sofa/0000775000113000011300000000000013027221062010747 5ustar bellsbellssofa/20160503_c/0000775000113000011300000000000013027221062012151 5ustar bellsbellssofa/20160503_c/c/0000775000113000011300000000000013027221063012374 5ustar bellsbellssofa/20160503_c/c/src/0000775000113000011300000000000013027221063013163 5ustar bellsbellssofa/20160503_c/c/src/a2af.c0000644000113000011300000001450413027221062014141 0ustar bellsbells#include "sofa.h" void iauA2af(int ndp, double angle, char *sign, int idmsf[4]) /* ** - - - - - - - - ** i a u A 2 a f ** - - - - - - - - ** ** Decompose radians into degrees, arcminutes, arcseconds, fraction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** ndp int resolution (Note 1) ** angle double angle in radians ** ** Returned: ** sign char '+' or '-' ** idmsf int[4] degrees, arcminutes, arcseconds, fraction ** ** Called: ** iauD2tf decompose days to hms ** ** Notes: ** ** 1) The argument ndp is interpreted as follows: ** ** ndp resolution ** : ...0000 00 00 ** -7 1000 00 00 ** -6 100 00 00 ** -5 10 00 00 ** -4 1 00 00 ** -3 0 10 00 ** -2 0 01 00 ** -1 0 00 10 ** 0 0 00 01 ** 1 0 00 00.1 ** 2 0 00 00.01 ** 3 0 00 00.001 ** : 0 00 00.000... ** ** 2) The largest positive useful value for ndp is determined by the ** size of angle, the format of doubles on the target platform, and ** the risk of overflowing idmsf[3]. On a typical platform, for ** angle up to 2pi, the available floating-point precision might ** correspond to ndp=12. However, the practical limit is typically ** ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is ** only 16 bits. ** ** 3) The absolute value of angle may exceed 2pi. In cases where it ** does not, it is up to the caller to test for and handle the ** case where angle is very nearly 2pi and rounds up to 360 degrees, ** by testing for idmsf[0]=360 and setting idmsf[0-3] to zero. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Hours to degrees * radians to turns */ const double F = 15.0 / D2PI; /* Scale then use days to h,m,s function. */ iauD2tf(ndp, angle*F, sign, idmsf); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/a2tf.c0000644000113000011300000001434613027221062014170 0ustar bellsbells#include "sofa.h" void iauA2tf(int ndp, double angle, char *sign, int ihmsf[4]) /* ** - - - - - - - - ** i a u A 2 t f ** - - - - - - - - ** ** Decompose radians into hours, minutes, seconds, fraction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** ndp int resolution (Note 1) ** angle double angle in radians ** ** Returned: ** sign char '+' or '-' ** ihmsf int[4] hours, minutes, seconds, fraction ** ** Called: ** iauD2tf decompose days to hms ** ** Notes: ** ** 1) The argument ndp is interpreted as follows: ** ** ndp resolution ** : ...0000 00 00 ** -7 1000 00 00 ** -6 100 00 00 ** -5 10 00 00 ** -4 1 00 00 ** -3 0 10 00 ** -2 0 01 00 ** -1 0 00 10 ** 0 0 00 01 ** 1 0 00 00.1 ** 2 0 00 00.01 ** 3 0 00 00.001 ** : 0 00 00.000... ** ** 2) The largest positive useful value for ndp is determined by the ** size of angle, the format of doubles on the target platform, and ** the risk of overflowing ihmsf[3]. On a typical platform, for ** angle up to 2pi, the available floating-point precision might ** correspond to ndp=12. However, the practical limit is typically ** ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is ** only 16 bits. ** ** 3) The absolute value of angle may exceed 2pi. In cases where it ** does not, it is up to the caller to test for and handle the ** case where angle is very nearly 2pi and rounds up to 24 hours, ** by testing for ihmsf[0]=24 and setting ihmsf[0-3] to zero. ** ** This revision: 2013 July 31 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Scale then use days to h,m,s function. */ iauD2tf(ndp, angle/D2PI, sign, ihmsf); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ab.c0000644000113000011300000001472413027221062013716 0ustar bellsbells#include "sofa.h" void iauAb(double pnat[3], double v[3], double s, double bm1, double ppr[3]) /* ** - - - - - - ** i a u A b ** - - - - - - ** ** Apply aberration to transform natural direction into proper ** direction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** pnat double[3] natural direction to the source (unit vector) ** v double[3] observer barycentric velocity in units of c ** s double distance between the Sun and the observer (au) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** ** Returned: ** ppr double[3] proper direction to source (unit vector) ** ** Notes: ** ** 1) The algorithm is based on Expr. (7.40) in the Explanatory ** Supplement (Urban & Seidelmann 2013), but with the following ** changes: ** ** o Rigorous rather than approximate normalization is applied. ** ** o The gravitational potential term from Expr. (7) in ** Klioner (2003) is added, taking into account only the Sun's ** contribution. This has a maximum effect of about ** 0.4 microarcsecond. ** ** 2) In almost all cases, the maximum accuracy will be limited by the ** supplied velocity. For example, if the SOFA iauEpv00 function is ** used, errors of up to 5 microarcseconds could occur. ** ** References: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013). ** ** Klioner, Sergei A., "A practical relativistic model for micro- ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). ** ** Called: ** iauPdp scalar product of two p-vectors ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int i; double pdv, w1, w2, r2, w, p[3], r; pdv = iauPdp(pnat, v); w1 = 1.0 + pdv/(1.0 + bm1); w2 = SRS/s; r2 = 0.0; for (i = 0; i < 3; i++) { w = pnat[i]*bm1 + w1*v[i] + w2*(v[i] - pdv*pnat[i]); p[i] = w; r2 = r2 + w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { ppr[i] = p[i]/r; } /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/af2a.c0000644000113000011300000001370713027221062014145 0ustar bellsbells#include "sofa.h" #include int iauAf2a(char s, int ideg, int iamin, double asec, double *rad) /* ** - - - - - - - - ** i a u A f 2 a ** - - - - - - - - ** ** Convert degrees, arcminutes, arcseconds to radians. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** s char sign: '-' = negative, otherwise positive ** ideg int degrees ** iamin int arcminutes ** asec double arcseconds ** ** Returned: ** rad double angle in radians ** ** Returned (function value): ** int status: 0 = OK ** 1 = ideg outside range 0-359 ** 2 = iamin outside range 0-59 ** 3 = asec outside range 0-59.999... ** ** Notes: ** ** 1) The result is computed even if any of the range checks fail. ** ** 2) Negative ideg, iamin and/or asec produce a warning status, but ** the absolute value is used in the conversion. ** ** 3) If there are multiple errors, the status value reflects only the ** first, the smallest taking precedence. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Compute the interval. */ *rad = ( s == '-' ? -1.0 : 1.0 ) * ( 60.0 * ( 60.0 * ( (double) abs(ideg) ) + ( (double) abs(iamin) ) ) + fabs(asec) ) * DAS2R; /* Validate arguments and return status. */ if ( ideg < 0 || ideg > 359 ) return 1; if ( iamin < 0 || iamin > 59 ) return 2; if ( asec < 0.0 || asec >= 60.0 ) return 3; return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/anp.c0000644000113000011300000001153313027221062014105 0ustar bellsbells#include "sofa.h" double iauAnp(double a) /* ** - - - - - - - ** i a u A n p ** - - - - - - - ** ** Normalize angle into the range 0 <= a < 2pi. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double angle (radians) ** ** Returned (function value): ** double angle in range 0-2pi ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double w; w = fmod(a, D2PI); if (w < 0) w += D2PI; return w; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/anpm.c0000644000113000011300000001156713027221062014271 0ustar bellsbells#include "sofa.h" double iauAnpm(double a) /* ** - - - - - - - - ** i a u A n p m ** - - - - - - - - ** ** Normalize angle into the range -pi <= a < +pi. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double angle (radians) ** ** Returned (function value): ** double angle in range +/-pi ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double w; w = fmod(a, D2PI); if (fabs(w) >= DPI) w -= dsign(D2PI, a); return w; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/apcg13.c0000644000113000011300000002207713027221062014412 0ustar bellsbells#include "sofa.h" void iauApcg13(double date1, double date2, iauASTROM *astrom) /* ** - - - - - - - - - - ** i a u A p c g 1 3 ** - - - - - - - - - - ** ** For a geocentric observer, prepare star-independent astrometry ** parameters for transformations between ICRS and GCRS coordinates. ** The caller supplies the date, and SOFA models are used to predict ** the Earth ephemeris. ** ** The parameters produced by this function are required in the ** parallax, light deflection and aberration parts of the astrometric ** transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) In cases where the caller wishes to supply his own Earth ** ephemeris, the function iauApcg can be used instead of the present ** function. ** ** 4) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 5) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauEpv00 Earth position and velocity ** iauApcg astrometry parameters, ICRS-GCRS, geocenter ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double ehpv[2][3], ebpv[2][3]; /* Earth barycentric & heliocentric position/velocity (au, au/d). */ (void) iauEpv00(date1, date2, ehpv, ebpv); /* Compute the star-independent astrometry parameters. */ iauApcg(date1, date2, ebpv, ehpv[0], astrom); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/apcg.c0000644000113000011300000002172613027221062014246 0ustar bellsbells#include "sofa.h" void iauApcg(double date1, double date2, double ebpv[2][3], double ehp[3], iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p c g ** - - - - - - - - ** ** For a geocentric observer, prepare star-independent astrometry ** parameters for transformations between ICRS and GCRS coordinates. ** The Earth ephemeris is supplied by the caller. ** ** The parameters produced by this function are required in the ** parallax, light deflection and aberration parts of the astrometric ** transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ebpv double[2][3] Earth barycentric pos/vel (au, au/day) ** ehp double[3] Earth heliocentric position (au) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 4) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauApcs astrometry parameters, ICRS-GCRS, space observer ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Geocentric observer */ double pv[2][3] = { { 0.0, 0.0, 0.0 }, { 0.0, 0.0, 0.0 } }; /* Compute the star-independent astrometry parameters. */ iauApcs(date1, date2, pv, ebpv, ehp, astrom); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/apci13.c0000644000113000011300000002334313027221062014411 0ustar bellsbells#include "sofa.h" void iauApci13(double date1, double date2, iauASTROM *astrom, double *eo) /* ** - - - - - - - - - - ** i a u A p c i 1 3 ** - - - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between ICRS and geocentric CIRS ** coordinates. The caller supplies the date, and SOFA models are used ** to predict the Earth ephemeris and CIP/CIO. ** ** The parameters produced by this function are required in the ** parallax, light deflection, aberration, and bias-precession-nutation ** parts of the astrometric transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** eo double* equation of the origins (ERA-GST) ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) In cases where the caller wishes to supply his own Earth ** ephemeris and CIP/CIO, the function iauApci can be used instead ** of the present function. ** ** 4) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 5) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauEpv00 Earth position and velocity ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** iauApci astrometry parameters, ICRS-CIRS ** iauEors equation of the origins, given NPB matrix and s ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double ehpv[2][3], ebpv[2][3], r[3][3], x, y, s; /* Earth barycentric & heliocentric position/velocity (au, au/d). */ (void) iauEpv00(date1, date2, ehpv, ebpv); /* Form the equinox based BPN matrix, IAU 2006/2000A. */ iauPnm06a(date1, date2, r); /* Extract CIP X,Y. */ iauBpn2xy(r, &x, &y); /* Obtain CIO locator s. */ s = iauS06(date1, date2, x, y); /* Compute the star-independent astrometry parameters. */ iauApci(date1, date2, ebpv, ehpv[0], x, y, s, astrom); /* Equation of the origins. */ *eo = iauEors(r, s); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/apci.c0000644000113000011300000002270613027221062014247 0ustar bellsbells#include "sofa.h" void iauApci(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p c i ** - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between ICRS and geocentric CIRS ** coordinates. The Earth ephemeris and CIP/CIO are supplied by the ** caller. ** ** The parameters produced by this function are required in the ** parallax, light deflection, aberration, and bias-precession-nutation ** parts of the astrometric transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ebpv double[2][3] Earth barycentric position/velocity (au, au/day) ** ehp double[3] Earth heliocentric position (au) ** x,y double CIP X,Y (components of unit vector) ** s double the CIO locator s (radians) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) In cases where the caller does not wish to provide the Earth ** ephemeris and CIP/CIO, the function iauApci13 can be used instead ** of the present function. This computes the required quantities ** using other SOFA functions. ** ** 4) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 5) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauApcg astrometry parameters, ICRS-GCRS, geocenter ** iauC2ixys celestial-to-intermediate matrix, given X,Y and s ** ** This revision: 2013 September 25 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Star-independent astrometry parameters for geocenter. */ iauApcg(date1, date2, ebpv, ehp, astrom); /* CIO based BPN matrix. */ iauC2ixys(x, y, s, astrom->bpn); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/apco13.c0000644000113000011300000003353513027221062014423 0ustar bellsbells#include "sofa.h" int iauApco13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom, double *eo) /* ** - - - - - - - - - - ** i a u A p c o 1 3 ** - - - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between ICRS and observed ** coordinates. The caller supplies UTC, site coordinates, ambient air ** conditions and observing wavelength, and SOFA models are used to ** obtain the Earth ephemeris, CIP/CIO and refraction constants. ** ** The parameters produced by this function are required in the ** parallax, light deflection, aberration, and bias-precession-nutation ** parts of the ICRS/CIRS transformations. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 1,2) ** dut1 double UT1-UTC (seconds, Note 3) ** elong double longitude (radians, east +ve, Note 4) ** phi double latitude (geodetic, radians, Note 4) ** hm double height above ellipsoid (m, geodetic, Notes 4,6) ** xp,yp double polar motion coordinates (radians, Note 5) ** phpa double pressure at the observer (hPa = mB, Note 6) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 7) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** eo double* equation of the origins (ERA-GST) ** ** Returned (function value): ** int status: +1 = dubious year (Note 2) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 2) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the ** future to be trusted. See iauDat for further details. ** ** 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 4) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 5) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many ** applications, xp and yp can be set to zero. ** ** Internally, the polar motion is stored in a form rotated onto ** the local meridian. ** ** 6) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to ** the pressure and that an accurate phpa value is important for ** precise work. ** ** 7) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 8) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 9) In cases where the caller wishes to supply his own Earth ** ephemeris, Earth rotation information and refraction constants, ** the function iauApco can be used instead of the present function. ** ** 10) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 11) The context structure astrom produced by this function is used ** by iauAtioq, iauAtoiq, iauAtciq* and iauAticq*. ** ** Called: ** iauUtctai UTC to TAI ** iauTaitt TAI to TT ** iauUtcut1 UTC to UT1 ** iauEpv00 Earth position and velocity ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** iauEra00 Earth rotation angle, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauRefco refraction constants for given ambient conditions ** iauApco astrometry parameters, ICRS-observed ** iauEors equation of the origins, given NPB matrix and s ** ** This revision: 2013 December 5 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j; double tai1, tai2, tt1, tt2, ut11, ut12, ehpv[2][3], ebpv[2][3], r[3][3], x, y, s, theta, sp, refa, refb; /* UTC to other time scales. */ j = iauUtctai(utc1, utc2, &tai1, &tai2); if ( j < 0 ) return -1; j = iauTaitt(tai1, tai2, &tt1, &tt2); j = iauUtcut1(utc1, utc2, dut1, &ut11, &ut12); if ( j < 0 ) return -1; /* Earth barycentric & heliocentric position/velocity (au, au/d). */ (void) iauEpv00(tt1, tt2, ehpv, ebpv); /* Form the equinox based BPN matrix, IAU 2006/2000A. */ iauPnm06a(tt1, tt2, r); /* Extract CIP X,Y. */ iauBpn2xy(r, &x, &y); /* Obtain CIO locator s. */ s = iauS06(tt1, tt2, x, y); /* Earth rotation angle. */ theta = iauEra00(ut11, ut12); /* TIO locator s'. */ sp = iauSp00(tt1, tt2); /* Refraction constants A and B. */ iauRefco(phpa, tc, rh, wl, &refa, &refb); /* Compute the star-independent astrometry parameters. */ iauApco(tt1, tt2, ebpv, ehpv[0], x, y, s, theta, elong, phi, hm, xp, yp, sp, refa, refb, astrom); /* Equation of the origins. */ *eo = iauEors(r, s); /* Return any warning status. */ return j; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/apco.c0000644000113000011300000003110113027221062014242 0ustar bellsbells#include "sofa.h" void iauApco(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, double theta, double elong, double phi, double hm, double xp, double yp, double sp, double refa, double refb, iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p c o ** - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between ICRS and observed ** coordinates. The caller supplies the Earth ephemeris, the Earth ** rotation information and the refraction constants as well as the ** site coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ebpv double[2][3] Earth barycentric PV (au, au/day, Note 2) ** ehp double[3] Earth heliocentric P (au, Note 2) ** x,y double CIP X,Y (components of unit vector) ** s double the CIO locator s (radians) ** theta double Earth rotation angle (radians) ** elong double longitude (radians, east +ve, Note 3) ** phi double latitude (geodetic, radians, Note 3) ** hm double height above ellipsoid (m, geodetic, Note 3) ** xp,yp double polar motion coordinates (radians, Note 4) ** sp double the TIO locator s' (radians, Note 4) ** refa double refraction constant A (radians, Note 5) ** refb double refraction constant B (radians, Note 5) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) The vectors eb, eh, and all the astrom vectors, are with respect ** to BCRS axes. ** ** 3) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN ** CONVENTION: the longitude required by the present function is ** right-handed, i.e. east-positive, in accordance with geographical ** convention. ** ** 4) xp and yp are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions), measured along the ** meridians 0 and 90 deg west respectively. sp is the TIO locator ** s', in radians, which positions the Terrestrial Intermediate ** Origin on the equator. For many applications, xp, yp and ** (especially) sp can be set to zero. ** ** Internally, the polar motion is stored in a form rotated onto the ** local meridian. ** ** 5) The refraction constants refa and refb are for use in a ** dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed ** (i.e. refracted) zenith distance and dZ is the amount of ** refraction. ** ** 6) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 7) In cases where the caller does not wish to provide the Earth ** Ephemeris, the Earth rotation information and refraction ** constants, the function iauApco13 can be used instead of the ** present function. This starts from UTC and weather readings etc. ** and computes suitable values using other SOFA functions. ** ** 8) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 9) The context structure astrom produced by this function is used by ** iauAtioq, iauAtoiq, iauAtciq* and iauAticq*. ** ** Called: ** iauAper astrometry parameters: update ERA ** iauC2ixys celestial-to-intermediate matrix, given X,Y and s ** iauPvtob position/velocity of terrestrial station ** iauTrxpv product of transpose of r-matrix and pv-vector ** iauApcs astrometry parameters, ICRS-GCRS, space observer ** iauCr copy r-matrix ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double sl, cl, r[3][3], pvc[2][3], pv[2][3]; /* Longitude with adjustment for TIO locator s'. */ astrom->along = elong + sp; /* Polar motion, rotated onto the local meridian. */ sl = sin(astrom->along); cl = cos(astrom->along); astrom->xpl = xp*cl - yp*sl; astrom->ypl = xp*sl + yp*cl; /* Functions of latitude. */ astrom->sphi = sin(phi); astrom->cphi = cos(phi); /* Refraction constants. */ astrom->refa = refa; astrom->refb = refb; /* Local Earth rotation angle. */ iauAper(theta, astrom); /* Disable the (redundant) diurnal aberration step. */ astrom->diurab = 0.0; /* CIO based BPN matrix. */ iauC2ixys(x, y, s, r); /* Observer's geocentric position and velocity (m, m/s, CIRS). */ iauPvtob(elong, phi, hm, xp, yp, sp, theta, pvc); /* Rotate into GCRS. */ iauTrxpv(r, pvc, pv); /* ICRS <-> GCRS parameters. */ iauApcs(date1, date2, pv, ebpv, ehp, astrom); /* Store the CIO based BPN matrix. */ iauCr(r, astrom->bpn ); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/apcs13.c0000644000113000011300000002272713027221062014430 0ustar bellsbells#include "sofa.h" void iauApcs13(double date1, double date2, double pv[2][3], iauASTROM *astrom) /* ** - - - - - - - - - - ** i a u A p c s 1 3 ** - - - - - - - - - - ** ** For an observer whose geocentric position and velocity are known, ** prepare star-independent astrometry parameters for transformations ** between ICRS and GCRS. The Earth ephemeris is from SOFA models. ** ** The parameters produced by this function are required in the space ** motion, parallax, light deflection and aberration parts of the ** astrometric transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** pv double[2][3] observer's geocentric pos/vel (Note 3) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) The observer's position and velocity pv are geocentric but with ** respect to BCRS axes, and in units of m and m/s. No assumptions ** are made about proximity to the Earth, and the function can be ** used for deep space applications as well as Earth orbit and ** terrestrial. ** ** 4) In cases where the caller wishes to supply his own Earth ** ephemeris, the function iauApcs can be used instead of the present ** function. ** ** 5) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 6) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauEpv00 Earth position and velocity ** iauApcs astrometry parameters, ICRS-GCRS, space observer ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double ehpv[2][3], ebpv[2][3]; /* Earth barycentric & heliocentric position/velocity (au, au/d). */ (void) iauEpv00(date1, date2, ehpv, ebpv); /* Compute the star-independent astrometry parameters. */ iauApcs(date1, date2, pv, ebpv, ehpv[0], astrom); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/apcs.c0000644000113000011300000002537613027221062014267 0ustar bellsbells#include "sofa.h" void iauApcs(double date1, double date2, double pv[2][3], double ebpv[2][3], double ehp[3], iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p c s ** - - - - - - - - ** ** For an observer whose geocentric position and velocity are known, ** prepare star-independent astrometry parameters for transformations ** between ICRS and GCRS. The Earth ephemeris is supplied by the ** caller. ** ** The parameters produced by this function are required in the space ** motion, parallax, light deflection and aberration parts of the ** astrometric transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** pv double[2][3] observer's geocentric pos/vel (m, m/s) ** ebpv double[2][3] Earth barycentric PV (au, au/day) ** ehp double[3] Earth heliocentric P (au) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) Providing separate arguments for (i) the observer's geocentric ** position and velocity and (ii) the Earth ephemeris is done for ** convenience in the geocentric, terrestrial and Earth orbit cases. ** For deep space applications it maybe more convenient to specify ** zero geocentric position and velocity and to supply the ** observer's position and velocity information directly instead of ** with respect to the Earth. However, note the different units: ** m and m/s for the geocentric vectors, au and au/day for the ** heliocentric and barycentric vectors. ** ** 4) In cases where the caller does not wish to provide the Earth ** ephemeris, the function iauApcs13 can be used instead of the ** present function. This computes the Earth ephemeris using the ** SOFA function iauEpv00. ** ** 5) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 6) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauCp copy p-vector ** iauPm modulus of p-vector ** iauPn decompose p-vector into modulus and direction ** iauIr initialize r-matrix to identity ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* au/d to m/s */ const double AUDMS = DAU/DAYSEC; /* Light time for 1 AU (day) */ const double CR = AULT/DAYSEC; int i; double dp, dv, pb[3], vb[3], ph[3], v2, w; /* Time since reference epoch, years (for proper motion calculation). */ astrom->pmt = ( (date1 - DJ00) + date2 ) / DJY; /* Adjust Earth ephemeris to observer. */ for (i = 0; i < 3; i++) { dp = pv[0][i] / DAU; dv = pv[1][i] / AUDMS; pb[i] = ebpv[0][i] + dp; vb[i] = ebpv[1][i] + dv; ph[i] = ehp[i] + dp; } /* Barycentric position of observer (au). */ iauCp(pb, astrom->eb); /* Heliocentric direction and distance (unit vector and au). */ iauPn(ph, &astrom->em, astrom->eh); /* Barycentric vel. in units of c, and reciprocal of Lorenz factor. */ v2 = 0.0; for (i = 0; i < 3; i++) { w = vb[i] * CR; astrom->v[i] = w; v2 += w*w; } astrom->bm1 = sqrt(1.0 - v2); /* Reset the NPB matrix. */ iauIr(astrom->bpn); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/aper13.c0000644000113000011300000002177013027221062014426 0ustar bellsbells#include "sofa.h" void iauAper13(double ut11, double ut12, iauASTROM *astrom) /* ** - - - - - - - - - - ** i a u A p e r 1 3 ** - - - - - - - - - - ** ** In the star-independent astrometry parameters, update only the ** Earth rotation angle. The caller provides UT1, (n.b. not UTC). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ut11 double UT1 as a 2-part... ** ut12 double ...Julian Date (Note 1) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double not used ** eb double[3] not used ** eh double[3] not used ** em double not used ** v double[3] not used ** bm1 double not used ** bpn double[3][3] not used ** along double longitude + s' (radians) ** xpl double not used ** ypl double not used ** sphi double not used ** cphi double not used ** diurab double not used ** eral double not used ** refa double not used ** refb double not used ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double unchanged ** eb double[3] unchanged ** eh double[3] unchanged ** em double unchanged ** v double[3] unchanged ** bm1 double unchanged ** bpn double[3][3] unchanged ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double "local" Earth rotation angle (radians) ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The UT1 date (n.b. not UTC) ut11+ut12 is a Julian Date, ** apportioned in any convenient way between the arguments ut11 and ** ut12. For example, JD(UT1)=2450123.7 could be expressed in any ** of these ways, among others: ** ** ut11 ut12 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. The date & time method is ** best matched to the algorithm used: maximum precision is ** delivered when the ut11 argument is for 0hrs UT1 on the day in ** question and the ut12 argument lies in the range 0 to 1, or vice ** versa. ** ** 2) If the caller wishes to provide the Earth rotation angle itself, ** the function iauAper can be used instead. One use of this ** technique is to substitute Greenwich apparent sidereal time and ** thereby to support equinox based transformations directly. ** ** 3) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** Called: ** iauAper astrometry parameters: update ERA ** iauEra00 Earth rotation angle, IAU 2000 ** ** This revision: 2013 September 25 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauAper(iauEra00(ut11,ut12), astrom); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/aper.c0000644000113000011300000002013613027221062014255 0ustar bellsbells#include "sofa.h" void iauAper(double theta, iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p e r ** - - - - - - - - ** ** In the star-independent astrometry parameters, update only the ** Earth rotation angle, supplied by the caller explicitly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** theta double Earth rotation angle (radians, Note 2) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double not used ** eb double[3] not used ** eh double[3] not used ** em double not used ** v double[3] not used ** bm1 double not used ** bpn double[3][3] not used ** along double longitude + s' (radians) ** xpl double not used ** ypl double not used ** sphi double not used ** cphi double not used ** diurab double not used ** eral double not used ** refa double not used ** refb double not used ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double unchanged ** eb double[3] unchanged ** eh double[3] unchanged ** em double unchanged ** v double[3] unchanged ** bm1 double unchanged ** bpn double[3][3] unchanged ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double "local" Earth rotation angle (radians) ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) This function exists to enable sidereal-tracking applications to ** avoid wasteful recomputation of the bulk of the astrometry ** parameters: only the Earth rotation is updated. ** ** 2) For targets expressed as equinox based positions, such as ** classical geocentric apparent (RA,Dec), the supplied theta can be ** Greenwich apparent sidereal time rather than Earth rotation ** angle. ** ** 3) The function iauAper13 can be used instead of the present ** function, and starts from UT1 rather than ERA itself. ** ** 4) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** This revision: 2013 September 25 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { astrom->eral = theta + astrom->along; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/apio13.c0000644000113000011300000003105313027221062014422 0ustar bellsbells#include "sofa.h" int iauApio13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom) /* ** - - - - - - - - - - ** i a u A p i o 1 3 ** - - - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between CIRS and observed ** coordinates. The caller supplies UTC, site coordinates, ambient air ** conditions and observing wavelength. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 1,2) ** dut1 double UT1-UTC (seconds) ** elong double longitude (radians, east +ve, Note 3) ** phi double geodetic latitude (radians, Note 3) ** hm double height above ellipsoid (m, geodetic Notes 4,6) ** xp,yp double polar motion coordinates (radians, Note 5) ** phpa double pressure at the observer (hPa = mB, Note 6) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 7) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double unchanged ** eb double[3] unchanged ** eh double[3] unchanged ** em double unchanged ** v double[3] unchanged ** bm1 double unchanged ** bpn double[3][3] unchanged ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned (function value): ** int status: +1 = dubious year (Note 2) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 2) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 4) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 5) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many applications, ** xp and yp can be set to zero. ** ** Internally, the polar motion is stored in a form rotated onto ** the local meridian. ** ** 6) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to the ** pressure and that an accurate phpa value is important for ** precise work. ** ** 7) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 8) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 9) In cases where the caller wishes to supply his own Earth ** rotation information and refraction constants, the function ** iauApc can be used instead of the present function. ** ** 10) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 11) The context structure astrom produced by this function is used ** by iauAtioq and iauAtoiq. ** ** Called: ** iauUtctai UTC to TAI ** iauTaitt TAI to TT ** iauUtcut1 UTC to UT1 ** iauSp00 the TIO locator s', IERS 2000 ** iauEra00 Earth rotation angle, IAU 2000 ** iauRefco refraction constants for given ambient conditions ** iauApio astrometry parameters, CIRS-observed ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j; double tai1, tai2, tt1, tt2, ut11, ut12, sp, theta, refa, refb; /* UTC to other time scales. */ j = iauUtctai(utc1, utc2, &tai1, &tai2); if ( j < 0 ) return -1; j = iauTaitt(tai1, tai2, &tt1, &tt2); j = iauUtcut1(utc1, utc2, dut1, &ut11, &ut12); if ( j < 0 ) return -1; /* TIO locator s'. */ sp = iauSp00(tt1, tt2); /* Earth rotation angle. */ theta = iauEra00(ut11, ut12); /* Refraction constants A and B. */ iauRefco(phpa, tc, rh, wl, &refa, &refb); /* CIRS <-> observed astrometry parameters. */ iauApio(sp, theta, elong, phi, hm, xp, yp, refa, refb, astrom); /* Return any warning status. */ return j; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/apio.c0000644000113000011300000002453513027221062014265 0ustar bellsbells#include "sofa.h" void iauApio(double sp, double theta, double elong, double phi, double hm, double xp, double yp, double refa, double refb, iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p i o ** - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between CIRS and observed ** coordinates. The caller supplies the Earth orientation information ** and the refraction constants as well as the site coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** sp double the TIO locator s' (radians, Note 1) ** theta double Earth rotation angle (radians) ** elong double longitude (radians, east +ve, Note 2) ** phi double geodetic latitude (radians, Note 2) ** hm double height above ellipsoid (m, geodetic Note 2) ** xp,yp double polar motion coordinates (radians, Note 3) ** refa double refraction constant A (radians, Note 4) ** refb double refraction constant B (radians, Note 4) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double unchanged ** eb double[3] unchanged ** eh double[3] unchanged ** em double unchanged ** v double[3] unchanged ** bm1 double unchanged ** bpn double[3][3] unchanged ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Notes: ** ** 1) sp, the TIO locator s', is a tiny quantity needed only by the ** most precise applications. It can either be set to zero or ** predicted using the SOFA function iauSp00. ** ** 2) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 3) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many applications, ** xp and yp can be set to zero. ** ** Internally, the polar motion is stored in a form rotated onto the ** local meridian. ** ** 4) The refraction constants refa and refb are for use in a ** dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed ** (i.e. refracted) zenith distance and dZ is the amount of ** refraction. ** ** 5) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 6) In cases where the caller does not wish to provide the Earth ** rotation information and refraction constants, the function ** iauApio13 can be used instead of the present function. This ** starts from UTC and weather readings etc. and computes suitable ** values using other SOFA functions. ** ** 7) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 8) The context structure astrom produced by this function is used by ** iauAtioq and iauAtoiq. ** ** Called: ** iauPvtob position/velocity of terrestrial station ** iauAper astrometry parameters: update ERA ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double sl, cl, pv[2][3]; /* Longitude with adjustment for TIO locator s'. */ astrom->along = elong + sp; /* Polar motion, rotated onto the local meridian. */ sl = sin(astrom->along); cl = cos(astrom->along); astrom->xpl = xp*cl - yp*sl; astrom->ypl = xp*sl + yp*cl; /* Functions of latitude. */ astrom->sphi = sin(phi); astrom->cphi = cos(phi); /* Observer's geocentric position and velocity (m, m/s, CIRS). */ iauPvtob(elong, phi, hm, xp, yp, sp, theta, pv); /* Magnitude of diurnal aberration vector. */ astrom->diurab = sqrt(pv[1][0]*pv[1][0]+pv[1][1]*pv[1][1]) / CMPS; /* Refraction constants. */ astrom->refa = refa; astrom->refb = refb; /* Local Earth rotation angle. */ iauAper(theta, astrom); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atci13.c0000644000113000011300000002010513027221062014406 0ustar bellsbells#include "sofa.h" void iauAtci13(double rc, double dc, double pr, double pd, double px, double rv, double date1, double date2, double *ri, double *di, double *eo) /* ** - - - - - - - - - - ** i a u A t c i 1 3 ** - - - - - - - - - - ** ** Transform ICRS star data, epoch J2000.0, to CIRS. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc double ICRS right ascension at J2000.0 (radians, Note 1) ** dc double ICRS declination at J2000.0 (radians, Note 1) ** pr double RA proper motion (radians/year; Note 2) ** pd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, +ve if receding) ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 3) ** ** Returned: ** ri,di double* CIRS geocentric RA,Dec (radians) ** eo double* equation of the origins (ERA-GST, Note 5) ** ** Notes: ** ** 1) Star data for an epoch other than J2000.0 (for example from the ** Hipparcos catalog, which has an epoch of J1991.25) will require a ** preliminary call to iauPmsafe before use. ** ** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 3) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.8g could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.8g 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 4) The available accuracy is better than 1 milliarcsecond, limited ** mainly by the precession-nutation model that is used, namely ** IAU 2000A/2006. Very close to solar system bodies, additional ** errors of up to several milliarcseconds can occur because of ** unmodeled light deflection; however, the Sun's contribution is ** taken into account, to first order. The accuracy limitations of ** the SOFA function iauEpv00 (used to compute Earth position and ** velocity) can contribute aberration errors of up to ** 5 microarcseconds. Light deflection at the Sun's limb is ** uncertain at the 0.4 mas level. ** ** 5) Should the transformation to (equinox based) apparent place be ** required rather than (CIO based) intermediate place, subtract the ** equation of the origins from the returned right ascension: ** RA = RI - EO. (The iauAnp function can then be applied, as ** required, to keep the result in the conventional 0-2pi range.) ** ** Called: ** iauApci13 astrometry parameters, ICRS-CIRS, 2013 ** iauAtciq quick ICRS to CIRS ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Star-independent astrometry parameters */ iauASTROM astrom; /* The transformation parameters. */ iauApci13(date1, date2, &astrom, eo); /* ICRS (epoch J2000.0) to CIRS. */ iauAtciq(rc, dc, pr, pd, px, rv, &astrom, ri, di); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atciq.c0000644000113000011300000001745313027221062014437 0ustar bellsbells#include "sofa.h" void iauAtciq(double rc, double dc, double pr, double pd, double px, double rv, iauASTROM *astrom, double *ri, double *di) /* ** - - - - - - - - - ** i a u A t c i q ** - - - - - - - - - ** ** Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed ** star-independent astrometry parameters. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are to be transformed for one date. The ** star-independent parameters can be obtained by calling one of the ** functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13]. ** ** If the parallax and proper motions are zero the iauAtciqz function ** can be used instead. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc,dc double ICRS RA,Dec at J2000.0 (radians) ** pr double RA proper motion (radians/year; Note 3) ** pd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, +ve if receding) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** ri,di double CIRS RA,Dec (radians) ** ** Notes: ** ** 1) All the vectors are with respect to BCRS axes. ** ** 2) Star data for an epoch other than J2000.0 (for example from the ** Hipparcos catalog, which has an epoch of J1991.25) will require a ** preliminary call to iauPmsafe before use. ** ** 3) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** Called: ** iauPmpx proper motion and parallax ** iauLdsun light deflection by the Sun ** iauAb stellar aberration ** iauRxp product of r-matrix and pv-vector ** iauC2s p-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double pco[3], pnat[3], ppr[3], pi[3], w; /* Proper motion and parallax, giving BCRS coordinate direction. */ iauPmpx(rc, dc, pr, pd, px, rv, astrom->pmt, astrom->eb, pco); /* Light deflection by the Sun, giving BCRS natural direction. */ iauLdsun(pco, astrom->eh, astrom->em, pnat); /* Aberration, giving GCRS proper direction. */ iauAb(pnat, astrom->v, astrom->em, astrom->bm1, ppr); /* Bias-precession-nutation, giving CIRS proper direction. */ iauRxp(astrom->bpn, ppr, pi); /* CIRS RA,Dec. */ iauC2s(pi, &w, di); *ri = iauAnp(w); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atciqn.c0000644000113000011300000002314313027221062014606 0ustar bellsbells#include "sofa.h" void iauAtciqn(double rc, double dc, double pr, double pd, double px, double rv, iauASTROM *astrom, int n, iauLDBODY b[], double *ri, double *di) /* ** - - - - - - - - - - ** i a u A t c i q n ** - - - - - - - - - - ** ** Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed ** star-independent astrometry parameters plus a list of light- ** deflecting bodies. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are to be transformed for one date. The ** star-independent parameters can be obtained by calling one of the ** functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13]. ** ** ** If the only light-deflecting body to be taken into account is the ** Sun, the iauAtciq function can be used instead. If in addition the ** parallax and proper motions are zero, the iauAtciqz function can be ** used. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc,dc double ICRS RA,Dec at J2000.0 (radians) ** pr double RA proper motion (radians/year; Note 3) ** pd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, +ve if receding) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** n int number of bodies (Note 3) ** b iauLDBODY[n] data for each of the n bodies (Notes 3,4): ** bm double mass of the body (solar masses, Note 5) ** dl double deflection limiter (Note 6) ** pv [2][3] barycentric PV of the body (au, au/day) ** ** Returned: ** ri,di double CIRS RA,Dec (radians) ** ** Notes: ** ** 1) Star data for an epoch other than J2000.0 (for example from the ** Hipparcos catalog, which has an epoch of J1991.25) will require a ** preliminary call to iauPmsafe before use. ** ** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 3) The struct b contains n entries, one for each body to be ** considered. If n = 0, no gravitational light deflection will be ** applied, not even for the Sun. ** ** 4) The struct b should include an entry for the Sun as well as for ** any planet or other body to be taken into account. The entries ** should be in the order in which the light passes the body. ** ** 5) In the entry in the b struct for body i, the mass parameter ** b[i].bm can, as required, be adjusted in order to allow for such ** effects as quadrupole field. ** ** 6) The deflection limiter parameter b[i].dl is phi^2/2, where phi is ** the angular separation (in radians) between star and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. Example values suitable for a terrestrial ** observer, together with masses, are as follows: ** ** body i b[i].bm b[i].dl ** ** Sun 1.0 6e-6 ** Jupiter 0.00095435 3e-9 ** Saturn 0.00028574 3e-10 ** ** 7) For efficiency, validation of the contents of the b array is ** omitted. The supplied masses must be greater than zero, the ** position and velocity vectors must be right, and the deflection ** limiter greater than zero. ** ** Called: ** iauPmpx proper motion and parallax ** iauLdn light deflection by n bodies ** iauAb stellar aberration ** iauRxp product of r-matrix and pv-vector ** iauC2s p-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double pco[3], pnat[3], ppr[3], pi[3], w; /* Proper motion and parallax, giving BCRS coordinate direction. */ iauPmpx(rc, dc, pr, pd, px, rv, astrom->pmt, astrom->eb, pco); /* Light deflection, giving BCRS natural direction. */ iauLdn(n, b, astrom->eb, pco, pnat); /* Aberration, giving GCRS proper direction. */ iauAb(pnat, astrom->v, astrom->em, astrom->bm1, ppr); /* Bias-precession-nutation, giving CIRS proper direction. */ iauRxp(astrom->bpn, ppr, pi); /* CIRS RA,Dec. */ iauC2s(pi, &w, di); *ri = iauAnp(w); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atciqz.c0000644000113000011300000001706213027221062014625 0ustar bellsbells#include "sofa.h" void iauAtciqz(double rc, double dc, iauASTROM *astrom, double *ri, double *di) /* ** - - - - - - - - - - ** i a u A t c i q z ** - - - - - - - - - - ** ** Quick ICRS to CIRS transformation, given precomputed star- ** independent astrometry parameters, and assuming zero parallax and ** proper motion. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are to be transformed for one date. The ** star-independent parameters can be obtained by calling one of the ** functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13]. ** ** The corresponding function for the case of non-zero parallax and ** proper motion is iauAtciq. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc,dc double ICRS astrometric RA,Dec (radians) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** ri,di double CIRS RA,Dec (radians) ** ** Note: ** ** All the vectors are with respect to BCRS axes. ** ** References: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013). ** ** Klioner, Sergei A., "A practical relativistic model for micro- ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauLdsun light deflection due to Sun ** iauAb stellar aberration ** iauRxp product of r-matrix and p-vector ** iauC2s p-vector to spherical ** iauAnp normalize angle into range +/- pi ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double pco[3], pnat[3], ppr[3], pi[3], w; /* BCRS coordinate direction (unit vector). */ iauS2c(rc, dc, pco); /* Light deflection by the Sun, giving BCRS natural direction. */ iauLdsun(pco, astrom->eh, astrom->em, pnat); /* Aberration, giving GCRS proper direction. */ iauAb(pnat, astrom->v, astrom->em, astrom->bm1, ppr); /* Bias-precession-nutation, giving CIRS proper direction. */ iauRxp(astrom->bpn, ppr, pi); /* CIRS RA,Dec. */ iauC2s(pi, &w, di); *ri = iauAnp(w); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atco13.c0000644000113000011300000003027313027221062014423 0ustar bellsbells#include "sofa.h" int iauAtco13(double rc, double dc, double pr, double pd, double px, double rv, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *aob, double *zob, double *hob, double *dob, double *rob, double *eo) /* ** - - - - - - - - - - ** i a u A t c o 1 3 ** - - - - - - - - - - ** ** ICRS RA,Dec to observed place. The caller supplies UTC, site ** coordinates, ambient air conditions and observing wavelength. ** ** SOFA models are used for the Earth ephemeris, bias-precession- ** nutation, Earth orientation and refraction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc,dc double ICRS right ascension at J2000.0 (radians, Note 1) ** pr double RA proper motion (radians/year; Note 2) ** pd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, +ve if receding) ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 3-4) ** dut1 double UT1-UTC (seconds, Note 5) ** elong double longitude (radians, east +ve, Note 6) ** phi double latitude (geodetic, radians, Note 6) ** hm double height above ellipsoid (m, geodetic, Notes 6,8) ** xp,yp double polar motion coordinates (radians, Note 7) ** phpa double pressure at the observer (hPa = mB, Note 8) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 9) ** ** Returned: ** aob double* observed azimuth (radians: N=0,E=90) ** zob double* observed zenith distance (radians) ** hob double* observed hour angle (radians) ** dob double* observed declination (radians) ** rob double* observed right ascension (CIO-based, radians) ** eo double* equation of the origins (ERA-GST) ** ** Returned (function value): ** int status: +1 = dubious year (Note 4) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) Star data for an epoch other than J2000.0 (for example from the ** Hipparcos catalog, which has an epoch of J1991.25) will require ** a preliminary call to iauPmsafe before use. ** ** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 3) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 4) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the ** future to be trusted. See iauDat for further details. ** ** 5) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 6) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 7) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many ** applications, xp and yp can be set to zero. ** ** 8) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), ** is available, an adequate estimate of hm can be obtained from ** the expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to ** the pressure and that an accurate phpa value is important for ** precise work. ** ** 9) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 10) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted observed ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better ** than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions iauAtco13 and ** iauAtoc13 are self-consistent to better than 1 microarcsecond ** all over the celestial sphere. With refraction included, ** consistency falls off at high zenith distances, but is still ** better than 0.05 arcsec at 85 degrees. ** ** 11) "Observed" Az,ZD means the position that would be seen by a ** perfect geodetically aligned theodolite. (Zenith distance is ** used rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) This is ** related to the observed HA,Dec via the standard rotation, using ** the geodetic latitude (corrected for polar motion), while the ** observed HA and RA are related simply through the Earth rotation ** angle and the site longitude. "Observed" RA,Dec or HA,Dec thus ** means the position that would be seen by a perfect equatorial ** with its polar axis aligned to the Earth's axis of rotation. ** ** 12) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** iauApco13 astrometry parameters, ICRS-observed, 2013 ** iauAtciq quick ICRS to CIRS ** iauAtioq quick CIRS to observed ** ** This revision: 2016 February 2 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j; iauASTROM astrom; double ri, di; /* Star-independent astrometry parameters. */ j = iauApco13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom, eo); /* Abort if bad UTC. */ if ( j < 0 ) return j; /* Transform ICRS to CIRS. */ iauAtciq(rc, dc, pr, pd, px, rv, &astrom, &ri, &di); /* Transform CIRS to observed. */ iauAtioq(ri, di, &astrom, aob, zob, hob, dob, rob); /* Return OK/warning status. */ return j; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atic13.c0000644000113000011300000001736013027221062014417 0ustar bellsbells#include "sofa.h" void iauAtic13(double ri, double di, double date1, double date2, double *rc, double *dc, double *eo) /* ** - - - - - - - - - - ** i a u A t i c 1 3 ** - - - - - - - - - - ** ** Transform star RA,Dec from geocentric CIRS to ICRS astrometric. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri,di double CIRS geocentric RA,Dec (radians) ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ** Returned: ** rc,dc double ICRS astrometric RA,Dec (radians) ** eo double equation of the origins (ERA-GST, Note 4) ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) Iterative techniques are used for the aberration and light ** deflection corrections so that the functions iauAtic13 (or ** iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses; ** even at the edge of the Sun's disk the discrepancy is only about ** 1 nanoarcsecond. ** ** 3) The available accuracy is better than 1 milliarcsecond, limited ** mainly by the precession-nutation model that is used, namely ** IAU 2000A/2006. Very close to solar system bodies, additional ** errors of up to several milliarcseconds can occur because of ** unmodeled light deflection; however, the Sun's contribution is ** taken into account, to first order. The accuracy limitations of ** the SOFA function iauEpv00 (used to compute Earth position and ** velocity) can contribute aberration errors of up to ** 5 microarcseconds. Light deflection at the Sun's limb is ** uncertain at the 0.4 mas level. ** ** 4) Should the transformation to (equinox based) J2000.0 mean place ** be required rather than (CIO based) ICRS coordinates, subtract the ** equation of the origins from the returned right ascension: ** RA = RI - EO. (The iauAnp function can then be applied, as ** required, to keep the result in the conventional 0-2pi range.) ** ** Called: ** iauApci13 astrometry parameters, ICRS-CIRS, 2013 ** iauAticq quick CIRS to ICRS astrometric ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Star-independent astrometry parameters */ iauASTROM astrom; /* Star-independent astrometry parameters. */ iauApci13(date1, date2, &astrom, eo); /* CIRS to ICRS astrometric. */ iauAticq(ri, di, &astrom, rc, dc); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/aticq.c0000644000113000011300000002104013027221062014422 0ustar bellsbells#include "sofa.h" void iauAticq(double ri, double di, iauASTROM *astrom, double *rc, double *dc) /* ** - - - - - - - - - ** i a u A t i c q ** - - - - - - - - - ** ** Quick CIRS RA,Dec to ICRS astrometric place, given the star- ** independent astrometry parameters. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are all to be transformed for one date. ** The star-independent astrometry parameters can be obtained by ** calling one of the functions iauApci[13], iauApcg[13], iauApco[13] ** or iauApcs[13]. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri,di double CIRS RA,Dec (radians) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** rc,dc double ICRS astrometric RA,Dec (radians) ** ** Notes: ** ** 1) Only the Sun is taken into account in the light deflection ** correction. ** ** 2) Iterative techniques are used for the aberration and light ** deflection corrections so that the functions iauAtic13 (or ** iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses; ** even at the edge of the Sun's disk the discrepancy is only about ** 1 nanoarcsecond. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauTrxp product of transpose of r-matrix and p-vector ** iauZp zero p-vector ** iauAb stellar aberration ** iauLdsun light deflection by the Sun ** iauC2s p-vector to spherical ** iauAnp normalize angle into range +/- pi ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j, i; double pi[3], ppr[3], pnat[3], pco[3], w, d[3], before[3], r2, r, after[3]; /* CIRS RA,Dec to Cartesian. */ iauS2c(ri, di, pi); /* Bias-precession-nutation, giving GCRS proper direction. */ iauTrxp(astrom->bpn, pi, ppr); /* Aberration, giving GCRS natural direction. */ iauZp(d); for (j = 0; j < 2; j++) { r2 = 0.0; for (i = 0; i < 3; i++) { w = ppr[i] - d[i]; before[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { before[i] /= r; } iauAb(before, astrom->v, astrom->em, astrom->bm1, after); r2 = 0.0; for (i = 0; i < 3; i++) { d[i] = after[i] - before[i]; w = ppr[i] - d[i]; pnat[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { pnat[i] /= r; } } /* Light deflection by the Sun, giving BCRS coordinate direction. */ iauZp(d); for (j = 0; j < 5; j++) { r2 = 0.0; for (i = 0; i < 3; i++) { w = pnat[i] - d[i]; before[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { before[i] /= r; } iauLdsun(before, astrom->eh, astrom->em, after); r2 = 0.0; for (i = 0; i < 3; i++) { d[i] = after[i] - before[i]; w = pnat[i] - d[i]; pco[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { pco[i] /= r; } } /* ICRS astrometric RA,Dec. */ iauC2s(pco, &w, dc); *rc = iauAnp(w); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/aticqn.c0000644000113000011300000002460513027221062014612 0ustar bellsbells#include "sofa.h" void iauAticqn(double ri, double di, iauASTROM *astrom, int n, iauLDBODY b[], double *rc, double *dc) /* ** - - - - - - - - - ** i a u A t i c q n ** - - - - - - - - - ** ** Quick CIRS to ICRS astrometric place transformation, given the star- ** independent astrometry parameters plus a list of light-deflecting ** bodies. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are all to be transformed for one date. ** The star-independent astrometry parameters can be obtained by ** calling one of the functions iauApci[13], iauApcg[13], iauApco[13] ** or iauApcs[13]. * * If the only light-deflecting body to be taken into account is the * Sun, the iauAticq function can be used instead. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri,di double CIRS RA,Dec (radians) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** n int number of bodies (Note 3) ** b iauLDBODY[n] data for each of the n bodies (Notes 3,4): ** bm double mass of the body (solar masses, Note 5) ** dl double deflection limiter (Note 6) ** pv [2][3] barycentric PV of the body (au, au/day) ** ** Returned: ** rc,dc double ICRS astrometric RA,Dec (radians) ** ** Notes: ** ** 1) Iterative techniques are used for the aberration and light ** deflection corrections so that the functions iauAticqn and ** iauAtciqn are accurate inverses; even at the edge of the Sun's ** disk the discrepancy is only about 1 nanoarcsecond. ** ** 2) If the only light-deflecting body to be taken into account is the ** Sun, the iauAticq function can be used instead. ** ** 3) The struct b contains n entries, one for each body to be ** considered. If n = 0, no gravitational light deflection will be ** applied, not even for the Sun. ** ** 4) The struct b should include an entry for the Sun as well as for ** any planet or other body to be taken into account. The entries ** should be in the order in which the light passes the body. ** ** 5) In the entry in the b struct for body i, the mass parameter ** b[i].bm can, as required, be adjusted in order to allow for such ** effects as quadrupole field. ** ** 6) The deflection limiter parameter b[i].dl is phi^2/2, where phi is ** the angular separation (in radians) between star and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. Example values suitable for a terrestrial ** observer, together with masses, are as follows: ** ** body i b[i].bm b[i].dl ** ** Sun 1.0 6e-6 ** Jupiter 0.00095435 3e-9 ** Saturn 0.00028574 3e-10 ** ** 7) For efficiency, validation of the contents of the b array is ** omitted. The supplied masses must be greater than zero, the ** position and velocity vectors must be right, and the deflection ** limiter greater than zero. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauTrxp product of transpose of r-matrix and p-vector ** iauZp zero p-vector ** iauAb stellar aberration ** iauLdn light deflection by n bodies ** iauC2s p-vector to spherical ** iauAnp normalize angle into range +/- pi ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j, i; double pi[3], ppr[3], pnat[3], pco[3], w, d[3], before[3], r2, r, after[3]; /* CIRS RA,Dec to Cartesian. */ iauS2c(ri, di, pi); /* Bias-precession-nutation, giving GCRS proper direction. */ iauTrxp(astrom->bpn, pi, ppr); /* Aberration, giving GCRS natural direction. */ iauZp(d); for (j = 0; j < 2; j++) { r2 = 0.0; for (i = 0; i < 3; i++) { w = ppr[i] - d[i]; before[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { before[i] /= r; } iauAb(before, astrom->v, astrom->em, astrom->bm1, after); r2 = 0.0; for (i = 0; i < 3; i++) { d[i] = after[i] - before[i]; w = ppr[i] - d[i]; pnat[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { pnat[i] /= r; } } /* Light deflection, giving BCRS coordinate direction. */ iauZp(d); for (j = 0; j < 5; j++) { r2 = 0.0; for (i = 0; i < 3; i++) { w = pnat[i] - d[i]; before[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { before[i] /= r; } iauLdn(n, b, astrom->eb, before, after); r2 = 0.0; for (i = 0; i < 3; i++) { d[i] = after[i] - before[i]; w = pnat[i] - d[i]; pco[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { pco[i] /= r; } } /* ICRS astrometric RA,Dec. */ iauC2s(pco, &w, dc); *rc = iauAnp(w); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atio13.c0000644000113000011300000002633713027221062014437 0ustar bellsbells#include "sofa.h" int iauAtio13(double ri, double di, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *aob, double *zob, double *hob, double *dob, double *rob) /* ** - - - - - - - - - - ** i a u A t i o 1 3 ** - - - - - - - - - - ** ** CIRS RA,Dec to observed place. The caller supplies UTC, site ** coordinates, ambient air conditions and observing wavelength. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri double CIRS right ascension (CIO-based, radians) ** di double CIRS declination (radians) ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 1,2) ** dut1 double UT1-UTC (seconds, Note 3) ** elong double longitude (radians, east +ve, Note 4) ** phi double geodetic latitude (radians, Note 4) ** hm double height above ellipsoid (m, geodetic Notes 4,6) ** xp,yp double polar motion coordinates (radians, Note 5) ** phpa double pressure at the observer (hPa = mB, Note 6) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 7) ** ** Returned: ** aob double* observed azimuth (radians: N=0,E=90) ** zob double* observed zenith distance (radians) ** hob double* observed hour angle (radians) ** dob double* observed declination (radians) ** rob double* observed right ascension (CIO-based, radians) ** ** Returned (function value): ** int status: +1 = dubious year (Note 2) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 2) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the ** future to be trusted. See iauDat for further details. ** ** 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 4) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 5) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many ** applications, xp and yp can be set to zero. ** ** 6) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to ** the pressure and that an accurate phpa value is important for ** precise work. ** ** 7) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 8) "Observed" Az,ZD means the position that would be seen by a ** perfect geodetically aligned theodolite. (Zenith distance is ** used rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) This is ** related to the observed HA,Dec via the standard rotation, using ** the geodetic latitude (corrected for polar motion), while the ** observed HA and RA are related simply through the Earth rotation ** angle and the site longitude. "Observed" RA,Dec or HA,Dec thus ** means the position that would be seen by a perfect equatorial ** with its polar axis aligned to the Earth's axis of rotation. ** ** 9) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted astrometric ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better ** than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** 10) The complementary functions iauAtio13 and iauAtoi13 are self- ** consistent to better than 1 microarcsecond all over the ** celestial sphere. ** ** 11) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** iauApio13 astrometry parameters, CIRS-observed, 2013 ** iauAtioq quick CIRS to observed ** ** This revision: 2016 February 2 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j; iauASTROM astrom; /* Star-independent astrometry parameters for CIRS->observed. */ j = iauApio13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom); /* Abort if bad UTC. */ if ( j < 0 ) return j; /* Transform CIRS to observed. */ iauAtioq(ri, di, &astrom, aob, zob, hob, dob, rob); /* Return OK/warning status. */ return j; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atioq.c0000644000113000011300000002617613027221062014455 0ustar bellsbells#include "sofa.h" void iauAtioq(double ri, double di, iauASTROM *astrom, double *aob, double *zob, double *hob, double *dob, double *rob) /* ** - - - - - - - - - ** i a u A t i o q ** - - - - - - - - - ** ** Quick CIRS to observed place transformation. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are all to be transformed for one date. ** The star-independent astrometry parameters can be obtained by ** calling iauApio[13] or iauApco[13]. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri double CIRS right ascension ** di double CIRS declination ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** aob double* observed azimuth (radians: N=0,E=90) ** zob double* observed zenith distance (radians) ** hob double* observed hour angle (radians) ** dob double* observed declination (radians) ** rob double* observed right ascension (CIO-based, radians) ** ** Notes: ** ** 1) This function returns zenith distance rather than altitude in ** order to reflect the fact that no allowance is made for ** depression of the horizon. ** ** 2) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted observed ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better ** than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions iauAtioq and ** iauAtoiq are self-consistent to better than 1 microarcsecond all ** over the celestial sphere. With refraction included, consistency ** falls off at high zenith distances, but is still better than ** 0.05 arcsec at 85 degrees. ** ** 3) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 4) The CIRS RA,Dec is obtained from a star catalog mean place by ** allowing for space motion, parallax, the Sun's gravitational lens ** effect, annual aberration and precession-nutation. For star ** positions in the ICRS, these effects can be applied by means of ** the iauAtci13 (etc.) functions. Starting from classical "mean ** place" systems, additional transformations will be needed first. ** ** 5) "Observed" Az,El means the position that would be seen by a ** perfect geodetically aligned theodolite. This is obtained from ** the CIRS RA,Dec by allowing for Earth orientation and diurnal ** aberration, rotating from equator to horizon coordinates, and ** then adjusting for refraction. The HA,Dec is obtained by ** rotating back into equatorial coordinates, and is the position ** that would be seen by a perfect equatorial with its polar axis ** aligned to the Earth's axis of rotation. Finally, the RA is ** obtained by subtracting the HA from the local ERA. ** ** 6) The star-independent CIRS-to-observed-place parameters in ASTROM ** may be computed with iauApio[13] or iauApco[13]. If nothing has ** changed significantly except the time, iauAper[13] may be used to ** perform the requisite adjustment to the astrom structure. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauC2s p-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** This revision: 2016 March 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Minimum cos(alt) and sin(alt) for refraction purposes */ const double CELMIN = 1e-6; const double SELMIN = 0.05; double v[3], x, y, z, xhd, yhd, zhd, f, xhdt, yhdt, zhdt, xaet, yaet, zaet, azobs, r, tz, w, del, cosdel, xaeo, yaeo, zaeo, zdobs, hmobs, dcobs, raobs; /* CIRS RA,Dec to Cartesian -HA,Dec. */ iauS2c(ri-astrom->eral, di, v); x = v[0]; y = v[1]; z = v[2]; /* Polar motion. */ xhd = x + astrom->xpl*z; yhd = y - astrom->ypl*z; zhd = z - astrom->xpl*x + astrom->ypl*y; /* Diurnal aberration. */ f = ( 1.0 - astrom->diurab*yhd ); xhdt = f * xhd; yhdt = f * ( yhd + astrom->diurab ); zhdt = f * zhd; /* Cartesian -HA,Dec to Cartesian Az,El (S=0,E=90). */ xaet = astrom->sphi*xhdt - astrom->cphi*zhdt; yaet = yhdt; zaet = astrom->cphi*xhdt + astrom->sphi*zhdt; /* Azimuth (N=0,E=90). */ azobs = ( xaet != 0.0 || yaet != 0.0 ) ? atan2(yaet,-xaet) : 0.0; /* ---------- */ /* Refraction */ /* ---------- */ /* Cosine and sine of altitude, with precautions. */ r = sqrt(xaet*xaet + yaet*yaet); r = r > CELMIN ? r : CELMIN; z = zaet > SELMIN ? zaet : SELMIN; /* A*tan(z)+B*tan^3(z) model, with Newton-Raphson correction. */ tz = r/z; w = astrom->refb*tz*tz; del = ( astrom->refa + w ) * tz / ( 1.0 + ( astrom->refa + 3.0*w ) / ( z*z ) ); /* Apply the change, giving observed vector. */ cosdel = 1.0 - del*del/2.0; f = cosdel - del*z/r; xaeo = xaet*f; yaeo = yaet*f; zaeo = cosdel*zaet + del*r; /* Observed ZD. */ zdobs = atan2(sqrt(xaeo*xaeo+yaeo*yaeo), zaeo); /* Az/El vector to HA,Dec vector (both right-handed). */ v[0] = astrom->sphi*xaeo + astrom->cphi*zaeo; v[1] = yaeo; v[2] = - astrom->cphi*xaeo + astrom->sphi*zaeo; /* To spherical -HA,Dec. */ iauC2s ( v, &hmobs, &dcobs ); /* Right ascension (with respect to CIO). */ raobs = astrom->eral + hmobs; /* Return the results. */ *aob = iauAnp(azobs); *zob = zdobs; *hob = -hmobs; *dob = dcobs; *rob = iauAnp(raobs); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atoc13.c0000644000113000011300000002734413027221062014430 0ustar bellsbells#include "sofa.h" int iauAtoc13(const char *type, double ob1, double ob2, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *rc, double *dc) /* ** - - - - - - - - - - ** i a u A t o c 1 3 ** - - - - - - - - - - ** ** Observed place at a groundbased site to to ICRS astrometric RA,Dec. ** The caller supplies UTC, site coordinates, ambient air conditions ** and observing wavelength. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** type char[] type of coordinates - "R", "H" or "A" (Notes 1,2) ** ob1 double observed Az, HA or RA (radians; Az is N=0,E=90) ** ob2 double observed ZD or Dec (radians) ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 3,4) ** dut1 double UT1-UTC (seconds, Note 5) ** elong double longitude (radians, east +ve, Note 6) ** phi double geodetic latitude (radians, Note 6) ** hm double height above ellipsoid (m, geodetic Notes 6,8) ** xp,yp double polar motion coordinates (radians, Note 7) ** phpa double pressure at the observer (hPa = mB, Note 8) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 9) ** ** Returned: ** rc,dc double ICRS astrometric RA,Dec (radians) ** ** Returned (function value): ** int status: +1 = dubious year (Note 4) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) "Observed" Az,ZD means the position that would be seen by a ** perfect geodetically aligned theodolite. (Zenith distance is ** used rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) This is ** related to the observed HA,Dec via the standard rotation, using ** the geodetic latitude (corrected for polar motion), while the ** observed HA and RA are related simply through the Earth rotation ** angle and the site longitude. "Observed" RA,Dec or HA,Dec thus ** means the position that would be seen by a perfect equatorial ** with its polar axis aligned to the Earth's axis of rotation. ** ** 2) Only the first character of the type argument is significant. ** "R" or "r" indicates that ob1 and ob2 are the observed right ** ascension and declination; "H" or "h" indicates that they are ** hour angle (west +ve) and declination; anything else ("A" or ** "a" is recommended) indicates that ob1 and ob2 are azimuth ** (north zero, east 90 deg) and zenith distance. ** ** 3) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 4) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the ** future to be trusted. See iauDat for further details. ** ** 5) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 6) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 7) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many ** applications, xp and yp can be set to zero. ** ** 8) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to ** the pressure and that an accurate phpa value is important for ** precise work. ** ** 9) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 10) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted astrometric ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better ** than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions iauAtco13 and ** iauAtoc13 are self-consistent to better than 1 microarcsecond ** all over the celestial sphere. With refraction included, ** consistency falls off at high zenith distances, but is still ** better than 0.05 arcsec at 85 degrees. ** ** 11) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** iauApco13 astrometry parameters, ICRS-observed ** iauAtoiq quick observed to CIRS ** iauAticq quick CIRS to ICRS ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j; iauASTROM astrom; double eo, ri, di; /* Star-independent astrometry parameters. */ j = iauApco13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom, &eo); /* Abort if bad UTC. */ if ( j < 0 ) return j; /* Transform observed to CIRS. */ iauAtoiq(type, ob1, ob2, &astrom, &ri, &di); /* Transform CIRS to ICRS. */ iauAticq(ri, di, &astrom, rc, dc); /* Return OK/warning status. */ return j; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atoi13.c0000644000113000011300000002717713027221062014442 0ustar bellsbells#include "sofa.h" int iauAtoi13(const char *type, double ob1, double ob2, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *ri, double *di) /* ** - - - - - - - - - - ** i a u A t o i 1 3 ** - - - - - - - - - - ** ** Observed place to CIRS. The caller supplies UTC, site coordinates, ** ambient air conditions and observing wavelength. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** type char[] type of coordinates - "R", "H" or "A" (Notes 1,2) ** ob1 double observed Az, HA or RA (radians; Az is N=0,E=90) ** ob2 double observed ZD or Dec (radians) ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 3,4) ** dut1 double UT1-UTC (seconds, Note 5) ** elong double longitude (radians, east +ve, Note 6) ** phi double geodetic latitude (radians, Note 6) ** hm double height above the ellipsoid (meters, Notes 6,8) ** xp,yp double polar motion coordinates (radians, Note 7) ** phpa double pressure at the observer (hPa = mB, Note 8) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 9) ** ** Returned: ** ri double* CIRS right ascension (CIO-based, radians) ** di double* CIRS declination (radians) ** ** Returned (function value): ** int status: +1 = dubious year (Note 2) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) "Observed" Az,ZD means the position that would be seen by a ** perfect geodetically aligned theodolite. (Zenith distance is ** used rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) This is ** related to the observed HA,Dec via the standard rotation, using ** the geodetic latitude (corrected for polar motion), while the ** observed HA and RA are related simply through the Earth rotation ** angle and the site longitude. "Observed" RA,Dec or HA,Dec thus ** means the position that would be seen by a perfect equatorial ** with its polar axis aligned to the Earth's axis of rotation. ** ** 2) Only the first character of the type argument is significant. ** "R" or "r" indicates that ob1 and ob2 are the observed right ** ascension and declination; "H" or "h" indicates that they are ** hour angle (west +ve) and declination; anything else ("A" or ** "a" is recommended) indicates that ob1 and ob2 are azimuth ** (north zero, east 90 deg) and zenith distance. ** ** 3) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 4) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the ** future to be trusted. See iauDat for further details. ** ** 5) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 6) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 7) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many ** applications, xp and yp can be set to zero. ** ** 8) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to ** the pressure and that an accurate phpa value is important for ** precise work. ** ** 9) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 10) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted astrometric ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better ** than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions iauAtio13 and ** iauAtoi13 are self-consistent to better than 1 microarcsecond ** all over the celestial sphere. With refraction included, ** consistency falls off at high zenith distances, but is still ** better than 0.05 arcsec at 85 degrees. ** ** 12) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** iauApio13 astrometry parameters, CIRS-observed, 2013 ** iauAtoiq quick observed to CIRS ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j; iauASTROM astrom; /* Star-independent astrometry parameters for CIRS->observed. */ j = iauApio13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom); /* Abort if bad UTC. */ if ( j < 0 ) return j; /* Transform observed to CIRS. */ iauAtoiq(type, ob1, ob2, &astrom, ri, di); /* Return OK/warning status. */ return j; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/atoiq.c0000644000113000011300000002555413027221062014454 0ustar bellsbells#include "sofa.h" void iauAtoiq(const char *type, double ob1, double ob2, iauASTROM *astrom, double *ri, double *di) /* ** - - - - - - - - - ** i a u A t o i q ** - - - - - - - - - ** ** Quick observed place to CIRS, given the star-independent astrometry ** parameters. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are all to be transformed for one date. ** The star-independent astrometry parameters can be obtained by ** calling iauApio[13] or iauApco[13]. ** ** Status: support function. ** ** Given: ** type char[] type of coordinates: "R", "H" or "A" (Note 1) ** ob1 double observed Az, HA or RA (radians; Az is N=0,E=90) ** ob2 double observed ZD or Dec (radians) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** ri double* CIRS right ascension (CIO-based, radians) ** di double* CIRS declination (radians) ** ** Notes: ** ** 1) "Observed" Az,El means the position that would be seen by a ** perfect geodetically aligned theodolite. This is related to ** the observed HA,Dec via the standard rotation, using the geodetic ** latitude (corrected for polar motion), while the observed HA and ** RA are related simply through the Earth rotation angle and the ** site longitude. "Observed" RA,Dec or HA,Dec thus means the ** position that would be seen by a perfect equatorial with its ** polar axis aligned to the Earth's axis of rotation. By removing ** from the observed place the effects of atmospheric refraction and ** diurnal aberration, the CIRS RA,Dec is obtained. ** ** 2) Only the first character of the type argument is significant. ** "R" or "r" indicates that ob1 and ob2 are the observed right ** ascension and declination; "H" or "h" indicates that they are ** hour angle (west +ve) and declination; anything else ("A" or ** "a" is recommended) indicates that ob1 and ob2 are azimuth (north ** zero, east 90 deg) and zenith distance. (Zenith distance is used ** rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) ** ** 3) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted observed ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better than ** 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions iauAtioq and ** iauAtoiq are self-consistent to better than 1 microarcsecond all ** over the celestial sphere. With refraction included, consistency ** falls off at high zenith distances, but is still better than ** 0.05 arcsec at 85 degrees. ** ** 4) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauC2s p-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int c; double c1, c2, sphi, cphi, ce, xaeo, yaeo, zaeo, v[3], xmhdo, ymhdo, zmhdo, az, sz, zdo, refa, refb, tz, dref, zdt, xaet, yaet, zaet, xmhda, ymhda, zmhda, f, xhd, yhd, zhd, xpl, ypl, w, hma; /* Coordinate type. */ c = (int) type[0]; /* Coordinates. */ c1 = ob1; c2 = ob2; /* Sin, cos of latitude. */ sphi = astrom->sphi; cphi = astrom->cphi; /* Standardize coordinate type. */ if ( c == 'r' || c == 'R' ) { c = 'R'; } else if ( c == 'h' || c == 'H' ) { c = 'H'; } else { c = 'A'; } /* If Az,ZD, convert to Cartesian (S=0,E=90). */ if ( c == 'A' ) { ce = sin(c2); xaeo = - cos(c1) * ce; yaeo = sin(c1) * ce; zaeo = cos(c2); } else { /* If RA,Dec, convert to HA,Dec. */ if ( c == 'R' ) c1 = astrom->eral - c1; /* To Cartesian -HA,Dec. */ iauS2c ( -c1, c2, v ); xmhdo = v[0]; ymhdo = v[1]; zmhdo = v[2]; /* To Cartesian Az,El (S=0,E=90). */ xaeo = sphi*xmhdo - cphi*zmhdo; yaeo = ymhdo; zaeo = cphi*xmhdo + sphi*zmhdo; } /* Azimuth (S=0,E=90). */ az = ( xaeo != 0.0 || yaeo != 0.0 ) ? atan2(yaeo,xaeo) : 0.0; /* Sine of observed ZD, and observed ZD. */ sz = sqrt ( xaeo*xaeo + yaeo*yaeo ); zdo = atan2 ( sz, zaeo ); /* ** Refraction ** ---------- */ /* Fast algorithm using two constant model. */ refa = astrom->refa; refb = astrom->refb; tz = sz / zaeo; dref = ( refa + refb*tz*tz ) * tz; zdt = zdo + dref; /* To Cartesian Az,ZD. */ ce = sin(zdt); xaet = cos(az) * ce; yaet = sin(az) * ce; zaet = cos(zdt); /* Cartesian Az,ZD to Cartesian -HA,Dec. */ xmhda = sphi*xaet + cphi*zaet; ymhda = yaet; zmhda = - cphi*xaet + sphi*zaet; /* Diurnal aberration. */ f = ( 1.0 + astrom->diurab*ymhda ); xhd = f * xmhda; yhd = f * ( ymhda - astrom->diurab ); zhd = f * zmhda; /* Polar motion. */ xpl = astrom->xpl; ypl = astrom->ypl; w = xpl*xhd - ypl*yhd + zhd; v[0] = xhd - xpl*w; v[1] = yhd + ypl*w; v[2] = w - ( xpl*xpl + ypl*ypl ) * zhd; /* To spherical -HA,Dec. */ iauC2s(v, &hma, di); /* Right ascension. */ *ri = iauAnp(astrom->eral + hma); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/bi00.c0000644000113000011300000001476013027221062014066 0ustar bellsbells#include "sofa.h" void iauBi00(double *dpsibi, double *depsbi, double *dra) /* ** - - - - - - - - ** i a u B i 0 0 ** - - - - - - - - ** ** Frame bias components of IAU 2000 precession-nutation models (part ** of MHB2000 with additions). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Returned: ** dpsibi,depsbi double longitude and obliquity corrections ** dra double the ICRS RA of the J2000.0 mean equinox ** ** Notes: ** ** 1) The frame bias corrections in longitude and obliquity (radians) ** are required in order to correct for the offset between the GCRS ** pole and the mean J2000.0 pole. They define, with respect to the ** GCRS frame, a J2000.0 mean pole that is consistent with the rest ** of the IAU 2000A precession-nutation model. ** ** 2) In addition to the displacement of the pole, the complete ** description of the frame bias requires also an offset in right ** ascension. This is not part of the IAU 2000A model, and is from ** Chapront et al. (2002). It is returned in radians. ** ** 3) This is a supplemented implementation of one aspect of the IAU ** 2000A nutation model, formally adopted by the IAU General ** Assembly in 2000, namely MHB2000 (Mathews et al. 2002). ** ** References: ** ** Chapront, J., Chapront-Touze, M. & Francou, G., Astron. ** Astrophys., 387, 700, 2002. ** ** Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation ** and precession New nutation series for nonrigid Earth and ** insights into the Earth's interior", J.Geophys.Res., 107, B4, ** 2002. The MHB2000 code itself was obtained on 9th September 2002 ** from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* The frame bias corrections in longitude and obliquity */ const double DPBIAS = -0.041775 * DAS2R, DEBIAS = -0.0068192 * DAS2R; /* The ICRS RA of the J2000.0 equinox (Chapront et al., 2002) */ const double DRA0 = -0.0146 * DAS2R; /* Return the results (which are fixed). */ *dpsibi = DPBIAS; *depsbi = DEBIAS; *dra = DRA0; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/bp00.c0000644000113000011300000002040613027221062014067 0ustar bellsbells#include "sofa.h" void iauBp00(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]) /* ** - - - - - - - - ** i a u B p 0 0 ** - - - - - - - - ** ** Frame bias and precession, IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rb double[3][3] frame bias matrix (Note 2) ** rp double[3][3] precession matrix (Note 3) ** rbp double[3][3] bias-precession matrix (Note 4) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rb transforms vectors from GCRS to mean J2000.0 by ** applying frame bias. ** ** 3) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 4) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 5) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the order given. ** ** Called: ** iauBi00 frame bias components, IAU 2000 ** iauPr00 IAU 2000 precession adjustments ** iauIr initialize r-matrix to identity ** iauRx rotate around X-axis ** iauRy rotate around Y-axis ** iauRz rotate around Z-axis ** iauCr copy r-matrix ** iauRxr product of two r-matrices ** ** Reference: ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** This revision: 2013 August 21 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* J2000.0 obliquity (Lieske et al. 1977) */ const double EPS0 = 84381.448 * DAS2R; double t, dpsibi, depsbi, dra0, psia77, oma77, chia, dpsipr, depspr, psia, oma, rbw[3][3]; /* Interval between fundamental epoch J2000.0 and current date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Frame bias. */ iauBi00(&dpsibi, &depsbi, &dra0); /* Precession angles (Lieske et al. 1977) */ psia77 = (5038.7784 + (-1.07259 + (-0.001147) * t) * t) * t * DAS2R; oma77 = EPS0 + ((0.05127 + (-0.007726) * t) * t) * t * DAS2R; chia = ( 10.5526 + (-2.38064 + (-0.001125) * t) * t) * t * DAS2R; /* Apply IAU 2000 precession corrections. */ iauPr00(date1, date2, &dpsipr, &depspr); psia = psia77 + dpsipr; oma = oma77 + depspr; /* Frame bias matrix: GCRS to J2000.0. */ iauIr(rbw); iauRz(dra0, rbw); iauRy(dpsibi*sin(EPS0), rbw); iauRx(-depsbi, rbw); iauCr(rbw, rb); /* Precession matrix: J2000.0 to mean of date. */ iauIr(rp); iauRx(EPS0, rp); iauRz(-psia, rp); iauRx(-oma, rp); iauRz(chia, rp); /* Bias-precession matrix: GCRS to mean of date. */ iauRxr(rp, rbw, rbp); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/bp06.c0000644000113000011300000001616013027221062014077 0ustar bellsbells#include "sofa.h" void iauBp06(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]) /* ** - - - - - - - - ** i a u B p 0 6 ** - - - - - - - - ** ** Frame bias and precession, IAU 2006. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rb double[3][3] frame bias matrix (Note 2) ** rp double[3][3] precession matrix (Note 3) ** rbp double[3][3] bias-precession matrix (Note 4) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rb transforms vectors from GCRS to mean J2000.0 by ** applying frame bias. ** ** 3) The matrix rp transforms vectors from mean J2000.0 to mean of ** date by applying precession. ** ** 4) The matrix rbp transforms vectors from GCRS to mean of date by ** applying frame bias then precession. It is the product rp x rb. ** ** 5) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the order given. ** ** Called: ** iauPfw06 bias-precession F-W angles, IAU 2006 ** iauFw2m F-W angles to r-matrix ** iauPmat06 PB matrix, IAU 2006 ** iauTr transpose r-matrix ** iauRxr product of two r-matrices ** iauCr copy r-matrix ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** This revision: 2013 August 21 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double gamb, phib, psib, epsa, rbpw[3][3], rbt[3][3]; /* B matrix. */ iauPfw06(DJM0, DJM00, &gamb, &phib, &psib, &epsa); iauFw2m(gamb, phib, psib, epsa, rb); /* PxB matrix (temporary). */ iauPmat06(date1, date2, rbpw); /* P matrix. */ iauTr(rb, rbt); iauRxr(rbpw, rbt, rp); /* PxB matrix. */ iauCr(rbpw, rbp); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/bpn2xy.c0000644000113000011300000001327613027221062014557 0ustar bellsbells#include "sofa.h" void iauBpn2xy(double rbpn[3][3], double *x, double *y) /* ** - - - - - - - - - - ** i a u B p n 2 x y ** - - - - - - - - - - ** ** Extract from the bias-precession-nutation matrix the X,Y coordinates ** of the Celestial Intermediate Pole. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rbpn double[3][3] celestial-to-true matrix (Note 1) ** ** Returned: ** x,y double Celestial Intermediate Pole (Note 2) ** ** Notes: ** ** 1) The matrix rbpn transforms vectors from GCRS to true equator (and ** CIO or equinox) of date, and therefore the Celestial Intermediate ** Pole unit vector is the bottom row of the matrix. ** ** 2) The arguments x,y are components of the Celestial Intermediate ** Pole unit vector in the Geocentric Celestial Reference System. ** ** Reference: ** ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 ** (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Extract the X,Y coordinates. */ *x = rbpn[2][0]; *y = rbpn[2][1]; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2i00a.c0000644000113000011300000001631713027221062014312 0ustar bellsbells#include "sofa.h" void iauC2i00a(double date1, double date2, double rc2i[3][3]) /* ** - - - - - - - - - - ** i a u C 2 i 0 0 a ** - - - - - - - - - - ** ** Form the celestial-to-intermediate matrix for a given date using the ** IAU 2000A precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 3) A faster, but slightly less accurate result (about 1 mas), can be ** obtained by using instead the iauC2i00b function. ** ** Called: ** iauPnm00a classical NPB matrix, IAU 2000A ** iauC2ibpn celestial-to-intermediate matrix, given NPB matrix ** ** References: ** ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 ** (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rbpn[3][3]; /* Obtain the celestial-to-true matrix (IAU 2000A). */ iauPnm00a(date1, date2, rbpn); /* Form the celestial-to-intermediate matrix. */ iauC2ibpn(date1, date2, rbpn, rc2i); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2i00b.c0000644000113000011300000001630213027221062014305 0ustar bellsbells#include "sofa.h" void iauC2i00b(double date1, double date2, double rc2i[3][3]) /* ** - - - - - - - - - - ** i a u C 2 i 0 0 b ** - - - - - - - - - - ** ** Form the celestial-to-intermediate matrix for a given date using the ** IAU 2000B precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 3) The present function is faster, but slightly less accurate (about ** 1 mas), than the iauC2i00a function. ** ** Called: ** iauPnm00b classical NPB matrix, IAU 2000B ** iauC2ibpn celestial-to-intermediate matrix, given NPB matrix ** ** References: ** ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 ** (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rbpn[3][3]; /* Obtain the celestial-to-true matrix (IAU 2000B). */ iauPnm00b(date1, date2, rbpn); /* Form the celestial-to-intermediate matrix. */ iauC2ibpn(date1, date2, rbpn, rc2i); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2i06a.c0000644000113000011300000001577513027221062014327 0ustar bellsbells#include "sofa.h" void iauC2i06a(double date1, double date2, double rc2i[3][3]) /* ** - - - - - - - - - - ** i a u C 2 i 0 6 a ** - - - - - - - - - - ** ** Form the celestial-to-intermediate matrix for a given date using the ** IAU 2006 precession and IAU 2000A nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = RC2T * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** Called: ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** iauC2ixys celestial-to-intermediate matrix, given X,Y and s ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rbpn[3][3], x, y, s; /* Obtain the celestial-to-true matrix (IAU 2006/2000A). */ iauPnm06a(date1, date2, rbpn); /* Extract the X,Y coordinates. */ iauBpn2xy(rbpn, &x, &y); /* Obtain the CIO locator. */ s = iauS06(date1, date2, x, y); /* Form the celestial-to-intermediate matrix. */ iauC2ixys(x, y, s, rc2i); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2ibpn.c0000644000113000011300000001665013027221062014511 0ustar bellsbells#include "sofa.h" void iauC2ibpn(double date1, double date2, double rbpn[3][3], double rc2i[3][3]) /* ** - - - - - - - - - - ** i a u C 2 i b p n ** - - - - - - - - - - ** ** Form the celestial-to-intermediate matrix for a given date given ** the bias-precession-nutation matrix. IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** rbpn double[3][3] celestial-to-true matrix (Note 2) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 3) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rbpn transforms vectors from GCRS to true equator (and ** CIO or equinox) of date. Only the CIP (bottom row) is used. ** ** 3) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = RC2T * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 4) Although its name does not include "00", This function is in fact ** specific to the IAU 2000 models. ** ** Called: ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauC2ixy celestial-to-intermediate matrix, given X,Y ** ** References: ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double x, y; /* Extract the X,Y coordinates. */ iauBpn2xy(rbpn, &x, &y); /* Form the celestial-to-intermediate matrix (n.b. IAU 2000 specific). */ iauC2ixy(date1, date2, x, y, rc2i); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2ixy.c0000644000113000011300000001577213027221062014376 0ustar bellsbells#include "sofa.h" void iauC2ixy(double date1, double date2, double x, double y, double rc2i[3][3]) /* ** - - - - - - - - - ** i a u C 2 i x y ** - - - - - - - - - ** ** Form the celestial to intermediate-frame-of-date matrix for a given ** date when the CIP X,Y coordinates are known. IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** x,y double Celestial Intermediate Pole (Note 2) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 3) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y components ** of the unit vector in the Geocentric Celestial Reference System. ** ** 3) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = RC2T * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 4) Although its name does not include "00", This function is in fact ** specific to the IAU 2000 models. ** ** Called: ** iauC2ixys celestial-to-intermediate matrix, given X,Y and s ** iauS00 the CIO locator s, given X,Y, IAU 2000A ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Compute s and then the matrix. */ iauC2ixys(x, y, iauS00(date1, date2, x, y), rc2i); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2ixys.c0000644000113000011300000001436713027221062014560 0ustar bellsbells#include "sofa.h" void iauC2ixys(double x, double y, double s, double rc2i[3][3]) /* ** - - - - - - - - - - ** i a u C 2 i x y s ** - - - - - - - - - - ** ** Form the celestial to intermediate-frame-of-date matrix given the CIP ** X,Y and the CIO locator s. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** x,y double Celestial Intermediate Pole (Note 1) ** s double the CIO locator s (Note 2) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 3) ** ** Notes: ** ** 1) The Celestial Intermediate Pole coordinates are the x,y ** components of the unit vector in the Geocentric Celestial ** Reference System. ** ** 2) The CIO locator s (in radians) positions the Celestial ** Intermediate Origin on the equator of the CIP. ** ** 3) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = RC2T * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** Called: ** iauIr initialize r-matrix to identity ** iauRz rotate around Z-axis ** iauRy rotate around Y-axis ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2014 November 7 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double r2, e, d; /* Obtain the spherical angles E and d. */ r2 = x*x + y*y; e = (r2 > 0.0) ? atan2(y, x) : 0.0; d = atan(sqrt(r2 / (1.0 - r2))); /* Form the matrix. */ iauIr(rc2i); iauRz(e, rc2i); iauRy(d, rc2i); iauRz(-(e+s), rc2i); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2s.c0000644000113000011300000001231013027221062014010 0ustar bellsbells#include "sofa.h" void iauC2s(double p[3], double *theta, double *phi) /* ** - - - - - - - ** i a u C 2 s ** - - - - - - - ** ** P-vector to spherical coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector ** ** Returned: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** ** Notes: ** ** 1) The vector p can have any magnitude; only its direction is used. ** ** 2) If p is null, zero theta and phi are returned. ** ** 3) At either pole, zero theta is returned. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double x, y, z, d2; x = p[0]; y = p[1]; z = p[2]; d2 = x*x + y*y; *theta = (d2 == 0.0) ? 0.0 : atan2(y, x); *phi = (z == 0.0) ? 0.0 : atan2(z, sqrt(d2)); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2t00a.c0000644000113000011300000001762313027221062014326 0ustar bellsbells#include "sofa.h" void iauC2t00a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t 0 0 a ** - - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1 and ** the polar motion, using the IAU 2000A nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** xp,yp double coordinates of the pole (radians, Note 2) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any of ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 3) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), RC2I is the ** celestial-to-intermediate matrix, ERA is the Earth rotation ** angle and RPOM is the polar motion matrix. ** ** 4) A faster, but slightly less accurate result (about 1 mas), can ** be obtained by using instead the iauC2t00b function. ** ** Called: ** iauC2i00a celestial-to-intermediate matrix, IAU 2000A ** iauEra00 Earth rotation angle, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauPom00 polar motion matrix ** iauC2tcio form CIO-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rc2i[3][3], era, sp, rpom[3][3]; /* Form the celestial-to-intermediate matrix for this TT (IAU 2000A). */ iauC2i00a(tta, ttb, rc2i ); /* Predict the Earth rotation angle for this UT1. */ era = iauEra00(uta, utb); /* Estimate s'. */ sp = iauSp00(tta, ttb); /* Form the polar motion matrix. */ iauPom00(xp, yp, sp, rpom); /* Combine to form the celestial-to-terrestrial matrix. */ iauC2tcio(rc2i, era, rpom, rc2t); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2t00b.c0000644000113000011300000001746113027221062014327 0ustar bellsbells#include "sofa.h" void iauC2t00b(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t 0 0 b ** - - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1 and ** the polar motion, using the IAU 2000B nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** xp,yp double coordinates of the pole (radians, Note 2) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any of ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 3) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), RC2I is the ** celestial-to-intermediate matrix, ERA is the Earth rotation ** angle and RPOM is the polar motion matrix. ** ** 4) The present function is faster, but slightly less accurate (about ** 1 mas), than the iauC2t00a function. ** ** Called: ** iauC2i00b celestial-to-intermediate matrix, IAU 2000B ** iauEra00 Earth rotation angle, IAU 2000 ** iauPom00 polar motion matrix ** iauC2tcio form CIO-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rc2i[3][3], era, rpom[3][3]; /* Form the celestial-to-intermediate matrix for this TT (IAU 2000B). */ iauC2i00b(tta, ttb, rc2i); /* Predict the Earth rotation angle for this UT1. */ era = iauEra00(uta, utb); /* Form the polar motion matrix (neglecting s'). */ iauPom00(xp, yp, 0.0, rpom); /* Combine to form the celestial-to-terrestrial matrix. */ iauC2tcio(rc2i, era, rpom, rc2t); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2t06a.c0000644000113000011300000001744213027221062014333 0ustar bellsbells#include "sofa.h" void iauC2t06a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t 0 6 a ** - - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1 and ** the polar motion, using the IAU 2006 precession and IAU 2000A ** nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** xp,yp double coordinates of the pole (radians, Note 2) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any of ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 3) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), RC2I is the ** celestial-to-intermediate matrix, ERA is the Earth rotation ** angle and RPOM is the polar motion matrix. ** ** Called: ** iauC2i06a celestial-to-intermediate matrix, IAU 2006/2000A ** iauEra00 Earth rotation angle, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauPom00 polar motion matrix ** iauC2tcio form CIO-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rc2i[3][3], era, sp, rpom[3][3]; /* Form the celestial-to-intermediate matrix for this TT. */ iauC2i06a(tta, ttb, rc2i); /* Predict the Earth rotation angle for this UT1. */ era = iauEra00(uta, utb); /* Estimate s'. */ sp = iauSp00(tta, ttb); /* Form the polar motion matrix. */ iauPom00(xp, yp, sp, rpom); /* Combine to form the celestial-to-terrestrial matrix. */ iauC2tcio(rc2i, era, rpom, rc2t); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2tcio.c0000644000113000011300000001477413027221062014524 0ustar bellsbells#include "sofa.h" void iauC2tcio(double rc2i[3][3], double era, double rpom[3][3], double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t c i o ** - - - - - - - - - - ** ** Assemble the celestial to terrestrial matrix from CIO-based ** components (the celestial-to-intermediate matrix, the Earth Rotation ** Angle and the polar motion matrix). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc2i double[3][3] celestial-to-intermediate matrix ** era double Earth rotation angle (radians) ** rpom double[3][3] polar-motion matrix ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix ** ** Notes: ** ** 1) This function constructs the rotation matrix that transforms ** vectors in the celestial system into vectors in the terrestrial ** system. It does so starting from precomputed components, namely ** the matrix which rotates from celestial coordinates to the ** intermediate frame, the Earth rotation angle and the polar motion ** matrix. One use of the present function is when generating a ** series of celestial-to-terrestrial matrices where only the Earth ** Rotation Angle changes, avoiding the considerable overhead of ** recomputing the precession-nutation more often than necessary to ** achieve given accuracy objectives. ** ** 2) The relationship between the arguments is as follows: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003). ** ** Called: ** iauCr copy r-matrix ** iauRz rotate around Z-axis ** iauRxr product of two r-matrices ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** This revision: 2013 August 24 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double r[3][3]; /* Construct the matrix. */ iauCr(rc2i, r); iauRz(era, r); iauRxr(rpom, r, rc2t); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2teqx.c0000644000113000011300000001502713027221062014537 0ustar bellsbells#include "sofa.h" void iauC2teqx(double rbpn[3][3], double gst, double rpom[3][3], double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t e q x ** - - - - - - - - - - ** ** Assemble the celestial to terrestrial matrix from equinox-based ** components (the celestial-to-true matrix, the Greenwich Apparent ** Sidereal Time and the polar motion matrix). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rbpn double[3][3] celestial-to-true matrix ** gst double Greenwich (apparent) Sidereal Time (radians) ** rpom double[3][3] polar-motion matrix ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 2) ** ** Notes: ** ** 1) This function constructs the rotation matrix that transforms ** vectors in the celestial system into vectors in the terrestrial ** system. It does so starting from precomputed components, namely ** the matrix which rotates from celestial coordinates to the ** true equator and equinox of date, the Greenwich Apparent Sidereal ** Time and the polar motion matrix. One use of the present function ** is when generating a series of celestial-to-terrestrial matrices ** where only the Sidereal Time changes, avoiding the considerable ** overhead of recomputing the precession-nutation more often than ** necessary to achieve given accuracy objectives. ** ** 2) The relationship between the arguments is as follows: ** ** [TRS] = rpom * R_3(gst) * rbpn * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003). ** ** Called: ** iauCr copy r-matrix ** iauRz rotate around Z-axis ** iauRxr product of two r-matrices ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 August 24 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double r[3][3]; /* Construct the matrix. */ iauCr(rbpn, r); iauRz(gst, r); iauRxr(rpom, r, rc2t); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2tpe.c0000644000113000011300000002112213027221062014337 0ustar bellsbells#include "sofa.h" void iauC2tpe(double tta, double ttb, double uta, double utb, double dpsi, double deps, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - ** i a u C 2 t p e ** - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1, ** the nutation and the polar motion. IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** dpsi,deps double nutation (Note 2) ** xp,yp double coordinates of the pole (radians, Note 3) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 4) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any of ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The caller is responsible for providing the nutation components; ** they are in longitude and obliquity, in radians and are with ** respect to the equinox and ecliptic of date. For high-accuracy ** applications, free core nutation should be included as well as ** any other relevant corrections to the position of the CIP. ** ** 3) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 4) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(GST) * RBPN * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), RBPN is the ** bias-precession-nutation matrix, GST is the Greenwich (apparent) ** Sidereal Time and RPOM is the polar motion matrix. ** ** 5) Although its name does not include "00", This function is in fact ** specific to the IAU 2000 models. ** ** Called: ** iauPn00 bias/precession/nutation results, IAU 2000 ** iauGmst00 Greenwich mean sidereal time, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauEe00 equation of the equinoxes, IAU 2000 ** iauPom00 polar motion matrix ** iauC2teqx form equinox-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double epsa, rb[3][3], rp[3][3], rbp[3][3], rn[3][3], rbpn[3][3], gmst, ee, sp, rpom[3][3]; /* Form the celestial-to-true matrix for this TT. */ iauPn00(tta, ttb, dpsi, deps, &epsa, rb, rp, rbp, rn, rbpn); /* Predict the Greenwich Mean Sidereal Time for this UT1 and TT. */ gmst = iauGmst00(uta, utb, tta, ttb); /* Predict the equation of the equinoxes given TT and nutation. */ ee = iauEe00(tta, ttb, epsa, dpsi); /* Estimate s'. */ sp = iauSp00(tta, ttb); /* Form the polar motion matrix. */ iauPom00(xp, yp, sp, rpom); /* Combine to form the celestial-to-terrestrial matrix. */ iauC2teqx(rbpn, gmst + ee, rpom, rc2t); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/c2txy.c0000644000113000011300000002007113027221062014375 0ustar bellsbells#include "sofa.h" void iauC2txy(double tta, double ttb, double uta, double utb, double x, double y, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - ** i a u C 2 t x y ** - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1, ** the CIP coordinates and the polar motion. IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** x,y double Celestial Intermediate Pole (Note 2) ** xp,yp double coordinates of the pole (radians, Note 3) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 4) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any o ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y ** components of the unit vector in the Geocentric Celestial ** Reference System. ** ** 3) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 4) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 5) Although its name does not include "00", This function is in fact ** specific to the IAU 2000 models. ** ** Called: ** iauC2ixy celestial-to-intermediate matrix, given X,Y ** iauEra00 Earth rotation angle, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauPom00 polar motion matrix ** iauC2tcio form CIO-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rc2i[3][3], era, sp, rpom[3][3]; /* Form the celestial-to-intermediate matrix for this TT. */ iauC2ixy(tta, ttb, x, y, rc2i); /* Predict the Earth rotation angle for this UT1. */ era = iauEra00(uta, utb); /* Estimate s'. */ sp = iauSp00(tta, ttb); /* Form the polar motion matrix. */ iauPom00(xp, yp, sp, rpom); /* Combine to form the celestial-to-terrestrial matrix. */ iauC2tcio(rc2i, era, rpom, rc2t); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/cal2jd.c0000644000113000011300000001546213027221062014473 0ustar bellsbells#include "sofa.h" int iauCal2jd(int iy, int im, int id, double *djm0, double *djm) /* ** - - - - - - - - - - ** i a u C a l 2 j d ** - - - - - - - - - - ** ** Gregorian Calendar to Julian Date. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** iy,im,id int year, month, day in Gregorian calendar (Note 1) ** ** Returned: ** djm0 double MJD zero-point: always 2400000.5 ** djm double Modified Julian Date for 0 hrs ** ** Returned (function value): ** int status: ** 0 = OK ** -1 = bad year (Note 3: JD not computed) ** -2 = bad month (JD not computed) ** -3 = bad day (JD computed) ** ** Notes: ** ** 1) The algorithm used is valid from -4800 March 1, but this ** implementation rejects dates before -4799 January 1. ** ** 2) The Julian Date is returned in two pieces, in the usual SOFA ** manner, which is designed to preserve time resolution. The ** Julian Date is available as a single number by adding djm0 and ** djm. ** ** 3) In early eras the conversion is from the "Proleptic Gregorian ** Calendar"; no account is taken of the date(s) of adoption of ** the Gregorian Calendar, nor is the AD/BC numbering convention ** observed. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 12.92 (p604). ** ** This revision: 2013 August 7 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j, ly, my; long iypmy; /* Earliest year allowed (4800BC) */ const int IYMIN = -4799; /* Month lengths in days */ static const int mtab[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; /* Preset status. */ j = 0; /* Validate year and month. */ if (iy < IYMIN) return -1; if (im < 1 || im > 12) return -2; /* If February in a leap year, 1, otherwise 0. */ ly = ((im == 2) && !(iy%4) && (iy%100 || !(iy%400))); /* Validate day, taking into account leap years. */ if ( (id < 1) || (id > (mtab[im-1] + ly))) j = -3; /* Return result. */ my = (im - 14) / 12; iypmy = (long) (iy + my); *djm0 = DJM0; *djm = (double)((1461L * (iypmy + 4800L)) / 4L + (367L * (long) (im - 2 - 12 * my)) / 12L - (3L * ((iypmy + 4900L) / 100L)) / 4L + (long) id - 2432076L); /* Return status. */ return j; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/cp.c0000644000113000011300000001144113027221062013727 0ustar bellsbells#include "sofa.h" void iauCp(double p[3], double c[3]) /* ** - - - - - - ** i a u C p ** - - - - - - ** ** Copy a p-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector to be copied ** ** Returned: ** c double[3] copy ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { c[0] = p[0]; c[1] = p[1]; c[2] = p[2]; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/cpv.c0000644000113000011300000001157613027221062014126 0ustar bellsbells#include "sofa.h" void iauCpv(double pv[2][3], double c[2][3]) /* ** - - - - - - - ** i a u C p v ** - - - - - - - ** ** Copy a position/velocity vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** pv double[2][3] position/velocity vector to be copied ** ** Returned: ** c double[2][3] copy ** ** Called: ** iauCp copy p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauCp(pv[0], c[0]); iauCp(pv[1], c[1]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/cr.c0000644000113000011300000001155613027221062013740 0ustar bellsbells#include "sofa.h" void iauCr(double r[3][3], double c[3][3]) /* ** - - - - - - ** i a u C r ** - - - - - - ** ** Copy an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix to be copied ** ** Returned: ** c double[3][3] copy ** ** Called: ** iauCp copy p-vector ** ** This revision: 2016 May 19 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauCp(r[0], c[0]); iauCp(r[1], c[1]); iauCp(r[2], c[2]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/d2dtf.c0000644000113000011300000002310213027221062014325 0ustar bellsbells#include "sofa.h" #include int iauD2dtf(const char *scale, int ndp, double d1, double d2, int *iy, int *im, int *id, int ihmsf[4]) /* ** - - - - - - - - - ** i a u D 2 d t f ** - - - - - - - - - ** ** Format for output a 2-part Julian Date (or in the case of UTC a ** quasi-JD form that includes special provision for leap seconds). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** scale char[] time scale ID (Note 1) ** ndp int resolution (Note 2) ** d1,d2 double time as a 2-part Julian Date (Notes 3,4) ** ** Returned: ** iy,im,id int year, month, day in Gregorian calendar (Note 5) ** ihmsf int[4] hours, minutes, seconds, fraction (Note 1) ** ** Returned (function value): ** int status: +1 = dubious year (Note 5) ** 0 = OK ** -1 = unacceptable date (Note 6) ** ** Notes: ** ** 1) scale identifies the time scale. Only the value "UTC" (in upper ** case) is significant, and enables handling of leap seconds (see ** Note 4). ** ** 2) ndp is the number of decimal places in the seconds field, and can ** have negative as well as positive values, such as: ** ** ndp resolution ** -4 1 00 00 ** -3 0 10 00 ** -2 0 01 00 ** -1 0 00 10 ** 0 0 00 01 ** 1 0 00 00.1 ** 2 0 00 00.01 ** 3 0 00 00.001 ** ** The limits are platform dependent, but a safe range is -5 to +9. ** ** 3) d1+d2 is Julian Date, apportioned in any convenient way between ** the two arguments, for example where d1 is the Julian Day Number ** and d2 is the fraction of a day. In the case of UTC, where the ** use of JD is problematical, special conventions apply: see the ** next note. ** ** 4) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The SOFA internal convention is that ** the quasi-JD day represents UTC days whether the length is 86399, ** 86400 or 86401 SI seconds. In the 1960-1972 era there were ** smaller jumps (in either direction) each time the linear UTC(TAI) ** expression was changed, and these "mini-leaps" are also included ** in the SOFA convention. ** ** 5) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 6) For calendar conventions and limitations, see iauCal2jd. ** ** Called: ** iauJd2cal JD to Gregorian calendar ** iauD2tf decompose days to hms ** iauDat delta(AT) = TAI-UTC ** ** This revision: 2014 February 15 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int leap; char s; int iy1, im1, id1, js, iy2, im2, id2, ihmsf1[4], i; double a1, b1, fd, dat0, dat12, w, dat24, dleap; /* The two-part JD. */ a1 = d1; b1 = d2; /* Provisional calendar date. */ js = iauJd2cal(a1, b1, &iy1, &im1, &id1, &fd); if ( js ) return -1; /* Is this a leap second day? */ leap = 0; if ( ! strcmp(scale,"UTC") ) { /* TAI-UTC at 0h today. */ js = iauDat(iy1, im1, id1, 0.0, &dat0); if ( js < 0 ) return -1; /* TAI-UTC at 12h today (to detect drift). */ js = iauDat(iy1, im1, id1, 0.5, &dat12); if ( js < 0 ) return -1; /* TAI-UTC at 0h tomorrow (to detect jumps). */ js = iauJd2cal(a1+1.5, b1-fd, &iy2, &im2, &id2, &w); if ( js ) return -1; js = iauDat(iy2, im2, id2, 0.0, &dat24); if ( js < 0 ) return -1; /* Any sudden change in TAI-UTC (seconds). */ dleap = dat24 - (2.0*dat12 - dat0); /* If leap second day, scale the fraction of a day into SI. */ leap = (dleap != 0.0); if (leap) fd += fd * dleap/DAYSEC; } /* Provisional time of day. */ iauD2tf ( ndp, fd, &s, ihmsf1 ); /* Has the (rounded) time gone past 24h? */ if ( ihmsf1[0] > 23 ) { /* Yes. We probably need tomorrow's calendar date. */ js = iauJd2cal(a1+1.5, b1-fd, &iy2, &im2, &id2, &w); if ( js ) return -1; /* Is today a leap second day? */ if ( ! leap ) { /* No. Use 0h tomorrow. */ iy1 = iy2; im1 = im2; id1 = id2; ihmsf1[0] = 0; ihmsf1[1] = 0; ihmsf1[2] = 0; } else { /* Yes. Are we past the leap second itself? */ if ( ihmsf1[2] > 0 ) { /* Yes. Use tomorrow but allow for the leap second. */ iy1 = iy2; im1 = im2; id1 = id2; ihmsf1[0] = 0; ihmsf1[1] = 0; ihmsf1[2] = 0; } else { /* No. Use 23 59 60... today. */ ihmsf1[0] = 23; ihmsf1[1] = 59; ihmsf1[2] = 60; } /* If rounding to 10s or coarser always go up to new day. */ if ( ndp < 0 && ihmsf1[2] == 60 ) { iy1 = iy2; im1 = im2; id1 = id2; ihmsf1[0] = 0; ihmsf1[1] = 0; ihmsf1[2] = 0; } } } /* Results. */ *iy = iy1; *im = im1; *id = id1; for ( i = 0; i < 4; i++ ) { ihmsf[i] = ihmsf1[i]; } /* Status. */ return js; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/d2tf.c0000644000113000011300000001610713027221062014170 0ustar bellsbells#include "sofa.h" void iauD2tf(int ndp, double days, char *sign, int ihmsf[4]) /* ** - - - - - - - - ** i a u D 2 t f ** - - - - - - - - ** ** Decompose days to hours, minutes, seconds, fraction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** ndp int resolution (Note 1) ** days double interval in days ** ** Returned: ** sign char '+' or '-' ** ihmsf int[4] hours, minutes, seconds, fraction ** ** Notes: ** ** 1) The argument ndp is interpreted as follows: ** ** ndp resolution ** : ...0000 00 00 ** -7 1000 00 00 ** -6 100 00 00 ** -5 10 00 00 ** -4 1 00 00 ** -3 0 10 00 ** -2 0 01 00 ** -1 0 00 10 ** 0 0 00 01 ** 1 0 00 00.1 ** 2 0 00 00.01 ** 3 0 00 00.001 ** : 0 00 00.000... ** ** 2) The largest positive useful value for ndp is determined by the ** size of days, the format of double on the target platform, and ** the risk of overflowing ihmsf[3]. On a typical platform, for ** days up to 1.0, the available floating-point precision might ** correspond to ndp=12. However, the practical limit is typically ** ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is ** only 16 bits. ** ** 3) The absolute value of days may exceed 1.0. In cases where it ** does not, it is up to the caller to test for and handle the ** case where days is very nearly 1.0 and rounds up to 24 hours, ** by testing for ihmsf[0]=24 and setting ihmsf[0-3] to zero. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int nrs, n; double rs, rm, rh, a, w, ah, am, as, af; /* Handle sign. */ *sign = (char) ( ( days >= 0.0 ) ? '+' : '-' ); /* Interval in seconds. */ a = DAYSEC * fabs(days); /* Pre-round if resolution coarser than 1s (then pretend ndp=1). */ if (ndp < 0) { nrs = 1; for (n = 1; n <= -ndp; n++) { nrs *= (n == 2 || n == 4) ? 6 : 10; } rs = (double) nrs; w = a / rs; a = rs * dnint(w); } /* Express the unit of each field in resolution units. */ nrs = 1; for (n = 1; n <= ndp; n++) { nrs *= 10; } rs = (double) nrs; rm = rs * 60.0; rh = rm * 60.0; /* Round the interval and express in resolution units. */ a = dnint(rs * a); /* Break into fields. */ ah = a / rh; ah = dint(ah); a -= ah * rh; am = a / rm; am = dint(am); a -= am * rm; as = a / rs; as = dint(as); af = a - as * rs; /* Return results. */ ihmsf[0] = (int) ah; ihmsf[1] = (int) am; ihmsf[2] = (int) as; ihmsf[3] = (int) af; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/dat.c0000644000113000011300000003147313027221062014104 0ustar bellsbells#include "sofa.h" int iauDat(int iy, int im, int id, double fd, double *deltat ) /* ** - - - - - - - ** i a u D a t ** - - - - - - - ** ** For a given UTC date, calculate delta(AT) = TAI-UTC. ** ** :------------------------------------------: ** : : ** : IMPORTANT : ** : : ** : A new version of this function must be : ** : produced whenever a new leap second is : ** : announced. There are four items to : ** : change on each such occasion: : ** : : ** : 1) A new line must be added to the set : ** : of statements that initialize the : ** : array "changes". : ** : : ** : 2) The constant IYV must be set to the : ** : current year. : ** : : ** : 3) The "Latest leap second" comment : ** : below must be set to the new leap : ** : second date. : ** : : ** : 4) The "This revision" comment, later, : ** : must be set to the current date. : ** : : ** : Change (2) must also be carried out : ** : whenever the function is re-issued, : ** : even if no leap seconds have been : ** : added. : ** : : ** : Latest leap second: 2016 December 31 : ** : : ** :__________________________________________: ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** iy int UTC: year (Notes 1 and 2) ** im int month (Note 2) ** id int day (Notes 2 and 3) ** fd double fraction of day (Note 4) ** ** Returned: ** deltat double TAI minus UTC, seconds ** ** Returned (function value): ** int status (Note 5): ** 1 = dubious year (Note 1) ** 0 = OK ** -1 = bad year ** -2 = bad month ** -3 = bad day (Note 3) ** -4 = bad fraction (Note 4) ** -5 = internal error (Note 5) ** ** Notes: ** ** 1) UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper ** to call the function with an earlier date. If this is attempted, ** zero is returned together with a warning status. ** ** Because leap seconds cannot, in principle, be predicted in ** advance, a reliable check for dates beyond the valid range is ** impossible. To guard against gross errors, a year five or more ** after the release year of the present function (see the constant ** IYV) is considered dubious. In this case a warning status is ** returned but the result is computed in the normal way. ** ** For both too-early and too-late years, the warning status is +1. ** This is distinct from the error status -1, which signifies a year ** so early that JD could not be computed. ** ** 2) If the specified date is for a day which ends with a leap second, ** the UTC-TAI value returned is for the period leading up to the ** leap second. If the date is for a day which begins as a leap ** second ends, the UTC-TAI returned is for the period following the ** leap second. ** ** 3) The day number must be in the normal calendar range, for example ** 1 through 30 for April. The "almanac" convention of allowing ** such dates as January 0 and December 32 is not supported in this ** function, in order to avoid confusion near leap seconds. ** ** 4) The fraction of day is used only for dates before the ** introduction of leap seconds, the first of which occurred at the ** end of 1971. It is tested for validity (0 to 1 is the valid ** range) even if not used; if invalid, zero is used and status -4 ** is returned. For many applications, setting fd to zero is ** acceptable; the resulting error is always less than 3 ms (and ** occurs only pre-1972). ** ** 5) The status value returned in the case where there are multiple ** errors refers to the first error detected. For example, if the ** month and day are 13 and 32 respectively, status -2 (bad month) ** will be returned. The "internal error" status refers to a ** case that is impossible but causes some compilers to issue a ** warning. ** ** 6) In cases where a valid result is not available, zero is returned. ** ** References: ** ** 1) For dates from 1961 January 1 onwards, the expressions from the ** file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used. ** ** 2) The 5ms timestep at 1961 January 1 is taken from 2.58.1 (p87) of ** the 1992 Explanatory Supplement. ** ** Called: ** iauCal2jd Gregorian calendar to JD ** ** This revision: 2016 July 7 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Release year for this version of iauDat */ enum { IYV = 2016}; /* Reference dates (MJD) and drift rates (s/day), pre leap seconds */ static const double drift[][2] = { { 37300.0, 0.0012960 }, { 37300.0, 0.0012960 }, { 37300.0, 0.0012960 }, { 37665.0, 0.0011232 }, { 37665.0, 0.0011232 }, { 38761.0, 0.0012960 }, { 38761.0, 0.0012960 }, { 38761.0, 0.0012960 }, { 38761.0, 0.0012960 }, { 38761.0, 0.0012960 }, { 38761.0, 0.0012960 }, { 38761.0, 0.0012960 }, { 39126.0, 0.0025920 }, { 39126.0, 0.0025920 } }; /* Number of Delta(AT) expressions before leap seconds were introduced */ enum { NERA1 = (int) (sizeof drift / sizeof (double) / 2) }; /* Dates and Delta(AT)s */ static const struct { int iyear, month; double delat; } changes[] = { { 1960, 1, 1.4178180 }, { 1961, 1, 1.4228180 }, { 1961, 8, 1.3728180 }, { 1962, 1, 1.8458580 }, { 1963, 11, 1.9458580 }, { 1964, 1, 3.2401300 }, { 1964, 4, 3.3401300 }, { 1964, 9, 3.4401300 }, { 1965, 1, 3.5401300 }, { 1965, 3, 3.6401300 }, { 1965, 7, 3.7401300 }, { 1965, 9, 3.8401300 }, { 1966, 1, 4.3131700 }, { 1968, 2, 4.2131700 }, { 1972, 1, 10.0 }, { 1972, 7, 11.0 }, { 1973, 1, 12.0 }, { 1974, 1, 13.0 }, { 1975, 1, 14.0 }, { 1976, 1, 15.0 }, { 1977, 1, 16.0 }, { 1978, 1, 17.0 }, { 1979, 1, 18.0 }, { 1980, 1, 19.0 }, { 1981, 7, 20.0 }, { 1982, 7, 21.0 }, { 1983, 7, 22.0 }, { 1985, 7, 23.0 }, { 1988, 1, 24.0 }, { 1990, 1, 25.0 }, { 1991, 1, 26.0 }, { 1992, 7, 27.0 }, { 1993, 7, 28.0 }, { 1994, 7, 29.0 }, { 1996, 1, 30.0 }, { 1997, 7, 31.0 }, { 1999, 1, 32.0 }, { 2006, 1, 33.0 }, { 2009, 1, 34.0 }, { 2012, 7, 35.0 }, { 2015, 7, 36.0 }, { 2017, 1, 37.0 } }; /* Number of Delta(AT) changes */ enum { NDAT = (int) (sizeof changes / sizeof changes[0]) }; /* Miscellaneous local variables */ int j, i, m; double da, djm0, djm; /* Initialize the result to zero. */ *deltat = da = 0.0; /* If invalid fraction of a day, set error status and give up. */ if (fd < 0.0 || fd > 1.0) return -4; /* Convert the date into an MJD. */ j = iauCal2jd(iy, im, id, &djm0, &djm); /* If invalid year, month, or day, give up. */ if (j < 0) return j; /* If pre-UTC year, set warning status and give up. */ if (iy < changes[0].iyear) return 1; /* If suspiciously late year, set warning status but proceed. */ if (iy > IYV + 5) j = 1; /* Combine year and month to form a date-ordered integer... */ m = 12*iy + im; /* ...and use it to find the preceding table entry. */ for (i = NDAT-1; i >=0; i--) { if (m >= (12 * changes[i].iyear + changes[i].month)) break; } /* Prevent underflow warnings. */ if (i < 0) return -5; /* Get the Delta(AT). */ da = changes[i].delat; /* If pre-1972, adjust for drift. */ if (i < NERA1) da += (djm + fd - drift[i][0]) * drift[i][1]; /* Return the Delta(AT) value. */ *deltat = da; /* Return the status. */ return j; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/dtdb.c0000644000113000011300000017407113027221062014253 0ustar bellsbells#include "sofa.h" double iauDtdb(double date1, double date2, double ut, double elong, double u, double v) /* ** - - - - - - - - ** i a u D t d b ** - - - - - - - - ** ** An approximation to TDB-TT, the difference between barycentric ** dynamical time and terrestrial time, for an observer on the Earth. ** ** The different time scales - proper, coordinate and realized - are ** related to each other: ** ** TAI <- physically realized ** : ** offset <- observed (nominally +32.184s) ** : ** TT <- terrestrial time ** : ** rate adjustment (L_G) <- definition of TT ** : ** TCG <- time scale for GCRS ** : ** "periodic" terms <- iauDtdb is an implementation ** : ** rate adjustment (L_C) <- function of solar-system ephemeris ** : ** TCB <- time scale for BCRS ** : ** rate adjustment (-L_B) <- definition of TDB ** : ** TDB <- TCB scaled to track TT ** : ** "periodic" terms <- -iauDtdb is an approximation ** : ** TT <- terrestrial time ** ** Adopted values for the various constants can be found in the IERS ** Conventions (McCarthy & Petit 2003). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support routine. ** ** Given: ** date1,date2 double date, TDB (Notes 1-3) ** ut double universal time (UT1, fraction of one day) ** elong double longitude (east positive, radians) ** u double distance from Earth spin axis (km) ** v double distance north of equatorial plane (km) ** ** Returned (function value): ** double TDB-TT (seconds) ** ** Notes: ** ** 1) The date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** Although the date is, formally, barycentric dynamical time (TDB), ** the terrestrial dynamical time (TT) can be used with no practical ** effect on the accuracy of the prediction. ** ** 2) TT can be regarded as a coordinate time that is realized as an ** offset of 32.184s from International Atomic Time, TAI. TT is a ** specific linear transformation of geocentric coordinate time TCG, ** which is the time scale for the Geocentric Celestial Reference ** System, GCRS. ** ** 3) TDB is a coordinate time, and is a specific linear transformation ** of barycentric coordinate time TCB, which is the time scale for ** the Barycentric Celestial Reference System, BCRS. ** ** 4) The difference TCG-TCB depends on the masses and positions of the ** bodies of the solar system and the velocity of the Earth. It is ** dominated by a rate difference, the residual being of a periodic ** character. The latter, which is modeled by the present function, ** comprises a main (annual) sinusoidal term of amplitude ** approximately 0.00166 seconds, plus planetary terms up to about ** 20 microseconds, and lunar and diurnal terms up to 2 microseconds. ** These effects come from the changing transverse Doppler effect ** and gravitational red-shift as the observer (on the Earth's ** surface) experiences variations in speed (with respect to the ** BCRS) and gravitational potential. ** ** 5) TDB can be regarded as the same as TCB but with a rate adjustment ** to keep it close to TT, which is convenient for many applications. ** The history of successive attempts to define TDB is set out in ** Resolution 3 adopted by the IAU General Assembly in 2006, which ** defines a fixed TDB(TCB) transformation that is consistent with ** contemporary solar-system ephemerides. Future ephemerides will ** imply slightly changed transformations between TCG and TCB, which ** could introduce a linear drift between TDB and TT; however, any ** such drift is unlikely to exceed 1 nanosecond per century. ** ** 6) The geocentric TDB-TT model used in the present function is that of ** Fairhead & Bretagnon (1990), in its full form. It was originally ** supplied by Fairhead (private communications with P.T.Wallace, ** 1990) as a Fortran subroutine. The present C function contains an ** adaptation of the Fairhead code. The numerical results are ** essentially unaffected by the changes, the differences with ** respect to the Fairhead & Bretagnon original being at the 1e-20 s ** level. ** ** The topocentric part of the model is from Moyer (1981) and ** Murray (1983), with fundamental arguments adapted from ** Simon et al. 1994. It is an approximation to the expression ** ( v / c ) . ( r / c ), where v is the barycentric velocity of ** the Earth, r is the geocentric position of the observer and ** c is the speed of light. ** ** By supplying zeroes for u and v, the topocentric part of the ** model can be nullified, and the function will return the Fairhead ** & Bretagnon result alone. ** ** 7) During the interval 1950-2050, the absolute accuracy is better ** than +/- 3 nanoseconds relative to time ephemerides obtained by ** direct numerical integrations based on the JPL DE405 solar system ** ephemeris. ** ** 8) It must be stressed that the present function is merely a model, ** and that numerical integration of solar-system ephemerides is the ** definitive method for predicting the relationship between TCG and ** TCB and hence between TT and TDB. ** ** References: ** ** Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247 ** (1990). ** ** IAU 2006 Resolution 3. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Moyer, T.D., Cel.Mech., 23, 33 (1981). ** ** Murray, C.A., Vectorial Astrometry, Adam Hilger (1983). ** ** Seidelmann, P.K. et al., Explanatory Supplement to the ** Astronomical Almanac, Chapter 2, University Science Books (1992). ** ** Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, tsol, w, elsun, emsun, d, elj, els, wt, w0, w1, w2, w3, w4, wf, wj; int j; /* ** ===================== ** Fairhead et al. model ** ===================== ** ** 787 sets of three coefficients. ** ** Each set is ** amplitude (microseconds) ** frequency (radians per Julian millennium since J2000.0) ** phase (radians) ** ** Sets 1-474 are the T**0 terms ** " 475-679 " " T**1 ** " 680-764 " " T**2 ** " 765-784 " " T**3 ** " 785-787 " " T**4 */ static const double fairhd[787][3] = { /* 1, 10 */ { 1656.674564e-6, 6283.075849991, 6.240054195 }, { 22.417471e-6, 5753.384884897, 4.296977442 }, { 13.839792e-6, 12566.151699983, 6.196904410 }, { 4.770086e-6, 529.690965095, 0.444401603 }, { 4.676740e-6, 6069.776754553, 4.021195093 }, { 2.256707e-6, 213.299095438, 5.543113262 }, { 1.694205e-6, -3.523118349, 5.025132748 }, { 1.554905e-6, 77713.771467920, 5.198467090 }, { 1.276839e-6, 7860.419392439, 5.988822341 }, { 1.193379e-6, 5223.693919802, 3.649823730 }, /* 11, 20 */ { 1.115322e-6, 3930.209696220, 1.422745069 }, { 0.794185e-6, 11506.769769794, 2.322313077 }, { 0.447061e-6, 26.298319800, 3.615796498 }, { 0.435206e-6, -398.149003408, 4.349338347 }, { 0.600309e-6, 1577.343542448, 2.678271909 }, { 0.496817e-6, 6208.294251424, 5.696701824 }, { 0.486306e-6, 5884.926846583, 0.520007179 }, { 0.432392e-6, 74.781598567, 2.435898309 }, { 0.468597e-6, 6244.942814354, 5.866398759 }, { 0.375510e-6, 5507.553238667, 4.103476804 }, /* 21, 30 */ { 0.243085e-6, -775.522611324, 3.651837925 }, { 0.173435e-6, 18849.227549974, 6.153743485 }, { 0.230685e-6, 5856.477659115, 4.773852582 }, { 0.203747e-6, 12036.460734888, 4.333987818 }, { 0.143935e-6, -796.298006816, 5.957517795 }, { 0.159080e-6, 10977.078804699, 1.890075226 }, { 0.119979e-6, 38.133035638, 4.551585768 }, { 0.118971e-6, 5486.777843175, 1.914547226 }, { 0.116120e-6, 1059.381930189, 0.873504123 }, { 0.137927e-6, 11790.629088659, 1.135934669 }, /* 31, 40 */ { 0.098358e-6, 2544.314419883, 0.092793886 }, { 0.101868e-6, -5573.142801634, 5.984503847 }, { 0.080164e-6, 206.185548437, 2.095377709 }, { 0.079645e-6, 4694.002954708, 2.949233637 }, { 0.062617e-6, 20.775395492, 2.654394814 }, { 0.075019e-6, 2942.463423292, 4.980931759 }, { 0.064397e-6, 5746.271337896, 1.280308748 }, { 0.063814e-6, 5760.498431898, 4.167901731 }, { 0.048042e-6, 2146.165416475, 1.495846011 }, { 0.048373e-6, 155.420399434, 2.251573730 }, /* 41, 50 */ { 0.058844e-6, 426.598190876, 4.839650148 }, { 0.046551e-6, -0.980321068, 0.921573539 }, { 0.054139e-6, 17260.154654690, 3.411091093 }, { 0.042411e-6, 6275.962302991, 2.869567043 }, { 0.040184e-6, -7.113547001, 3.565975565 }, { 0.036564e-6, 5088.628839767, 3.324679049 }, { 0.040759e-6, 12352.852604545, 3.981496998 }, { 0.036507e-6, 801.820931124, 6.248866009 }, { 0.036955e-6, 3154.687084896, 5.071801441 }, { 0.042732e-6, 632.783739313, 5.720622217 }, /* 51, 60 */ { 0.042560e-6, 161000.685737473, 1.270837679 }, { 0.040480e-6, 15720.838784878, 2.546610123 }, { 0.028244e-6, -6286.598968340, 5.069663519 }, { 0.033477e-6, 6062.663207553, 4.144987272 }, { 0.034867e-6, 522.577418094, 5.210064075 }, { 0.032438e-6, 6076.890301554, 0.749317412 }, { 0.030215e-6, 7084.896781115, 3.389610345 }, { 0.029247e-6, -71430.695617928, 4.183178762 }, { 0.033529e-6, 9437.762934887, 2.404714239 }, { 0.032423e-6, 8827.390269875, 5.541473556 }, /* 61, 70 */ { 0.027567e-6, 6279.552731642, 5.040846034 }, { 0.029862e-6, 12139.553509107, 1.770181024 }, { 0.022509e-6, 10447.387839604, 1.460726241 }, { 0.020937e-6, 8429.241266467, 0.652303414 }, { 0.020322e-6, 419.484643875, 3.735430632 }, { 0.024816e-6, -1194.447010225, 1.087136918 }, { 0.025196e-6, 1748.016413067, 2.901883301 }, { 0.021691e-6, 14143.495242431, 5.952658009 }, { 0.017673e-6, 6812.766815086, 3.186129845 }, { 0.022567e-6, 6133.512652857, 3.307984806 }, /* 71, 80 */ { 0.016155e-6, 10213.285546211, 1.331103168 }, { 0.014751e-6, 1349.867409659, 4.308933301 }, { 0.015949e-6, -220.412642439, 4.005298270 }, { 0.015974e-6, -2352.866153772, 6.145309371 }, { 0.014223e-6, 17789.845619785, 2.104551349 }, { 0.017806e-6, 73.297125859, 3.475975097 }, { 0.013671e-6, -536.804512095, 5.971672571 }, { 0.011942e-6, 8031.092263058, 2.053414715 }, { 0.014318e-6, 16730.463689596, 3.016058075 }, { 0.012462e-6, 103.092774219, 1.737438797 }, /* 81, 90 */ { 0.010962e-6, 3.590428652, 2.196567739 }, { 0.015078e-6, 19651.048481098, 3.969480770 }, { 0.010396e-6, 951.718406251, 5.717799605 }, { 0.011707e-6, -4705.732307544, 2.654125618 }, { 0.010453e-6, 5863.591206116, 1.913704550 }, { 0.012420e-6, 4690.479836359, 4.734090399 }, { 0.011847e-6, 5643.178563677, 5.489005403 }, { 0.008610e-6, 3340.612426700, 3.661698944 }, { 0.011622e-6, 5120.601145584, 4.863931876 }, { 0.010825e-6, 553.569402842, 0.842715011 }, /* 91, 100 */ { 0.008666e-6, -135.065080035, 3.293406547 }, { 0.009963e-6, 149.563197135, 4.870690598 }, { 0.009858e-6, 6309.374169791, 1.061816410 }, { 0.007959e-6, 316.391869657, 2.465042647 }, { 0.010099e-6, 283.859318865, 1.942176992 }, { 0.007147e-6, -242.728603974, 3.661486981 }, { 0.007505e-6, 5230.807466803, 4.920937029 }, { 0.008323e-6, 11769.853693166, 1.229392026 }, { 0.007490e-6, -6256.777530192, 3.658444681 }, { 0.009370e-6, 149854.400134205, 0.673880395 }, /* 101, 110 */ { 0.007117e-6, 38.027672636, 5.294249518 }, { 0.007857e-6, 12168.002696575, 0.525733528 }, { 0.007019e-6, 6206.809778716, 0.837688810 }, { 0.006056e-6, 955.599741609, 4.194535082 }, { 0.008107e-6, 13367.972631107, 3.793235253 }, { 0.006731e-6, 5650.292110678, 5.639906583 }, { 0.007332e-6, 36.648562930, 0.114858677 }, { 0.006366e-6, 4164.311989613, 2.262081818 }, { 0.006858e-6, 5216.580372801, 0.642063318 }, { 0.006919e-6, 6681.224853400, 6.018501522 }, /* 111, 120 */ { 0.006826e-6, 7632.943259650, 3.458654112 }, { 0.005308e-6, -1592.596013633, 2.500382359 }, { 0.005096e-6, 11371.704689758, 2.547107806 }, { 0.004841e-6, 5333.900241022, 0.437078094 }, { 0.005582e-6, 5966.683980335, 2.246174308 }, { 0.006304e-6, 11926.254413669, 2.512929171 }, { 0.006603e-6, 23581.258177318, 5.393136889 }, { 0.005123e-6, -1.484472708, 2.999641028 }, { 0.004648e-6, 1589.072895284, 1.275847090 }, { 0.005119e-6, 6438.496249426, 1.486539246 }, /* 121, 130 */ { 0.004521e-6, 4292.330832950, 6.140635794 }, { 0.005680e-6, 23013.539539587, 4.557814849 }, { 0.005488e-6, -3.455808046, 0.090675389 }, { 0.004193e-6, 7234.794256242, 4.869091389 }, { 0.003742e-6, 7238.675591600, 4.691976180 }, { 0.004148e-6, -110.206321219, 3.016173439 }, { 0.004553e-6, 11499.656222793, 5.554998314 }, { 0.004892e-6, 5436.993015240, 1.475415597 }, { 0.004044e-6, 4732.030627343, 1.398784824 }, { 0.004164e-6, 12491.370101415, 5.650931916 }, /* 131, 140 */ { 0.004349e-6, 11513.883316794, 2.181745369 }, { 0.003919e-6, 12528.018664345, 5.823319737 }, { 0.003129e-6, 6836.645252834, 0.003844094 }, { 0.004080e-6, -7058.598461315, 3.690360123 }, { 0.003270e-6, 76.266071276, 1.517189902 }, { 0.002954e-6, 6283.143160294, 4.447203799 }, { 0.002872e-6, 28.449187468, 1.158692983 }, { 0.002881e-6, 735.876513532, 0.349250250 }, { 0.003279e-6, 5849.364112115, 4.893384368 }, { 0.003625e-6, 6209.778724132, 1.473760578 }, /* 141, 150 */ { 0.003074e-6, 949.175608970, 5.185878737 }, { 0.002775e-6, 9917.696874510, 1.030026325 }, { 0.002646e-6, 10973.555686350, 3.918259169 }, { 0.002575e-6, 25132.303399966, 6.109659023 }, { 0.003500e-6, 263.083923373, 1.892100742 }, { 0.002740e-6, 18319.536584880, 4.320519510 }, { 0.002464e-6, 202.253395174, 4.698203059 }, { 0.002409e-6, 2.542797281, 5.325009315 }, { 0.003354e-6, -90955.551694697, 1.942656623 }, { 0.002296e-6, 6496.374945429, 5.061810696 }, /* 151, 160 */ { 0.003002e-6, 6172.869528772, 2.797822767 }, { 0.003202e-6, 27511.467873537, 0.531673101 }, { 0.002954e-6, -6283.008539689, 4.533471191 }, { 0.002353e-6, 639.897286314, 3.734548088 }, { 0.002401e-6, 16200.772724501, 2.605547070 }, { 0.003053e-6, 233141.314403759, 3.029030662 }, { 0.003024e-6, 83286.914269554, 2.355556099 }, { 0.002863e-6, 17298.182327326, 5.240963796 }, { 0.002103e-6, -7079.373856808, 5.756641637 }, { 0.002303e-6, 83996.847317911, 2.013686814 }, /* 161, 170 */ { 0.002303e-6, 18073.704938650, 1.089100410 }, { 0.002381e-6, 63.735898303, 0.759188178 }, { 0.002493e-6, 6386.168624210, 0.645026535 }, { 0.002366e-6, 3.932153263, 6.215885448 }, { 0.002169e-6, 11015.106477335, 4.845297676 }, { 0.002397e-6, 6243.458341645, 3.809290043 }, { 0.002183e-6, 1162.474704408, 6.179611691 }, { 0.002353e-6, 6246.427287062, 4.781719760 }, { 0.002199e-6, -245.831646229, 5.956152284 }, { 0.001729e-6, 3894.181829542, 1.264976635 }, /* 171, 180 */ { 0.001896e-6, -3128.388765096, 4.914231596 }, { 0.002085e-6, 35.164090221, 1.405158503 }, { 0.002024e-6, 14712.317116458, 2.752035928 }, { 0.001737e-6, 6290.189396992, 5.280820144 }, { 0.002229e-6, 491.557929457, 1.571007057 }, { 0.001602e-6, 14314.168113050, 4.203664806 }, { 0.002186e-6, 454.909366527, 1.402101526 }, { 0.001897e-6, 22483.848574493, 4.167932508 }, { 0.001825e-6, -3738.761430108, 0.545828785 }, { 0.001894e-6, 1052.268383188, 5.817167450 }, /* 181, 190 */ { 0.001421e-6, 20.355319399, 2.419886601 }, { 0.001408e-6, 10984.192351700, 2.732084787 }, { 0.001847e-6, 10873.986030480, 2.903477885 }, { 0.001391e-6, -8635.942003763, 0.593891500 }, { 0.001388e-6, -7.046236698, 1.166145902 }, { 0.001810e-6, -88860.057071188, 0.487355242 }, { 0.001288e-6, -1990.745017041, 3.913022880 }, { 0.001297e-6, 23543.230504682, 3.063805171 }, { 0.001335e-6, -266.607041722, 3.995764039 }, { 0.001376e-6, 10969.965257698, 5.152914309 }, /* 191, 200 */ { 0.001745e-6, 244287.600007027, 3.626395673 }, { 0.001649e-6, 31441.677569757, 1.952049260 }, { 0.001416e-6, 9225.539273283, 4.996408389 }, { 0.001238e-6, 4804.209275927, 5.503379738 }, { 0.001472e-6, 4590.910180489, 4.164913291 }, { 0.001169e-6, 6040.347246017, 5.841719038 }, { 0.001039e-6, 5540.085789459, 2.769753519 }, { 0.001004e-6, -170.672870619, 0.755008103 }, { 0.001284e-6, 10575.406682942, 5.306538209 }, { 0.001278e-6, 71.812653151, 4.713486491 }, /* 201, 210 */ { 0.001321e-6, 18209.330263660, 2.624866359 }, { 0.001297e-6, 21228.392023546, 0.382603541 }, { 0.000954e-6, 6282.095528923, 0.882213514 }, { 0.001145e-6, 6058.731054289, 1.169483931 }, { 0.000979e-6, 5547.199336460, 5.448375984 }, { 0.000987e-6, -6262.300454499, 2.656486959 }, { 0.001070e-6, -154717.609887482, 1.827624012 }, { 0.000991e-6, 4701.116501708, 4.387001801 }, { 0.001155e-6, -14.227094002, 3.042700750 }, { 0.001176e-6, 277.034993741, 3.335519004 }, /* 211, 220 */ { 0.000890e-6, 13916.019109642, 5.601498297 }, { 0.000884e-6, -1551.045222648, 1.088831705 }, { 0.000876e-6, 5017.508371365, 3.969902609 }, { 0.000806e-6, 15110.466119866, 5.142876744 }, { 0.000773e-6, -4136.910433516, 0.022067765 }, { 0.001077e-6, 175.166059800, 1.844913056 }, { 0.000954e-6, -6284.056171060, 0.968480906 }, { 0.000737e-6, 5326.786694021, 4.923831588 }, { 0.000845e-6, -433.711737877, 4.749245231 }, { 0.000819e-6, 8662.240323563, 5.991247817 }, /* 221, 230 */ { 0.000852e-6, 199.072001436, 2.189604979 }, { 0.000723e-6, 17256.631536341, 6.068719637 }, { 0.000940e-6, 6037.244203762, 6.197428148 }, { 0.000885e-6, 11712.955318231, 3.280414875 }, { 0.000706e-6, 12559.038152982, 2.824848947 }, { 0.000732e-6, 2379.164473572, 2.501813417 }, { 0.000764e-6, -6127.655450557, 2.236346329 }, { 0.000908e-6, 131.541961686, 2.521257490 }, { 0.000907e-6, 35371.887265976, 3.370195967 }, { 0.000673e-6, 1066.495477190, 3.876512374 }, /* 231, 240 */ { 0.000814e-6, 17654.780539750, 4.627122566 }, { 0.000630e-6, 36.027866677, 0.156368499 }, { 0.000798e-6, 515.463871093, 5.151962502 }, { 0.000798e-6, 148.078724426, 5.909225055 }, { 0.000806e-6, 309.278322656, 6.054064447 }, { 0.000607e-6, -39.617508346, 2.839021623 }, { 0.000601e-6, 412.371096874, 3.984225404 }, { 0.000646e-6, 11403.676995575, 3.852959484 }, { 0.000704e-6, 13521.751441591, 2.300991267 }, { 0.000603e-6, -65147.619767937, 4.140083146 }, /* 241, 250 */ { 0.000609e-6, 10177.257679534, 0.437122327 }, { 0.000631e-6, 5767.611978898, 4.026532329 }, { 0.000576e-6, 11087.285125918, 4.760293101 }, { 0.000674e-6, 14945.316173554, 6.270510511 }, { 0.000726e-6, 5429.879468239, 6.039606892 }, { 0.000710e-6, 28766.924424484, 5.672617711 }, { 0.000647e-6, 11856.218651625, 3.397132627 }, { 0.000678e-6, -5481.254918868, 6.249666675 }, { 0.000618e-6, 22003.914634870, 2.466427018 }, { 0.000738e-6, 6134.997125565, 2.242668890 }, /* 251, 260 */ { 0.000660e-6, 625.670192312, 5.864091907 }, { 0.000694e-6, 3496.032826134, 2.668309141 }, { 0.000531e-6, 6489.261398429, 1.681888780 }, { 0.000611e-6, -143571.324284214, 2.424978312 }, { 0.000575e-6, 12043.574281889, 4.216492400 }, { 0.000553e-6, 12416.588502848, 4.772158039 }, { 0.000689e-6, 4686.889407707, 6.224271088 }, { 0.000495e-6, 7342.457780181, 3.817285811 }, { 0.000567e-6, 3634.621024518, 1.649264690 }, { 0.000515e-6, 18635.928454536, 3.945345892 }, /* 261, 270 */ { 0.000486e-6, -323.505416657, 4.061673868 }, { 0.000662e-6, 25158.601719765, 1.794058369 }, { 0.000509e-6, 846.082834751, 3.053874588 }, { 0.000472e-6, -12569.674818332, 5.112133338 }, { 0.000461e-6, 6179.983075773, 0.513669325 }, { 0.000641e-6, 83467.156352816, 3.210727723 }, { 0.000520e-6, 10344.295065386, 2.445597761 }, { 0.000493e-6, 18422.629359098, 1.676939306 }, { 0.000478e-6, 1265.567478626, 5.487314569 }, { 0.000472e-6, -18.159247265, 1.999707589 }, /* 271, 280 */ { 0.000559e-6, 11190.377900137, 5.783236356 }, { 0.000494e-6, 9623.688276691, 3.022645053 }, { 0.000463e-6, 5739.157790895, 1.411223013 }, { 0.000432e-6, 16858.482532933, 1.179256434 }, { 0.000574e-6, 72140.628666286, 1.758191830 }, { 0.000484e-6, 17267.268201691, 3.290589143 }, { 0.000550e-6, 4907.302050146, 0.864024298 }, { 0.000399e-6, 14.977853527, 2.094441910 }, { 0.000491e-6, 224.344795702, 0.878372791 }, { 0.000432e-6, 20426.571092422, 6.003829241 }, /* 281, 290 */ { 0.000481e-6, 5749.452731634, 4.309591964 }, { 0.000480e-6, 5757.317038160, 1.142348571 }, { 0.000485e-6, 6702.560493867, 0.210580917 }, { 0.000426e-6, 6055.549660552, 4.274476529 }, { 0.000480e-6, 5959.570433334, 5.031351030 }, { 0.000466e-6, 12562.628581634, 4.959581597 }, { 0.000520e-6, 39302.096962196, 4.788002889 }, { 0.000458e-6, 12132.439962106, 1.880103788 }, { 0.000470e-6, 12029.347187887, 1.405611197 }, { 0.000416e-6, -7477.522860216, 1.082356330 }, /* 291, 300 */ { 0.000449e-6, 11609.862544012, 4.179989585 }, { 0.000465e-6, 17253.041107690, 0.353496295 }, { 0.000362e-6, -4535.059436924, 1.583849576 }, { 0.000383e-6, 21954.157609398, 3.747376371 }, { 0.000389e-6, 17.252277143, 1.395753179 }, { 0.000331e-6, 18052.929543158, 0.566790582 }, { 0.000430e-6, 13517.870106233, 0.685827538 }, { 0.000368e-6, -5756.908003246, 0.731374317 }, { 0.000330e-6, 10557.594160824, 3.710043680 }, { 0.000332e-6, 20199.094959633, 1.652901407 }, /* 301, 310 */ { 0.000384e-6, 11933.367960670, 5.827781531 }, { 0.000387e-6, 10454.501386605, 2.541182564 }, { 0.000325e-6, 15671.081759407, 2.178850542 }, { 0.000318e-6, 138.517496871, 2.253253037 }, { 0.000305e-6, 9388.005909415, 0.578340206 }, { 0.000352e-6, 5749.861766548, 3.000297967 }, { 0.000311e-6, 6915.859589305, 1.693574249 }, { 0.000297e-6, 24072.921469776, 1.997249392 }, { 0.000363e-6, -640.877607382, 5.071820966 }, { 0.000323e-6, 12592.450019783, 1.072262823 }, /* 311, 320 */ { 0.000341e-6, 12146.667056108, 4.700657997 }, { 0.000290e-6, 9779.108676125, 1.812320441 }, { 0.000342e-6, 6132.028180148, 4.322238614 }, { 0.000329e-6, 6268.848755990, 3.033827743 }, { 0.000374e-6, 17996.031168222, 3.388716544 }, { 0.000285e-6, -533.214083444, 4.687313233 }, { 0.000338e-6, 6065.844601290, 0.877776108 }, { 0.000276e-6, 24.298513841, 0.770299429 }, { 0.000336e-6, -2388.894020449, 5.353796034 }, { 0.000290e-6, 3097.883822726, 4.075291557 }, /* 321, 330 */ { 0.000318e-6, 709.933048357, 5.941207518 }, { 0.000271e-6, 13095.842665077, 3.208912203 }, { 0.000331e-6, 6073.708907816, 4.007881169 }, { 0.000292e-6, 742.990060533, 2.714333592 }, { 0.000362e-6, 29088.811415985, 3.215977013 }, { 0.000280e-6, 12359.966151546, 0.710872502 }, { 0.000267e-6, 10440.274292604, 4.730108488 }, { 0.000262e-6, 838.969287750, 1.327720272 }, { 0.000250e-6, 16496.361396202, 0.898769761 }, { 0.000325e-6, 20597.243963041, 0.180044365 }, /* 331, 340 */ { 0.000268e-6, 6148.010769956, 5.152666276 }, { 0.000284e-6, 5636.065016677, 5.655385808 }, { 0.000301e-6, 6080.822454817, 2.135396205 }, { 0.000294e-6, -377.373607916, 3.708784168 }, { 0.000236e-6, 2118.763860378, 1.733578756 }, { 0.000234e-6, 5867.523359379, 5.575209112 }, { 0.000268e-6, -226858.238553767, 0.069432392 }, { 0.000265e-6, 167283.761587465, 4.369302826 }, { 0.000280e-6, 28237.233459389, 5.304829118 }, { 0.000292e-6, 12345.739057544, 4.096094132 }, /* 341, 350 */ { 0.000223e-6, 19800.945956225, 3.069327406 }, { 0.000301e-6, 43232.306658416, 6.205311188 }, { 0.000264e-6, 18875.525869774, 1.417263408 }, { 0.000304e-6, -1823.175188677, 3.409035232 }, { 0.000301e-6, 109.945688789, 0.510922054 }, { 0.000260e-6, 813.550283960, 2.389438934 }, { 0.000299e-6, 316428.228673312, 5.384595078 }, { 0.000211e-6, 5756.566278634, 3.789392838 }, { 0.000209e-6, 5750.203491159, 1.661943545 }, { 0.000240e-6, 12489.885628707, 5.684549045 }, /* 351, 360 */ { 0.000216e-6, 6303.851245484, 3.862942261 }, { 0.000203e-6, 1581.959348283, 5.549853589 }, { 0.000200e-6, 5642.198242609, 1.016115785 }, { 0.000197e-6, -70.849445304, 4.690702525 }, { 0.000227e-6, 6287.008003254, 2.911891613 }, { 0.000197e-6, 533.623118358, 1.048982898 }, { 0.000205e-6, -6279.485421340, 1.829362730 }, { 0.000209e-6, -10988.808157535, 2.636140084 }, { 0.000208e-6, -227.526189440, 4.127883842 }, { 0.000191e-6, 415.552490612, 4.401165650 }, /* 361, 370 */ { 0.000190e-6, 29296.615389579, 4.175658539 }, { 0.000264e-6, 66567.485864652, 4.601102551 }, { 0.000256e-6, -3646.350377354, 0.506364778 }, { 0.000188e-6, 13119.721102825, 2.032195842 }, { 0.000185e-6, -209.366942175, 4.694756586 }, { 0.000198e-6, 25934.124331089, 3.832703118 }, { 0.000195e-6, 4061.219215394, 3.308463427 }, { 0.000234e-6, 5113.487598583, 1.716090661 }, { 0.000188e-6, 1478.866574064, 5.686865780 }, { 0.000222e-6, 11823.161639450, 1.942386641 }, /* 371, 380 */ { 0.000181e-6, 10770.893256262, 1.999482059 }, { 0.000171e-6, 6546.159773364, 1.182807992 }, { 0.000206e-6, 70.328180442, 5.934076062 }, { 0.000169e-6, 20995.392966449, 2.169080622 }, { 0.000191e-6, 10660.686935042, 5.405515999 }, { 0.000228e-6, 33019.021112205, 4.656985514 }, { 0.000184e-6, -4933.208440333, 3.327476868 }, { 0.000220e-6, -135.625325010, 1.765430262 }, { 0.000166e-6, 23141.558382925, 3.454132746 }, { 0.000191e-6, 6144.558353121, 5.020393445 }, /* 381, 390 */ { 0.000180e-6, 6084.003848555, 0.602182191 }, { 0.000163e-6, 17782.732072784, 4.960593133 }, { 0.000225e-6, 16460.333529525, 2.596451817 }, { 0.000222e-6, 5905.702242076, 3.731990323 }, { 0.000204e-6, 227.476132789, 5.636192701 }, { 0.000159e-6, 16737.577236597, 3.600691544 }, { 0.000200e-6, 6805.653268085, 0.868220961 }, { 0.000187e-6, 11919.140866668, 2.629456641 }, { 0.000161e-6, 127.471796607, 2.862574720 }, { 0.000205e-6, 6286.666278643, 1.742882331 }, /* 391, 400 */ { 0.000189e-6, 153.778810485, 4.812372643 }, { 0.000168e-6, 16723.350142595, 0.027860588 }, { 0.000149e-6, 11720.068865232, 0.659721876 }, { 0.000189e-6, 5237.921013804, 5.245313000 }, { 0.000143e-6, 6709.674040867, 4.317625647 }, { 0.000146e-6, 4487.817406270, 4.815297007 }, { 0.000144e-6, -664.756045130, 5.381366880 }, { 0.000175e-6, 5127.714692584, 4.728443327 }, { 0.000162e-6, 6254.626662524, 1.435132069 }, { 0.000187e-6, 47162.516354635, 1.354371923 }, /* 401, 410 */ { 0.000146e-6, 11080.171578918, 3.369695406 }, { 0.000180e-6, -348.924420448, 2.490902145 }, { 0.000148e-6, 151.047669843, 3.799109588 }, { 0.000157e-6, 6197.248551160, 1.284375887 }, { 0.000167e-6, 146.594251718, 0.759969109 }, { 0.000133e-6, -5331.357443741, 5.409701889 }, { 0.000154e-6, 95.979227218, 3.366890614 }, { 0.000148e-6, -6418.140930027, 3.384104996 }, { 0.000128e-6, -6525.804453965, 3.803419985 }, { 0.000130e-6, 11293.470674356, 0.939039445 }, /* 411, 420 */ { 0.000152e-6, -5729.506447149, 0.734117523 }, { 0.000138e-6, 210.117701700, 2.564216078 }, { 0.000123e-6, 6066.595360816, 4.517099537 }, { 0.000140e-6, 18451.078546566, 0.642049130 }, { 0.000126e-6, 11300.584221356, 3.485280663 }, { 0.000119e-6, 10027.903195729, 3.217431161 }, { 0.000151e-6, 4274.518310832, 4.404359108 }, { 0.000117e-6, 6072.958148291, 0.366324650 }, { 0.000165e-6, -7668.637425143, 4.298212528 }, { 0.000117e-6, -6245.048177356, 5.379518958 }, /* 421, 430 */ { 0.000130e-6, -5888.449964932, 4.527681115 }, { 0.000121e-6, -543.918059096, 6.109429504 }, { 0.000162e-6, 9683.594581116, 5.720092446 }, { 0.000141e-6, 6219.339951688, 0.679068671 }, { 0.000118e-6, 22743.409379516, 4.881123092 }, { 0.000129e-6, 1692.165669502, 0.351407289 }, { 0.000126e-6, 5657.405657679, 5.146592349 }, { 0.000114e-6, 728.762966531, 0.520791814 }, { 0.000120e-6, 52.596639600, 0.948516300 }, { 0.000115e-6, 65.220371012, 3.504914846 }, /* 431, 440 */ { 0.000126e-6, 5881.403728234, 5.577502482 }, { 0.000158e-6, 163096.180360983, 2.957128968 }, { 0.000134e-6, 12341.806904281, 2.598576764 }, { 0.000151e-6, 16627.370915377, 3.985702050 }, { 0.000109e-6, 1368.660252845, 0.014730471 }, { 0.000131e-6, 6211.263196841, 0.085077024 }, { 0.000146e-6, 5792.741760812, 0.708426604 }, { 0.000146e-6, -77.750543984, 3.121576600 }, { 0.000107e-6, 5341.013788022, 0.288231904 }, { 0.000138e-6, 6281.591377283, 2.797450317 }, /* 441, 450 */ { 0.000113e-6, -6277.552925684, 2.788904128 }, { 0.000115e-6, -525.758811831, 5.895222200 }, { 0.000138e-6, 6016.468808270, 6.096188999 }, { 0.000139e-6, 23539.707386333, 2.028195445 }, { 0.000146e-6, -4176.041342449, 4.660008502 }, { 0.000107e-6, 16062.184526117, 4.066520001 }, { 0.000142e-6, 83783.548222473, 2.936315115 }, { 0.000128e-6, 9380.959672717, 3.223844306 }, { 0.000135e-6, 6205.325306007, 1.638054048 }, { 0.000101e-6, 2699.734819318, 5.481603249 }, /* 451, 460 */ { 0.000104e-6, -568.821874027, 2.205734493 }, { 0.000103e-6, 6321.103522627, 2.440421099 }, { 0.000119e-6, 6321.208885629, 2.547496264 }, { 0.000138e-6, 1975.492545856, 2.314608466 }, { 0.000121e-6, 137.033024162, 4.539108237 }, { 0.000123e-6, 19402.796952817, 4.538074405 }, { 0.000119e-6, 22805.735565994, 2.869040566 }, { 0.000133e-6, 64471.991241142, 6.056405489 }, { 0.000129e-6, -85.827298831, 2.540635083 }, { 0.000131e-6, 13613.804277336, 4.005732868 }, /* 461, 470 */ { 0.000104e-6, 9814.604100291, 1.959967212 }, { 0.000112e-6, 16097.679950283, 3.589026260 }, { 0.000123e-6, 2107.034507542, 1.728627253 }, { 0.000121e-6, 36949.230808424, 6.072332087 }, { 0.000108e-6, -12539.853380183, 3.716133846 }, { 0.000113e-6, -7875.671863624, 2.725771122 }, { 0.000109e-6, 4171.425536614, 4.033338079 }, { 0.000101e-6, 6247.911759770, 3.441347021 }, { 0.000113e-6, 7330.728427345, 0.656372122 }, { 0.000113e-6, 51092.726050855, 2.791483066 }, /* 471, 480 */ { 0.000106e-6, 5621.842923210, 1.815323326 }, { 0.000101e-6, 111.430161497, 5.711033677 }, { 0.000103e-6, 909.818733055, 2.812745443 }, { 0.000101e-6, 1790.642637886, 1.965746028 }, /* T */ { 102.156724e-6, 6283.075849991, 4.249032005 }, { 1.706807e-6, 12566.151699983, 4.205904248 }, { 0.269668e-6, 213.299095438, 3.400290479 }, { 0.265919e-6, 529.690965095, 5.836047367 }, { 0.210568e-6, -3.523118349, 6.262738348 }, { 0.077996e-6, 5223.693919802, 4.670344204 }, /* 481, 490 */ { 0.054764e-6, 1577.343542448, 4.534800170 }, { 0.059146e-6, 26.298319800, 1.083044735 }, { 0.034420e-6, -398.149003408, 5.980077351 }, { 0.032088e-6, 18849.227549974, 4.162913471 }, { 0.033595e-6, 5507.553238667, 5.980162321 }, { 0.029198e-6, 5856.477659115, 0.623811863 }, { 0.027764e-6, 155.420399434, 3.745318113 }, { 0.025190e-6, 5746.271337896, 2.980330535 }, { 0.022997e-6, -796.298006816, 1.174411803 }, { 0.024976e-6, 5760.498431898, 2.467913690 }, /* 491, 500 */ { 0.021774e-6, 206.185548437, 3.854787540 }, { 0.017925e-6, -775.522611324, 1.092065955 }, { 0.013794e-6, 426.598190876, 2.699831988 }, { 0.013276e-6, 6062.663207553, 5.845801920 }, { 0.011774e-6, 12036.460734888, 2.292832062 }, { 0.012869e-6, 6076.890301554, 5.333425680 }, { 0.012152e-6, 1059.381930189, 6.222874454 }, { 0.011081e-6, -7.113547001, 5.154724984 }, { 0.010143e-6, 4694.002954708, 4.044013795 }, { 0.009357e-6, 5486.777843175, 3.416081409 }, /* 501, 510 */ { 0.010084e-6, 522.577418094, 0.749320262 }, { 0.008587e-6, 10977.078804699, 2.777152598 }, { 0.008628e-6, 6275.962302991, 4.562060226 }, { 0.008158e-6, -220.412642439, 5.806891533 }, { 0.007746e-6, 2544.314419883, 1.603197066 }, { 0.007670e-6, 2146.165416475, 3.000200440 }, { 0.007098e-6, 74.781598567, 0.443725817 }, { 0.006180e-6, -536.804512095, 1.302642751 }, { 0.005818e-6, 5088.628839767, 4.827723531 }, { 0.004945e-6, -6286.598968340, 0.268305170 }, /* 511, 520 */ { 0.004774e-6, 1349.867409659, 5.808636673 }, { 0.004687e-6, -242.728603974, 5.154890570 }, { 0.006089e-6, 1748.016413067, 4.403765209 }, { 0.005975e-6, -1194.447010225, 2.583472591 }, { 0.004229e-6, 951.718406251, 0.931172179 }, { 0.005264e-6, 553.569402842, 2.336107252 }, { 0.003049e-6, 5643.178563677, 1.362634430 }, { 0.002974e-6, 6812.766815086, 1.583012668 }, { 0.003403e-6, -2352.866153772, 2.552189886 }, { 0.003030e-6, 419.484643875, 5.286473844 }, /* 521, 530 */ { 0.003210e-6, -7.046236698, 1.863796539 }, { 0.003058e-6, 9437.762934887, 4.226420633 }, { 0.002589e-6, 12352.852604545, 1.991935820 }, { 0.002927e-6, 5216.580372801, 2.319951253 }, { 0.002425e-6, 5230.807466803, 3.084752833 }, { 0.002656e-6, 3154.687084896, 2.487447866 }, { 0.002445e-6, 10447.387839604, 2.347139160 }, { 0.002990e-6, 4690.479836359, 6.235872050 }, { 0.002890e-6, 5863.591206116, 0.095197563 }, { 0.002498e-6, 6438.496249426, 2.994779800 }, /* 531, 540 */ { 0.001889e-6, 8031.092263058, 3.569003717 }, { 0.002567e-6, 801.820931124, 3.425611498 }, { 0.001803e-6, -71430.695617928, 2.192295512 }, { 0.001782e-6, 3.932153263, 5.180433689 }, { 0.001694e-6, -4705.732307544, 4.641779174 }, { 0.001704e-6, -1592.596013633, 3.997097652 }, { 0.001735e-6, 5849.364112115, 0.417558428 }, { 0.001643e-6, 8429.241266467, 2.180619584 }, { 0.001680e-6, 38.133035638, 4.164529426 }, { 0.002045e-6, 7084.896781115, 0.526323854 }, /* 541, 550 */ { 0.001458e-6, 4292.330832950, 1.356098141 }, { 0.001437e-6, 20.355319399, 3.895439360 }, { 0.001738e-6, 6279.552731642, 0.087484036 }, { 0.001367e-6, 14143.495242431, 3.987576591 }, { 0.001344e-6, 7234.794256242, 0.090454338 }, { 0.001438e-6, 11499.656222793, 0.974387904 }, { 0.001257e-6, 6836.645252834, 1.509069366 }, { 0.001358e-6, 11513.883316794, 0.495572260 }, { 0.001628e-6, 7632.943259650, 4.968445721 }, { 0.001169e-6, 103.092774219, 2.838496795 }, /* 551, 560 */ { 0.001162e-6, 4164.311989613, 3.408387778 }, { 0.001092e-6, 6069.776754553, 3.617942651 }, { 0.001008e-6, 17789.845619785, 0.286350174 }, { 0.001008e-6, 639.897286314, 1.610762073 }, { 0.000918e-6, 10213.285546211, 5.532798067 }, { 0.001011e-6, -6256.777530192, 0.661826484 }, { 0.000753e-6, 16730.463689596, 3.905030235 }, { 0.000737e-6, 11926.254413669, 4.641956361 }, { 0.000694e-6, 3340.612426700, 2.111120332 }, { 0.000701e-6, 3894.181829542, 2.760823491 }, /* 561, 570 */ { 0.000689e-6, -135.065080035, 4.768800780 }, { 0.000700e-6, 13367.972631107, 5.760439898 }, { 0.000664e-6, 6040.347246017, 1.051215840 }, { 0.000654e-6, 5650.292110678, 4.911332503 }, { 0.000788e-6, 6681.224853400, 4.699648011 }, { 0.000628e-6, 5333.900241022, 5.024608847 }, { 0.000755e-6, -110.206321219, 4.370971253 }, { 0.000628e-6, 6290.189396992, 3.660478857 }, { 0.000635e-6, 25132.303399966, 4.121051532 }, { 0.000534e-6, 5966.683980335, 1.173284524 }, /* 571, 580 */ { 0.000543e-6, -433.711737877, 0.345585464 }, { 0.000517e-6, -1990.745017041, 5.414571768 }, { 0.000504e-6, 5767.611978898, 2.328281115 }, { 0.000485e-6, 5753.384884897, 1.685874771 }, { 0.000463e-6, 7860.419392439, 5.297703006 }, { 0.000604e-6, 515.463871093, 0.591998446 }, { 0.000443e-6, 12168.002696575, 4.830881244 }, { 0.000570e-6, 199.072001436, 3.899190272 }, { 0.000465e-6, 10969.965257698, 0.476681802 }, { 0.000424e-6, -7079.373856808, 1.112242763 }, /* 581, 590 */ { 0.000427e-6, 735.876513532, 1.994214480 }, { 0.000478e-6, -6127.655450557, 3.778025483 }, { 0.000414e-6, 10973.555686350, 5.441088327 }, { 0.000512e-6, 1589.072895284, 0.107123853 }, { 0.000378e-6, 10984.192351700, 0.915087231 }, { 0.000402e-6, 11371.704689758, 4.107281715 }, { 0.000453e-6, 9917.696874510, 1.917490952 }, { 0.000395e-6, 149.563197135, 2.763124165 }, { 0.000371e-6, 5739.157790895, 3.112111866 }, { 0.000350e-6, 11790.629088659, 0.440639857 }, /* 591, 600 */ { 0.000356e-6, 6133.512652857, 5.444568842 }, { 0.000344e-6, 412.371096874, 5.676832684 }, { 0.000383e-6, 955.599741609, 5.559734846 }, { 0.000333e-6, 6496.374945429, 0.261537984 }, { 0.000340e-6, 6055.549660552, 5.975534987 }, { 0.000334e-6, 1066.495477190, 2.335063907 }, { 0.000399e-6, 11506.769769794, 5.321230910 }, { 0.000314e-6, 18319.536584880, 2.313312404 }, { 0.000424e-6, 1052.268383188, 1.211961766 }, { 0.000307e-6, 63.735898303, 3.169551388 }, /* 601, 610 */ { 0.000329e-6, 29.821438149, 6.106912080 }, { 0.000357e-6, 6309.374169791, 4.223760346 }, { 0.000312e-6, -3738.761430108, 2.180556645 }, { 0.000301e-6, 309.278322656, 1.499984572 }, { 0.000268e-6, 12043.574281889, 2.447520648 }, { 0.000257e-6, 12491.370101415, 3.662331761 }, { 0.000290e-6, 625.670192312, 1.272834584 }, { 0.000256e-6, 5429.879468239, 1.913426912 }, { 0.000339e-6, 3496.032826134, 4.165930011 }, { 0.000283e-6, 3930.209696220, 4.325565754 }, /* 611, 620 */ { 0.000241e-6, 12528.018664345, 3.832324536 }, { 0.000304e-6, 4686.889407707, 1.612348468 }, { 0.000259e-6, 16200.772724501, 3.470173146 }, { 0.000238e-6, 12139.553509107, 1.147977842 }, { 0.000236e-6, 6172.869528772, 3.776271728 }, { 0.000296e-6, -7058.598461315, 0.460368852 }, { 0.000306e-6, 10575.406682942, 0.554749016 }, { 0.000251e-6, 17298.182327326, 0.834332510 }, { 0.000290e-6, 4732.030627343, 4.759564091 }, { 0.000261e-6, 5884.926846583, 0.298259862 }, /* 621, 630 */ { 0.000249e-6, 5547.199336460, 3.749366406 }, { 0.000213e-6, 11712.955318231, 5.415666119 }, { 0.000223e-6, 4701.116501708, 2.703203558 }, { 0.000268e-6, -640.877607382, 0.283670793 }, { 0.000209e-6, 5636.065016677, 1.238477199 }, { 0.000193e-6, 10177.257679534, 1.943251340 }, { 0.000182e-6, 6283.143160294, 2.456157599 }, { 0.000184e-6, -227.526189440, 5.888038582 }, { 0.000182e-6, -6283.008539689, 0.241332086 }, { 0.000228e-6, -6284.056171060, 2.657323816 }, /* 631, 640 */ { 0.000166e-6, 7238.675591600, 5.930629110 }, { 0.000167e-6, 3097.883822726, 5.570955333 }, { 0.000159e-6, -323.505416657, 5.786670700 }, { 0.000154e-6, -4136.910433516, 1.517805532 }, { 0.000176e-6, 12029.347187887, 3.139266834 }, { 0.000167e-6, 12132.439962106, 3.556352289 }, { 0.000153e-6, 202.253395174, 1.463313961 }, { 0.000157e-6, 17267.268201691, 1.586837396 }, { 0.000142e-6, 83996.847317911, 0.022670115 }, { 0.000152e-6, 17260.154654690, 0.708528947 }, /* 641, 650 */ { 0.000144e-6, 6084.003848555, 5.187075177 }, { 0.000135e-6, 5756.566278634, 1.993229262 }, { 0.000134e-6, 5750.203491159, 3.457197134 }, { 0.000144e-6, 5326.786694021, 6.066193291 }, { 0.000160e-6, 11015.106477335, 1.710431974 }, { 0.000133e-6, 3634.621024518, 2.836451652 }, { 0.000134e-6, 18073.704938650, 5.453106665 }, { 0.000134e-6, 1162.474704408, 5.326898811 }, { 0.000128e-6, 5642.198242609, 2.511652591 }, { 0.000160e-6, 632.783739313, 5.628785365 }, /* 651, 660 */ { 0.000132e-6, 13916.019109642, 0.819294053 }, { 0.000122e-6, 14314.168113050, 5.677408071 }, { 0.000125e-6, 12359.966151546, 5.251984735 }, { 0.000121e-6, 5749.452731634, 2.210924603 }, { 0.000136e-6, -245.831646229, 1.646502367 }, { 0.000120e-6, 5757.317038160, 3.240883049 }, { 0.000134e-6, 12146.667056108, 3.059480037 }, { 0.000137e-6, 6206.809778716, 1.867105418 }, { 0.000141e-6, 17253.041107690, 2.069217456 }, { 0.000129e-6, -7477.522860216, 2.781469314 }, /* 661, 670 */ { 0.000116e-6, 5540.085789459, 4.281176991 }, { 0.000116e-6, 9779.108676125, 3.320925381 }, { 0.000129e-6, 5237.921013804, 3.497704076 }, { 0.000113e-6, 5959.570433334, 0.983210840 }, { 0.000122e-6, 6282.095528923, 2.674938860 }, { 0.000140e-6, -11.045700264, 4.957936982 }, { 0.000108e-6, 23543.230504682, 1.390113589 }, { 0.000106e-6, -12569.674818332, 0.429631317 }, { 0.000110e-6, -266.607041722, 5.501340197 }, { 0.000115e-6, 12559.038152982, 4.691456618 }, /* 671, 680 */ { 0.000134e-6, -2388.894020449, 0.577313584 }, { 0.000109e-6, 10440.274292604, 6.218148717 }, { 0.000102e-6, -543.918059096, 1.477842615 }, { 0.000108e-6, 21228.392023546, 2.237753948 }, { 0.000101e-6, -4535.059436924, 3.100492232 }, { 0.000103e-6, 76.266071276, 5.594294322 }, { 0.000104e-6, 949.175608970, 5.674287810 }, { 0.000101e-6, 13517.870106233, 2.196632348 }, { 0.000100e-6, 11933.367960670, 4.056084160 }, /* T^2 */ { 4.322990e-6, 6283.075849991, 2.642893748 }, /* 681, 690 */ { 0.406495e-6, 0.000000000, 4.712388980 }, { 0.122605e-6, 12566.151699983, 2.438140634 }, { 0.019476e-6, 213.299095438, 1.642186981 }, { 0.016916e-6, 529.690965095, 4.510959344 }, { 0.013374e-6, -3.523118349, 1.502210314 }, { 0.008042e-6, 26.298319800, 0.478549024 }, { 0.007824e-6, 155.420399434, 5.254710405 }, { 0.004894e-6, 5746.271337896, 4.683210850 }, { 0.004875e-6, 5760.498431898, 0.759507698 }, { 0.004416e-6, 5223.693919802, 6.028853166 }, /* 691, 700 */ { 0.004088e-6, -7.113547001, 0.060926389 }, { 0.004433e-6, 77713.771467920, 3.627734103 }, { 0.003277e-6, 18849.227549974, 2.327912542 }, { 0.002703e-6, 6062.663207553, 1.271941729 }, { 0.003435e-6, -775.522611324, 0.747446224 }, { 0.002618e-6, 6076.890301554, 3.633715689 }, { 0.003146e-6, 206.185548437, 5.647874613 }, { 0.002544e-6, 1577.343542448, 6.232904270 }, { 0.002218e-6, -220.412642439, 1.309509946 }, { 0.002197e-6, 5856.477659115, 2.407212349 }, /* 701, 710 */ { 0.002897e-6, 5753.384884897, 5.863842246 }, { 0.001766e-6, 426.598190876, 0.754113147 }, { 0.001738e-6, -796.298006816, 2.714942671 }, { 0.001695e-6, 522.577418094, 2.629369842 }, { 0.001584e-6, 5507.553238667, 1.341138229 }, { 0.001503e-6, -242.728603974, 0.377699736 }, { 0.001552e-6, -536.804512095, 2.904684667 }, { 0.001370e-6, -398.149003408, 1.265599125 }, { 0.001889e-6, -5573.142801634, 4.413514859 }, { 0.001722e-6, 6069.776754553, 2.445966339 }, /* 711, 720 */ { 0.001124e-6, 1059.381930189, 5.041799657 }, { 0.001258e-6, 553.569402842, 3.849557278 }, { 0.000831e-6, 951.718406251, 2.471094709 }, { 0.000767e-6, 4694.002954708, 5.363125422 }, { 0.000756e-6, 1349.867409659, 1.046195744 }, { 0.000775e-6, -11.045700264, 0.245548001 }, { 0.000597e-6, 2146.165416475, 4.543268798 }, { 0.000568e-6, 5216.580372801, 4.178853144 }, { 0.000711e-6, 1748.016413067, 5.934271972 }, { 0.000499e-6, 12036.460734888, 0.624434410 }, /* 721, 730 */ { 0.000671e-6, -1194.447010225, 4.136047594 }, { 0.000488e-6, 5849.364112115, 2.209679987 }, { 0.000621e-6, 6438.496249426, 4.518860804 }, { 0.000495e-6, -6286.598968340, 1.868201275 }, { 0.000456e-6, 5230.807466803, 1.271231591 }, { 0.000451e-6, 5088.628839767, 0.084060889 }, { 0.000435e-6, 5643.178563677, 3.324456609 }, { 0.000387e-6, 10977.078804699, 4.052488477 }, { 0.000547e-6, 161000.685737473, 2.841633844 }, { 0.000522e-6, 3154.687084896, 2.171979966 }, /* 731, 740 */ { 0.000375e-6, 5486.777843175, 4.983027306 }, { 0.000421e-6, 5863.591206116, 4.546432249 }, { 0.000439e-6, 7084.896781115, 0.522967921 }, { 0.000309e-6, 2544.314419883, 3.172606705 }, { 0.000347e-6, 4690.479836359, 1.479586566 }, { 0.000317e-6, 801.820931124, 3.553088096 }, { 0.000262e-6, 419.484643875, 0.606635550 }, { 0.000248e-6, 6836.645252834, 3.014082064 }, { 0.000245e-6, -1592.596013633, 5.519526220 }, { 0.000225e-6, 4292.330832950, 2.877956536 }, /* 741, 750 */ { 0.000214e-6, 7234.794256242, 1.605227587 }, { 0.000205e-6, 5767.611978898, 0.625804796 }, { 0.000180e-6, 10447.387839604, 3.499954526 }, { 0.000229e-6, 199.072001436, 5.632304604 }, { 0.000214e-6, 639.897286314, 5.960227667 }, { 0.000175e-6, -433.711737877, 2.162417992 }, { 0.000209e-6, 515.463871093, 2.322150893 }, { 0.000173e-6, 6040.347246017, 2.556183691 }, { 0.000184e-6, 6309.374169791, 4.732296790 }, { 0.000227e-6, 149854.400134205, 5.385812217 }, /* 751, 760 */ { 0.000154e-6, 8031.092263058, 5.120720920 }, { 0.000151e-6, 5739.157790895, 4.815000443 }, { 0.000197e-6, 7632.943259650, 0.222827271 }, { 0.000197e-6, 74.781598567, 3.910456770 }, { 0.000138e-6, 6055.549660552, 1.397484253 }, { 0.000149e-6, -6127.655450557, 5.333727496 }, { 0.000137e-6, 3894.181829542, 4.281749907 }, { 0.000135e-6, 9437.762934887, 5.979971885 }, { 0.000139e-6, -2352.866153772, 4.715630782 }, { 0.000142e-6, 6812.766815086, 0.513330157 }, /* 761, 770 */ { 0.000120e-6, -4705.732307544, 0.194160689 }, { 0.000131e-6, -71430.695617928, 0.000379226 }, { 0.000124e-6, 6279.552731642, 2.122264908 }, { 0.000108e-6, -6256.777530192, 0.883445696 }, /* T^3 */ { 0.143388e-6, 6283.075849991, 1.131453581 }, { 0.006671e-6, 12566.151699983, 0.775148887 }, { 0.001480e-6, 155.420399434, 0.480016880 }, { 0.000934e-6, 213.299095438, 6.144453084 }, { 0.000795e-6, 529.690965095, 2.941595619 }, { 0.000673e-6, 5746.271337896, 0.120415406 }, /* 771, 780 */ { 0.000672e-6, 5760.498431898, 5.317009738 }, { 0.000389e-6, -220.412642439, 3.090323467 }, { 0.000373e-6, 6062.663207553, 3.003551964 }, { 0.000360e-6, 6076.890301554, 1.918913041 }, { 0.000316e-6, -21.340641002, 5.545798121 }, { 0.000315e-6, -242.728603974, 1.884932563 }, { 0.000278e-6, 206.185548437, 1.266254859 }, { 0.000238e-6, -536.804512095, 4.532664830 }, { 0.000185e-6, 522.577418094, 4.578313856 }, { 0.000245e-6, 18849.227549974, 0.587467082 }, /* 781, 787 */ { 0.000180e-6, 426.598190876, 5.151178553 }, { 0.000200e-6, 553.569402842, 5.355983739 }, { 0.000141e-6, 5223.693919802, 1.336556009 }, { 0.000104e-6, 5856.477659115, 4.239842759 }, /* T^4 */ { 0.003826e-6, 6283.075849991, 5.705257275 }, { 0.000303e-6, 12566.151699983, 5.407132842 }, { 0.000209e-6, 155.420399434, 1.989815753 } }; /* Time since J2000.0 in Julian millennia. */ t = ((date1 - DJ00) + date2) / DJM; /* ================= */ /* Topocentric terms */ /* ================= */ /* Convert UT to local solar time in radians. */ tsol = fmod(ut, 1.0) * D2PI + elong; /* FUNDAMENTAL ARGUMENTS: Simon et al. 1994. */ /* Combine time argument (millennia) with deg/arcsec factor. */ w = t / 3600.0; /* Sun Mean Longitude. */ elsun = fmod(280.46645683 + 1296027711.03429 * w, 360.0) * DD2R; /* Sun Mean Anomaly. */ emsun = fmod(357.52910918 + 1295965810.481 * w, 360.0) * DD2R; /* Mean Elongation of Moon from Sun. */ d = fmod(297.85019547 + 16029616012.090 * w, 360.0) * DD2R; /* Mean Longitude of Jupiter. */ elj = fmod(34.35151874 + 109306899.89453 * w, 360.0) * DD2R; /* Mean Longitude of Saturn. */ els = fmod(50.07744430 + 44046398.47038 * w, 360.0) * DD2R; /* TOPOCENTRIC TERMS: Moyer 1981 and Murray 1983. */ wt = + 0.00029e-10 * u * sin(tsol + elsun - els) + 0.00100e-10 * u * sin(tsol - 2.0 * emsun) + 0.00133e-10 * u * sin(tsol - d) + 0.00133e-10 * u * sin(tsol + elsun - elj) - 0.00229e-10 * u * sin(tsol + 2.0 * elsun + emsun) - 0.02200e-10 * v * cos(elsun + emsun) + 0.05312e-10 * u * sin(tsol - emsun) - 0.13677e-10 * u * sin(tsol + 2.0 * elsun) - 1.31840e-10 * v * cos(elsun) + 3.17679e-10 * u * sin(tsol); /* ===================== */ /* Fairhead et al. model */ /* ===================== */ /* T**0 */ w0 = 0; for (j = 473; j >= 0; j--) { w0 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]); } /* T**1 */ w1 = 0; for (j = 678; j >= 474; j--) { w1 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]); } /* T**2 */ w2 = 0; for (j = 763; j >= 679; j--) { w2 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]); } /* T**3 */ w3 = 0; for (j = 783; j >= 764; j--) { w3 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]); } /* T**4 */ w4 = 0; for (j = 786; j >= 784; j--) { w4 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]); } /* Multiply by powers of T and combine. */ wf = t * (t * (t * (t * w4 + w3) + w2) + w1) + w0; /* Adjustments to use JPL planetary masses instead of IAU. */ wj = 0.00065e-6 * sin(6069.776754 * t + 4.021194) + 0.00033e-6 * sin( 213.299095 * t + 5.543132) + (-0.00196e-6 * sin(6208.294251 * t + 5.696701)) + (-0.00173e-6 * sin( 74.781599 * t + 2.435900)) + 0.03638e-6 * t * t; /* ============ */ /* Final result */ /* ============ */ /* TDB-TT in seconds. */ w = wt + wf + wj; return w; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/dtf2d.c0000644000113000011300000002223713027221062014335 0ustar bellsbells#include "sofa.h" #include int iauDtf2d(const char *scale, int iy, int im, int id, int ihr, int imn, double sec, double *d1, double *d2) /* ** - - - - - - - - - ** i a u D t f 2 d ** - - - - - - - - - ** ** Encode date and time fields into 2-part Julian Date (or in the case ** of UTC a quasi-JD form that includes special provision for leap ** seconds). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** scale char[] time scale ID (Note 1) ** iy,im,id int year, month, day in Gregorian calendar (Note 2) ** ihr,imn int hour, minute ** sec double seconds ** ** Returned: ** d1,d2 double 2-part Julian Date (Notes 3,4) ** ** Returned (function value): ** int status: +3 = both of next two ** +2 = time is after end of day (Note 5) ** +1 = dubious year (Note 6) ** 0 = OK ** -1 = bad year ** -2 = bad month ** -3 = bad day ** -4 = bad hour ** -5 = bad minute ** -6 = bad second (<0) ** ** Notes: ** ** 1) scale identifies the time scale. Only the value "UTC" (in upper ** case) is significant, and enables handling of leap seconds (see ** Note 4). ** ** 2) For calendar conventions and limitations, see iauCal2jd. ** ** 3) The sum of the results, d1+d2, is Julian Date, where normally d1 ** is the Julian Day Number and d2 is the fraction of a day. In the ** case of UTC, where the use of JD is problematical, special ** conventions apply: see the next note. ** ** 4) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The SOFA internal convention is that ** the quasi-JD day represents UTC days whether the length is 86399, ** 86400 or 86401 SI seconds. In the 1960-1972 era there were ** smaller jumps (in either direction) each time the linear UTC(TAI) ** expression was changed, and these "mini-leaps" are also included ** in the SOFA convention. ** ** 5) The warning status "time is after end of day" usually means that ** the sec argument is greater than 60.0. However, in a day ending ** in a leap second the limit changes to 61.0 (or 59.0 in the case ** of a negative leap second). ** ** 6) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 7) Only in the case of continuous and regular time scales (TAI, TT, ** TCG, TCB and TDB) is the result d1+d2 a Julian Date, strictly ** speaking. In the other cases (UT1 and UTC) the result must be ** used with circumspection; in particular the difference between ** two such results cannot be interpreted as a precise time ** interval. ** ** Called: ** iauCal2jd Gregorian calendar to JD ** iauDat delta(AT) = TAI-UTC ** iauJd2cal JD to Gregorian calendar ** ** This revision: 2013 July 26 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int js, iy2, im2, id2; double dj, w, day, seclim, dat0, dat12, dat24, dleap, time; /* Today's Julian Day Number. */ js = iauCal2jd(iy, im, id, &dj, &w); if ( js ) return js; dj += w; /* Day length and final minute length in seconds (provisional). */ day = DAYSEC; seclim = 60.0; /* Deal with the UTC leap second case. */ if ( ! strcmp(scale,"UTC") ) { /* TAI-UTC at 0h today. */ js = iauDat(iy, im, id, 0.0, &dat0); if ( js < 0 ) return js; /* TAI-UTC at 12h today (to detect drift). */ js = iauDat(iy, im, id, 0.5, &dat12); if ( js < 0 ) return js; /* TAI-UTC at 0h tomorrow (to detect jumps). */ js = iauJd2cal ( dj, 1.5, &iy2, &im2, &id2, &w); if ( js ) return js; js = iauDat(iy2, im2, id2, 0.0, &dat24); if ( js < 0 ) return js; /* Any sudden change in TAI-UTC between today and tomorrow. */ dleap = dat24 - (2.0*dat12 - dat0); /* If leap second day, correct the day and final minute lengths. */ day += dleap; if ( ihr == 23 && imn == 59 ) seclim += dleap; /* End of UTC-specific actions. */ } /* Validate the time. */ if ( ihr >= 0 && ihr <= 23 ) { if ( imn >= 0 && imn <= 59 ) { if ( sec >= 0 ) { if ( sec >= seclim ) { js += 2; } } else { js = -6; } } else { js = -5; } } else { js = -4; } if ( js < 0 ) return js; /* The time in days. */ time = ( 60.0 * ( (double) ( 60 * ihr + imn ) ) + sec ) / day; /* Return the date and time. */ *d1 = dj; *d2 = time; /* Status. */ return js; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/eceq06.c0000644000113000011300000001610613027221062014413 0ustar bellsbells#include "sofa.h" void iauEceq06(double date1, double date2, double dl, double db, double *dr, double *dd) /* ** - - - - - - - - - - ** i a u E c e q 0 6 ** - - - - - - - - - - ** ** Transformation from ecliptic coordinates (mean equinox and ecliptic ** of date) to ICRS RA,Dec, using the IAU 2006 precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian date (Note 1) ** dl,db double ecliptic longitude and latitude (radians) ** ** Returned: ** dr,dd double ICRS right ascension and declination (radians) ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) No assumptions are made about whether the coordinates represent ** starlight and embody astrometric effects such as parallax or ** aberration. ** ** 3) The transformation is approximately that from ecliptic longitude ** and latitude (mean equinox and ecliptic of date) to mean J2000.0 ** right ascension and declination, with only frame bias (always ** less than 25 mas) to disturb this classical picture. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauEcm06 J2000.0 to ecliptic rotation matrix, IAU 2006 ** iauTrxp product of transpose of r-matrix and p-vector ** iauC2s unit vector to spherical coordinates ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** ** This revision: 2016 February 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rm[3][3], v1[3], v2[3], a, b; /* Spherical to Cartesian. */ iauS2c(dl, db, v1); /* Rotation matrix, ICRS equatorial to ecliptic. */ iauEcm06(date1, date2, rm); /* The transformation from ecliptic to ICRS. */ iauTrxp(rm, v1, v2); /* Cartesian to spherical. */ iauC2s(v2, &a, &b); /* Express in conventional ranges. */ *dr = iauAnp(a); *dd = iauAnpm(b); /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ecm06.c0000644000113000011300000001612413027221062014242 0ustar bellsbells#include "sofa.h" void iauEcm06(double date1, double date2, double rm[3][3]) /* ** - - - - - - - - - ** i a u E c m 0 6 ** - - - - - - - - - ** ** ICRS equatorial to ecliptic rotation matrix, IAU 2006. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian date (Note 1) ** ** Returned: ** rm double[3][3] ICRS to ecliptic rotation matrix ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 1) The matrix is in the sense ** ** E_ep = rm x P_ICRS, ** ** where P_ICRS is a vector with respect to ICRS right ascension ** and declination axes and E_ep is the same vector with respect to ** the (inertial) ecliptic and equinox of date. ** ** 2) P_ICRS is a free vector, merely a direction, typically of unit ** magnitude, and not bound to any particular spatial origin, such ** as the Earth, Sun or SSB. No assumptions are made about whether ** it represents starlight and embodies astrometric effects such as ** parallax or aberration. The transformation is approximately that ** between mean J2000.0 right ascension and declination and ecliptic ** longitude and latitude, with only frame bias (always less than ** 25 mas) to disturb this classical picture. ** ** Called: ** iauObl06 mean obliquity, IAU 2006 ** iauPmat06 PB matrix, IAU 2006 ** iauIr initialize r-matrix to identity ** iauRx rotate around X-axis ** iauRxr product of two r-matrices ** ** This revision: 2015 December 11 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double ob, bp[3][3], e[3][3]; /* Obliquity, IAU 2006. */ ob = iauObl06(date1, date2); /* Precession-bias matrix, IAU 2006. */ iauPmat06(date1, date2, bp); /* Equatorial of date to ecliptic matrix. */ iauIr(e); iauRx(ob, e); /* ICRS to ecliptic coordinates rotation matrix, IAU 2006. */ iauRxr(e, bp, rm); /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ee00a.c0000644000113000011300000001570113027221062014222 0ustar bellsbells#include "sofa.h" double iauEe00a(double date1, double date2) /* ** - - - - - - - - - ** i a u E e 0 0 a ** - - - - - - - - - ** ** Equation of the equinoxes, compatible with IAU 2000 resolutions. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double equation of the equinoxes (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result, which is in radians, operates in the following sense: ** ** Greenwich apparent ST = GMST + equation of the equinoxes ** ** 3) The result is compatible with the IAU 2000 resolutions. For ** further details, see IERS Conventions 2003 and Capitaine et al. ** (2002). ** ** Called: ** iauPr00 IAU 2000 precession adjustments ** iauObl80 mean obliquity, IAU 1980 ** iauNut00a nutation, IAU 2000A ** iauEe00 equation of the equinoxes, IAU 2000 ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003). ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004). ** ** This revision: 2008 May 16 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dpsipr, depspr, epsa, dpsi, deps, ee; /* IAU 2000 precession-rate adjustments. */ iauPr00(date1, date2, &dpsipr, &depspr); /* Mean obliquity, consistent with IAU 2000 precession-nutation. */ epsa = iauObl80(date1, date2) + depspr; /* Nutation in longitude. */ iauNut00a(date1, date2, &dpsi, &deps); /* Equation of the equinoxes. */ ee = iauEe00(date1, date2, epsa, dpsi); return ee; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ee00b.c0000644000113000011300000001641413027221062014225 0ustar bellsbells#include "sofa.h" double iauEe00b(double date1, double date2) /* ** - - - - - - - - - ** i a u E e 0 0 b ** - - - - - - - - - ** ** Equation of the equinoxes, compatible with IAU 2000 resolutions but ** using the truncated nutation model IAU 2000B. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double equation of the equinoxes (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result, which is in radians, operates in the following sense: ** ** Greenwich apparent ST = GMST + equation of the equinoxes ** ** 3) The result is compatible with the IAU 2000 resolutions except ** that accuracy has been compromised for the sake of speed. For ** further details, see McCarthy & Luzum (2001), IERS Conventions ** 2003 and Capitaine et al. (2003). ** ** Called: ** iauPr00 IAU 2000 precession adjustments ** iauObl80 mean obliquity, IAU 1980 ** iauNut00b nutation, IAU 2000B ** iauEe00 equation of the equinoxes, IAU 2000 ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** McCarthy, D.D. & Luzum, B.J., "An abridged model of the ** precession-nutation of the celestial pole", Celestial Mechanics & ** Dynamical Astronomy, 85, 37-49 (2003) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2008 May 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dpsipr, depspr, epsa, dpsi, deps, ee; /* IAU 2000 precession-rate adjustments. */ iauPr00(date1, date2, &dpsipr, &depspr); /* Mean obliquity, consistent with IAU 2000 precession-nutation. */ epsa = iauObl80(date1, date2) + depspr; /* Nutation in longitude. */ iauNut00b(date1, date2, &dpsi, &deps); /* Equation of the equinoxes. */ ee = iauEe00(date1, date2, epsa, dpsi); return ee; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ee00.c0000644000113000011300000001542113027221062014060 0ustar bellsbells#include "sofa.h" double iauEe00(double date1, double date2, double epsa, double dpsi) /* ** - - - - - - - - ** i a u E e 0 0 ** - - - - - - - - ** ** The equation of the equinoxes, compatible with IAU 2000 resolutions, ** given the nutation in longitude and the mean obliquity. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** epsa double mean obliquity (Note 2) ** dpsi double nutation in longitude (Note 3) ** ** Returned (function value): ** double equation of the equinoxes (Note 4) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The obliquity, in radians, is mean of date. ** ** 3) The result, which is in radians, operates in the following sense: ** ** Greenwich apparent ST = GMST + equation of the equinoxes ** ** 4) The result is compatible with the IAU 2000 resolutions. For ** further details, see IERS Conventions 2003 and Capitaine et al. ** (2002). ** ** Called: ** iauEect00 equation of the equinoxes complementary terms ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2008 May 16 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double ee; /* Equation of the equinoxes. */ ee = dpsi * cos(epsa) + iauEect00(date1, date2); return ee; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ee06a.c0000644000113000011300000001475013027221062014233 0ustar bellsbells#include "sofa.h" double iauEe06a(double date1, double date2) /* ** - - - - - - - - - ** i a u E e 0 6 a ** - - - - - - - - - ** ** Equation of the equinoxes, compatible with IAU 2000 resolutions and ** IAU 2006/2000A precession-nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double equation of the equinoxes (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result, which is in radians, operates in the following sense: ** ** Greenwich apparent ST = GMST + equation of the equinoxes ** ** Called: ** iauAnpm normalize angle into range +/- pi ** iauGst06a Greenwich apparent sidereal time, IAU 2006/2000A ** iauGmst06 Greenwich mean sidereal time, IAU 2006 ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** This revision: 2008 May 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double gst06a, gmst06, ee; /* Apparent and mean sidereal times. */ gst06a = iauGst06a(0.0, 0.0, date1, date2); gmst06 = iauGmst06(0.0, 0.0, date1, date2); /* Equation of the equinoxes. */ ee = iauAnpm(gst06a - gmst06); return ee; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/eect00.c0000644000113000011300000003011613027221062014405 0ustar bellsbells#include "sofa.h" double iauEect00(double date1, double date2) /* ** - - - - - - - - - - ** i a u E e c t 0 0 ** - - - - - - - - - - ** ** Equation of the equinoxes complementary terms, consistent with ** IAU 2000 resolutions. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double complementary terms (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The "complementary terms" are part of the equation of the ** equinoxes (EE), classically the difference between apparent and ** mean Sidereal Time: ** ** GAST = GMST + EE ** ** with: ** ** EE = dpsi * cos(eps) ** ** where dpsi is the nutation in longitude and eps is the obliquity ** of date. However, if the rotation of the Earth were constant in ** an inertial frame the classical formulation would lead to ** apparent irregularities in the UT1 timescale traceable to side- ** effects of precession-nutation. In order to eliminate these ** effects from UT1, "complementary terms" were introduced in 1994 ** (IAU, 1994) and took effect from 1997 (Capitaine and Gontier, ** 1993): ** ** GAST = GMST + CT + EE ** ** By convention, the complementary terms are included as part of ** the equation of the equinoxes rather than as part of the mean ** Sidereal Time. This slightly compromises the "geometrical" ** interpretation of mean sidereal time but is otherwise ** inconsequential. ** ** The present function computes CT in the above expression, ** compatible with IAU 2000 resolutions (Capitaine et al., 2002, and ** IERS Conventions 2003). ** ** Called: ** iauFal03 mean anomaly of the Moon ** iauFalp03 mean anomaly of the Sun ** iauFaf03 mean argument of the latitude of the Moon ** iauFad03 mean elongation of the Moon from the Sun ** iauFaom03 mean longitude of the Moon's ascending node ** iauFave03 mean longitude of Venus ** iauFae03 mean longitude of Earth ** iauFapa03 general accumulated precession in longitude ** ** References: ** ** Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275, ** 645-650 (1993) ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** IAU Resolution C7, Recommendation 3 (1994) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Time since J2000.0, in Julian centuries */ double t; /* Miscellaneous */ int i, j; double a, s0, s1; /* Fundamental arguments */ double fa[14]; /* Returned value. */ double eect; /* ----------------------------------------- */ /* The series for the EE complementary terms */ /* ----------------------------------------- */ typedef struct { int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */ double s, c; /* sine and cosine coefficients */ } TERM; /* Terms of order t^0 */ static const TERM e0[] = { /* 1-10 */ {{ 0, 0, 0, 0, 1, 0, 0, 0}, 2640.96e-6, -0.39e-6 }, {{ 0, 0, 0, 0, 2, 0, 0, 0}, 63.52e-6, -0.02e-6 }, {{ 0, 0, 2, -2, 3, 0, 0, 0}, 11.75e-6, 0.01e-6 }, {{ 0, 0, 2, -2, 1, 0, 0, 0}, 11.21e-6, 0.01e-6 }, {{ 0, 0, 2, -2, 2, 0, 0, 0}, -4.55e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 3, 0, 0, 0}, 2.02e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.98e-6, 0.00e-6 }, {{ 0, 0, 0, 0, 3, 0, 0, 0}, -1.72e-6, 0.00e-6 }, {{ 0, 1, 0, 0, 1, 0, 0, 0}, -1.41e-6, -0.01e-6 }, {{ 0, 1, 0, 0, -1, 0, 0, 0}, -1.26e-6, -0.01e-6 }, /* 11-20 */ {{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.63e-6, 0.00e-6 }, {{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.63e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 3, 0, 0, 0}, 0.46e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 1, 0, 0, 0}, 0.45e-6, 0.00e-6 }, {{ 0, 0, 4, -4, 4, 0, 0, 0}, 0.36e-6, 0.00e-6 }, {{ 0, 0, 1, -1, 1, -8, 12, 0}, -0.24e-6, -0.12e-6 }, {{ 0, 0, 2, 0, 0, 0, 0, 0}, 0.32e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 2, 0, 0, 0}, 0.28e-6, 0.00e-6 }, {{ 1, 0, 2, 0, 3, 0, 0, 0}, 0.27e-6, 0.00e-6 }, {{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.26e-6, 0.00e-6 }, /* 21-30 */ {{ 0, 0, 2, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 }, {{ 0, 1, -2, 2, -3, 0, 0, 0}, 0.19e-6, 0.00e-6 }, {{ 0, 1, -2, 2, -1, 0, 0, 0}, 0.18e-6, 0.00e-6 }, {{ 0, 0, 0, 0, 0, 8,-13, -1}, -0.10e-6, 0.05e-6 }, {{ 0, 0, 0, 2, 0, 0, 0, 0}, 0.15e-6, 0.00e-6 }, {{ 2, 0, -2, 0, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 }, {{ 1, 0, 0, -2, 1, 0, 0, 0}, 0.14e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 2, 0, 0, 0}, -0.14e-6, 0.00e-6 }, {{ 1, 0, 0, -2, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 }, {{ 0, 0, 4, -2, 4, 0, 0, 0}, 0.13e-6, 0.00e-6 }, /* 31-33 */ {{ 0, 0, 2, -2, 4, 0, 0, 0}, -0.11e-6, 0.00e-6 }, {{ 1, 0, -2, 0, -3, 0, 0, 0}, 0.11e-6, 0.00e-6 }, {{ 1, 0, -2, 0, -1, 0, 0, 0}, 0.11e-6, 0.00e-6 } }; /* Terms of order t^1 */ static const TERM e1[] = { {{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.87e-6, 0.00e-6 } }; /* Number of terms in the series */ const int NE0 = (int) (sizeof e0 / sizeof (TERM)); const int NE1 = (int) (sizeof e1 / sizeof (TERM)); /*--------------------------------------------------------------------*/ /* Interval between fundamental epoch J2000.0 and current date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Fundamental Arguments (from IERS Conventions 2003) */ /* Mean anomaly of the Moon. */ fa[0] = iauFal03(t); /* Mean anomaly of the Sun. */ fa[1] = iauFalp03(t); /* Mean longitude of the Moon minus that of the ascending node. */ fa[2] = iauFaf03(t); /* Mean elongation of the Moon from the Sun. */ fa[3] = iauFad03(t); /* Mean longitude of the ascending node of the Moon. */ fa[4] = iauFaom03(t); /* Mean longitude of Venus. */ fa[5] = iauFave03(t); /* Mean longitude of Earth. */ fa[6] = iauFae03(t); /* General precession in longitude. */ fa[7] = iauFapa03(t); /* Evaluate the EE complementary terms. */ s0 = 0.0; s1 = 0.0; for (i = NE0-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)(e0[i].nfa[j]) * fa[j]; } s0 += e0[i].s * sin(a) + e0[i].c * cos(a); } for (i = NE1-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)(e1[i].nfa[j]) * fa[j]; } s1 += e1[i].s * sin(a) + e1[i].c * cos(a); } eect = (s0 + s1 * t ) * DAS2R; return eect; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/eform.c0000644000113000011300000001504113027221062014435 0ustar bellsbells#include "sofa.h" int iauEform ( int n, double *a, double *f ) /* ** - - - - - - - - - ** i a u E f o r m ** - - - - - - - - - ** ** Earth reference ellipsoids. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** n int ellipsoid identifier (Note 1) ** ** Returned: ** a double equatorial radius (meters, Note 2) ** f double flattening (Note 2) ** ** Returned (function value): ** int status: 0 = OK ** -1 = illegal identifier (Note 3) ** ** Notes: ** ** 1) The identifier n is a number that specifies the choice of ** reference ellipsoid. The following are supported: ** ** n ellipsoid ** ** 1 WGS84 ** 2 GRS80 ** 3 WGS72 ** ** The n value has no significance outside the SOFA software. For ** convenience, symbols WGS84 etc. are defined in sofam.h. ** ** 2) The ellipsoid parameters are returned in the form of equatorial ** radius in meters (a) and flattening (f). The latter is a number ** around 0.00335, i.e. around 1/298. ** ** 3) For the case where an unsupported n value is supplied, zero a and ** f are returned, as well as error status. ** ** References: ** ** Department of Defense World Geodetic System 1984, National ** Imagery and Mapping Agency Technical Report 8350.2, Third ** Edition, p3-2. ** ** Moritz, H., Bull. Geodesique 66-2, 187 (1992). ** ** The Department of Defense World Geodetic System 1972, World ** Geodetic System Committee, May 1974. ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** p220. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Look up a and f for the specified reference ellipsoid. */ switch ( n ) { case WGS84: *a = 6378137.0; *f = 1.0 / 298.257223563; break; case GRS80: *a = 6378137.0; *f = 1.0 / 298.257222101; break; case WGS72: *a = 6378135.0; *f = 1.0 / 298.26; break; default: /* Invalid identifier. */ *a = 0.0; *f = 0.0; return -1; } /* OK status. */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/eo06a.c0000644000113000011300000001553013027221062014242 0ustar bellsbells#include "sofa.h" double iauEo06a(double date1, double date2) /* ** - - - - - - - - - ** i a u E o 0 6 a ** - - - - - - - - - ** ** Equation of the origins, IAU 2006 precession and IAU 2000A nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double equation of the origins in radians ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The equation of the origins is the distance between the true ** equinox and the celestial intermediate origin and, equivalently, ** the difference between Earth rotation angle and Greenwich ** apparent sidereal time (ERA-GST). It comprises the precession ** (since J2000.0) in right ascension plus the equation of the ** equinoxes (including the small correction terms). ** ** Called: ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** iauEors equation of the origins, given NPB matrix and s ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double r[3][3], x, y, s, eo; /* Classical nutation x precession x bias matrix. */ iauPnm06a(date1, date2, r); /* Extract CIP coordinates. */ iauBpn2xy(r, &x, &y); /* The CIO locator, s. */ s = iauS06(date1, date2, x, y); /* Solve for the EO. */ eo = iauEors(r, s); return eo; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/eors.c0000644000113000011300000001370213027221062014277 0ustar bellsbells#include "sofa.h" double iauEors(double rnpb[3][3], double s) /* ** - - - - - - - - ** i a u E o r s ** - - - - - - - - ** ** Equation of the origins, given the classical NPB matrix and the ** quantity s. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rnpb double[3][3] classical nutation x precession x bias matrix ** s double the quantity s (the CIO locator) ** ** Returned (function value): ** double the equation of the origins in radians. ** ** Notes: ** ** 1) The equation of the origins is the distance between the true ** equinox and the celestial intermediate origin and, equivalently, ** the difference between Earth rotation angle and Greenwich ** apparent sidereal time (ERA-GST). It comprises the precession ** (since J2000.0) in right ascension plus the equation of the ** equinoxes (including the small correction terms). ** ** 2) The algorithm is from Wallace & Capitaine (2006). ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double x, ax, xs, ys, zs, p, q, eo; /* Evaluate Wallace & Capitaine (2006) expression (16). */ x = rnpb[2][0]; ax = x / (1.0 + rnpb[2][2]); xs = 1.0 - ax * x; ys = -ax * rnpb[2][1]; zs = -x; p = rnpb[0][0] * xs + rnpb[0][1] * ys + rnpb[0][2] * zs; q = rnpb[1][0] * xs + rnpb[1][1] * ys + rnpb[1][2] * zs; eo = ((p != 0) || (q != 0)) ? s - atan2(q, p) : s; return eo; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/epb2jd.c0000644000113000011300000001233613027221062014477 0ustar bellsbells#include "sofa.h" void iauEpb2jd(double epb, double *djm0, double *djm) /* ** - - - - - - - - - - ** i a u E p b 2 j d ** - - - - - - - - - - ** ** Besselian Epoch to Julian Date. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epb double Besselian Epoch (e.g. 1957.3) ** ** Returned: ** djm0 double MJD zero-point: always 2400000.5 ** djm double Modified Julian Date ** ** Note: ** ** The Julian Date is returned in two pieces, in the usual SOFA ** manner, which is designed to preserve time resolution. The ** Julian Date is available as a single number by adding djm0 and ** djm. ** ** Reference: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282. ** ** This revision: 2013 August 13 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { *djm0 = DJM0; *djm = 15019.81352 + (epb - 1900.0) * DTY; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/epb.c0000644000113000011300000001242613027221062014077 0ustar bellsbells#include "sofa.h" double iauEpb(double dj1, double dj2) /* ** - - - - - - - ** i a u E p b ** - - - - - - - ** ** Julian Date to Besselian Epoch. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** dj1,dj2 double Julian Date (see note) ** ** Returned (function value): ** double Besselian Epoch. ** ** Note: ** ** The Julian Date is supplied in two pieces, in the usual SOFA ** manner, which is designed to preserve time resolution. The ** Julian Date is available as a single number by adding dj1 and ** dj2. The maximum resolution is achieved if dj1 is 2451545.0 ** (J2000.0). ** ** Reference: ** ** Lieske, J.H., 1979. Astron.Astrophys., 73, 282. ** ** This revision: 2013 August 21 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* J2000.0-B1900.0 (2415019.81352) in days */ const double D1900 = 36524.68648; return 1900.0 + ((dj1 - DJ00) + (dj2 + D1900)) / DTY; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/epj2jd.c0000644000113000011300000001232213027221062014502 0ustar bellsbells#include "sofa.h" void iauEpj2jd(double epj, double *djm0, double *djm) /* ** - - - - - - - - - - ** i a u E p j 2 j d ** - - - - - - - - - - ** ** Julian Epoch to Julian Date. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian Epoch (e.g. 1996.8) ** ** Returned: ** djm0 double MJD zero-point: always 2400000.5 ** djm double Modified Julian Date ** ** Note: ** ** The Julian Date is returned in two pieces, in the usual SOFA ** manner, which is designed to preserve time resolution. The ** Julian Date is available as a single number by adding djm0 and ** djm. ** ** Reference: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282. ** ** This revision: 2013 August 7 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { *djm0 = DJM0; *djm = DJM00 + (epj - 2000.0) * 365.25; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/epj.c0000644000113000011300000001231713027221062014106 0ustar bellsbells#include "sofa.h" double iauEpj(double dj1, double dj2) /* ** - - - - - - - ** i a u E p j ** - - - - - - - ** ** Julian Date to Julian Epoch. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** dj1,dj2 double Julian Date (see note) ** ** Returned (function value): ** double Julian Epoch ** ** Note: ** ** The Julian Date is supplied in two pieces, in the usual SOFA ** manner, which is designed to preserve time resolution. The ** Julian Date is available as a single number by adding dj1 and ** dj2. The maximum resolution is achieved if dj1 is 2451545.0 ** (J2000.0). ** ** Reference: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282. ** ** This revision: 2013 August 7 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double epj; epj = 2000.0 + ((dj1 - DJ00) + dj2) / DJY; return epj; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/epv00.c0000644000113000011300000045073013027221062014267 0ustar bellsbells#include "sofa.h" int iauEpv00(double date1, double date2, double pvh[2][3], double pvb[2][3]) /* ** - - - - - - - - - ** i a u E p v 0 0 ** - - - - - - - - - ** ** Earth position and velocity, heliocentric and barycentric, with ** respect to the Barycentric Celestial Reference System. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TDB date (Note 1) ** ** Returned: ** pvh double[2][3] heliocentric Earth position/velocity ** pvb double[2][3] barycentric Earth position/velocity ** ** Returned (function value): ** int status: 0 = OK ** +1 = warning: date outside ** the range 1900-2100 AD ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. However, ** the accuracy of the result is more likely to be limited by the ** algorithm itself than the way the date has been expressed. ** ** n.b. TT can be used instead of TDB in most applications. ** ** 2) On return, the arrays pvh and pvb contain the following: ** ** pvh[0][0] x } ** pvh[0][1] y } heliocentric position, AU ** pvh[0][2] z } ** ** pvh[1][0] xdot } ** pvh[1][1] ydot } heliocentric velocity, AU/d ** pvh[1][2] zdot } ** ** pvb[0][0] x } ** pvb[0][1] y } barycentric position, AU ** pvb[0][2] z } ** ** pvb[1][0] xdot } ** pvb[1][1] ydot } barycentric velocity, AU/d ** pvb[1][2] zdot } ** ** The vectors are with respect to the Barycentric Celestial ** Reference System. The time unit is one day in TDB. ** ** 3) The function is a SIMPLIFIED SOLUTION from the planetary theory ** VSOP2000 (X. Moisson, P. Bretagnon, 2001, Celes. Mechanics & ** Dyn. Astron., 80, 3/4, 205-213) and is an adaptation of original ** Fortran code supplied by P. Bretagnon (private comm., 2000). ** ** 4) Comparisons over the time span 1900-2100 with this simplified ** solution and the JPL DE405 ephemeris give the following results: ** ** RMS max ** Heliocentric: ** position error 3.7 11.2 km ** velocity error 1.4 5.0 mm/s ** ** Barycentric: ** position error 4.6 13.4 km ** velocity error 1.4 4.9 mm/s ** ** Comparisons with the JPL DE406 ephemeris show that by 1800 and ** 2200 the position errors are approximately double their 1900-2100 ** size. By 1500 and 2500 the deterioration is a factor of 10 and ** by 1000 and 3000 a factor of 60. The velocity accuracy falls off ** at about half that rate. ** ** 5) It is permissible to use the same array for pvh and pvb, which ** will receive the barycentric values. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* ** Matrix elements for orienting the analytical model to DE405. ** ** The corresponding Euler angles are: ** ** d ' " ** 1st rotation - 23 26 21.4091 about the x-axis (obliquity) ** 2nd rotation + 0.0475 about the z-axis (RA offset) ** ** These were obtained empirically, by comparisons with DE405 over ** 1900-2100. */ static const double am12 = 0.000000211284, am13 = -0.000000091603, am21 = -0.000000230286, am22 = 0.917482137087, am23 = -0.397776982902, am32 = 0.397776982902, am33 = 0.917482137087; /* ** ---------------------- ** Ephemeris Coefficients ** ---------------------- ** ** The ephemeris consists of harmonic terms for predicting (i) the Sun ** to Earth vector and (ii) the Solar-System-barycenter to Sun vector ** respectively. The coefficients are stored in arrays which, although ** 1-demensional, contain groups of three. Each triplet of ** coefficients is the amplitude, phase and frequency for one term in ** the model, and each array contains the number of terms called for by ** the model. ** ** There are eighteen such arrays, named as follows: ** ** array model power of T component ** ** e0x Sun-to-Earth 0 x ** e0y Sun-to-Earth 0 y ** e0z Sun-to-Earth 0 z ** ** e1x Sun-to-Earth 1 x ** e1y Sun-to-Earth 1 y ** e1z Sun-to-Earth 1 z ** ** e2x Sun-to-Earth 2 x ** e2y Sun-to-Earth 2 y ** e2z Sun-to-Earth 2 z ** ** s0x SSB-to-Sun 0 x ** s0y SSB-to-Sun 0 y ** s0z SSB-to-Sun 0 z ** ** s1x SSB-to-Sun 1 x ** s1y SSB-to-Sun 1 y ** s1z SSB-to-Sun 1 z ** ** s2x SSB-to-Sun 2 x ** s2y SSB-to-Sun 2 y ** s2z SSB-to-Sun 2 z */ /* Sun-to-Earth, T^0, X */ static const double e0x[] = { 0.9998292878132e+00, 0.1753485171504e+01, 0.6283075850446e+01, 0.8352579567414e-02, 0.1710344404582e+01, 0.1256615170089e+02, 0.5611445335148e-02, 0.0000000000000e+00, 0.0000000000000e+00, 0.1046664295572e-03, 0.1667225416770e+01, 0.1884922755134e+02, 0.3110842534677e-04, 0.6687513390251e+00, 0.8399684731857e+02, 0.2552413503550e-04, 0.5830637358413e+00, 0.5296909721118e+00, 0.2137207845781e-04, 0.1092330954011e+01, 0.1577343543434e+01, 0.1680240182951e-04, 0.4955366134987e+00, 0.6279552690824e+01, 0.1679012370795e-04, 0.6153014091901e+01, 0.6286599010068e+01, 0.1445526946777e-04, 0.3472744100492e+01, 0.2352866153506e+01, 0.1091038246184e-04, 0.3689845786119e+01, 0.5223693906222e+01, 0.9344399733932e-05, 0.6073934645672e+01, 0.1203646072878e+02, 0.8993182910652e-05, 0.3175705249069e+01, 0.1021328554739e+02, 0.5665546034116e-05, 0.2152484672246e+01, 0.1059381944224e+01, 0.6844146703035e-05, 0.1306964099750e+01, 0.5753384878334e+01, 0.7346610905565e-05, 0.4354980070466e+01, 0.3981490189893e+00, 0.6815396474414e-05, 0.2218229211267e+01, 0.4705732307012e+01, 0.6112787253053e-05, 0.5384788425458e+01, 0.6812766822558e+01, 0.4518120711239e-05, 0.6087604012291e+01, 0.5884926831456e+01, 0.4521963430706e-05, 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0.7130726476180e-07, 0.7674871987661e+00, 0.6321103546637e+01, 0.6650894461162e-07, 0.6987129150116e+00, 0.5327476111629e+01, 0.7396888823688e-07, 0.3576824794443e+01, 0.5368044267797e+00, 0.7420588884775e-07, 0.5033615245369e+01, 0.2354323048545e+02, 0.6141181642908e-07, 0.9449927045673e+00, 0.1296430071988e+02, 0.6373557924058e-07, 0.6206342280341e+01, 0.9517183207817e+00, 0.6359474329261e-07, 0.5036079095757e+01, 0.1990745094947e+01, 0.5740173582646e-07, 0.6105106371350e+01, 0.9555997388169e+00, 0.7019864084602e-07, 0.7237747359018e+00, 0.5225775174439e+00, 0.6398054487042e-07, 0.3976367969666e+01, 0.2407292145756e+02, 0.7797092650498e-07, 0.4305423910623e+01, 0.2200391463820e+02, 0.6466760000900e-07, 0.3500136825200e+01, 0.5230807360890e+01, 0.7529417043890e-07, 0.3514779246100e+01, 0.1842262939178e+02, 0.6924571140892e-07, 0.2743457928679e+01, 0.1554202828031e+00, 0.6220798650222e-07, 0.2242598118209e+01, 0.1845107853235e+02, 0.5870209391853e-07, 0.2332832707527e+01, 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0.3598484186267e-08, 0.3505282086105e+01, 0.6147450479709e+01, 0.3694594027310e-08, 0.2286651088141e+01, 0.2636725487657e+01, 0.2680444152969e-08, 0.1871816775482e+00, 0.6816289982179e+01, 0.3497574865641e-08, 0.3143251755431e+01, 0.6418701221183e+01, 0.3130274129494e-08, 0.2462167316018e+01, 0.1235996607578e+02, 0.3241119069551e-08, 0.4256374004686e+01, 0.1652265972112e+02, 0.2601960842061e-08, 0.4970362941425e+01, 0.1045450126711e+02, 0.2690601527504e-08, 0.2372657824898e+01, 0.3163918923335e+00, 0.2908688152664e-08, 0.4232652627721e+01, 0.2828699048865e+02, 0.3120456131875e-08, 0.3925747001137e+00, 0.2195415756911e+02, 0.3148855423384e-08, 0.3093478330445e+01, 0.1172006883645e+02, 0.3051044261017e-08, 0.5560948248212e+01, 0.6055599646783e+01, 0.2826006876660e-08, 0.5072790310072e+01, 0.5120601093667e+01, 0.3100034191711e-08, 0.4998530231096e+01, 0.1799603123222e+02, 0.2398771640101e-08, 0.2561739802176e+01, 0.6255674361143e+01, 0.2384002842728e-08, 0.4087420284111e+01, 0.6310477339748e+01, 0.2842146517568e-08, 0.2515048217955e+01, 0.5469525544182e+01, 0.2847674371340e-08, 0.5235326497443e+01, 0.1034429499989e+02, 0.2903722140764e-08, 0.1088200795797e+01, 0.6510552054109e+01, 0.3187610710605e-08, 0.4710624424816e+01, 0.1693792562116e+03, 0.3048869992813e-08, 0.2857975896445e+00, 0.8390110365991e+01, 0.2860216950984e-08, 0.2241619020815e+01, 0.2243449970715e+00, 0.2701117683113e-08, 0.6651573305272e-01, 0.6129297044991e+01, 0.2509891590152e-08, 0.1285135324585e+01, 0.1044027435778e+02, 0.2623200252223e-08, 0.2981229834530e+00, 0.6436854655901e+01, 0.2622541669202e-08, 0.6122470726189e+01, 0.9380959548977e+01, 0.2818435667099e-08, 0.4251087148947e+01, 0.5934151399930e+01, 0.2365196797465e-08, 0.3465070460790e+01, 0.2470570524223e+02, 0.2358704646143e-08, 0.5791603815350e+01, 0.8671969964381e+01, 0.2388299481390e-08, 0.4142483772941e+01, 0.7096626156709e+01, 0.1996041217224e-08, 0.2101901889496e+01, 0.1727188400790e+02, 0.2687593060336e-08, 0.1526689456959e+01, 0.7075506709219e+02, 0.2618913670810e-08, 0.2397684236095e+01, 0.6632000300961e+01, 0.2571523050364e-08, 0.5751929456787e+00, 0.6206810014183e+01, 0.2582135006946e-08, 0.5595464352926e+01, 0.4873985990671e+02, 0.2372530190361e-08, 0.5092689490655e+01, 0.1590676413561e+02, 0.2357178484712e-08, 0.4444363527851e+01, 0.3097883698531e+01, 0.2451590394723e-08, 0.3108251687661e+01, 0.6612329252343e+00, 0.2370045949608e-08, 0.2608133861079e+01, 0.3459636466239e+02, 0.2268997267358e-08, 0.3639717753384e+01, 0.2844914056730e-01, 0.1731432137906e-08, 0.1741898445707e+00, 0.2019909489111e+02, 0.1629869741622e-08, 0.3902225646724e+01, 0.3035599730800e+02, 0.2206215801974e-08, 0.4971131250731e+01, 0.6281667977667e+01, 0.2205469554680e-08, 0.1677462357110e+01, 0.6284483723224e+01, 0.2148792362509e-08, 0.4236259604006e+01, 0.1980482729015e+02, 0.1873733657847e-08, 0.5926814998687e+01, 0.2876692439167e+02, 0.2026573758959e-08, 0.4349643351962e+01, 0.2449240616245e+02, 0.1807770325110e-08, 0.5700940482701e+01, 0.2045286941806e+02, 0.1881174408581e-08, 0.6601286363430e+00, 0.2358125818164e+02, 0.1368023671690e-08, 0.2211098592752e+01, 0.2473415438279e+02, 0.1720017916280e-08, 0.4942488551129e+01, 0.1679593901136e+03, 0.1702427665131e-08, 0.1452233856386e+01, 0.3338575901272e+03, 0.1414032510054e-08, 0.5525357721439e+01, 0.1624205518357e+03, 0.1652626045364e-08, 0.4108794283624e+01, 0.8956999012000e+02, 0.1642957769686e-08, 0.7344335209984e+00, 0.5267006960365e+02, 0.1614952403624e-08, 0.3541213951363e+01, 0.3332657872986e+02, 0.1535988291188e-08, 0.4031094072151e+01, 0.3852657435933e+02, 0.1593193738177e-08, 0.4185136203609e+01, 0.2282781046519e+03, 0.1074569126382e-08, 0.1720485636868e+01, 0.8397383534231e+02, 0.1074408214509e-08, 0.2758613420318e+01, 0.8401985929482e+02, 0.9700199670465e-09, 0.4216686842097e+01, 0.7826370942180e+02, 0.1258433517061e-08, 0.2575068876639e+00, 0.3115650189215e+03, 0.1240303229539e-08, 0.4800844956756e+00, 0.1784300471910e+03, 0.9018345948127e-09, 0.3896756361552e+00, 0.5886454391678e+02, 0.1135301432805e-08, 0.3700805023550e+00, 0.7842370451713e+02, 0.9215887951370e-09, 0.4364579276638e+01, 0.1014262087719e+03, 0.1055401054147e-08, 0.2156564222111e+01, 0.5660027930059e+02, 0.1008725979831e-08, 0.5454015785234e+01, 0.4245678405627e+02, 0.7217398104321e-09, 0.1597772562175e+01, 0.2457074661053e+03, 0.6912033134447e-09, 0.5824090621461e+01, 0.1679936946371e+03, 0.6833881523549e-09, 0.3578778482835e+01, 0.6053048899753e+02, 0.4887304205142e-09, 0.3724362812423e+01, 0.9656299901946e+02, 0.5173709754788e-09, 0.5422427507933e+01, 0.2442876000072e+03, 0.4671353097145e-09, 0.2396106924439e+01, 0.1435713242844e+03, 0.5652608439480e-09, 0.2804028838685e+01, 0.8365903305582e+02, 0.5604061331253e-09, 0.1638816006247e+01, 0.8433466158131e+02, 0.4712723365400e-09, 0.8979003224474e+00, 0.3164282286739e+03, 0.4909967465112e-09, 0.3210426725516e+01, 0.4059982187939e+03, 0.4771358267658e-09, 0.5308027211629e+01, 0.1805255418145e+03, 0.3943451445989e-09, 0.2195145341074e+01, 0.2568537517081e+03, 0.3952109120244e-09, 0.5081189491586e+01, 0.2449975330562e+03, 0.3788134594789e-09, 0.4345171264441e+01, 0.1568131045107e+03, 0.3738330190479e-09, 0.2613062847997e+01, 0.3948519331910e+03, 0.3099866678136e-09, 0.2846760817689e+01, 0.1547176098872e+03, 0.2002962716768e-09, 0.4921360989412e+01, 0.2268582385539e+03, 0.2198291338754e-09, 0.1130360117454e+00, 0.1658638954901e+03, 0.1491958330784e-09, 0.4228195232278e+01, 0.2219950288015e+03, 0.1475384076173e-09, 0.3005721811604e+00, 0.3052819430710e+03, 0.1661626624624e-09, 0.7830125621203e+00, 0.2526661704812e+03, 0.9015823460025e-10, 0.3807792942715e+01, 0.4171445043968e+03 }; /* Sun-to-Earth, T^0, Y */ static const double e0y[] = { 0.9998921098898e+00, 0.1826583913846e+00, 0.6283075850446e+01, -0.2442700893735e-01, 0.0000000000000e+00, 0.0000000000000e+00, 0.8352929742915e-02, 0.1395277998680e+00, 0.1256615170089e+02, 0.1046697300177e-03, 0.9641423109763e-01, 0.1884922755134e+02, 0.3110841876663e-04, 0.5381140401712e+01, 0.8399684731857e+02, 0.2570269094593e-04, 0.5301016407128e+01, 0.5296909721118e+00, 0.2147389623610e-04, 0.2662510869850e+01, 0.1577343543434e+01, 0.1680344384050e-04, 0.5207904119704e+01, 0.6279552690824e+01, 0.1679117312193e-04, 0.4582187486968e+01, 0.6286599010068e+01, 0.1440512068440e-04, 0.1900688517726e+01, 0.2352866153506e+01, 0.1135139664999e-04, 0.5273108538556e+01, 0.5223693906222e+01, 0.9345482571018e-05, 0.4503047687738e+01, 0.1203646072878e+02, 0.9007418719568e-05, 0.1605621059637e+01, 0.1021328554739e+02, 0.5671536712314e-05, 0.5812849070861e+00, 0.1059381944224e+01, 0.7451401861666e-05, 0.2807346794836e+01, 0.3981490189893e+00, 0.6393470057114e-05, 0.6029224133855e+01, 0.5753384878334e+01, 0.6814275881697e-05, 0.6472990145974e+00, 0.4705732307012e+01, 0.6113705628887e-05, 0.3813843419700e+01, 0.6812766822558e+01, 0.4503851367273e-05, 0.4527804370996e+01, 0.5884926831456e+01, 0.4522249141926e-05, 0.5991783029224e+01, 0.6256777527156e+01, 0.4501794307018e-05, 0.3798703844397e+01, 0.6309374173736e+01, 0.5514927480180e-05, 0.3961257833388e+01, 0.5507553240374e+01, 0.4062862799995e-05, 0.5256247296369e+01, 0.6681224869435e+01, 0.5414900429712e-05, 0.5499032014097e+01, 0.7755226100720e+00, 0.5463153987424e-05, 0.6173092454097e+01, 0.1414349524433e+02, 0.5071611859329e-05, 0.2870244247651e+01, 0.7860419393880e+01, 0.2195112094455e-05, 0.2952338617201e+01, 0.1150676975667e+02, 0.2279139233919e-05, 0.5951775132933e+01, 0.7058598460518e+01, 0.2278386100876e-05, 0.4845456398785e+01, 0.4694002934110e+01, 0.2559088003308e-05, 0.6945321117311e+00, 0.1216800268190e+02, 0.2561079286856e-05, 0.6167224608301e+01, 0.7099330490126e+00, 0.1792755796387e-05, 0.1400122509632e+01, 0.7962980379786e+00, 0.1818715656502e-05, 0.4703347611830e+01, 0.6283142985870e+01, 0.1818744924791e-05, 0.5086748900237e+01, 0.6283008715021e+01, 0.1554518791390e-05, 0.5331008042713e-01, 0.2513230340178e+02, 0.2063265737239e-05, 0.4283680484178e+01, 0.1179062909082e+02, 0.1497613520041e-05, 0.6074207826073e+01, 0.5486777812467e+01, 0.2000617940427e-05, 0.2501426281450e+01, 0.1778984560711e+02, 0.1289731195580e-05, 0.3646340599536e+01, 0.7079373888424e+01, 0.1282657998934e-05, 0.3232864804902e+01, 0.3738761453707e+01, 0.1528915968658e-05, 0.5581433416669e+01, 0.2132990797783e+00, 0.1187304098432e-05, 0.5453576453694e+01, 0.9437762937313e+01, 0.7842782928118e-06, 0.2823953922273e+00, 0.8827390247185e+01, 0.7352892280868e-06, 0.1124369580175e+01, 0.1589072916335e+01, 0.6570189360797e-06, 0.2089154042840e+01, 0.1176985366291e+02, 0.6324967590410e-06, 0.6704855581230e+00, 0.6262300422539e+01, 0.6298289872283e-06, 0.2836414855840e+01, 0.6303851278352e+01, 0.6476686465855e-06, 0.4852433866467e+00, 0.7113454667900e-02, 0.8587034651234e-06, 0.1453511005668e+01, 0.1672837615881e+03, 0.8068948788113e-06, 0.9224087798609e+00, 0.6069776770667e+01, 0.8353786011661e-06, 0.4631707184895e+01, 0.3340612434717e+01, 0.6009324532132e-06, 0.1829498827726e+01, 0.4136910472696e+01, 0.7558158559566e-06, 0.2588596800317e+01, 0.6496374930224e+01, 0.5809279504503e-06, 0.5516818853476e+00, 0.1097707878456e+02, 0.5374131950254e-06, 0.6275674734960e+01, 0.1194447056968e+01, 0.5711160507326e-06, 0.1091905956872e+01, 0.6282095334605e+01, 0.5710183170746e-06, 0.2415001635090e+01, 0.6284056366286e+01, 0.5144373590610e-06, 0.6020336443438e+01, 0.6290189305114e+01, 0.5103108927267e-06, 0.3775634564605e+01, 0.6275962395778e+01, 0.4960654697891e-06, 0.1073450946756e+01, 0.6127655567643e+01, 0.4786385689280e-06, 0.2431178012310e+01, 0.6438496133249e+01, 0.6109911263665e-06, 0.5343356157914e+01, 0.3154687086868e+01, 0.4839898944024e-06, 0.5830833594047e-01, 0.8018209333619e+00, 0.4734822623919e-06, 0.4536080134821e+01, 0.3128388763578e+01, 0.4834741473290e-06, 0.2585090489754e+00, 0.7084896783808e+01, 0.5134858581156e-06, 0.4213317172603e+01, 0.1235285262111e+02, 0.5064004264978e-06, 0.4814418806478e+00, 0.1185621865188e+02, 0.3753476772761e-06, 0.1599953399788e+01, 0.8429241228195e+01, 0.4935264014283e-06, 0.2157417556873e+01, 0.2544314396739e+01, 0.3950929600897e-06, 0.3359394184254e+01, 0.5481254917084e+01, 0.4895849789777e-06, 0.5165704376558e+01, 0.9225539266174e+01, 0.4215241688886e-06, 0.2065368800993e+01, 0.1726015463500e+02, 0.3796773731132e-06, 0.1468606346612e+01, 0.4265981595566e+00, 0.3114178142515e-06, 0.3615638079474e+01, 0.2146165377750e+01, 0.3260664220838e-06, 0.4417134922435e+01, 0.4164311961999e+01, 0.3976996123008e-06, 0.4700866883004e+01, 0.5856477690889e+01, 0.2801459672924e-06, 0.4538902060922e+01, 0.1256967486051e+02, 0.3638931868861e-06, 0.1334197991475e+01, 0.1807370494127e+02, 0.2487013269476e-06, 0.3749275558275e+01, 0.2629832328990e-01, 0.3034165481994e-06, 0.4236622030873e+00, 0.4535059491685e+01, 0.2676278825586e-06, 0.5970848007811e+01, 0.3930209696940e+01, 0.2764903818918e-06, 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0.6281591679874e+01, 0.8995601652048e-08, 0.2224439106766e+01, 0.6284560021018e+01, 0.8288040568796e-08, 0.5234914433867e+01, 0.1241658836951e+02, 0.6359381347255e-08, 0.4137989441490e+01, 0.1596186371003e+01, 0.8699572228626e-08, 0.1758411009497e+01, 0.6133512519065e+01, 0.6456797542736e-08, 0.5919285089994e+01, 0.1685848245639e+02, 0.7424573475452e-08, 0.5414616938827e+01, 0.4061219149443e+01, 0.7235671196168e-08, 0.1496516557134e+01, 0.1610006857377e+03, 0.8104015182733e-08, 0.1919918242764e+01, 0.8460828644453e+00, 0.8098576535937e-08, 0.3819615855458e+01, 0.3894181736510e+01, 0.6275292346625e-08, 0.6244264115141e+01, 0.8531963191132e+00, 0.6052432989112e-08, 0.5037731872610e+00, 0.1567108171867e+02, 0.5705651535817e-08, 0.2984557271995e+01, 0.1258692712880e+02, 0.5789650115138e-08, 0.6087038140697e+01, 0.1193336791622e+02, 0.5512132153377e-08, 0.5855668994076e+01, 0.1232342296471e+02, 0.7388890819102e-08, 0.2443128574740e+01, 0.4907302013889e+01, 0.5467593991798e-08, 0.3017561234194e+01, 0.1884211409667e+02, 0.6388519802999e-08, 0.5887386712935e+01, 0.5217580628120e+02, 0.6106777149944e-08, 0.3483461059895e+00, 0.1422690933580e-01, 0.7383420275489e-08, 0.5417387056707e+01, 0.2358125818164e+02, 0.5505208141738e-08, 0.2848193644783e+01, 0.1151388321134e+02, 0.6310757462877e-08, 0.2349882520828e+01, 0.1041998632314e+02, 0.6166904929691e-08, 0.5728575944077e+00, 0.6151533897323e+01, 0.5263442042754e-08, 0.4495796125937e+01, 0.1885275071096e+02, 0.5591828082629e-08, 0.1355441967677e+01, 0.4337116142245e+00, 0.5397051680497e-08, 0.1673422864307e+01, 0.6286362197481e+01, 0.5396992745159e-08, 0.1833502206373e+01, 0.6279789503410e+01, 0.6572913000726e-08, 0.3331122065824e+01, 0.1176433076753e+02, 0.5123421866413e-08, 0.2165327142679e+01, 0.1245594543367e+02, 0.5930495725999e-08, 0.2931146089284e+01, 0.6414617803568e+01, 0.6431797403933e-08, 0.4134407994088e+01, 0.1350651127443e+00, 0.5003182207604e-08, 0.3805420303749e+01, 0.1096996532989e+02, 0.5587731032504e-08, 0.1082469260599e+01, 0.6062663316000e+01, 0.5935263407816e-08, 0.8384333678401e+00, 0.5326786718777e+01, 0.4756019827760e-08, 0.3552588749309e+01, 0.3104930017775e+01, 0.6599951172637e-08, 0.4320826409528e+01, 0.4087944051283e+02, 0.5902606868464e-08, 0.4811879454445e+01, 0.5849364236221e+01, 0.5921147809031e-08, 0.9942628922396e-01, 0.1581959461667e+01, 0.5505382581266e-08, 0.2466557607764e+01, 0.6503488384892e+01, 0.5353771071862e-08, 0.4551978748683e+01, 0.1735668374386e+03, 0.5063282210946e-08, 0.5710812312425e+01, 0.1248988586463e+02, 0.5926120403383e-08, 0.1333998428358e+01, 0.2673594526851e+02, 0.5211016176149e-08, 0.4649315360760e+01, 0.2460261242967e+02, 0.5347075084894e-08, 0.5512754081205e+01, 0.4171425416666e+01, 0.4872609773574e-08, 0.1308025299938e+01, 0.5333900173445e+01, 0.4727711321420e-08, 0.2144908368062e+01, 0.7232251527446e+01, 0.6029426018652e-08, 0.5567259412084e+01, 0.3227113045244e+03, 0.4321485284369e-08, 0.5230667156451e+01, 0.9388005868221e+01, 0.4476406760553e-08, 0.6134081115303e+01, 0.5547199253223e+01, 0.5835268277420e-08, 0.4783808492071e+01, 0.7285056171570e+02, 0.5172183602748e-08, 0.5161817911099e+01, 0.1884570439172e+02, 0.5693571465184e-08, 0.1381646203111e+01, 0.9723862754494e+02, 0.4060634965349e-08, 0.3876705259495e+00, 0.4274518229222e+01, 0.3967398770473e-08, 0.5029491776223e+01, 0.3496032717521e+01, 0.3943754005255e-08, 0.1923162955490e+01, 0.6244942932314e+01, 0.4781323427824e-08, 0.4633332586423e+01, 0.2929661536378e+02, 0.3871483781204e-08, 0.1616650009743e+01, 0.6321208768577e+01, 0.5141741733997e-08, 0.9817316704659e-01, 0.1232032006293e+02, 0.4002385978497e-08, 0.3656161212139e+01, 0.7018952447668e+01, 0.4901092604097e-08, 0.4404098713092e+01, 0.1478866649112e+01, 0.3740932630345e-08, 0.5181188732639e+00, 0.6922973089781e+01, 0.4387283718538e-08, 0.3254859566869e+01, 0.2331413144044e+03, 0.5019197802033e-08, 0.3086773224677e+01, 0.1715706182245e+02, 0.3834931695175e-08, 0.2797882673542e+01, 0.1491901785440e+02, 0.3760413942497e-08, 0.2892676280217e+01, 0.1726726808967e+02, 0.3719717204628e-08, 0.5861046025739e+01, 0.6297302759782e+01, 0.4145623530149e-08, 0.2168239627033e+01, 0.1376059875786e+02, 0.3932788425380e-08, 0.6271811124181e+01, 0.7872148766781e+01, 0.3686377476857e-08, 0.3936853151404e+01, 0.6268848941110e+01, 0.3779077950339e-08, 0.1404148734043e+01, 0.4157198507331e+01, 0.4091334550598e-08, 0.2452436180854e+01, 0.9779108567966e+01, 0.3926694536146e-08, 0.6102292739040e+01, 0.1098419223922e+02, 0.4841000253289e-08, 0.6072760457276e+01, 0.1252801878276e+02, 0.4949340130240e-08, 0.1154832815171e+01, 0.1617106187867e+03, 0.3761557737360e-08, 0.5527545321897e+01, 0.3185192151914e+01, 0.3647396268188e-08, 0.1525035688629e+01, 0.6271346477544e+01, 0.3932405074189e-08, 0.5570681040569e+01, 0.2139354194808e+02, 0.3631322501141e-08, 0.1981240601160e+01, 0.6294805223347e+01, 0.4130007425139e-08, 0.2050060880201e+01, 0.2195415756911e+02, 0.4433905965176e-08, 0.3277477970321e+01, 0.7445550607224e+01, 0.3851814176947e-08, 0.5210690074886e+01, 0.9562891316684e+00, 0.3485807052785e-08, 0.6653274904611e+00, 0.1161697602389e+02, 0.3979772816991e-08, 0.1767941436148e+01, 0.2277943724828e+02, 0.3402607460500e-08, 0.3421746306465e+01, 0.1087398597200e+02, 0.4049993000926e-08, 0.1127144787547e+01, 0.3163918923335e+00, 0.3420511182382e-08, 0.4214794779161e+01, 0.1362553364512e+02, 0.3640772365012e-08, 0.5324905497687e+01, 0.1725304118033e+02, 0.3323037987501e-08, 0.6135761838271e+01, 0.6279143387820e+01, 0.4503141663637e-08, 0.1802305450666e+01, 0.1385561574497e+01, 0.4314560055588e-08, 0.4812299731574e+01, 0.4176041334900e+01, 0.3294226949110e-08, 0.3657547059723e+01, 0.6287008313071e+01, 0.3215657197281e-08, 0.4866676894425e+01, 0.5749861718712e+01, 0.4129362656266e-08, 0.3809342558906e+01, 0.5905702259363e+01, 0.3137762976388e-08, 0.2494635174443e+01, 0.2099539292909e+02, 0.3514010952384e-08, 0.2699961831678e+01, 0.7335344340001e+01, 0.3327607571530e-08, 0.3318457714816e+01, 0.5436992986000e+01, 0.3541066946675e-08, 0.4382703582466e+01, 0.1234573916645e+02, 0.3216179847052e-08, 0.5271066317054e+01, 0.3802769619140e-01, 0.2959045059570e-08, 0.5819591585302e+01, 0.2670964694522e+02, 0.3884040326665e-08, 0.5980934960428e+01, 0.6660449441528e+01, 0.2922027539886e-08, 0.3337290282483e+01, 0.1375773836557e+01, 0.4110846382042e-08, 0.5742978187327e+01, 0.4480965020977e+02, 0.2934508411032e-08, 0.2278075804200e+01, 0.6408777551755e+00, 0.3966896193000e-08, 0.5835747858477e+01, 0.3773735910827e+00, 0.3286695827610e-08, 0.5838898193902e+01, 0.3932462625300e-02, 0.3720643094196e-08, 0.1122212337858e+01, 0.1646033343740e+02, 0.3285508906174e-08, 0.9182250996416e+00, 0.1081813534213e+02, 0.3753880575973e-08, 0.5174761973266e+01, 0.5642198095270e+01, 0.3022129385587e-08, 0.3381611020639e+01, 0.2982630633589e+02, 0.2798569205621e-08, 0.3546193723922e+01, 0.1937891852345e+02, 0.3397872070505e-08, 0.4533203197934e+01, 0.6923953605621e+01, 0.3708099772977e-08, 0.2756168198616e+01, 0.3066615496545e+02, 0.3599283541510e-08, 0.1934395469918e+01, 0.6147450479709e+01, 0.3688702753059e-08, 0.7149920971109e+00, 0.2636725487657e+01, 0.2681084724003e-08, 0.4899819493154e+01, 0.6816289982179e+01, 0.3495993460759e-08, 0.1572418915115e+01, 0.6418701221183e+01, 0.3130770324995e-08, 0.8912190180489e+00, 0.1235996607578e+02, 0.2744353821941e-08, 0.3800821940055e+01, 0.2059724391010e+02, 0.2842732906341e-08, 0.2644717440029e+01, 0.2828699048865e+02, 0.3046882682154e-08, 0.3987793020179e+01, 0.6055599646783e+01, 0.2399072455143e-08, 0.9908826440764e+00, 0.6255674361143e+01, 0.2384306274204e-08, 0.2516149752220e+01, 0.6310477339748e+01, 0.2977324500559e-08, 0.5849195642118e+01, 0.1652265972112e+02, 0.3062835258972e-08, 0.1681660100162e+01, 0.1172006883645e+02, 0.3109682589231e-08, 0.5804143987737e+00, 0.2751146787858e+02, 0.2903920355299e-08, 0.5800768280123e+01, 0.6510552054109e+01, 0.2823221989212e-08, 0.9241118370216e+00, 0.5469525544182e+01, 0.3187949696649e-08, 0.3139776445735e+01, 0.1693792562116e+03, 0.2922559771655e-08, 0.3549440782984e+01, 0.2630839062450e+00, 0.2436302066603e-08, 0.4735540696319e+01, 0.3946258593675e+00, 0.3049473043606e-08, 0.4998289124561e+01, 0.8390110365991e+01, 0.2863682575784e-08, 0.6709515671102e+00, 0.2243449970715e+00, 0.2641750517966e-08, 0.5410978257284e+01, 0.2986433403208e+02, 0.2704093466243e-08, 0.4778317207821e+01, 0.6129297044991e+01, 0.2445522177011e-08, 0.6009020662222e+01, 0.1171295538178e+02, 0.2623608810230e-08, 0.5010449777147e+01, 0.6436854655901e+01, 0.2079259704053e-08, 0.5980943768809e+01, 0.2019909489111e+02, 0.2820225596771e-08, 0.2679965110468e+01, 0.5934151399930e+01, 0.2365221950927e-08, 0.1894231148810e+01, 0.2470570524223e+02, 0.2359682077149e-08, 0.4220752950780e+01, 0.8671969964381e+01, 0.2387577137206e-08, 0.2571783940617e+01, 0.7096626156709e+01, 0.1982102089816e-08, 0.5169765997119e+00, 0.1727188400790e+02, 0.2687502389925e-08, 0.6239078264579e+01, 0.7075506709219e+02, 0.2207751669135e-08, 0.2031184412677e+01, 0.4377611041777e+01, 0.2618370214274e-08, 0.8266079985979e+00, 0.6632000300961e+01, 0.2591951887361e-08, 0.8819350522008e+00, 0.4873985990671e+02, 0.2375055656248e-08, 0.3520944177789e+01, 0.1590676413561e+02, 0.2472019978911e-08, 0.1551431908671e+01, 0.6612329252343e+00, 0.2368157127199e-08, 0.4178610147412e+01, 0.3459636466239e+02, 0.1764846605693e-08, 0.1506764000157e+01, 0.1980094587212e+02, 0.2291769608798e-08, 0.2118250611782e+01, 0.2844914056730e-01, 0.2209997316943e-08, 0.3363255261678e+01, 0.2666070658668e+00, 0.2292699097923e-08, 0.4200423956460e+00, 0.1484170571900e-02, 0.1629683015329e-08, 0.2331362582487e+01, 0.3035599730800e+02, 0.2206492862426e-08, 0.3400274026992e+01, 0.6281667977667e+01, 0.2205746568257e-08, 0.1066051230724e+00, 0.6284483723224e+01, 0.2026310767991e-08, 0.2779066487979e+01, 0.2449240616245e+02, 0.1762977622163e-08, 0.9951450691840e+00, 0.2045286941806e+02, 0.1368535049606e-08, 0.6402447365817e+00, 0.2473415438279e+02, 0.1720598775450e-08, 0.2303524214705e+00, 0.1679593901136e+03, 0.1702429015449e-08, 0.6164622655048e+01, 0.3338575901272e+03, 0.1414033197685e-08, 0.3954561185580e+01, 0.1624205518357e+03, 0.1573768958043e-08, 0.2028286308984e+01, 0.3144167757552e+02, 0.1650705184447e-08, 0.2304040666128e+01, 0.5267006960365e+02, 0.1651087618855e-08, 0.2538461057280e+01, 0.8956999012000e+02, 0.1616409518983e-08, 0.5111054348152e+01, 0.3332657872986e+02, 0.1537175173581e-08, 0.5601130666603e+01, 0.3852657435933e+02, 0.1593191980553e-08, 0.2614340453411e+01, 0.2282781046519e+03, 0.1499480170643e-08, 0.3624721577264e+01, 0.2823723341956e+02, 0.1493807843235e-08, 0.4214569879008e+01, 0.2876692439167e+02, 0.1074571199328e-08, 0.1496911744704e+00, 0.8397383534231e+02, 0.1074406983417e-08, 0.1187817671922e+01, 0.8401985929482e+02, 0.9757576855851e-09, 0.2655703035858e+01, 0.7826370942180e+02, 0.1258432887565e-08, 0.4969896184844e+01, 0.3115650189215e+03, 0.1240336343282e-08, 0.5192460776926e+01, 0.1784300471910e+03, 0.9016107005164e-09, 0.1960356923057e+01, 0.5886454391678e+02, 0.1135392360918e-08, 0.5082427809068e+01, 0.7842370451713e+02, 0.9216046089565e-09, 0.2793775037273e+01, 0.1014262087719e+03, 0.1061276615030e-08, 0.3726144311409e+01, 0.5660027930059e+02, 0.1010110596263e-08, 0.7404080708937e+00, 0.4245678405627e+02, 0.7217424756199e-09, 0.2697449980577e-01, 0.2457074661053e+03, 0.6912003846756e-09, 0.4253296276335e+01, 0.1679936946371e+03, 0.6871814664847e-09, 0.5148072412354e+01, 0.6053048899753e+02, 0.4887158016343e-09, 0.2153581148294e+01, 0.9656299901946e+02, 0.5161802866314e-09, 0.3852750634351e+01, 0.2442876000072e+03, 0.5652599559057e-09, 0.1233233356270e+01, 0.8365903305582e+02, 0.4710812608586e-09, 0.5610486976767e+01, 0.3164282286739e+03, 0.4909977500324e-09, 0.1639629524123e+01, 0.4059982187939e+03, 0.4772641839378e-09, 0.3737100368583e+01, 0.1805255418145e+03, 0.4487562567153e-09, 0.1158417054478e+00, 0.8433466158131e+02, 0.3943441230497e-09, 0.6243502862796e+00, 0.2568537517081e+03, 0.3952236913598e-09, 0.3510377382385e+01, 0.2449975330562e+03, 0.3788898363417e-09, 0.5916128302299e+01, 0.1568131045107e+03, 0.3738329328831e-09, 0.1042266763456e+01, 0.3948519331910e+03, 0.2451199165151e-09, 0.1166788435700e+01, 0.1435713242844e+03, 0.2436734402904e-09, 0.3254726114901e+01, 0.2268582385539e+03, 0.2213605274325e-09, 0.1687210598530e+01, 0.1658638954901e+03, 0.1491521204829e-09, 0.2657541786794e+01, 0.2219950288015e+03, 0.1474995329744e-09, 0.5013089805819e+01, 0.3052819430710e+03, 0.1661939475656e-09, 0.5495315428418e+01, 0.2526661704812e+03, 0.9015946748003e-10, 0.2236989966505e+01, 0.4171445043968e+03 }; /* Sun-to-Earth, T^0, Z */ static const double e0z[] = { 0.2796207639075e-05, 0.3198701560209e+01, 0.8433466158131e+02, 0.1016042198142e-05, 0.5422360395913e+01, 0.5507553240374e+01, 0.8044305033647e-06, 0.3880222866652e+01, 0.5223693906222e+01, 0.4385347909274e-06, 0.3704369937468e+01, 0.2352866153506e+01, 0.3186156414906e-06, 0.3999639363235e+01, 0.1577343543434e+01, 0.2272412285792e-06, 0.3984738315952e+01, 0.1047747311755e+01, 0.1645620103007e-06, 0.3565412516841e+01, 0.5856477690889e+01, 0.1815836921166e-06, 0.4984507059020e+01, 0.6283075850446e+01, 0.1447461676364e-06, 0.3702753570108e+01, 0.9437762937313e+01, 0.1430760876382e-06, 0.3409658712357e+01, 0.1021328554739e+02, 0.1120445753226e-06, 0.4829561570246e+01, 0.1414349524433e+02, 0.1090232840797e-06, 0.2080729178066e+01, 0.6812766822558e+01, 0.9715727346551e-07, 0.3476295881948e+01, 0.4694002934110e+01, 0.1036267136217e-06, 0.4056639536648e+01, 0.7109288135493e+02, 0.8752665271340e-07, 0.4448159519911e+01, 0.5753384878334e+01, 0.8331864956004e-07, 0.4991704044208e+01, 0.7084896783808e+01, 0.6901658670245e-07, 0.4325358994219e+01, 0.6275962395778e+01, 0.9144536848998e-07, 0.1141826375363e+01, 0.6620890113188e+01, 0.7205085037435e-07, 0.3624344170143e+01, 0.5296909721118e+00, 0.7697874654176e-07, 0.5554257458998e+01, 0.1676215758509e+03, 0.5197545738384e-07, 0.6251760961735e+01, 0.1807370494127e+02, 0.5031345378608e-07, 0.2497341091913e+01, 0.4705732307012e+01, 0.4527110205840e-07, 0.2335079920992e+01, 0.6309374173736e+01, 0.4753355798089e-07, 0.7094148987474e+00, 0.5884926831456e+01, 0.4296951977516e-07, 0.1101916352091e+01, 0.6681224869435e+01, 0.3855341568387e-07, 0.1825495405486e+01, 0.5486777812467e+01, 0.5253930970990e-07, 0.4424740687208e+01, 0.7860419393880e+01, 0.4024630496471e-07, 0.5120498157053e+01, 0.1336797263425e+02, 0.4061069791453e-07, 0.6029771435451e+01, 0.3930209696940e+01, 0.3797883804205e-07, 0.4435193600836e+00, 0.3154687086868e+01, 0.2933033225587e-07, 0.5124157356507e+01, 0.1059381944224e+01, 0.3503000930426e-07, 0.5421830162065e+01, 0.6069776770667e+01, 0.3670096214050e-07, 0.4582101667297e+01, 0.1219403291462e+02, 0.2905609437008e-07, 0.1926566420072e+01, 0.1097707878456e+02, 0.2466827821713e-07, 0.6090174539834e+00, 0.6496374930224e+01, 0.2691647295332e-07, 0.1393432595077e+01, 0.2200391463820e+02, 0.2150554667946e-07, 0.4308671715951e+01, 0.5643178611111e+01, 0.2237481922680e-07, 0.8133968269414e+00, 0.8635942003952e+01, 0.1817741038157e-07, 0.3755205127454e+01, 0.3340612434717e+01, 0.2227820762132e-07, 0.2759558596664e+01, 0.1203646072878e+02, 0.1944713772307e-07, 0.5699645869121e+01, 0.1179062909082e+02, 0.1527340520662e-07, 0.1986749091746e+01, 0.3981490189893e+00, 0.1577282574914e-07, 0.3205017217983e+01, 0.5088628793478e+01, 0.1424738825424e-07, 0.6256747903666e+01, 0.2544314396739e+01, 0.1616563121701e-07, 0.2601671259394e+00, 0.1729818233119e+02, 0.1401210391692e-07, 0.4686939173506e+01, 0.7058598460518e+01, 0.1488726974214e-07, 0.2815862451372e+01, 0.2593412433514e+02, 0.1692626442388e-07, 0.4956894109797e+01, 0.1564752902480e+03, 0.1123571582910e-07, 0.2381192697696e+01, 0.3738761453707e+01, 0.9903308606317e-08, 0.4294851657684e+01, 0.9225539266174e+01, 0.9174533187191e-08, 0.3075171510642e+01, 0.4164311961999e+01, 0.8645985631457e-08, 0.5477534821633e+00, 0.8429241228195e+01, -0.1085876492688e-07, 0.0000000000000e+00, 0.0000000000000e+00, 0.9264309077815e-08, 0.5968571670097e+01, 0.7079373888424e+01, 0.8243116984954e-08, 0.1489098777643e+01, 0.1044738781244e+02, 0.8268102113708e-08, 0.3512977691983e+01, 0.1150676975667e+02, 0.9043613988227e-08, 0.1290704408221e+00, 0.1101510648075e+02, 0.7432912038789e-08, 0.1991086893337e+01, 0.2608790314060e+02, 0.8586233727285e-08, 0.4238357924414e+01, 0.2986433403208e+02, 0.7612230060131e-08, 0.2911090150166e+01, 0.4732030630302e+01, 0.7097787751408e-08, 0.1908938392390e+01, 0.8031092209206e+01, 0.7640237040175e-08, 0.6129219000168e+00, 0.7962980379786e+00, 0.7070445688081e-08, 0.1380417036651e+01, 0.2146165377750e+01, 0.7690770957702e-08, 0.1680504249084e+01, 0.2122839202813e+02, 0.8051292542594e-08, 0.5127423484511e+01, 0.2942463415728e+01, 0.5902709104515e-08, 0.2020274190917e+01, 0.7755226100720e+00, 0.5134567496462e-08, 0.2606778676418e+01, 0.1256615170089e+02, 0.5525802046102e-08, 0.1613011769663e+01, 0.8018209333619e+00, 0.5880724784221e-08, 0.4604483417236e+01, 0.4690479774488e+01, 0.5211699081370e-08, 0.5718964114193e+01, 0.8827390247185e+01, 0.4891849573562e-08, 0.3689658932196e+01, 0.2132990797783e+00, 0.5150246069997e-08, 0.4099769855122e+01, 0.6480980550449e+02, 0.5102434319633e-08, 0.5660834602509e+01, 0.3379454372902e+02, 0.5083405254252e-08, 0.9842221218974e+00, 0.4136910472696e+01, 0.4206562585682e-08, 0.1341363634163e+00, 0.3128388763578e+01, 0.4663249683579e-08, 0.8130132735866e+00, 0.5216580451554e+01, 0.4099474416530e-08, 0.5791497770644e+01, 0.4265981595566e+00, 0.4628251220767e-08, 0.1249802769331e+01, 0.1572083878776e+02, 0.5024068728142e-08, 0.4795684802743e+01, 0.6290189305114e+01, 0.5120234327758e-08, 0.3810420387208e+01, 0.5230807360890e+01, 0.5524029815280e-08, 0.1029264714351e+01, 0.2397622045175e+03, 0.4757415718860e-08, 0.3528044781779e+01, 0.1649636139783e+02, 0.3915786131127e-08, 0.5593889282646e+01, 0.1589072916335e+01, 0.4869053149991e-08, 0.3299636454433e+01, 0.7632943190217e+01, 0.3649365703729e-08, 0.1286049002584e+01, 0.6206810014183e+01, 0.3992493949002e-08, 0.3100307589464e+01, 0.2515860172507e+02, 0.3320247477418e-08, 0.6212683940807e+01, 0.1216800268190e+02, 0.3287123739696e-08, 0.4699118445928e+01, 0.7234794171227e+01, 0.3472776811103e-08, 0.2630507142004e+01, 0.7342457794669e+01, 0.3423253294767e-08, 0.2946432844305e+01, 0.9623688285163e+01, 0.3896173898244e-08, 0.1224834179264e+01, 0.6438496133249e+01, 0.3388455337924e-08, 0.1543807616351e+01, 0.1494531617769e+02, 0.3062704716523e-08, 0.1191777572310e+01, 0.8662240327241e+01, 0.3270075600400e-08, 0.5483498767737e+01, 0.1194447056968e+01, 0.3101209215259e-08, 0.8000833804348e+00, 0.3772475342596e+02, 0.2780883347311e-08, 0.4077980721888e+00, 0.5863591145557e+01, 0.2903605931824e-08, 0.2617490302147e+01, 0.1965104848470e+02, 0.2682014743119e-08, 0.2634703158290e+01, 0.7238675589263e+01, 0.2534360108492e-08, 0.6102446114873e+01, 0.6836645152238e+01, 0.2392564882509e-08, 0.3681820208691e+01, 0.5849364236221e+01, 0.2656667254856e-08, 0.6216045388886e+01, 0.6133512519065e+01, 0.2331242096773e-08, 0.5864949777744e+01, 0.4535059491685e+01, 0.2287898363668e-08, 0.4566628532802e+01, 0.7477522907414e+01, 0.2336944521306e-08, 0.2442722126930e+01, 0.1137170464392e+02, 0.3156632236269e-08, 0.1626628050682e+01, 0.2509084901204e+03, 0.2982612402766e-08, 0.2803604512609e+01, 0.1748016358760e+01, 0.2774031674807e-08, 0.4654002897158e+01, 0.8223916695780e+02, 0.2295236548638e-08, 0.4326518333253e+01, 0.3378142627421e+00, 0.2190714699873e-08, 0.4519614578328e+01, 0.2908881142201e+02, 0.2191495845045e-08, 0.3012626912549e+01, 0.1673046366289e+02, 0.2492901628386e-08, 0.1290101424052e+00, 0.1543797956245e+03, 0.1993778064319e-08, 0.3864046799414e+01, 0.1778984560711e+02, 0.1898146479022e-08, 0.5053777235891e+01, 0.2042657109477e+02, 0.1918280127634e-08, 0.2222470192548e+01, 0.4165496312290e+02, 0.1916351061607e-08, 0.8719067257774e+00, 0.7737595720538e+02, 0.1834720181466e-08, 0.4031491098040e+01, 0.2358125818164e+02, 0.1249201523806e-08, 0.5938379466835e+01, 0.3301902111895e+02, 0.1477304050539e-08, 0.6544722606797e+00, 0.9548094718417e+02, 0.1264316431249e-08, 0.2059072853236e+01, 0.8399684731857e+02, 0.1203526495039e-08, 0.3644813532605e+01, 0.4558517281984e+02, 0.9221681059831e-09, 0.3241815055602e+01, 0.7805158573086e+02, 0.7849278367646e-09, 0.5043812342457e+01, 0.5217580628120e+02, 0.7983392077387e-09, 0.5000024502753e+01, 0.1501922143975e+03, 0.7925395431654e-09, 0.1398734871821e-01, 0.9061773743175e+02, 0.7640473285886e-09, 0.5067111723130e+01, 0.4951538251678e+02, 0.5398937754482e-09, 0.5597382200075e+01, 0.1613385000004e+03, 0.5626247550193e-09, 0.2601338209422e+01, 0.7318837597844e+02, 0.5525197197855e-09, 0.5814832109256e+01, 0.1432335100216e+03, 0.5407629837898e-09, 0.3384820609076e+01, 0.3230491187871e+03, 0.3856739119801e-09, 0.1072391840473e+01, 0.2334791286671e+03, 0.3856425239987e-09, 0.2369540393327e+01, 0.1739046517013e+03, 0.4350867755983e-09, 0.5255575751082e+01, 0.1620484330494e+03, 0.3844113924996e-09, 0.5482356246182e+01, 0.9757644180768e+02, 0.2854869155431e-09, 0.9573634763143e+00, 0.1697170704744e+03, 0.1719227671416e-09, 0.1887203025202e+01, 0.2265204242912e+03, 0.1527846879755e-09, 0.3982183931157e+01, 0.3341954043900e+03, 0.1128229264847e-09, 0.2787457156298e+01, 0.3119028331842e+03 }; /* Sun-to-Earth, T^1, X */ static const double e1x[] = { 0.1234046326004e-05, 0.0000000000000e+00, 0.0000000000000e+00, 0.5150068824701e-06, 0.6002664557501e+01, 0.1256615170089e+02, 0.1290743923245e-07, 0.5959437664199e+01, 0.1884922755134e+02, 0.1068615564952e-07, 0.2015529654209e+01, 0.6283075850446e+01, 0.2079619142538e-08, 0.1732960531432e+01, 0.6279552690824e+01, 0.2078009243969e-08, 0.4915604476996e+01, 0.6286599010068e+01, 0.6206330058856e-09, 0.3616457953824e+00, 0.4705732307012e+01, 0.5989335313746e-09, 0.3802607304474e+01, 0.6256777527156e+01, 0.5958495663840e-09, 0.2845866560031e+01, 0.6309374173736e+01, 0.4866923261539e-09, 0.5213203771824e+01, 0.7755226100720e+00, 0.4267785823142e-09, 0.4368189727818e+00, 0.1059381944224e+01, 0.4610675141648e-09, 0.1837249181372e-01, 0.7860419393880e+01, 0.3626989993973e-09, 0.2161590545326e+01, 0.5753384878334e+01, 0.3563071194389e-09, 0.1452631954746e+01, 0.5884926831456e+01, 0.3557015642807e-09, 0.4470593393054e+01, 0.6812766822558e+01, 0.3210412089122e-09, 0.5195926078314e+01, 0.6681224869435e+01, 0.2875473577986e-09, 0.5916256610193e+01, 0.2513230340178e+02, 0.2842913681629e-09, 0.1149902426047e+01, 0.6127655567643e+01, 0.2751248215916e-09, 0.5502088574662e+01, 0.6438496133249e+01, 0.2481432881127e-09, 0.2921989846637e+01, 0.5486777812467e+01, 0.2059885976560e-09, 0.3718070376585e+01, 0.7079373888424e+01, 0.2015522342591e-09, 0.5979395259740e+01, 0.6290189305114e+01, 0.1995364084253e-09, 0.6772087985494e+00, 0.6275962395778e+01, 0.1957436436943e-09, 0.2899210654665e+01, 0.5507553240374e+01, 0.1651609818948e-09, 0.6228206482192e+01, 0.1150676975667e+02, 0.1822980550699e-09, 0.1469348746179e+01, 0.1179062909082e+02, 0.1675223159760e-09, 0.3813910555688e+01, 0.7058598460518e+01, 0.1706491764745e-09, 0.3004380506684e+00, 0.7113454667900e-02, 0.1392952362615e-09, 0.1440393973406e+01, 0.7962980379786e+00, 0.1209868266342e-09, 0.4150425791727e+01, 0.4694002934110e+01, 0.1009827202611e-09, 0.3290040429843e+01, 0.3738761453707e+01, 0.1047261388602e-09, 0.4229590090227e+01, 0.6282095334605e+01, 0.1047006652004e-09, 0.2418967680575e+01, 0.6284056366286e+01, 0.9609993143095e-10, 0.4627943659201e+01, 0.6069776770667e+01, 0.9590900593873e-10, 0.1894393939924e+01, 0.4136910472696e+01, 0.9146249188071e-10, 0.2010647519562e+01, 0.6496374930224e+01, 0.8545274480290e-10, 0.5529846956226e-01, 0.1194447056968e+01, 0.8224377881194e-10, 0.1254304102174e+01, 0.1589072916335e+01, 0.6183529510410e-10, 0.3360862168815e+01, 0.8827390247185e+01, 0.6259255147141e-10, 0.4755628243179e+01, 0.8429241228195e+01, 0.5539291694151e-10, 0.5371746955142e+01, 0.4933208510675e+01, 0.7328259466314e-10, 0.4927699613906e+00, 0.4535059491685e+01, 0.6017835843560e-10, 0.5776682001734e-01, 0.1255903824622e+02, 0.7079827775243e-10, 0.4395059432251e+01, 0.5088628793478e+01, 0.5170358878213e-10, 0.5154062619954e+01, 0.1176985366291e+02, 0.4872301838682e-10, 0.6289611648973e+00, 0.6040347114260e+01, 0.5249869411058e-10, 0.5617272046949e+01, 0.3154687086868e+01, 0.4716172354411e-10, 0.3965901800877e+01, 0.5331357529664e+01, 0.4871214940964e-10, 0.4627507050093e+01, 0.1256967486051e+02, 0.4598076850751e-10, 0.6023631226459e+01, 0.6525804586632e+01, 0.4562196089485e-10, 0.4138562084068e+01, 0.3930209696940e+01, 0.4325493872224e-10, 0.1330845906564e+01, 0.7632943190217e+01, 0.5673781176748e-10, 0.2558752615657e+01, 0.5729506548653e+01, 0.3961436642503e-10, 0.2728071734630e+01, 0.7234794171227e+01, 0.5101868209058e-10, 0.4113444965144e+01, 0.6836645152238e+01, 0.5257043167676e-10, 0.6195089830590e+01, 0.8031092209206e+01, 0.5076613989393e-10, 0.2305124132918e+01, 0.7477522907414e+01, 0.3342169352778e-10, 0.5415998155071e+01, 0.1097707878456e+02, 0.3545881983591e-10, 0.3727160564574e+01, 0.4164311961999e+01, 0.3364063738599e-10, 0.2901121049204e+00, 0.1137170464392e+02, 0.3357039670776e-10, 0.1652229354331e+01, 0.5223693906222e+01, 0.4307412268687e-10, 0.4938909587445e+01, 0.1592596075957e+01, 0.3405769115435e-10, 0.2408890766511e+01, 0.3128388763578e+01, 0.3001926198480e-10, 0.4862239006386e+01, 0.1748016358760e+01, 0.2778264787325e-10, 0.5241168661353e+01, 0.7342457794669e+01, 0.2676159480666e-10, 0.3423593942199e+01, 0.2146165377750e+01, 0.2954273399939e-10, 0.1881721265406e+01, 0.5368044267797e+00, 0.3309362888795e-10, 0.1931525677349e+01, 0.8018209333619e+00, 0.2810283608438e-10, 0.2414659495050e+01, 0.5225775174439e+00, 0.3378045637764e-10, 0.4238019163430e+01, 0.1554202828031e+00, 0.2558134979840e-10, 0.1828225235805e+01, 0.5230807360890e+01, 0.2273755578447e-10, 0.5858184283998e+01, 0.7084896783808e+01, 0.2294176037690e-10, 0.4514589779057e+01, 0.1726015463500e+02, 0.2533506099435e-10, 0.2355717851551e+01, 0.5216580451554e+01, 0.2716685375812e-10, 0.2221003625100e+01, 0.8635942003952e+01, 0.2419043435198e-10, 0.5955704951635e+01, 0.4690479774488e+01, 0.2521232544812e-10, 0.1395676848521e+01, 0.5481254917084e+01, 0.2630195021491e-10, 0.5727468918743e+01, 0.2629832328990e-01, 0.2548395840944e-10, 0.2628351859400e-03, 0.1349867339771e+01 }; /* Sun-to-Earth, T^1, Y */ static const double e1y[] = { 0.9304690546528e-06, 0.0000000000000e+00, 0.0000000000000e+00, 0.5150715570663e-06, 0.4431807116294e+01, 0.1256615170089e+02, 0.1290825411056e-07, 0.4388610039678e+01, 0.1884922755134e+02, 0.4645466665386e-08, 0.5827263376034e+01, 0.6283075850446e+01, 0.2079625310718e-08, 0.1621698662282e+00, 0.6279552690824e+01, 0.2078189850907e-08, 0.3344713435140e+01, 0.6286599010068e+01, 0.6207190138027e-09, 0.5074049319576e+01, 0.4705732307012e+01, 0.5989826532569e-09, 0.2231842216620e+01, 0.6256777527156e+01, 0.5961360812618e-09, 0.1274975769045e+01, 0.6309374173736e+01, 0.4874165471016e-09, 0.3642277426779e+01, 0.7755226100720e+00, 0.4283834034360e-09, 0.5148765510106e+01, 0.1059381944224e+01, 0.4652389287529e-09, 0.4715794792175e+01, 0.7860419393880e+01, 0.3751707476401e-09, 0.6617207370325e+00, 0.5753384878334e+01, 0.3559998806198e-09, 0.6155548875404e+01, 0.5884926831456e+01, 0.3558447558857e-09, 0.2898827297664e+01, 0.6812766822558e+01, 0.3211116927106e-09, 0.3625813502509e+01, 0.6681224869435e+01, 0.2875609914672e-09, 0.4345435813134e+01, 0.2513230340178e+02, 0.2843109704069e-09, 0.5862263940038e+01, 0.6127655567643e+01, 0.2744676468427e-09, 0.3926419475089e+01, 0.6438496133249e+01, 0.2481285237789e-09, 0.1351976572828e+01, 0.5486777812467e+01, 0.2060338481033e-09, 0.2147556998591e+01, 0.7079373888424e+01, 0.2015822358331e-09, 0.4408358972216e+01, 0.6290189305114e+01, 0.2001195944195e-09, 0.5385829822531e+01, 0.6275962395778e+01, 0.1953667642377e-09, 0.1304933746120e+01, 0.5507553240374e+01, 0.1839744078713e-09, 0.6173567228835e+01, 0.1179062909082e+02, 0.1643334294845e-09, 0.4635942997523e+01, 0.1150676975667e+02, 0.1768051018652e-09, 0.5086283558874e+01, 0.7113454667900e-02, 0.1674874205489e-09, 0.2243332137241e+01, 0.7058598460518e+01, 0.1421445397609e-09, 0.6186899771515e+01, 0.7962980379786e+00, 0.1255163958267e-09, 0.5730238465658e+01, 0.4694002934110e+01, 0.1013945281961e-09, 0.1726055228402e+01, 0.3738761453707e+01, 0.1047294335852e-09, 0.2658801228129e+01, 0.6282095334605e+01, 0.1047103879392e-09, 0.8481047835035e+00, 0.6284056366286e+01, 0.9530343962826e-10, 0.3079267149859e+01, 0.6069776770667e+01, 0.9604637611690e-10, 0.3258679792918e+00, 0.4136910472696e+01, 0.9153518537177e-10, 0.4398599886584e+00, 0.6496374930224e+01, 0.8562458214922e-10, 0.4772686794145e+01, 0.1194447056968e+01, 0.8232525360654e-10, 0.5966220721679e+01, 0.1589072916335e+01, 0.6150223411438e-10, 0.1780985591923e+01, 0.8827390247185e+01, 0.6272087858000e-10, 0.3184305429012e+01, 0.8429241228195e+01, 0.5540476311040e-10, 0.3801260595433e+01, 0.4933208510675e+01, 0.7331901699361e-10, 0.5205948591865e+01, 0.4535059491685e+01, 0.6018528702791e-10, 0.4770139083623e+01, 0.1255903824622e+02, 0.5150530724804e-10, 0.3574796899585e+01, 0.1176985366291e+02, 0.6471933741811e-10, 0.2679787266521e+01, 0.5088628793478e+01, 0.5317460644174e-10, 0.9528763345494e+00, 0.3154687086868e+01, 0.4832187748783e-10, 0.5329322498232e+01, 0.6040347114260e+01, 0.4716763555110e-10, 0.2395235316466e+01, 0.5331357529664e+01, 0.4871509139861e-10, 0.3056663648823e+01, 0.1256967486051e+02, 0.4598417696768e-10, 0.4452762609019e+01, 0.6525804586632e+01, 0.5674189533175e-10, 0.9879680872193e+00, 0.5729506548653e+01, 0.4073560328195e-10, 0.5939127696986e+01, 0.7632943190217e+01, 0.5040994945359e-10, 0.4549875824510e+01, 0.8031092209206e+01, 0.5078185134679e-10, 0.7346659893982e+00, 0.7477522907414e+01, 0.3769343537061e-10, 0.1071317188367e+01, 0.7234794171227e+01, 0.4980331365299e-10, 0.2500345341784e+01, 0.6836645152238e+01, 0.3458236594757e-10, 0.3825159450711e+01, 0.1097707878456e+02, 0.3578859493602e-10, 0.5299664791549e+01, 0.4164311961999e+01, 0.3370504646419e-10, 0.5002316301593e+01, 0.1137170464392e+02, 0.3299873338428e-10, 0.2526123275282e+01, 0.3930209696940e+01, 0.4304917318409e-10, 0.3368078557132e+01, 0.1592596075957e+01, 0.3402418753455e-10, 0.8385495425800e+00, 0.3128388763578e+01, 0.2778460572146e-10, 0.3669905203240e+01, 0.7342457794669e+01, 0.2782710128902e-10, 0.2691664812170e+00, 0.1748016358760e+01, 0.2711725179646e-10, 0.4707487217718e+01, 0.5296909721118e+00, 0.2981760946340e-10, 0.3190260867816e+00, 0.5368044267797e+00, 0.2811672977772e-10, 0.3196532315372e+01, 0.7084896783808e+01, 0.2863454474467e-10, 0.2263240324780e+00, 0.5223693906222e+01, 0.3333464634051e-10, 0.3498451685065e+01, 0.8018209333619e+00, 0.3312991747609e-10, 0.5839154477412e+01, 0.1554202828031e+00, 0.2813255564006e-10, 0.8268044346621e+00, 0.5225775174439e+00, 0.2665098083966e-10, 0.3934021725360e+01, 0.5216580451554e+01, 0.2349795705216e-10, 0.5197620913779e+01, 0.2146165377750e+01, 0.2330352293961e-10, 0.2984999231807e+01, 0.1726015463500e+02, 0.2728001683419e-10, 0.6521679638544e+00, 0.8635942003952e+01, 0.2484061007669e-10, 0.3468955561097e+01, 0.5230807360890e+01, 0.2646328768427e-10, 0.1013724533516e+01, 0.2629832328990e-01, 0.2518630264831e-10, 0.6108081057122e+01, 0.5481254917084e+01, 0.2421901455384e-10, 0.1651097776260e+01, 0.1349867339771e+01, 0.6348533267831e-11, 0.3220226560321e+01, 0.8433466158131e+02 }; /* Sun-to-Earth, T^1, Z */ static const double e1z[] = { 0.2278290449966e-05, 0.3413716033863e+01, 0.6283075850446e+01, 0.5429458209830e-07, 0.0000000000000e+00, 0.0000000000000e+00, 0.1903240492525e-07, 0.3370592358297e+01, 0.1256615170089e+02, 0.2385409276743e-09, 0.3327914718416e+01, 0.1884922755134e+02, 0.8676928342573e-10, 0.1824006811264e+01, 0.5223693906222e+01, 0.7765442593544e-10, 0.3888564279247e+01, 0.5507553240374e+01, 0.7066158332715e-10, 0.5194267231944e+01, 0.2352866153506e+01, 0.7092175288657e-10, 0.2333246960021e+01, 0.8399684731857e+02, 0.5357582213535e-10, 0.2224031176619e+01, 0.5296909721118e+00, 0.3828035865021e-10, 0.2156710933584e+01, 0.6279552690824e+01, 0.3824857220427e-10, 0.1529755219915e+01, 0.6286599010068e+01, 0.3286995181628e-10, 0.4879512900483e+01, 0.1021328554739e+02 }; /* Sun-to-Earth, T^2, X */ static const double e2x[] = { -0.4143818297913e-10, 0.0000000000000e+00, 0.0000000000000e+00, 0.2171497694435e-10, 0.4398225628264e+01, 0.1256615170089e+02, 0.9845398442516e-11, 0.2079720838384e+00, 0.6283075850446e+01, 0.9256833552682e-12, 0.4191264694361e+01, 0.1884922755134e+02, 0.1022049384115e-12, 0.5381133195658e+01, 0.8399684731857e+02 }; /* Sun-to-Earth, T^2, Y */ static const double e2y[] = { 0.5063375872532e-10, 0.0000000000000e+00, 0.0000000000000e+00, 0.2173815785980e-10, 0.2827805833053e+01, 0.1256615170089e+02, 0.1010231999920e-10, 0.4634612377133e+01, 0.6283075850446e+01, 0.9259745317636e-12, 0.2620612076189e+01, 0.1884922755134e+02, 0.1022202095812e-12, 0.3809562326066e+01, 0.8399684731857e+02 }; /* Sun-to-Earth, T^2, Z */ static const double e2z[] = { 0.9722666114891e-10, 0.5152219582658e+01, 0.6283075850446e+01, -0.3494819171909e-11, 0.0000000000000e+00, 0.0000000000000e+00, 0.6713034376076e-12, 0.6440188750495e+00, 0.1256615170089e+02 }; /* SSB-to-Sun, T^0, X */ static const double s0x[] = { 0.4956757536410e-02, 0.3741073751789e+01, 0.5296909721118e+00, 0.2718490072522e-02, 0.4016011511425e+01, 0.2132990797783e+00, 0.1546493974344e-02, 0.2170528330642e+01, 0.3813291813120e-01, 0.8366855276341e-03, 0.2339614075294e+01, 0.7478166569050e-01, 0.2936777942117e-03, 0.0000000000000e+00, 0.0000000000000e+00, 0.1201317439469e-03, 0.4090736353305e+01, 0.1059381944224e+01, 0.7578550887230e-04, 0.3241518088140e+01, 0.4265981595566e+00, 0.1941787367773e-04, 0.1012202064330e+01, 0.2061856251104e+00, 0.1889227765991e-04, 0.3892520416440e+01, 0.2204125344462e+00, 0.1937896968613e-04, 0.4797779441161e+01, 0.1495633313810e+00, 0.1434506110873e-04, 0.3868960697933e+01, 0.5225775174439e+00, 0.1406659911580e-04, 0.4759766557397e+00, 0.5368044267797e+00, 0.1179022300202e-04, 0.7774961520598e+00, 0.7626583626240e-01, 0.8085864460959e-05, 0.3254654471465e+01, 0.3664874755930e-01, 0.7622752967615e-05, 0.4227633103489e+01, 0.3961708870310e-01, 0.6209171139066e-05, 0.2791828325711e+00, 0.7329749511860e-01, 0.4366435633970e-05, 0.4440454875925e+01, 0.1589072916335e+01, 0.3792124889348e-05, 0.5156393842356e+01, 0.7113454667900e-02, 0.3154548963402e-05, 0.6157005730093e+01, 0.4194847048887e+00, 0.3088359882942e-05, 0.2494567553163e+01, 0.6398972393349e+00, 0.2788440902136e-05, 0.4934318747989e+01, 0.1102062672231e+00, 0.3039928456376e-05, 0.4895077702640e+01, 0.6283075850446e+01, 0.2272258457679e-05, 0.5278394064764e+01, 0.1030928125552e+00, 0.2162007057957e-05, 0.5802978019099e+01, 0.3163918923335e+00, 0.1767632855737e-05, 0.3415346595193e-01, 0.1021328554739e+02, 0.1349413459362e-05, 0.2001643230755e+01, 0.1484170571900e-02, 0.1170141900476e-05, 0.2424750491620e+01, 0.6327837846670e+00, 0.1054355266820e-05, 0.3123311487576e+01, 0.4337116142245e+00, 0.9800822461610e-06, 0.3026258088130e+01, 0.1052268489556e+01, 0.1091203749931e-05, 0.3157811670347e+01, 0.1162474756779e+01, 0.6960236715913e-06, 0.8219570542313e+00, 0.1066495398892e+01, 0.5689257296909e-06, 0.1323052375236e+01, 0.9491756770005e+00, 0.6613172135802e-06, 0.2765348881598e+00, 0.8460828644453e+00, 0.6277702517571e-06, 0.5794064466382e+01, 0.1480791608091e+00, 0.6304884066699e-06, 0.7323555380787e+00, 0.2243449970715e+00, 0.4897850467382e-06, 0.3062464235399e+01, 0.3340612434717e+01, 0.3759148598786e-06, 0.4588290469664e+01, 0.3516457698740e-01, 0.3110520548195e-06, 0.1374299536572e+01, 0.6373574839730e-01, 0.3064708359780e-06, 0.4222267485047e+01, 0.1104591729320e-01, 0.2856347168241e-06, 0.3714202944973e+01, 0.1510475019529e+00, 0.2840945514288e-06, 0.2847972875882e+01, 0.4110125927500e-01, 0.2378951599405e-06, 0.3762072563388e+01, 0.2275259891141e+00, 0.2714229481417e-06, 0.1036049980031e+01, 0.2535050500000e-01, 0.2323551717307e-06, 0.4682388599076e+00, 0.8582758298370e-01, 0.1881790512219e-06, 0.4790565425418e+01, 0.2118763888447e+01, 0.2261353968371e-06, 0.1669144912212e+01, 0.7181332454670e-01, 0.2214546389848e-06, 0.3937717281614e+01, 0.2968341143800e-02, 0.2184915594933e-06, 0.1129169845099e+00, 0.7775000683430e-01, 0.2000164937936e-06, 0.4030009638488e+01, 0.2093666171530e+00, 0.1966105136719e-06, 0.8745955786834e+00, 0.2172315424036e+00, 0.1904742332624e-06, 0.5919743598964e+01, 0.2022531624851e+00, 0.1657399705031e-06, 0.2549141484884e+01, 0.7358765972222e+00, 0.1574070533987e-06, 0.5277533020230e+01, 0.7429900518901e+00, 0.1832261651039e-06, 0.3064688127777e+01, 0.3235053470014e+00, 0.1733615346569e-06, 0.3011432799094e+01, 0.1385174140878e+00, 0.1549124014496e-06, 0.4005569132359e+01, 0.5154640627760e+00, 0.1637044713838e-06, 0.1831375966632e+01, 0.8531963191132e+00, 0.1123420082383e-06, 0.1180270407578e+01, 0.1990721704425e+00, 0.1083754165740e-06, 0.3414101320863e+00, 0.5439178814476e+00, 0.1156638012655e-06, 0.6130479452594e+00, 0.5257585094865e+00, 0.1142548785134e-06, 0.3724761948846e+01, 0.5336234347371e+00, 0.7921463895965e-07, 0.2435425589361e+01, 0.1478866649112e+01, 0.7428600285231e-07, 0.3542144398753e+01, 0.2164800718209e+00, 0.8323211246747e-07, 0.3525058072354e+01, 0.1692165728891e+01, 0.7257595116312e-07, 0.1364299431982e+01, 0.2101180877357e+00, 0.7111185833236e-07, 0.2460478875808e+01, 0.4155522422634e+00, 0.6868090383716e-07, 0.4397327670704e+01, 0.1173197218910e+00, 0.7226419974175e-07, 0.4042647308905e+01, 0.1265567569334e+01, 0.6955642383177e-07, 0.2865047906085e+01, 0.9562891316684e+00, 0.7492139296331e-07, 0.5014278994215e+01, 0.1422690933580e-01, 0.6598363128857e-07, 0.2376730020492e+01, 0.6470106940028e+00, 0.7381147293385e-07, 0.3272990384244e+01, 0.1581959461667e+01, 0.6402909624032e-07, 0.5302290955138e+01, 0.9597935788730e-01, 0.6237454263857e-07, 0.5444144425332e+01, 0.7084920306520e-01, 0.5241198544016e-07, 0.4215359579205e+01, 0.5265099800692e+00, 0.5144463853918e-07, 0.1218916689916e+00, 0.5328719641544e+00, 0.5868164772299e-07, 0.2369402002213e+01, 0.7871412831580e-01, 0.6233195669151e-07, 0.1254922242403e+01, 0.2608790314060e+02, 0.6068463791422e-07, 0.5679713760431e+01, 0.1114304132498e+00, 0.4359361135065e-07, 0.6097219641646e+00, 0.1375773836557e+01, 0.4686510366826e-07, 0.4786231041431e+01, 0.1143987543936e+00, 0.3758977287225e-07, 0.1167368068139e+01, 0.1596186371003e+01, 0.4282051974778e-07, 0.1519471064319e+01, 0.2770348281756e+00, 0.5153765386113e-07, 0.1860532322984e+01, 0.2228608264996e+00, 0.4575129387188e-07, 0.7632857887158e+00, 0.1465949902372e+00, 0.3326844933286e-07, 0.1298219485285e+01, 0.5070101000000e-01, 0.3748617450984e-07, 0.1046510321062e+01, 0.4903339079539e+00, 0.2816756661499e-07, 0.3434522346190e+01, 0.2991266627620e+00, 0.3412750405039e-07, 0.2523766270318e+01, 0.3518164938661e+00, 0.2655796761776e-07, 0.2904422260194e+01, 0.6256703299991e+00, 0.2963597929458e-07, 0.5923900431149e+00, 0.1099462426779e+00, 0.2539523734781e-07, 0.4851947722567e+01, 0.1256615170089e+02, 0.2283087914139e-07, 0.3400498595496e+01, 0.6681224869435e+01, 0.2321309799331e-07, 0.5789099148673e+01, 0.3368040641550e-01, 0.2549657649750e-07, 0.3991856479792e-01, 0.1169588211447e+01, 0.2290462303977e-07, 0.2788567577052e+01, 0.1045155034888e+01, 0.1945398522914e-07, 0.3290896998176e+01, 0.1155361302111e+01, 0.1849171512638e-07, 0.2698060129367e+01, 0.4452511715700e-02, 0.1647199834254e-07, 0.3016735644085e+01, 0.4408250688924e+00, 0.1529530765273e-07, 0.5573043116178e+01, 0.6521991896920e-01, 0.1433199339978e-07, 0.1481192356147e+01, 0.9420622223326e+00, 0.1729134193602e-07, 0.1422817538933e+01, 0.2108507877249e+00, 0.1716463931346e-07, 0.3469468901855e+01, 0.2157473718317e+00, 0.1391206061378e-07, 0.6122436220547e+01, 0.4123712502208e+00, 0.1404746661924e-07, 0.1647765641936e+01, 0.4258542984690e-01, 0.1410452399455e-07, 0.5989729161964e+01, 0.2258291676434e+00, 0.1089828772168e-07, 0.2833705509371e+01, 0.4226656969313e+00, 0.1047374564948e-07, 0.5090690007331e+00, 0.3092784376656e+00, 0.1358279126532e-07, 0.5128990262836e+01, 0.7923417740620e-01, 0.1020456476148e-07, 0.9632772880808e+00, 0.1456308687557e+00, 0.1033428735328e-07, 0.3223779318418e+01, 0.1795258541446e+01, 0.1412435841540e-07, 0.2410271572721e+01, 0.1525316725248e+00, 0.9722759371574e-08, 0.2333531395690e+01, 0.8434341241180e-01, 0.9657334084704e-08, 0.6199270974168e+01, 0.1272681024002e+01, 0.1083641148690e-07, 0.2864222292929e+01, 0.7032915397480e-01, 0.1067318403838e-07, 0.5833458866568e+00, 0.2123349582968e+00, 0.1062366201976e-07, 0.4307753989494e+01, 0.2142632012598e+00, 0.1236364149266e-07, 0.2873917870593e+01, 0.1847279083684e+00, 0.1092759489593e-07, 0.2959887266733e+01, 0.1370332435159e+00, 0.8912069362899e-08, 0.5141213702562e+01, 0.2648454860559e+01, 0.9656467707970e-08, 0.4532182462323e+01, 0.4376440768498e+00, 0.8098386150135e-08, 0.2268906338379e+01, 0.2880807454688e+00, 0.7857714675000e-08, 0.4055544260745e+01, 0.2037373330570e+00, 0.7288455940646e-08, 0.5357901655142e+01, 0.1129145838217e+00, 0.9450595950552e-08, 0.4264926963939e+01, 0.5272426800584e+00, 0.9381718247537e-08, 0.7489366976576e-01, 0.5321392641652e+00, 0.7079052646038e-08, 0.1923311052874e+01, 0.6288513220417e+00, 0.9259004415344e-08, 0.2970256853438e+01, 0.1606092486742e+00, 0.8259801499742e-08, 0.3327056314697e+01, 0.8389694097774e+00, 0.6476334355779e-08, 0.2954925505727e+01, 0.2008557621224e+01, 0.5984021492007e-08, 0.9138753105829e+00, 0.2042657109477e+02, 0.5989546863181e-08, 0.3244464082031e+01, 0.2111650433779e+01, 0.6233108606023e-08, 0.4995232638403e+00, 0.4305306221819e+00, 0.6877299149965e-08, 0.2834987233449e+01, 0.9561746721300e-02, 0.8311234227190e-08, 0.2202951835758e+01, 0.3801276407308e+00, 0.6599472832414e-08, 0.4478581462618e+01, 0.1063314406849e+01, 0.6160491096549e-08, 0.5145858696411e+01, 0.1368660381889e+01, 0.6164772043891e-08, 0.3762976697911e+00, 0.4234171675140e+00, 0.6363248684450e-08, 0.3162246718685e+01, 0.1253008786510e-01, 0.6448587520999e-08, 0.3442693302119e+01, 0.5287268506303e+00, 0.6431662283977e-08, 0.8977549136606e+00, 0.5306550935933e+00, 0.6351223158474e-08, 0.4306447410369e+01, 0.5217580628120e+02, 0.5476721393451e-08, 0.3888529177855e+01, 0.2221856701002e+01, 0.5341772572619e-08, 0.2655560662512e+01, 0.7466759693650e-01, 0.5337055758302e-08, 0.5164990735946e+01, 0.7489573444450e-01, 0.5373120816787e-08, 0.6041214553456e+01, 0.1274714967946e+00, 0.5392351705426e-08, 0.9177763485932e+00, 0.1055449481598e+01, 0.6688495850205e-08, 0.3089608126937e+01, 0.2213766559277e+00, 0.5072003660362e-08, 0.4311316541553e+01, 0.2132517061319e+00, 0.5070726650455e-08, 0.5790675464444e+00, 0.2133464534247e+00, 0.5658012950032e-08, 0.2703945510675e+01, 0.7287631425543e+00, 0.4835509924854e-08, 0.2975422976065e+01, 0.7160067364790e-01, 0.6479821978012e-08, 0.1324168733114e+01, 0.2209183458640e-01, 0.6230636494980e-08, 0.2860103632836e+01, 0.3306188016693e+00, 0.4649239516213e-08, 0.4832259763403e+01, 0.7796265773310e-01, 0.6487325792700e-08, 0.2726165825042e+01, 0.3884652414254e+00, 0.4682823682770e-08, 0.6966602455408e+00, 0.1073608853559e+01, 0.5704230804976e-08, 0.5669634104606e+01, 0.8731175355560e-01, 0.6125413585489e-08, 0.1513386538915e+01, 0.7605151500000e-01, 0.6035825038187e-08, 0.1983509168227e+01, 0.9846002785331e+00, 0.4331123462303e-08, 0.2782892992807e+01, 0.4297791515992e+00, 0.4681107685143e-08, 0.5337232886836e+01, 0.2127790306879e+00, 0.4669105829655e-08, 0.5837133792160e+01, 0.2138191288687e+00, 0.5138823602365e-08, 0.3080560200507e+01, 0.7233337363710e-01, 0.4615856664534e-08, 0.1661747897471e+01, 0.8603097737811e+00, 0.4496916702197e-08, 0.2112508027068e+01, 0.7381754420900e-01, 0.4278479042945e-08, 0.5716528462627e+01, 0.7574578717200e-01, 0.3840525503932e-08, 0.6424172726492e+00, 0.3407705765729e+00, 0.4866636509685e-08, 0.4919244697715e+01, 0.7722995774390e-01, 0.3526100639296e-08, 0.2550821052734e+01, 0.6225157782540e-01, 0.3939558488075e-08, 0.3939331491710e+01, 0.5268983110410e-01, 0.4041268772576e-08, 0.2275337571218e+01, 0.3503323232942e+00, 0.3948761842853e-08, 0.1999324200790e+01, 0.1451108196653e+00, 0.3258394550029e-08, 0.9121001378200e+00, 0.5296435984654e+00, 0.3257897048761e-08, 0.3428428660869e+01, 0.5297383457582e+00, 0.3842559031298e-08, 0.6132927720035e+01, 0.9098186128426e+00, 0.3109920095448e-08, 0.7693650193003e+00, 0.3932462625300e-02, 0.3132237775119e-08, 0.3621293854908e+01, 0.2346394437820e+00, 0.3942189421510e-08, 0.4841863659733e+01, 0.3180992042600e-02, 0.3796972285340e-08, 0.1814174994268e+01, 0.1862120789403e+00, 0.3995640233688e-08, 0.1386990406091e+01, 0.4549093064213e+00, 0.2875013727414e-08, 0.9178318587177e+00, 0.1905464808669e+01, 0.3073719932844e-08, 0.2688923811835e+01, 0.3628624111593e+00, 0.2731016580075e-08, 0.1188259127584e+01, 0.2131850110243e+00, 0.2729549896546e-08, 0.3702160634273e+01, 0.2134131485323e+00, 0.3339372892449e-08, 0.7199163960331e+00, 0.2007689919132e+00, 0.2898833764204e-08, 0.1916709364999e+01, 0.5291709230214e+00, 0.2894536549362e-08, 0.2424043195547e+01, 0.5302110212022e+00, 0.3096872473843e-08, 0.4445894977497e+01, 0.2976424921901e+00, 0.2635672326810e-08, 0.3814366984117e+01, 0.1485980103780e+01, 0.3649302697001e-08, 0.2924200596084e+01, 0.6044726378023e+00, 0.3127954585895e-08, 0.1842251648327e+01, 0.1084620721060e+00, 0.2616040173947e-08, 0.4155841921984e+01, 0.1258454114666e+01, 0.2597395859860e-08, 0.1158045978874e+00, 0.2103781122809e+00, 0.2593286172210e-08, 0.4771850408691e+01, 0.2162200472757e+00, 0.2481823585747e-08, 0.4608842558889e+00, 0.1062562936266e+01, 0.2742219550725e-08, 0.1538781127028e+01, 0.5651155736444e+00, 0.3199558469610e-08, 0.3226647822878e+00, 0.7036329877322e+00, 0.2666088542957e-08, 0.1967991731219e+00, 0.1400015846597e+00, 0.2397067430580e-08, 0.3707036669873e+01, 0.2125476091956e+00, 0.2376570772738e-08, 0.1182086628042e+01, 0.2140505503610e+00, 0.2547228007887e-08, 0.4906256820629e+01, 0.1534957940063e+00, 0.2265575594114e-08, 0.3414949866857e+01, 0.2235935264888e+00, 0.2464381430585e-08, 0.4599122275378e+01, 0.2091065926078e+00, 0.2433408527044e-08, 0.2830751145445e+00, 0.2174915669488e+00, 0.2443605509076e-08, 0.4212046432538e+01, 0.1739420156204e+00, 0.2319779262465e-08, 0.9881978408630e+00, 0.7530171478090e-01, 0.2284622835465e-08, 0.5565347331588e+00, 0.7426161660010e-01, 0.2467268750783e-08, 0.5655708150766e+00, 0.2526561439362e+00, 0.2808513492782e-08, 0.1418405053408e+01, 0.5636314030725e+00, 0.2329528932532e-08, 0.4069557545675e+01, 0.1056200952181e+01, 0.9698639532817e-09, 0.1074134313634e+01, 0.7826370942180e+02 }; /* SSB-to-Sun, T^0, Y */ static const double s0y[] = { 0.4955392320126e-02, 0.2170467313679e+01, 0.5296909721118e+00, 0.2722325167392e-02, 0.2444433682196e+01, 0.2132990797783e+00, 0.1546579925346e-02, 0.5992779281546e+00, 0.3813291813120e-01, 0.8363140252966e-03, 0.7687356310801e+00, 0.7478166569050e-01, 0.3385792683603e-03, 0.0000000000000e+00, 0.0000000000000e+00, 0.1201192221613e-03, 0.2520035601514e+01, 0.1059381944224e+01, 0.7587125720554e-04, 0.1669954006449e+01, 0.4265981595566e+00, 0.1964155361250e-04, 0.5707743963343e+01, 0.2061856251104e+00, 0.1891900364909e-04, 0.2320960679937e+01, 0.2204125344462e+00, 0.1937373433356e-04, 0.3226940689555e+01, 0.1495633313810e+00, 0.1437139941351e-04, 0.2301626908096e+01, 0.5225775174439e+00, 0.1406267683099e-04, 0.5188579265542e+01, 0.5368044267797e+00, 0.1178703080346e-04, 0.5489483248476e+01, 0.7626583626240e-01, 0.8079835186041e-05, 0.1683751835264e+01, 0.3664874755930e-01, 0.7623253594652e-05, 0.2656400462961e+01, 0.3961708870310e-01, 0.6248667483971e-05, 0.4992775362055e+01, 0.7329749511860e-01, 0.4366353695038e-05, 0.2869706279678e+01, 0.1589072916335e+01, 0.3829101568895e-05, 0.3572131359950e+01, 0.7113454667900e-02, 0.3175733773908e-05, 0.4535372530045e+01, 0.4194847048887e+00, 0.3092437902159e-05, 0.9230153317909e+00, 0.6398972393349e+00, 0.2874168812154e-05, 0.3363143761101e+01, 0.1102062672231e+00, 0.3040119321826e-05, 0.3324250895675e+01, 0.6283075850446e+01, 0.2699723308006e-05, 0.2917882441928e+00, 0.1030928125552e+00, 0.2134832683534e-05, 0.4220997202487e+01, 0.3163918923335e+00, 0.1770412139433e-05, 0.4747318496462e+01, 0.1021328554739e+02, 0.1377264209373e-05, 0.4305058462401e+00, 0.1484170571900e-02, 0.1127814538960e-05, 0.8538177240740e+00, 0.6327837846670e+00, 0.1055608090130e-05, 0.1551800742580e+01, 0.4337116142245e+00, 0.9802673861420e-06, 0.1459646735377e+01, 0.1052268489556e+01, 0.1090329461951e-05, 0.1587351228711e+01, 0.1162474756779e+01, 0.6959590025090e-06, 0.5534442628766e+01, 0.1066495398892e+01, 0.5664914529542e-06, 0.6030673003297e+01, 0.9491756770005e+00, 0.6607787763599e-06, 0.4989507233927e+01, 0.8460828644453e+00, 0.6269725742838e-06, 0.4222951804572e+01, 0.1480791608091e+00, 0.6301889697863e-06, 0.5444316669126e+01, 0.2243449970715e+00, 0.4891042662861e-06, 0.1490552839784e+01, 0.3340612434717e+01, 0.3457083123290e-06, 0.3030475486049e+01, 0.3516457698740e-01, 0.3032559967314e-06, 0.2652038793632e+01, 0.1104591729320e-01, 0.2841133988903e-06, 0.1276744786829e+01, 0.4110125927500e-01, 0.2855564444432e-06, 0.2143368674733e+01, 0.1510475019529e+00, 0.2765157135038e-06, 0.5444186109077e+01, 0.6373574839730e-01, 0.2382312465034e-06, 0.2190521137593e+01, 0.2275259891141e+00, 0.2808060365077e-06, 0.5735195064841e+01, 0.2535050500000e-01, 0.2332175234405e-06, 0.9481985524859e-01, 0.7181332454670e-01, 0.2322488199659e-06, 0.5180499361533e+01, 0.8582758298370e-01, 0.1881850258423e-06, 0.3219788273885e+01, 0.2118763888447e+01, 0.2196111392808e-06, 0.2366941159761e+01, 0.2968341143800e-02, 0.2183810335519e-06, 0.4825445110915e+01, 0.7775000683430e-01, 0.2002733093326e-06, 0.2457148995307e+01, 0.2093666171530e+00, 0.1967111767229e-06, 0.5586291545459e+01, 0.2172315424036e+00, 0.1568473250543e-06, 0.3708003123320e+01, 0.7429900518901e+00, 0.1852528314300e-06, 0.4310638151560e+01, 0.2022531624851e+00, 0.1832111226447e-06, 0.1494665322656e+01, 0.3235053470014e+00, 0.1746805502310e-06, 0.1451378500784e+01, 0.1385174140878e+00, 0.1555730966650e-06, 0.1068040418198e+01, 0.7358765972222e+00, 0.1554883462559e-06, 0.2442579035461e+01, 0.5154640627760e+00, 0.1638380568746e-06, 0.2597913420625e+00, 0.8531963191132e+00, 0.1159938593640e-06, 0.5834512021280e+01, 0.1990721704425e+00, 0.1083427965695e-06, 0.5054033177950e+01, 0.5439178814476e+00, 0.1156480369431e-06, 0.5325677432457e+01, 0.5257585094865e+00, 0.1141308860095e-06, 0.2153403923857e+01, 0.5336234347371e+00, 0.7913146470946e-07, 0.8642846847027e+00, 0.1478866649112e+01, 0.7439752463733e-07, 0.1970628496213e+01, 0.2164800718209e+00, 0.7280277104079e-07, 0.6073307250609e+01, 0.2101180877357e+00, 0.8319567719136e-07, 0.1954371928334e+01, 0.1692165728891e+01, 0.7137705549290e-07, 0.8904989440909e+00, 0.4155522422634e+00, 0.6900825396225e-07, 0.2825717714977e+01, 0.1173197218910e+00, 0.7245757216635e-07, 0.2481677513331e+01, 0.1265567569334e+01, 0.6961165696255e-07, 0.1292955312978e+01, 0.9562891316684e+00, 0.7571804456890e-07, 0.3427517575069e+01, 0.1422690933580e-01, 0.6605425721904e-07, 0.8052192701492e+00, 0.6470106940028e+00, 0.7375477357248e-07, 0.1705076390088e+01, 0.1581959461667e+01, 0.7041664951470e-07, 0.4848356967891e+00, 0.9597935788730e-01, 0.6322199535763e-07, 0.3878069473909e+01, 0.7084920306520e-01, 0.5244380279191e-07, 0.2645560544125e+01, 0.5265099800692e+00, 0.5143125704988e-07, 0.4834486101370e+01, 0.5328719641544e+00, 0.5871866319373e-07, 0.7981472548900e+00, 0.7871412831580e-01, 0.6300822573871e-07, 0.5979398788281e+01, 0.2608790314060e+02, 0.6062154271548e-07, 0.4108655402756e+01, 0.1114304132498e+00, 0.4361912339976e-07, 0.5322624319280e+01, 0.1375773836557e+01, 0.4417005920067e-07, 0.6240817359284e+01, 0.2770348281756e+00, 0.4686806749936e-07, 0.3214977301156e+01, 0.1143987543936e+00, 0.3758892132305e-07, 0.5879809634765e+01, 0.1596186371003e+01, 0.5151351332319e-07, 0.2893377688007e+00, 0.2228608264996e+00, 0.4554683578572e-07, 0.5475427144122e+01, 0.1465949902372e+00, 0.3442381385338e-07, 0.5992034796640e+01, 0.5070101000000e-01, 0.2831093954933e-07, 0.5367350273914e+01, 0.3092784376656e+00, 0.3756267090084e-07, 0.5758171285420e+01, 0.4903339079539e+00, 0.2816374679892e-07, 0.1863718700923e+01, 0.2991266627620e+00, 0.3419307025569e-07, 0.9524347534130e+00, 0.3518164938661e+00, 0.2904250494239e-07, 0.5304471615602e+01, 0.1099462426779e+00, 0.2471734511206e-07, 0.1297069793530e+01, 0.6256703299991e+00, 0.2539620831872e-07, 0.3281126083375e+01, 0.1256615170089e+02, 0.2281017868007e-07, 0.1829122133165e+01, 0.6681224869435e+01, 0.2275319473335e-07, 0.5797198160181e+01, 0.3932462625300e-02, 0.2547755368442e-07, 0.4752697708330e+01, 0.1169588211447e+01, 0.2285979669317e-07, 0.1223205292886e+01, 0.1045155034888e+01, 0.1913386560994e-07, 0.1757532993389e+01, 0.1155361302111e+01, 0.1809020525147e-07, 0.4246116108791e+01, 0.3368040641550e-01, 0.1649213300201e-07, 0.1445162890627e+01, 0.4408250688924e+00, 0.1834972793932e-07, 0.1126917567225e+01, 0.4452511715700e-02, 0.1439550648138e-07, 0.6160756834764e+01, 0.9420622223326e+00, 0.1487645457041e-07, 0.4358761931792e+01, 0.4123712502208e+00, 0.1731729516660e-07, 0.6134456753344e+01, 0.2108507877249e+00, 0.1717747163567e-07, 0.1898186084455e+01, 0.2157473718317e+00, 0.1418190430374e-07, 0.4180286741266e+01, 0.6521991896920e-01, 0.1404844134873e-07, 0.7654053565412e-01, 0.4258542984690e-01, 0.1409842846538e-07, 0.4418612420312e+01, 0.2258291676434e+00, 0.1090948346291e-07, 0.1260615686131e+01, 0.4226656969313e+00, 0.1357577323612e-07, 0.3558248818690e+01, 0.7923417740620e-01, 0.1018154061960e-07, 0.5676087241256e+01, 0.1456308687557e+00, 0.1412073972109e-07, 0.8394392632422e+00, 0.1525316725248e+00, 0.1030938326496e-07, 0.1653593274064e+01, 0.1795258541446e+01, 0.1180081567104e-07, 0.1285802592036e+01, 0.7032915397480e-01, 0.9708510575650e-08, 0.7631889488106e+00, 0.8434341241180e-01, 0.9637689663447e-08, 0.4630642649176e+01, 0.1272681024002e+01, 0.1068910429389e-07, 0.5294934032165e+01, 0.2123349582968e+00, 0.1063716179336e-07, 0.2736266800832e+01, 0.2142632012598e+00, 0.1234858713814e-07, 0.1302891146570e+01, 0.1847279083684e+00, 0.8912631189738e-08, 0.3570415993621e+01, 0.2648454860559e+01, 0.1036378285534e-07, 0.4236693440949e+01, 0.1370332435159e+00, 0.9667798501561e-08, 0.2960768892398e+01, 0.4376440768498e+00, 0.8108314201902e-08, 0.6987781646841e+00, 0.2880807454688e+00, 0.7648364324628e-08, 0.2499017863863e+01, 0.2037373330570e+00, 0.7286136828406e-08, 0.3787426951665e+01, 0.1129145838217e+00, 0.9448237743913e-08, 0.2694354332983e+01, 0.5272426800584e+00, 0.9374276106428e-08, 0.4787121277064e+01, 0.5321392641652e+00, 0.7100226287462e-08, 0.3530238792101e+00, 0.6288513220417e+00, 0.9253056659571e-08, 0.1399478925664e+01, 0.1606092486742e+00, 0.6636432145504e-08, 0.3479575438447e+01, 0.1368660381889e+01, 0.6469975312932e-08, 0.1383669964800e+01, 0.2008557621224e+01, 0.7335849729765e-08, 0.1243698166898e+01, 0.9561746721300e-02, 0.8743421205855e-08, 0.3776164289301e+01, 0.3801276407308e+00, 0.5993635744494e-08, 0.5627122113596e+01, 0.2042657109477e+02, 0.5981008479693e-08, 0.1674336636752e+01, 0.2111650433779e+01, 0.6188535145838e-08, 0.5214925208672e+01, 0.4305306221819e+00, 0.6596074017566e-08, 0.2907653268124e+01, 0.1063314406849e+01, 0.6630815126226e-08, 0.2127643669658e+01, 0.8389694097774e+00, 0.6156772830040e-08, 0.5082160803295e+01, 0.4234171675140e+00, 0.6446960563014e-08, 0.1872100916905e+01, 0.5287268506303e+00, 0.6429324424668e-08, 0.5610276103577e+01, 0.5306550935933e+00, 0.6302232396465e-08, 0.1592152049607e+01, 0.1253008786510e-01, 0.6399244436159e-08, 0.2746214421532e+01, 0.5217580628120e+02, 0.5474965172558e-08, 0.2317666374383e+01, 0.2221856701002e+01, 0.5339293190692e-08, 0.1084724961156e+01, 0.7466759693650e-01, 0.5334733683389e-08, 0.3594106067745e+01, 0.7489573444450e-01, 0.5392665782110e-08, 0.5630254365606e+01, 0.1055449481598e+01, 0.6682075673789e-08, 0.1518480041732e+01, 0.2213766559277e+00, 0.5079130495960e-08, 0.2739765115711e+01, 0.2132517061319e+00, 0.5077759793261e-08, 0.5290711290094e+01, 0.2133464534247e+00, 0.4832037368310e-08, 0.1404473217200e+01, 0.7160067364790e-01, 0.6463279674802e-08, 0.6038381695210e+01, 0.2209183458640e-01, 0.6240592771560e-08, 0.1290170653666e+01, 0.3306188016693e+00, 0.4672013521493e-08, 0.3261895939677e+01, 0.7796265773310e-01, 0.6500650750348e-08, 0.1154522312095e+01, 0.3884652414254e+00, 0.6344161389053e-08, 0.6206111545062e+01, 0.7605151500000e-01, 0.4682518370646e-08, 0.5409118796685e+01, 0.1073608853559e+01, 0.5329460015591e-08, 0.1202985784864e+01, 0.7287631425543e+00, 0.5701588675898e-08, 0.4098715257064e+01, 0.8731175355560e-01, 0.6030690867211e-08, 0.4132033218460e+00, 0.9846002785331e+00, 0.4336256312655e-08, 0.1211415991827e+01, 0.4297791515992e+00, 0.4688498808975e-08, 0.3765479072409e+01, 0.2127790306879e+00, 0.4675578609335e-08, 0.4265540037226e+01, 0.2138191288687e+00, 0.4225578112158e-08, 0.5237566010676e+01, 0.3407705765729e+00, 0.5139422230028e-08, 0.1507173079513e+01, 0.7233337363710e-01, 0.4619995093571e-08, 0.9023957449848e-01, 0.8603097737811e+00, 0.4494776255461e-08, 0.5414930552139e+00, 0.7381754420900e-01, 0.4274026276788e-08, 0.4145735303659e+01, 0.7574578717200e-01, 0.5018141789353e-08, 0.3344408829055e+01, 0.3180992042600e-02, 0.4866163952181e-08, 0.3348534657607e+01, 0.7722995774390e-01, 0.4111986020501e-08, 0.4198823597220e+00, 0.1451108196653e+00, 0.3356142784950e-08, 0.5609144747180e+01, 0.1274714967946e+00, 0.4070575554551e-08, 0.7028411059224e+00, 0.3503323232942e+00, 0.3257451857278e-08, 0.5624697983086e+01, 0.5296435984654e+00, 0.3256973703026e-08, 0.1857842076707e+01, 0.5297383457582e+00, 0.3830771508640e-08, 0.4562887279931e+01, 0.9098186128426e+00, 0.3725024005962e-08, 0.2358058692652e+00, 0.1084620721060e+00, 0.3136763921756e-08, 0.2049731526845e+01, 0.2346394437820e+00, 0.3795147256194e-08, 0.2432356296933e+00, 0.1862120789403e+00, 0.2877342229911e-08, 0.5631101279387e+01, 0.1905464808669e+01, 0.3076931798805e-08, 0.1117615737392e+01, 0.3628624111593e+00, 0.2734765945273e-08, 0.5899826516955e+01, 0.2131850110243e+00, 0.2733405296885e-08, 0.2130562964070e+01, 0.2134131485323e+00, 0.2898552353410e-08, 0.3462387048225e+00, 0.5291709230214e+00, 0.2893736103681e-08, 0.8534352781543e+00, 0.5302110212022e+00, 0.3095717734137e-08, 0.2875061429041e+01, 0.2976424921901e+00, 0.2636190425832e-08, 0.2242512846659e+01, 0.1485980103780e+01, 0.3645512095537e-08, 0.1354016903958e+01, 0.6044726378023e+00, 0.2808173547723e-08, 0.6705114365631e-01, 0.6225157782540e-01, 0.2625012866888e-08, 0.4775705748482e+01, 0.5268983110410e-01, 0.2572233995651e-08, 0.2638924216139e+01, 0.1258454114666e+01, 0.2604238824792e-08, 0.4826358927373e+01, 0.2103781122809e+00, 0.2596886385239e-08, 0.3200388483118e+01, 0.2162200472757e+00, 0.3228057304264e-08, 0.5384848409563e+01, 0.2007689919132e+00, 0.2481601798252e-08, 0.5173373487744e+01, 0.1062562936266e+01, 0.2745977498864e-08, 0.6250966149853e+01, 0.5651155736444e+00, 0.2669878833811e-08, 0.4906001352499e+01, 0.1400015846597e+00, 0.3203986611711e-08, 0.5034333010005e+01, 0.7036329877322e+00, 0.3354961227212e-08, 0.6108262423137e+01, 0.4549093064213e+00, 0.2400407324558e-08, 0.2135399294955e+01, 0.2125476091956e+00, 0.2379905859802e-08, 0.5893721933961e+01, 0.2140505503610e+00, 0.2550844302187e-08, 0.3331940762063e+01, 0.1534957940063e+00, 0.2268824211001e-08, 0.1843418461035e+01, 0.2235935264888e+00, 0.2464700891204e-08, 0.3029548547230e+01, 0.2091065926078e+00, 0.2436814726024e-08, 0.4994717970364e+01, 0.2174915669488e+00, 0.2443623894745e-08, 0.2645102591375e+01, 0.1739420156204e+00, 0.2318701783838e-08, 0.5700547397897e+01, 0.7530171478090e-01, 0.2284448700256e-08, 0.5268898905872e+01, 0.7426161660010e-01, 0.2468848123510e-08, 0.5276280575078e+01, 0.2526561439362e+00, 0.2814052350303e-08, 0.6130168623475e+01, 0.5636314030725e+00, 0.2243662755220e-08, 0.6631692457995e+00, 0.8886590321940e-01, 0.2330795855941e-08, 0.2499435487702e+01, 0.1056200952181e+01, 0.9757679038404e-09, 0.5796846023126e+01, 0.7826370942180e+02 }; /* SSB-to-Sun, T^0, Z */ static const double s0z[] = { 0.1181255122986e-03, 0.4607918989164e+00, 0.2132990797783e+00, 0.1127777651095e-03, 0.4169146331296e+00, 0.5296909721118e+00, 0.4777754401806e-04, 0.4582657007130e+01, 0.3813291813120e-01, 0.1129354285772e-04, 0.5758735142480e+01, 0.7478166569050e-01, -0.1149543637123e-04, 0.0000000000000e+00, 0.0000000000000e+00, 0.3298730512306e-05, 0.5978801994625e+01, 0.4265981595566e+00, 0.2733376706079e-05, 0.7665413691040e+00, 0.1059381944224e+01, 0.9426389657270e-06, 0.3710201265838e+01, 0.2061856251104e+00, 0.8187517749552e-06, 0.3390675605802e+00, 0.2204125344462e+00, 0.4080447871819e-06, 0.4552296640088e+00, 0.5225775174439e+00, 0.3169973017028e-06, 0.3445455899321e+01, 0.5368044267797e+00, 0.2438098615549e-06, 0.5664675150648e+01, 0.3664874755930e-01, 0.2601897517235e-06, 0.1931894095697e+01, 0.1495633313810e+00, 0.2314558080079e-06, 0.3666319115574e+00, 0.3961708870310e-01, 0.1962549548002e-06, 0.3167411699020e+01, 0.7626583626240e-01, 0.2180518287925e-06, 0.1544420746580e+01, 0.7113454667900e-02, 0.1451382442868e-06, 0.1583756740070e+01, 0.1102062672231e+00, 0.1358439007389e-06, 0.5239941758280e+01, 0.6398972393349e+00, 0.1050585898028e-06, 0.2266958352859e+01, 0.3163918923335e+00, 0.1050029870186e-06, 0.2711495250354e+01, 0.4194847048887e+00, 0.9934920679800e-07, 0.1116208151396e+01, 0.1589072916335e+01, 0.1048395331560e-06, 0.3408619600206e+01, 0.1021328554739e+02, 0.8370147196668e-07, 0.3810459401087e+01, 0.2535050500000e-01, 0.7989856510998e-07, 0.3769910473647e+01, 0.7329749511860e-01, 0.5441221655233e-07, 0.2416994903374e+01, 0.1030928125552e+00, 0.4610812906784e-07, 0.5858503336994e+01, 0.4337116142245e+00, 0.3923022803444e-07, 0.3354170010125e+00, 0.1484170571900e-02, 0.2610725582128e-07, 0.5410600646324e+01, 0.6327837846670e+00, 0.2455279767721e-07, 0.6120216681403e+01, 0.1162474756779e+01, 0.2375530706525e-07, 0.6055443426143e+01, 0.1052268489556e+01, 0.1782967577553e-07, 0.3146108708004e+01, 0.8460828644453e+00, 0.1581687095238e-07, 0.6255496089819e+00, 0.3340612434717e+01, 0.1594657672461e-07, 0.3782604300261e+01, 0.1066495398892e+01, 0.1563448615040e-07, 0.1997775733196e+01, 0.2022531624851e+00, 0.1463624258525e-07, 0.1736316792088e+00, 0.3516457698740e-01, 0.1331585056673e-07, 0.4331941830747e+01, 0.9491756770005e+00, 0.1130634557637e-07, 0.6152017751825e+01, 0.2968341143800e-02, 0.1028949607145e-07, 0.2101792614637e+00, 0.2275259891141e+00, 0.1024074971618e-07, 0.4071833211074e+01, 0.5070101000000e-01, 0.8826956060303e-08, 0.4861633688145e+00, 0.2093666171530e+00, 0.8572230171541e-08, 0.5268190724302e+01, 0.4110125927500e-01, 0.7649332643544e-08, 0.5134543417106e+01, 0.2608790314060e+02, 0.8581673291033e-08, 0.2920218146681e+01, 0.1480791608091e+00, 0.8430589300938e-08, 0.3604576619108e+01, 0.2172315424036e+00, 0.7776165501012e-08, 0.3772942249792e+01, 0.6373574839730e-01, 0.8311070234408e-08, 0.6200412329888e+01, 0.3235053470014e+00, 0.6927365212582e-08, 0.4543353113437e+01, 0.8531963191132e+00, 0.6791574208598e-08, 0.2882188406238e+01, 0.7181332454670e-01, 0.5593100811839e-08, 0.1776646892780e+01, 0.7429900518901e+00, 0.4553381853021e-08, 0.3949617611240e+01, 0.7775000683430e-01, 0.5758000450068e-08, 0.3859251775075e+01, 0.1990721704425e+00, 0.4281283457133e-08, 0.1466294631206e+01, 0.2118763888447e+01, 0.4206935661097e-08, 0.5421776011706e+01, 0.1104591729320e-01, 0.4213751641837e-08, 0.3412048993322e+01, 0.2243449970715e+00, 0.5310506239878e-08, 0.5421641370995e+00, 0.5154640627760e+00, 0.3827450341320e-08, 0.8887314524995e+00, 0.1510475019529e+00, 0.4292435241187e-08, 0.1405043757194e+01, 0.1422690933580e-01, 0.3189780702289e-08, 0.1060049293445e+01, 0.1173197218910e+00, 0.3226611928069e-08, 0.6270858897442e+01, 0.2164800718209e+00, 0.2893897608830e-08, 0.5117563223301e+01, 0.6470106940028e+00, 0.3239852024578e-08, 0.4079092237983e+01, 0.2101180877357e+00, 0.2956892222200e-08, 0.1594917021704e+01, 0.3092784376656e+00, 0.2980177912437e-08, 0.5258787667564e+01, 0.4155522422634e+00, 0.3163725690776e-08, 0.3854589225479e+01, 0.8582758298370e-01, 0.2662262399118e-08, 0.3561326430187e+01, 0.5257585094865e+00, 0.2766689135729e-08, 0.3180732086830e+00, 0.1385174140878e+00, 0.2411600278464e-08, 0.3324798335058e+01, 0.5439178814476e+00, 0.2483527695131e-08, 0.4169069291947e+00, 0.5336234347371e+00, 0.7788777276590e-09, 0.1900569908215e+01, 0.5217580628120e+02 }; /* SSB-to-Sun, T^1, X */ static const double s1x[] = { -0.1296310361520e-07, 0.0000000000000e+00, 0.0000000000000e+00, 0.8975769009438e-08, 0.1128891609250e+01, 0.4265981595566e+00, 0.7771113441307e-08, 0.2706039877077e+01, 0.2061856251104e+00, 0.7538303866642e-08, 0.2191281289498e+01, 0.2204125344462e+00, 0.6061384579336e-08, 0.3248167319958e+01, 0.1059381944224e+01, 0.5726994235594e-08, 0.5569981398610e+01, 0.5225775174439e+00, 0.5616492836424e-08, 0.5057386614909e+01, 0.5368044267797e+00, 0.1010881584769e-08, 0.3473577116095e+01, 0.7113454667900e-02, 0.7259606157626e-09, 0.3651858593665e+00, 0.6398972393349e+00, 0.8755095026935e-09, 0.1662835408338e+01, 0.4194847048887e+00, 0.5370491182812e-09, 0.1327673878077e+01, 0.4337116142245e+00, 0.5743773887665e-09, 0.4250200846687e+01, 0.2132990797783e+00, 0.4408103140300e-09, 0.3598752574277e+01, 0.1589072916335e+01, 0.3101892374445e-09, 0.4887822983319e+01, 0.1052268489556e+01, 0.3209453713578e-09, 0.9702272295114e+00, 0.5296909721118e+00, 0.3017228286064e-09, 0.5484462275949e+01, 0.1066495398892e+01, 0.3200700038601e-09, 0.2846613338643e+01, 0.1495633313810e+00, 0.2137637279911e-09, 0.5692163292729e+00, 0.3163918923335e+00, 0.1899686386727e-09, 0.2061077157189e+01, 0.2275259891141e+00, 0.1401994545308e-09, 0.4177771136967e+01, 0.1102062672231e+00, 0.1578057810499e-09, 0.5782460597335e+01, 0.7626583626240e-01, 0.1237713253351e-09, 0.5705900866881e+01, 0.5154640627760e+00, 0.1313076837395e-09, 0.5163438179576e+01, 0.3664874755930e-01, 0.1184963304860e-09, 0.3054804427242e+01, 0.6327837846670e+00, 0.1238130878565e-09, 0.2317292575962e+01, 0.3961708870310e-01, 0.1015959527736e-09, 0.2194643645526e+01, 0.7329749511860e-01, 0.9017954423714e-10, 0.2868603545435e+01, 0.1990721704425e+00, 0.8668024955603e-10, 0.4923849675082e+01, 0.5439178814476e+00, 0.7756083930103e-10, 0.3014334135200e+01, 0.9491756770005e+00, 0.7536503401741e-10, 0.2704886279769e+01, 0.1030928125552e+00, 0.5483308679332e-10, 0.6010983673799e+01, 0.8531963191132e+00, 0.5184339620428e-10, 0.1952704573291e+01, 0.2093666171530e+00, 0.5108658712030e-10, 0.2958575786649e+01, 0.2172315424036e+00, 0.5019424524650e-10, 0.1736317621318e+01, 0.2164800718209e+00, 0.4909312625978e-10, 0.3167216416257e+01, 0.2101180877357e+00, 0.4456638901107e-10, 0.7697579923471e+00, 0.3235053470014e+00, 0.4227030350925e-10, 0.3490910137928e+01, 0.6373574839730e-01, 0.4095456040093e-10, 0.5178888984491e+00, 0.6470106940028e+00, 0.4990537041422e-10, 0.3323887668974e+01, 0.1422690933580e-01, 0.4321170010845e-10, 0.4288484987118e+01, 0.7358765972222e+00, 0.3544072091802e-10, 0.6021051579251e+01, 0.5265099800692e+00, 0.3480198638687e-10, 0.4600027054714e+01, 0.5328719641544e+00, 0.3440287244435e-10, 0.4349525970742e+01, 0.8582758298370e-01, 0.3330628322713e-10, 0.2347391505082e+01, 0.1104591729320e-01, 0.2973060707184e-10, 0.4789409286400e+01, 0.5257585094865e+00, 0.2932606766089e-10, 0.5831693799927e+01, 0.5336234347371e+00, 0.2876972310953e-10, 0.2692638514771e+01, 0.1173197218910e+00, 0.2827488278556e-10, 0.2056052487960e+01, 0.2022531624851e+00, 0.2515028239756e-10, 0.7411863262449e+00, 0.9597935788730e-01, 0.2853033744415e-10, 0.3948481024894e+01, 0.2118763888447e+01 }; /* SSB-to-Sun, T^1, Y */ static const double s1y[] = { 0.8989047573576e-08, 0.5840593672122e+01, 0.4265981595566e+00, 0.7815938401048e-08, 0.1129664707133e+01, 0.2061856251104e+00, 0.7550926713280e-08, 0.6196589104845e+00, 0.2204125344462e+00, 0.6056556925895e-08, 0.1677494667846e+01, 0.1059381944224e+01, 0.5734142698204e-08, 0.4000920852962e+01, 0.5225775174439e+00, 0.5614341822459e-08, 0.3486722577328e+01, 0.5368044267797e+00, 0.1028678147656e-08, 0.1877141024787e+01, 0.7113454667900e-02, 0.7270792075266e-09, 0.5077167301739e+01, 0.6398972393349e+00, 0.8734141726040e-09, 0.9069550282609e-01, 0.4194847048887e+00, 0.5377371402113e-09, 0.6039381844671e+01, 0.4337116142245e+00, 0.4729719431571e-09, 0.2153086311760e+01, 0.2132990797783e+00, 0.4458052820973e-09, 0.5059830025565e+01, 0.5296909721118e+00, 0.4406855467908e-09, 0.2027971692630e+01, 0.1589072916335e+01, 0.3101659310977e-09, 0.3317677981860e+01, 0.1052268489556e+01, 0.3016749232545e-09, 0.3913703482532e+01, 0.1066495398892e+01, 0.3198541352656e-09, 0.1275513098525e+01, 0.1495633313810e+00, 0.2142065389871e-09, 0.5301351614597e+01, 0.3163918923335e+00, 0.1902615247592e-09, 0.4894943352736e+00, 0.2275259891141e+00, 0.1613410990871e-09, 0.2449891130437e+01, 0.1102062672231e+00, 0.1576992165097e-09, 0.4211421447633e+01, 0.7626583626240e-01, 0.1241637259894e-09, 0.4140803368133e+01, 0.5154640627760e+00, 0.1313974830355e-09, 0.3591920305503e+01, 0.3664874755930e-01, 0.1181697118258e-09, 0.1506314382788e+01, 0.6327837846670e+00, 0.1238239742779e-09, 0.7461405378404e+00, 0.3961708870310e-01, 0.1010107068241e-09, 0.6271010795475e+00, 0.7329749511860e-01, 0.9226316616509e-10, 0.1259158839583e+01, 0.1990721704425e+00, 0.8664946419555e-10, 0.3353244696934e+01, 0.5439178814476e+00, 0.7757230468978e-10, 0.1447677295196e+01, 0.9491756770005e+00, 0.7693168628139e-10, 0.1120509896721e+01, 0.1030928125552e+00, 0.5487897454612e-10, 0.4439380426795e+01, 0.8531963191132e+00, 0.5196118677218e-10, 0.3788856619137e+00, 0.2093666171530e+00, 0.5110853339935e-10, 0.1386879372016e+01, 0.2172315424036e+00, 0.5027804534813e-10, 0.1647881805466e+00, 0.2164800718209e+00, 0.4922485922674e-10, 0.1594315079862e+01, 0.2101180877357e+00, 0.6155599524400e-10, 0.0000000000000e+00, 0.0000000000000e+00, 0.4447147832161e-10, 0.5480720918976e+01, 0.3235053470014e+00, 0.4144691276422e-10, 0.1931371033660e+01, 0.6373574839730e-01, 0.4099950625452e-10, 0.5229611294335e+01, 0.6470106940028e+00, 0.5060541682953e-10, 0.1731112486298e+01, 0.1422690933580e-01, 0.4293615946300e-10, 0.2714571038925e+01, 0.7358765972222e+00, 0.3545659845763e-10, 0.4451041444634e+01, 0.5265099800692e+00, 0.3479112041196e-10, 0.3029385448081e+01, 0.5328719641544e+00, 0.3438516493570e-10, 0.2778507143731e+01, 0.8582758298370e-01, 0.3297341285033e-10, 0.7898709807584e+00, 0.1104591729320e-01, 0.2972585818015e-10, 0.3218785316973e+01, 0.5257585094865e+00, 0.2931707295017e-10, 0.4260731012098e+01, 0.5336234347371e+00, 0.2897198149403e-10, 0.1120753978101e+01, 0.1173197218910e+00, 0.2832293240878e-10, 0.4597682717827e+00, 0.2022531624851e+00, 0.2864348326612e-10, 0.2169939928448e+01, 0.9597935788730e-01, 0.2852714675471e-10, 0.2377659870578e+01, 0.2118763888447e+01 }; /* SSB-to-Sun, T^1, Z */ static const double s1z[] = { 0.5444220475678e-08, 0.1803825509310e+01, 0.2132990797783e+00, 0.3883412695596e-08, 0.4668616389392e+01, 0.5296909721118e+00, 0.1334341434551e-08, 0.0000000000000e+00, 0.0000000000000e+00, 0.3730001266883e-09, 0.5401405918943e+01, 0.2061856251104e+00, 0.2894929197956e-09, 0.4932415609852e+01, 0.2204125344462e+00, 0.2857950357701e-09, 0.3154625362131e+01, 0.7478166569050e-01, 0.2499226432292e-09, 0.3657486128988e+01, 0.4265981595566e+00, 0.1937705443593e-09, 0.5740434679002e+01, 0.1059381944224e+01, 0.1374894396320e-09, 0.1712857366891e+01, 0.5368044267797e+00, 0.1217248678408e-09, 0.2312090870932e+01, 0.5225775174439e+00, 0.7961052740870e-10, 0.5283368554163e+01, 0.3813291813120e-01, 0.4979225949689e-10, 0.4298290471860e+01, 0.4194847048887e+00, 0.4388552286597e-10, 0.6145515047406e+01, 0.7113454667900e-02, 0.2586835212560e-10, 0.3019448001809e+01, 0.6398972393349e+00 }; /* SSB-to-Sun, T^2, X */ static const double s2x[] = { 0.1603551636587e-11, 0.4404109410481e+01, 0.2061856251104e+00, 0.1556935889384e-11, 0.4818040873603e+00, 0.2204125344462e+00, 0.1182594414915e-11, 0.9935762734472e+00, 0.5225775174439e+00, 0.1158794583180e-11, 0.3353180966450e+01, 0.5368044267797e+00, 0.9597358943932e-12, 0.5567045358298e+01, 0.2132990797783e+00, 0.6511516579605e-12, 0.5630872420788e+01, 0.4265981595566e+00, 0.7419792747688e-12, 0.2156188581957e+01, 0.5296909721118e+00, 0.3951972655848e-12, 0.1981022541805e+01, 0.1059381944224e+01, 0.4478223877045e-12, 0.0000000000000e+00, 0.0000000000000e+00 }; /* SSB-to-Sun, T^2, Y */ static const double s2y[] = { 0.1609114495091e-11, 0.2831096993481e+01, 0.2061856251104e+00, 0.1560330784946e-11, 0.5193058213906e+01, 0.2204125344462e+00, 0.1183535479202e-11, 0.5707003443890e+01, 0.5225775174439e+00, 0.1158183066182e-11, 0.1782400404928e+01, 0.5368044267797e+00, 0.1032868027407e-11, 0.4036925452011e+01, 0.2132990797783e+00, 0.6540142847741e-12, 0.4058241056717e+01, 0.4265981595566e+00, 0.7305236491596e-12, 0.6175401942957e+00, 0.5296909721118e+00, -0.5580725052968e-12, 0.0000000000000e+00, 0.0000000000000e+00, 0.3946122651015e-12, 0.4108265279171e+00, 0.1059381944224e+01 }; /* SSB-to-Sun, T^2, Z */ static const double s2z[] = { 0.3749920358054e-12, 0.3230285558668e+01, 0.2132990797783e+00, 0.2735037220939e-12, 0.6154322683046e+01, 0.5296909721118e+00 }; /* Pointers to coefficient arrays, in x,y,z sets */ static const double *ce0[] = { e0x, e0y, e0z }, *ce1[] = { e1x, e1y, e1z }, *ce2[] = { e2x, e2y, e2z }, *cs0[] = { s0x, s0y, s0z }, *cs1[] = { s1x, s1y, s1z }, *cs2[] = { s2x, s2y, s2z }; const double *coeffs; /* Numbers of terms for each component of the model, in x,y,z sets */ static const int ne0[3] = {(int)(sizeof e0x / sizeof (double) / 3), (int)(sizeof e0y / sizeof (double) / 3), (int)(sizeof e0z / sizeof (double) / 3) }, ne1[3] = {(int)(sizeof e1x / sizeof (double) / 3), (int)(sizeof e1y / sizeof (double) / 3), (int)(sizeof e1z / sizeof (double) / 3) }, ne2[3] = {(int)(sizeof e2x / sizeof (double) / 3), (int)(sizeof e2y / sizeof (double) / 3), (int)(sizeof e2z / sizeof (double) / 3) }, ns0[3] = {(int)(sizeof s0x / sizeof (double) / 3), (int)(sizeof s0y / sizeof (double) / 3), (int)(sizeof s0z / sizeof (double) / 3) }, ns1[3] = {(int)(sizeof s1x / sizeof (double) / 3), (int)(sizeof s1y / sizeof (double) / 3), (int)(sizeof s1z / sizeof (double) / 3) }, ns2[3] = {(int)(sizeof s2x / sizeof (double) / 3), (int)(sizeof s2y / sizeof (double) / 3), (int)(sizeof s2z / sizeof (double) / 3) }; int nterms; /* Miscellaneous */ int jstat, i, j; double t, t2, xyz, xyzd, a, b, c, ct, p, cp, ph[3], vh[3], pb[3], vb[3], x, y, z; /*--------------------------------------------------------------------*/ /* Time since reference epoch, Julian years. */ t = ((date1 - DJ00) + date2) / DJY; t2 = t*t; /* Set status. */ jstat = fabs(t) <= 100.0 ? 0 : 1; /* X then Y then Z. */ for (i = 0; i < 3; i++) { /* Initialize position and velocity component. */ xyz = 0.0; xyzd = 0.0; /* ------------------------------------------------ */ /* Obtain component of Sun to Earth ecliptic vector */ /* ------------------------------------------------ */ /* Sun to Earth, T^0 terms. */ coeffs = ce0[i]; nterms = ne0[i]; for (j = 0; j < nterms; j++) { a = *coeffs++; b = *coeffs++; c = *coeffs++; p = b + c*t; xyz += a*cos(p); xyzd -= a*c*sin(p); } /* Sun to Earth, T^1 terms. */ coeffs = ce1[i]; nterms = ne1[i]; for (j = 0; j < nterms; j++) { a = *coeffs++; b = *coeffs++; c = *coeffs++; ct = c*t; p = b + ct; cp = cos(p); xyz += a*t*cp; xyzd += a*( cp - ct*sin(p) ); } /* Sun to Earth, T^2 terms. */ coeffs = ce2[i]; nterms = ne2[i]; for (j = 0; j < nterms; j++) { a = *coeffs++; b = *coeffs++; c = *coeffs++; ct = c*t; p = b + ct; cp = cos(p); xyz += a*t2*cp; xyzd += a*t*( 2.0*cp - ct*sin(p) ); } /* Heliocentric Earth position and velocity component. */ ph[i] = xyz; vh[i] = xyzd / DJY; /* ------------------------------------------------ */ /* Obtain component of SSB to Earth ecliptic vector */ /* ------------------------------------------------ */ /* SSB to Sun, T^0 terms. */ coeffs = cs0[i]; nterms = ns0[i]; for (j = 0; j < nterms; j++) { a = *coeffs++; b = *coeffs++; c = *coeffs++; p = b + c*t; xyz += a*cos(p); xyzd -= a*c*sin(p); } /* SSB to Sun, T^1 terms. */ coeffs = cs1[i]; nterms = ns1[i]; for (j = 0; j < nterms; j++) { a = *coeffs++; b = *coeffs++; c = *coeffs++; ct = c*t; p = b + ct; cp = cos(p); xyz += a*t*cp; xyzd += a*(cp - ct*sin(p)); } /* SSB to Sun, T^2 terms. */ coeffs = cs2[i]; nterms = ns2[i]; for (j = 0; j < nterms; j++) { a = *coeffs++; b = *coeffs++; c = *coeffs++; ct = c*t; p = b + ct; cp = cos(p); xyz += a*t2*cp; xyzd += a*t*(2.0*cp - ct*sin(p)); } /* Barycentric Earth position and velocity component. */ pb[i] = xyz; vb[i] = xyzd / DJY; /* Next Cartesian component. */ } /* Rotate from ecliptic to BCRS coordinates. */ x = ph[0]; y = ph[1]; z = ph[2]; pvh[0][0] = x + am12*y + am13*z; pvh[0][1] = am21*x + am22*y + am23*z; pvh[0][2] = am32*y + am33*z; x = vh[0]; y = vh[1]; z = vh[2]; pvh[1][0] = x + am12*y + am13*z; pvh[1][1] = am21*x + am22*y + am23*z; pvh[1][2] = am32*y + am33*z; x = pb[0]; y = pb[1]; z = pb[2]; pvb[0][0] = x + am12*y + am13*z; pvb[0][1] = am21*x + am22*y + am23*z; pvb[0][2] = am32*y + am33*z; x = vb[0]; y = vb[1]; z = vb[2]; pvb[1][0] = x + am12*y + am13*z; pvb[1][1] = am21*x + am22*y + am23*z; pvb[1][2] = am32*y + am33*z; /* Return the status. */ return jstat; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/eqec06.c0000644000113000011300000001610713027221062014414 0ustar bellsbells#include "sofa.h" void iauEqec06(double date1, double date2, double dr, double dd, double *dl, double *db) /* ** - - - - - - - - - - ** i a u E q e c 0 6 ** - - - - - - - - - - ** ** Transformation from ICRS equatorial coordinates to ecliptic ** coordinates (mean equinox and ecliptic of date) using IAU 2006 ** precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian date (Note 1) ** dr,dd double ICRS right ascension and declination (radians) ** ** Returned: ** dl,db double ecliptic longitude and latitude (radians) ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) No assumptions are made about whether the coordinates represent ** starlight and embody astrometric effects such as parallax or ** aberration. ** ** 3) The transformation is approximately that from mean J2000.0 right ** ascension and declination to ecliptic longitude and latitude ** (mean equinox and ecliptic of date), with only frame bias (always ** less than 25 mas) to disturb this classical picture. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauEcm06 J2000.0 to ecliptic rotation matrix, IAU 2006 ** iauRxp product of r-matrix and p-vector ** iauC2s unit vector to spherical coordinates ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** ** This revision: 2016 February 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rm[3][3], v1[3], v2[3], a, b; /* Spherical to Cartesian. */ iauS2c(dr, dd, v1); /* Rotation matrix, ICRS equatorial to ecliptic. */ iauEcm06(date1, date2, rm); /* The transformation from ICRS to ecliptic. */ iauRxp(rm, v1, v2); /* Cartesian to spherical. */ iauC2s(v2, &a, &b); /* Express in conventional ranges. */ *dl = iauAnp(a); *db = iauAnpm(b); /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/eqeq94.c0000644000113000011300000001545113027221062014442 0ustar bellsbells#include "sofa.h" double iauEqeq94(double date1, double date2) /* ** - - - - - - - - - - ** i a u E q e q 9 4 ** - - - - - - - - - - ** ** Equation of the equinoxes, IAU 1994 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TDB date (Note 1) ** ** Returned (function value): ** double equation of the equinoxes (Note 2) ** ** Notes: ** ** 1) The date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result, which is in radians, operates in the following sense: ** ** Greenwich apparent ST = GMST + equation of the equinoxes ** ** Called: ** iauAnpm normalize angle into range +/- pi ** iauNut80 nutation, IAU 1980 ** iauObl80 mean obliquity, IAU 1980 ** ** References: ** ** IAU Resolution C7, Recommendation 3 (1994). ** ** Capitaine, N. & Gontier, A.-M., 1993, Astron. Astrophys., 275, ** 645-650. ** ** This revision: 2013 August 31 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, om, dpsi, deps, eps0, ee; /* Interval between fundamental epoch J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Longitude of the mean ascending node of the lunar orbit on the */ /* ecliptic, measured from the mean equinox of date. */ om = iauAnpm((450160.280 + (-482890.539 + (7.455 + 0.008 * t) * t) * t) * DAS2R + fmod(-5.0 * t, 1.0) * D2PI); /* Nutation components and mean obliquity. */ iauNut80(date1, date2, &dpsi, &deps); eps0 = iauObl80(date1, date2); /* Equation of the equinoxes. */ ee = dpsi*cos(eps0) + DAS2R*(0.00264*sin(om) + 0.000063*sin(om+om)); return ee; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/era00.c0000644000113000011300000001550213027221062014236 0ustar bellsbells#include "sofa.h" double iauEra00(double dj1, double dj2) /* ** - - - - - - - - - ** i a u E r a 0 0 ** - - - - - - - - - ** ** Earth rotation angle (IAU 2000 model). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** dj1,dj2 double UT1 as a 2-part Julian Date (see note) ** ** Returned (function value): ** double Earth rotation angle (radians), range 0-2pi ** ** Notes: ** ** 1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any ** convenient way between the arguments dj1 and dj2. For example, ** JD(UT1)=2450123.7 could be expressed in any of these ways, ** among others: ** ** dj1 dj2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. The date & time method is ** best matched to the algorithm used: maximum precision is ** delivered when the dj1 argument is for 0hrs UT1 on the day in ** question and the dj2 argument lies in the range 0 to 1, or vice ** versa. ** ** 2) The algorithm is adapted from Expression 22 of Capitaine et al. ** 2000. The time argument has been expressed in days directly, ** and, to retain precision, integer contributions have been ** eliminated. The same formulation is given in IERS Conventions ** (2003), Chap. 5, Eq. 14. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Capitaine N., Guinot B. and McCarthy D.D, 2000, Astron. ** Astrophys., 355, 398-405. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double d1, d2, t, f, theta; /* Days since fundamental epoch. */ if (dj1 < dj2) { d1 = dj1; d2 = dj2; } else { d1 = dj2; d2 = dj1; } t = d1 + (d2- DJ00); /* Fractional part of T (days). */ f = fmod(d1, 1.0) + fmod(d2, 1.0); /* Earth rotation angle at this UT1. */ theta = iauAnp(D2PI * (f + 0.7790572732640 + 0.00273781191135448 * t)); return theta; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fad03.c0000644000113000011300000001323513027221062014225 0ustar bellsbells#include "sofa.h" double iauFad03(double t) /* ** - - - - - - - - - ** i a u F a d 0 3 ** - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean elongation of the Moon from the Sun. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double D, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean elongation of the Moon from the Sun (IERS Conventions 2003). */ a = fmod( 1072260.703692 + t * ( 1602961601.2090 + t * ( - 6.3706 + t * ( 0.006593 + t * ( - 0.00003169 ) ) ) ), TURNAS ) * DAS2R; return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fae03.c0000644000113000011300000001317413027221062014230 0ustar bellsbells#include "sofa.h" double iauFae03(double t) /* ** - - - - - - - - - ** i a u F a e 0 3 ** - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Earth. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Earth, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean longitude of Earth (IERS Conventions 2003). */ a = fmod(1.753470314 + 628.3075849991 * t, D2PI); return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/faf03.c0000644000113000011300000001337313027221062014232 0ustar bellsbells#include "sofa.h" double iauFaf03(double t) /* ** - - - - - - - - - ** i a u F a f 0 3 ** - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of the Moon minus mean longitude of the ascending ** node. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double F, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean longitude of the Moon minus that of the ascending node */ /* (IERS Conventions 2003). */ a = fmod( 335779.526232 + t * ( 1739527262.8478 + t * ( - 12.7512 + t * ( - 0.001037 + t * ( 0.00000417 ) ) ) ), TURNAS ) * DAS2R; return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/faju03.c0000644000113000011300000001321013027221062014411 0ustar bellsbells#include "sofa.h" double iauFaju03(double t) /* ** - - - - - - - - - - ** i a u F a j u 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Jupiter. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Jupiter, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean longitude of Jupiter (IERS Conventions 2003). */ a = fmod(0.599546497 + 52.9690962641 * t, D2PI); return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fal03.c0000644000113000011300000001317613027221062014241 0ustar bellsbells#include "sofa.h" double iauFal03(double t) /* ** - - - - - - - - - ** i a u F a l 0 3 ** - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean anomaly of the Moon. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double l, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean anomaly of the Moon (IERS Conventions 2003). */ a = fmod( 485868.249036 + t * ( 1717915923.2178 + t * ( 31.8792 + t * ( 0.051635 + t * ( - 0.00024470 ) ) ) ), TURNAS ) * DAS2R; return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/falp03.c0000644000113000011300000001317613027221062014421 0ustar bellsbells#include "sofa.h" double iauFalp03(double t) /* ** - - - - - - - - - - ** i a u F a l p 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean anomaly of the Sun. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double l', radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean anomaly of the Sun (IERS Conventions 2003). */ a = fmod( 1287104.793048 + t * ( 129596581.0481 + t * ( - 0.5532 + t * ( 0.000136 + t * ( - 0.00001149 ) ) ) ), TURNAS ) * DAS2R; return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fama03.c0000644000113000011300000001320013027221062014367 0ustar bellsbells#include "sofa.h" double iauFama03(double t) /* ** - - - - - - - - - - ** i a u F a m a 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Mars. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Mars, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean longitude of Mars (IERS Conventions 2003). */ a = fmod(6.203480913 + 334.0612426700 * t, D2PI); return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fame03.c0000644000113000011300000001321213027221062014376 0ustar bellsbells#include "sofa.h" double iauFame03(double t) /* ** - - - - - - - - - - ** i a u F a m e 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Mercury. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Mercury, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean longitude of Mercury (IERS Conventions 2003). */ a = fmod(4.402608842 + 2608.7903141574 * t, D2PI); return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fane03.c0000644000113000011300000001277713027221062014416 0ustar bellsbells#include "sofa.h" double iauFane03(double t) /* ** - - - - - - - - - - ** i a u F a n e 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Neptune. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Neptune, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is adapted from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean longitude of Neptune (IERS Conventions 2003). */ a = fmod(5.311886287 + 3.8133035638 * t, D2PI); return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/faom03.c0000644000113000011300000001330213027221062014410 0ustar bellsbells#include "sofa.h" double iauFaom03(double t) /* ** - - - - - - - - - - ** i a u F a o m 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of the Moon's ascending node. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double Omega, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean longitude of the Moon's ascending node */ /* (IERS Conventions 2003). */ a = fmod( 450160.398036 + t * ( - 6962890.5431 + t * ( 7.4722 + t * ( 0.007702 + t * ( - 0.00005939 ) ) ) ), TURNAS ) * DAS2R; return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fapa03.c0000644000113000011300000001317213027221062014402 0ustar bellsbells#include "sofa.h" double iauFapa03(double t) /* ** - - - - - - - - - - ** i a u F a p a 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** general accumulated precession in longitude. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double general precession in longitude, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003). It ** is taken from Kinoshita & Souchay (1990) and comes originally ** from Lieske et al. (1977). ** ** References: ** ** Kinoshita, H. and Souchay J. 1990, Celest.Mech. and Dyn.Astron. ** 48, 187 ** ** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, ** Astron.Astrophys. 58, 1-16 ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* General accumulated precession in longitude. */ a = (0.024381750 + 0.00000538691 * t) * t; return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fasa03.c0000644000113000011300000001320513027221062014402 0ustar bellsbells#include "sofa.h" double iauFasa03(double t) /* ** - - - - - - - - - - ** i a u F a s a 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Saturn. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Saturn, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean longitude of Saturn (IERS Conventions 2003). */ a = fmod(0.874016757 + 21.3299104960 * t, D2PI); return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/faur03.c0000644000113000011300000001277513027221062014440 0ustar bellsbells#include "sofa.h" double iauFaur03(double t) /* ** - - - - - - - - - - ** i a u F a u r 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Uranus. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Uranus, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is adapted from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean longitude of Uranus (IERS Conventions 2003). */ a = fmod(5.481293872 + 7.4781598567 * t, D2PI); return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fave03.c0000644000113000011300000001320413027221062014410 0ustar bellsbells#include "sofa.h" double iauFave03(double t) /* ** - - - - - - - - - - ** i a u F a v e 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Venus. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Venus, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double a; /* Mean longitude of Venus (IERS Conventions 2003). */ a = fmod(3.176146697 + 1021.3285546211 * t, D2PI); return a; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fk52h.c0000644000113000011300000001637313027221062014255 0ustar bellsbells#include "sofa.h" void iauFk52h(double r5, double d5, double dr5, double dd5, double px5, double rv5, double *rh, double *dh, double *drh, double *ddh, double *pxh, double *rvh) /* ** - - - - - - - - - ** i a u F k 5 2 h ** - - - - - - - - - ** ** Transform FK5 (J2000.0) star data into the Hipparcos system. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given (all FK5, equinox J2000.0, epoch J2000.0): ** r5 double RA (radians) ** d5 double Dec (radians) ** dr5 double proper motion in RA (dRA/dt, rad/Jyear) ** dd5 double proper motion in Dec (dDec/dt, rad/Jyear) ** px5 double parallax (arcsec) ** rv5 double radial velocity (km/s, positive = receding) ** ** Returned (all Hipparcos, epoch J2000.0): ** rh double RA (radians) ** dh double Dec (radians) ** drh double proper motion in RA (dRA/dt, rad/Jyear) ** ddh double proper motion in Dec (dDec/dt, rad/Jyear) ** pxh double parallax (arcsec) ** rvh double radial velocity (km/s, positive = receding) ** ** Notes: ** ** 1) This function transforms FK5 star positions and proper motions ** into the system of the Hipparcos catalog. ** ** 2) The proper motions in RA are dRA/dt rather than ** cos(Dec)*dRA/dt, and are per year rather than per century. ** ** 3) The FK5 to Hipparcos transformation is modeled as a pure ** rotation and spin; zonal errors in the FK5 catalog are not ** taken into account. ** ** 4) See also iauH2fk5, iauFk5hz, iauHfk5z. ** ** Called: ** iauStarpv star catalog data to space motion pv-vector ** iauFk5hip FK5 to Hipparcos rotation and spin ** iauRxp product of r-matrix and p-vector ** iauPxp vector product of two p-vectors ** iauPpp p-vector plus p-vector ** iauPvstar space motion pv-vector to star catalog data ** ** Reference: ** ** F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int i; double pv5[2][3], r5h[3][3], s5h[3], wxp[3], vv[3], pvh[2][3]; /* FK5 barycentric position/velocity pv-vector (normalized). */ iauStarpv(r5, d5, dr5, dd5, px5, rv5, pv5); /* FK5 to Hipparcos orientation matrix and spin vector. */ iauFk5hip(r5h, s5h); /* Make spin units per day instead of per year. */ for ( i = 0; i < 3; s5h[i++] /= 365.25 ); /* Orient the FK5 position into the Hipparcos system. */ iauRxp(r5h, pv5[0], pvh[0]); /* Apply spin to the position giving an extra space motion component. */ iauPxp(pv5[0], s5h, wxp); /* Add this component to the FK5 space motion. */ iauPpp(wxp, pv5[1], vv); /* Orient the FK5 space motion into the Hipparcos system. */ iauRxp(r5h, vv, pvh[1]); /* Hipparcos pv-vector to spherical. */ iauPvstar(pvh, rh, dh, drh, ddh, pxh, rvh); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fk5hip.c0000644000113000011300000001406313027221062014516 0ustar bellsbells#include "sofa.h" void iauFk5hip(double r5h[3][3], double s5h[3]) /* ** - - - - - - - - - - ** i a u F k 5 h i p ** - - - - - - - - - - ** ** FK5 to Hipparcos rotation and spin. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Returned: ** r5h double[3][3] r-matrix: FK5 rotation wrt Hipparcos (Note 2) ** s5h double[3] r-vector: FK5 spin wrt Hipparcos (Note 3) ** ** Notes: ** ** 1) This function models the FK5 to Hipparcos transformation as a ** pure rotation and spin; zonal errors in the FK5 catalogue are ** not taken into account. ** ** 2) The r-matrix r5h operates in the sense: ** ** P_Hipparcos = r5h x P_FK5 ** ** where P_FK5 is a p-vector in the FK5 frame, and P_Hipparcos is ** the equivalent Hipparcos p-vector. ** ** 3) The r-vector s5h represents the time derivative of the FK5 to ** Hipparcos rotation. The units are radians per year (Julian, ** TDB). ** ** Called: ** iauRv2m r-vector to r-matrix ** ** Reference: ** ** F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double v[3]; /* FK5 wrt Hipparcos orientation and spin (radians, radians/year) */ double epx, epy, epz; double omx, omy, omz; epx = -19.9e-3 * DAS2R; epy = -9.1e-3 * DAS2R; epz = 22.9e-3 * DAS2R; omx = -0.30e-3 * DAS2R; omy = 0.60e-3 * DAS2R; omz = 0.70e-3 * DAS2R; /* FK5 to Hipparcos orientation expressed as an r-vector. */ v[0] = epx; v[1] = epy; v[2] = epz; /* Re-express as an r-matrix. */ iauRv2m(v, r5h); /* Hipparcos wrt FK5 spin expressed as an r-vector. */ s5h[0] = omx; s5h[1] = omy; s5h[2] = omz; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fk5hz.c0000644000113000011300000001763513027221062014367 0ustar bellsbells#include "sofa.h" void iauFk5hz(double r5, double d5, double date1, double date2, double *rh, double *dh) /* ** - - - - - - - - - ** i a u F k 5 h z ** - - - - - - - - - ** ** Transform an FK5 (J2000.0) star position into the system of the ** Hipparcos catalogue, assuming zero Hipparcos proper motion. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** r5 double FK5 RA (radians), equinox J2000.0, at date ** d5 double FK5 Dec (radians), equinox J2000.0, at date ** date1,date2 double TDB date (Notes 1,2) ** ** Returned: ** rh double Hipparcos RA (radians) ** dh double Hipparcos Dec (radians) ** ** Notes: ** ** 1) This function converts a star position from the FK5 system to ** the Hipparcos system, in such a way that the Hipparcos proper ** motion is zero. Because such a star has, in general, a non-zero ** proper motion in the FK5 system, the function requires the date ** at which the position in the FK5 system was determined. ** ** 2) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 3) The FK5 to Hipparcos transformation is modeled as a pure ** rotation and spin; zonal errors in the FK5 catalogue are not ** taken into account. ** ** 4) The position returned by this function is in the Hipparcos ** reference system but at date date1+date2. ** ** 5) See also iauFk52h, iauH2fk5, iauHfk5z. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauFk5hip FK5 to Hipparcos rotation and spin ** iauSxp multiply p-vector by scalar ** iauRv2m r-vector to r-matrix ** iauTrxp product of transpose of r-matrix and p-vector ** iauPxp vector product of two p-vectors ** iauC2s p-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, p5e[3], r5h[3][3], s5h[3], vst[3], rst[3][3], p5[3], ph[3], w; /* Interval from given date to fundamental epoch J2000.0 (JY). */ t = - ((date1 - DJ00) + date2) / DJY; /* FK5 barycentric position vector. */ iauS2c(r5, d5, p5e); /* FK5 to Hipparcos orientation matrix and spin vector. */ iauFk5hip(r5h, s5h); /* Accumulated Hipparcos wrt FK5 spin over that interval. */ iauSxp(t, s5h, vst); /* Express the accumulated spin as a rotation matrix. */ iauRv2m(vst, rst); /* Derotate the vector's FK5 axes back to date. */ iauTrxp(rst, p5e, p5); /* Rotate the vector into the Hipparcos system. */ iauRxp(r5h, p5, ph); /* Hipparcos vector to spherical. */ iauC2s(ph, &w, dh); *rh = iauAnp(w); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fw2m.c0000644000113000011300000001516213027221062014204 0ustar bellsbells#include "sofa.h" void iauFw2m(double gamb, double phib, double psi, double eps, double r[3][3]) /* ** - - - - - - - - ** i a u F w 2 m ** - - - - - - - - ** ** Form rotation matrix given the Fukushima-Williams angles. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** gamb double F-W angle gamma_bar (radians) ** phib double F-W angle phi_bar (radians) ** psi double F-W angle psi (radians) ** eps double F-W angle epsilon (radians) ** ** Returned: ** r double[3][3] rotation matrix ** ** Notes: ** ** 1) Naming the following points: ** ** e = J2000.0 ecliptic pole, ** p = GCRS pole, ** E = ecliptic pole of date, ** and P = CIP, ** ** the four Fukushima-Williams angles are as follows: ** ** gamb = gamma = epE ** phib = phi = pE ** psi = psi = pEP ** eps = epsilon = EP ** ** 2) The matrix representing the combined effects of frame bias, ** precession and nutation is: ** ** NxPxB = R_1(-eps).R_3(-psi).R_1(phib).R_3(gamb) ** ** 3) Three different matrices can be constructed, depending on the ** supplied angles: ** ** o To obtain the nutation x precession x frame bias matrix, ** generate the four precession angles, generate the nutation ** components and add them to the psi_bar and epsilon_A angles, ** and call the present function. ** ** o To obtain the precession x frame bias matrix, generate the ** four precession angles and call the present function. ** ** o To obtain the frame bias matrix, generate the four precession ** angles for date J2000.0 and call the present function. ** ** The nutation-only and precession-only matrices can if necessary ** be obtained by combining these three appropriately. ** ** Called: ** iauIr initialize r-matrix to identity ** iauRz rotate around Z-axis ** iauRx rotate around X-axis ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Construct the matrix. */ iauIr(r); iauRz(gamb, r); iauRx(phib, r); iauRz(-psi, r); iauRx(-eps, r); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/fw2xy.c0000644000113000011300000001400313027221062014401 0ustar bellsbells#include "sofa.h" void iauFw2xy(double gamb, double phib, double psi, double eps, double *x, double *y) /* ** - - - - - - - - - ** i a u F w 2 x y ** - - - - - - - - - ** ** CIP X,Y given Fukushima-Williams bias-precession-nutation angles. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** gamb double F-W angle gamma_bar (radians) ** phib double F-W angle phi_bar (radians) ** psi double F-W angle psi (radians) ** eps double F-W angle epsilon (radians) ** ** Returned: ** x,y double CIP unit vector X,Y ** ** Notes: ** ** 1) Naming the following points: ** ** e = J2000.0 ecliptic pole, ** p = GCRS pole ** E = ecliptic pole of date, ** and P = CIP, ** ** the four Fukushima-Williams angles are as follows: ** ** gamb = gamma = epE ** phib = phi = pE ** psi = psi = pEP ** eps = epsilon = EP ** ** 2) The matrix representing the combined effects of frame bias, ** precession and nutation is: ** ** NxPxB = R_1(-epsA).R_3(-psi).R_1(phib).R_3(gamb) ** ** The returned values x,y are elements [2][0] and [2][1] of the ** matrix. Near J2000.0, they are essentially angles in radians. ** ** Called: ** iauFw2m F-W angles to r-matrix ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** ** This revision: 2013 September 2 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double r[3][3]; /* Form NxPxB matrix. */ iauFw2m(gamb, phib, psi, eps, r); /* Extract CIP X,Y. */ iauBpn2xy(r, x, y); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/g2icrs.c0000644000113000011300000002031513027221062014516 0ustar bellsbells#include "sofa.h" void iauG2icrs ( double dl, double db, double *dr, double *dd ) /* ** - - - - - - - - - - ** i a u G 2 i c r s ** - - - - - - - - - - ** ** Transformation from Galactic Coordinates to ICRS. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support routine. ** ** Given: ** dl double galactic longitude (radians) ** db double galactic latitude (radians) ** ** Returned: ** dr double ICRS right ascension (radians) ** dd double ICRS declination (radians) ** ** Notes: ** ** 1) The IAU 1958 system of Galactic coordinates was defined with ** respect to the now obsolete reference system FK4 B1950.0. When ** interpreting the system in a modern context, several factors have ** to be taken into account: ** ** . The inclusion in FK4 positions of the E-terms of aberration. ** ** . The distortion of the FK4 proper motion system by differential ** Galactic rotation. ** ** . The use of the B1950.0 equinox rather than the now-standard ** J2000.0. ** ** . The frame bias between ICRS and the J2000.0 mean place system. ** ** The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation ** matrix that transforms directly between ICRS and Galactic ** coordinates with the above factors taken into account. The ** matrix is derived from three angles, namely the ICRS coordinates ** of the Galactic pole and the longitude of the ascending node of ** the galactic equator on the ICRS equator. They are given in ** degrees to five decimal places and for canonical purposes are ** regarded as exact. In the Hipparcos Catalogue the matrix ** elements are given to 10 decimal places (about 20 microarcsec). ** In the present SOFA function the matrix elements have been ** recomputed from the canonical three angles and are given to 30 ** decimal places. ** ** 2) The inverse transformation is performed by the function iauIcrs2g. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** iauS2c spherical coordinates to unit vector ** iauTrxp product of transpose of r-matrix and p-vector ** iauC2s p-vector to spherical ** ** Reference: ** Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho ** catalogues. Astrometric and photometric star catalogues ** derived from the ESA Hipparcos Space Astrometry Mission. ESA ** Publications Division, Noordwijk, Netherlands. ** ** This revision: 2015 January 20 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double v1[3], v2[3]; /* ** L2,B2 system of galactic coordinates in the form presented in the ** Hipparcos Catalogue. In degrees: ** ** P = 192.85948 right ascension of the Galactic north pole in ICRS ** Q = 27.12825 declination of the Galactic north pole in ICRS ** R = 32.93192 longitude of the ascending node of the Galactic ** plane on the ICRS equator ** ** ICRS to galactic rotation matrix, obtained by computing ** R_3(-R) R_1(pi/2-Q) R_3(pi/2+P) to the full precision shown: */ double r[3][3] = { { -0.054875560416215368492398900454, -0.873437090234885048760383168409, -0.483835015548713226831774175116 }, { +0.494109427875583673525222371358, -0.444829629960011178146614061616, +0.746982244497218890527388004556 }, { -0.867666149019004701181616534570, -0.198076373431201528180486091412, +0.455983776175066922272100478348 } }; /* Spherical to Cartesian. */ iauS2c(dl, db, v1); /* Galactic to ICRS. */ iauTrxp(r, v1, v2); /* Cartesian to spherical. */ iauC2s(v2, dr, dd); /* Express in conventional ranges. */ *dr = iauAnp(*dr); *dd = iauAnpm(*dd); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gc2gd.c0000644000113000011300000001506713027221062014323 0ustar bellsbells#include "sofa.h" int iauGc2gd ( int n, double xyz[3], double *elong, double *phi, double *height ) /* ** - - - - - - - - - ** i a u G c 2 g d ** - - - - - - - - - ** ** Transform geocentric coordinates to geodetic using the specified ** reference ellipsoid. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical transformation. ** ** Given: ** n int ellipsoid identifier (Note 1) ** xyz double[3] geocentric vector (Note 2) ** ** Returned: ** elong double longitude (radians, east +ve, Note 3) ** phi double latitude (geodetic, radians, Note 3) ** height double height above ellipsoid (geodetic, Notes 2,3) ** ** Returned (function value): ** int status: 0 = OK ** -1 = illegal identifier (Note 3) ** -2 = internal error (Note 3) ** ** Notes: ** ** 1) The identifier n is a number that specifies the choice of ** reference ellipsoid. The following are supported: ** ** n ellipsoid ** ** 1 WGS84 ** 2 GRS80 ** 3 WGS72 ** ** The n value has no significance outside the SOFA software. For ** convenience, symbols WGS84 etc. are defined in sofam.h. ** ** 2) The geocentric vector (xyz, given) and height (height, returned) ** are in meters. ** ** 3) An error status -1 means that the identifier n is illegal. An ** error status -2 is theoretically impossible. In all error cases, ** all three results are set to -1e9. ** ** 4) The inverse transformation is performed in the function iauGd2gc. ** ** Called: ** iauEform Earth reference ellipsoids ** iauGc2gde geocentric to geodetic transformation, general ** ** This revision: 2013 September 1 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j; double a, f; /* Obtain reference ellipsoid parameters. */ j = iauEform ( n, &a, &f ); /* If OK, transform x,y,z to longitude, geodetic latitude, height. */ if ( j == 0 ) { j = iauGc2gde ( a, f, xyz, elong, phi, height ); if ( j < 0 ) j = -2; } /* Deal with any errors. */ if ( j < 0 ) { *elong = -1e9; *phi = -1e9; *height = -1e9; } /* Return the status. */ return j; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gc2gde.c0000644000113000011300000002022313027221062014456 0ustar bellsbells#include "sofa.h" int iauGc2gde ( double a, double f, double xyz[3], double *elong, double *phi, double *height ) /* ** - - - - - - - - - - ** i a u G c 2 g d e ** - - - - - - - - - - ** ** Transform geocentric coordinates to geodetic for a reference ** ellipsoid of specified form. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** a double equatorial radius (Notes 2,4) ** f double flattening (Note 3) ** xyz double[3] geocentric vector (Note 4) ** ** Returned: ** elong double longitude (radians, east +ve) ** phi double latitude (geodetic, radians) ** height double height above ellipsoid (geodetic, Note 4) ** ** Returned (function value): ** int status: 0 = OK ** -1 = illegal f ** -2 = illegal a ** ** Notes: ** ** 1) This function is based on the GCONV2H Fortran subroutine by ** Toshio Fukushima (see reference). ** ** 2) The equatorial radius, a, can be in any units, but meters is ** the conventional choice. ** ** 3) The flattening, f, is (for the Earth) a value around 0.00335, ** i.e. around 1/298. ** ** 4) The equatorial radius, a, and the geocentric vector, xyz, ** must be given in the same units, and determine the units of ** the returned height, height. ** ** 5) If an error occurs (status < 0), elong, phi and height are ** unchanged. ** ** 6) The inverse transformation is performed in the function ** iauGd2gce. ** ** 7) The transformation for a standard ellipsoid (such as WGS84) can ** more conveniently be performed by calling iauGc2gd, which uses a ** numerical code to identify the required A and F values. ** ** Reference: ** ** Fukushima, T., "Transformation from Cartesian to geodetic ** coordinates accelerated by Halley's method", J.Geodesy (2006) ** 79: 689-693 ** ** This revision: 2014 November 7 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double aeps2, e2, e4t, ec2, ec, b, x, y, z, p2, absz, p, s0, pn, zc, c0, c02, c03, s02, s03, a02, a0, a03, d0, f0, b0, s1, cc, s12, cc2; /* ------------- */ /* Preliminaries */ /* ------------- */ /* Validate ellipsoid parameters. */ if ( f < 0.0 || f >= 1.0 ) return -1; if ( a <= 0.0 ) return -2; /* Functions of ellipsoid parameters (with further validation of f). */ aeps2 = a*a * 1e-32; e2 = (2.0 - f) * f; e4t = e2*e2 * 1.5; ec2 = 1.0 - e2; if ( ec2 <= 0.0 ) return -1; ec = sqrt(ec2); b = a * ec; /* Cartesian components. */ x = xyz[0]; y = xyz[1]; z = xyz[2]; /* Distance from polar axis squared. */ p2 = x*x + y*y; /* Longitude. */ *elong = p2 > 0.0 ? atan2(y, x) : 0.0; /* Unsigned z-coordinate. */ absz = fabs(z); /* Proceed unless polar case. */ if ( p2 > aeps2 ) { /* Distance from polar axis. */ p = sqrt(p2); /* Normalization. */ s0 = absz / a; pn = p / a; zc = ec * s0; /* Prepare Newton correction factors. */ c0 = ec * pn; c02 = c0 * c0; c03 = c02 * c0; s02 = s0 * s0; s03 = s02 * s0; a02 = c02 + s02; a0 = sqrt(a02); a03 = a02 * a0; d0 = zc*a03 + e2*s03; f0 = pn*a03 - e2*c03; /* Prepare Halley correction factor. */ b0 = e4t * s02 * c02 * pn * (a0 - ec); s1 = d0*f0 - b0*s0; cc = ec * (f0*f0 - b0*c0); /* Evaluate latitude and height. */ *phi = atan(s1/cc); s12 = s1 * s1; cc2 = cc * cc; *height = (p*cc + absz*s1 - a * sqrt(ec2*s12 + cc2)) / sqrt(s12 + cc2); } else { /* Exception: pole. */ *phi = DPI / 2.0; *height = absz - b; } /* Restore sign of latitude. */ if ( z < 0 ) *phi = -*phi; /* OK status. */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gd2gc.c0000644000113000011300000001520013027221062014310 0ustar bellsbells#include "sofa.h" int iauGd2gc ( int n, double elong, double phi, double height, double xyz[3] ) /* ** - - - - - - - - - ** i a u G d 2 g c ** - - - - - - - - - ** ** Transform geodetic coordinates to geocentric using the specified ** reference ellipsoid. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical transformation. ** ** Given: ** n int ellipsoid identifier (Note 1) ** elong double longitude (radians, east +ve) ** phi double latitude (geodetic, radians, Note 3) ** height double height above ellipsoid (geodetic, Notes 2,3) ** ** Returned: ** xyz double[3] geocentric vector (Note 2) ** ** Returned (function value): ** int status: 0 = OK ** -1 = illegal identifier (Note 3) ** -2 = illegal case (Note 3) ** ** Notes: ** ** 1) The identifier n is a number that specifies the choice of ** reference ellipsoid. The following are supported: ** ** n ellipsoid ** ** 1 WGS84 ** 2 GRS80 ** 3 WGS72 ** ** The n value has no significance outside the SOFA software. For ** convenience, symbols WGS84 etc. are defined in sofam.h. ** ** 2) The height (height, given) and the geocentric vector (xyz, ** returned) are in meters. ** ** 3) No validation is performed on the arguments elong, phi and ** height. An error status -1 means that the identifier n is ** illegal. An error status -2 protects against cases that would ** lead to arithmetic exceptions. In all error cases, xyz is set ** to zeros. ** ** 4) The inverse transformation is performed in the function iauGc2gd. ** ** Called: ** iauEform Earth reference ellipsoids ** iauGd2gce geodetic to geocentric transformation, general ** iauZp zero p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j; double a, f; /* Obtain reference ellipsoid parameters. */ j = iauEform ( n, &a, &f ); /* If OK, transform longitude, geodetic latitude, height to x,y,z. */ if ( j == 0 ) { j = iauGd2gce ( a, f, elong, phi, height, xyz ); if ( j != 0 ) j = -2; } /* Deal with any errors. */ if ( j != 0 ) iauZp ( xyz ); /* Return the status. */ return j; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gd2gce.c0000644000113000011300000001547113027221062014467 0ustar bellsbells#include "sofa.h" int iauGd2gce ( double a, double f, double elong, double phi, double height, double xyz[3] ) /* ** - - - - - - - - - - ** i a u G d 2 g c e ** - - - - - - - - - - ** ** Transform geodetic coordinates to geocentric for a reference ** ellipsoid of specified form. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** a double equatorial radius (Notes 1,4) ** f double flattening (Notes 2,4) ** elong double longitude (radians, east +ve) ** phi double latitude (geodetic, radians, Note 4) ** height double height above ellipsoid (geodetic, Notes 3,4) ** ** Returned: ** xyz double[3] geocentric vector (Note 3) ** ** Returned (function value): ** int status: 0 = OK ** -1 = illegal case (Note 4) ** Notes: ** ** 1) The equatorial radius, a, can be in any units, but meters is ** the conventional choice. ** ** 2) The flattening, f, is (for the Earth) a value around 0.00335, ** i.e. around 1/298. ** ** 3) The equatorial radius, a, and the height, height, must be ** given in the same units, and determine the units of the ** returned geocentric vector, xyz. ** ** 4) No validation is performed on individual arguments. The error ** status -1 protects against (unrealistic) cases that would lead ** to arithmetic exceptions. If an error occurs, xyz is unchanged. ** ** 5) The inverse transformation is performed in the function ** iauGc2gde. ** ** 6) The transformation for a standard ellipsoid (such as WGS84) can ** more conveniently be performed by calling iauGd2gc, which uses a ** numerical code to identify the required a and f values. ** ** References: ** ** Green, R.M., Spherical Astronomy, Cambridge University Press, ** (1985) Section 4.5, p96. ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 4.22, p202. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double sp, cp, w, d, ac, as, r; /* Functions of geodetic latitude. */ sp = sin(phi); cp = cos(phi); w = 1.0 - f; w = w * w; d = cp*cp + w*sp*sp; if ( d <= 0.0 ) return -1; ac = a / sqrt(d); as = w * ac; /* Geocentric vector. */ r = (ac + height) * cp; xyz[0] = r * cos(elong); xyz[1] = r * sin(elong); xyz[2] = (as + height) * sp; /* Success. */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gmst00.c0000644000113000011300000001702313027221062014441 0ustar bellsbells#include "sofa.h" double iauGmst00(double uta, double utb, double tta, double ttb) /* ** - - - - - - - - - - ** i a u G m s t 0 0 ** - - - - - - - - - - ** ** Greenwich mean sidereal time (model consistent with IAU 2000 ** resolutions). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** tta,ttb double TT as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich mean sidereal time (radians) ** ** Notes: ** ** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both ** Julian Dates, apportioned in any convenient way between the ** argument pairs. For example, JD=2450123.7 could be expressed in ** any of these ways, among others: ** ** Part A Part B ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable (in the case of UT; the TT is not at all critical ** in this respect). The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** Rotation Angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation ** and TT to predict the effects of precession. If UT1 is used for ** both purposes, errors of order 100 microarcseconds result. ** ** 3) This GMST is compatible with the IAU 2000 resolutions and must be ** used only in conjunction with other IAU 2000 compatible ** components such as precession-nutation and equation of the ** equinoxes. ** ** 4) The result is returned in the range 0 to 2pi. ** ** 5) The algorithm is from Capitaine et al. (2003) and IERS ** Conventions 2003. ** ** Called: ** iauEra00 Earth rotation angle, IAU 2000 ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, gmst; /* TT Julian centuries since J2000.0. */ t = ((tta - DJ00) + ttb) / DJC; /* Greenwich Mean Sidereal Time, IAU 2000. */ gmst = iauAnp(iauEra00(uta, utb) + ( 0.014506 + ( 4612.15739966 + ( 1.39667721 + ( -0.00009344 + ( 0.00001882 ) * t) * t) * t) * t) * DAS2R); return gmst; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gmst06.c0000644000113000011300000001625113027221062014451 0ustar bellsbells#include "sofa.h" double iauGmst06(double uta, double utb, double tta, double ttb) /* ** - - - - - - - - - - ** i a u G m s t 0 6 ** - - - - - - - - - - ** ** Greenwich mean sidereal time (consistent with IAU 2006 precession). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** tta,ttb double TT as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich mean sidereal time (radians) ** ** Notes: ** ** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both ** Julian Dates, apportioned in any convenient way between the ** argument pairs. For example, JD=2450123.7 could be expressed in ** any of these ways, among others: ** ** Part A Part B ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable (in the case of UT; the TT is not at all critical ** in this respect). The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** rotation angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation ** and TT to predict the effects of precession. If UT1 is used for ** both purposes, errors of order 100 microarcseconds result. ** ** 3) This GMST is compatible with the IAU 2006 precession and must not ** be used with other precession models. ** ** 4) The result is returned in the range 0 to 2pi. ** ** Called: ** iauEra00 Earth rotation angle, IAU 2000 ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** Capitaine, N., Wallace, P.T. & Chapront, J., 2005, ** Astron.Astrophys. 432, 355 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, gmst; /* TT Julian centuries since J2000.0. */ t = ((tta - DJ00) + ttb) / DJC; /* Greenwich mean sidereal time, IAU 2006. */ gmst = iauAnp(iauEra00(uta, utb) + ( 0.014506 + ( 4612.156534 + ( 1.3915817 + ( -0.00000044 + ( -0.000029956 + ( -0.0000000368 ) * t) * t) * t) * t) * t) * DAS2R); return gmst; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gmst82.c0000644000113000011300000001707313027221062014460 0ustar bellsbells#include "sofa.h" double iauGmst82(double dj1, double dj2) /* ** - - - - - - - - - - ** i a u G m s t 8 2 ** - - - - - - - - - - ** ** Universal Time to Greenwich mean sidereal time (IAU 1982 model). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** dj1,dj2 double UT1 Julian Date (see note) ** ** Returned (function value): ** double Greenwich mean sidereal time (radians) ** ** Notes: ** ** 1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any ** convenient way between the arguments dj1 and dj2. For example, ** JD(UT1)=2450123.7 could be expressed in any of these ways, ** among others: ** ** dj1 dj2 ** ** 2450123.7 0 (JD method) ** 2451545 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. The date & time method is ** best matched to the algorithm used: maximum accuracy (or, at ** least, minimum noise) is delivered when the dj1 argument is for ** 0hrs UT1 on the day in question and the dj2 argument lies in the ** range 0 to 1, or vice versa. ** ** 2) The algorithm is based on the IAU 1982 expression. This is ** always described as giving the GMST at 0 hours UT1. In fact, it ** gives the difference between the GMST and the UT, the steady ** 4-minutes-per-day drawing-ahead of ST with respect to UT. When ** whole days are ignored, the expression happens to equal the GMST ** at 0 hours UT1 each day. ** ** 3) In this function, the entire UT1 (the sum of the two arguments ** dj1 and dj2) is used directly as the argument for the standard ** formula, the constant term of which is adjusted by 12 hours to ** take account of the noon phasing of Julian Date. The UT1 is then ** added, but omitting whole days to conserve accuracy. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Transactions of the International Astronomical Union, ** XVIII B, 67 (1983). ** ** Aoki et al., Astron. Astrophys. 105, 359-361 (1982). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Coefficients of IAU 1982 GMST-UT1 model */ double A = 24110.54841 - DAYSEC / 2.0; double B = 8640184.812866; double C = 0.093104; double D = -6.2e-6; /* Note: the first constant, A, has to be adjusted by 12 hours */ /* because the UT1 is supplied as a Julian date, which begins */ /* at noon. */ double d1, d2, t, f, gmst; /* Julian centuries since fundamental epoch. */ if (dj1 < dj2) { d1 = dj1; d2 = dj2; } else { d1 = dj2; d2 = dj1; } t = (d1 + (d2 - DJ00)) / DJC; /* Fractional part of JD(UT1), in seconds. */ f = DAYSEC * (fmod(d1, 1.0) + fmod(d2, 1.0)); /* GMST at this UT1. */ gmst = iauAnp(DS2R * ((A + (B + (C + D * t) * t) * t) + f)); return gmst; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gst00a.c0000644000113000011300000001645613027221062014436 0ustar bellsbells#include "sofa.h" double iauGst00a(double uta, double utb, double tta, double ttb) /* ** - - - - - - - - - - ** i a u G s t 0 0 a ** - - - - - - - - - - ** ** Greenwich apparent sidereal time (consistent with IAU 2000 ** resolutions). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** tta,ttb double TT as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich apparent sidereal time (radians) ** ** Notes: ** ** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both ** Julian Dates, apportioned in any convenient way between the ** argument pairs. For example, JD=2450123.7 could be expressed in ** any of these ways, among others: ** ** Part A Part B ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable (in the case of UT; the TT is not at all critical ** in this respect). The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** Rotation Angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation ** and TT to predict the effects of precession-nutation. If UT1 is ** used for both purposes, errors of order 100 microarcseconds ** result. ** ** 3) This GAST is compatible with the IAU 2000 resolutions and must be ** used only in conjunction with other IAU 2000 compatible ** components such as precession-nutation. ** ** 4) The result is returned in the range 0 to 2pi. ** ** 5) The algorithm is from Capitaine et al. (2003) and IERS ** Conventions 2003. ** ** Called: ** iauGmst00 Greenwich mean sidereal time, IAU 2000 ** iauEe00a equation of the equinoxes, IAU 2000A ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double gmst00, ee00a, gst; gmst00 = iauGmst00(uta, utb, tta, ttb); ee00a = iauEe00a(tta, ttb); gst = iauAnp(gmst00 + ee00a); return gst; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gst00b.c0000644000113000011300000001713213027221062014427 0ustar bellsbells#include "sofa.h" double iauGst00b(double uta, double utb) /* ** - - - - - - - - - - ** i a u G s t 0 0 b ** - - - - - - - - - - ** ** Greenwich apparent sidereal time (consistent with IAU 2000 ** resolutions but using the truncated nutation model IAU 2000B). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich apparent sidereal time (radians) ** ** Notes: ** ** 1) The UT1 date uta+utb is a Julian Date, apportioned in any ** convenient way between the argument pair. For example, ** JD=2450123.7 could be expressed in any of these ways, among ** others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** Rotation Angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) The result is compatible with the IAU 2000 resolutions, except ** that accuracy has been compromised for the sake of speed and ** convenience in two respects: ** ** . UT is used instead of TDB (or TT) to compute the precession ** component of GMST and the equation of the equinoxes. This ** results in errors of order 0.1 mas at present. ** ** . The IAU 2000B abridged nutation model (McCarthy & Luzum, 2001) ** is used, introducing errors of up to 1 mas. ** ** 3) This GAST is compatible with the IAU 2000 resolutions and must be ** used only in conjunction with other IAU 2000 compatible ** components such as precession-nutation. ** ** 4) The result is returned in the range 0 to 2pi. ** ** 5) The algorithm is from Capitaine et al. (2003) and IERS ** Conventions 2003. ** ** Called: ** iauGmst00 Greenwich mean sidereal time, IAU 2000 ** iauEe00b equation of the equinoxes, IAU 2000B ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** McCarthy, D.D. & Luzum, B.J., "An abridged model of the ** precession-nutation of the celestial pole", Celestial Mechanics & ** Dynamical Astronomy, 85, 37-49 (2003) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double gmst00, ee00b, gst; gmst00 = iauGmst00(uta, utb, uta, utb); ee00b = iauEe00b(uta, utb); gst = iauAnp(gmst00 + ee00b); return gst; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gst06a.c0000644000113000011300000001600613027221062014433 0ustar bellsbells#include "sofa.h" double iauGst06a(double uta, double utb, double tta, double ttb) /* ** - - - - - - - - - - ** i a u G s t 0 6 a ** - - - - - - - - - - ** ** Greenwich apparent sidereal time (consistent with IAU 2000 and 2006 ** resolutions). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** tta,ttb double TT as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich apparent sidereal time (radians) ** ** Notes: ** ** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both ** Julian Dates, apportioned in any convenient way between the ** argument pairs. For example, JD=2450123.7 could be expressed in ** any of these ways, among others: ** ** Part A Part B ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable (in the case of UT; the TT is not at all critical ** in this respect). The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** rotation angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation ** and TT to predict the effects of precession-nutation. If UT1 is ** used for both purposes, errors of order 100 microarcseconds ** result. ** ** 3) This GAST is compatible with the IAU 2000/2006 resolutions and ** must be used only in conjunction with IAU 2006 precession and ** IAU 2000A nutation. ** ** 4) The result is returned in the range 0 to 2pi. ** ** Called: ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauGst06 Greenwich apparent ST, IAU 2006, given NPB matrix ** ** Reference: ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rnpb[3][3], gst; /* Classical nutation x precession x bias matrix, IAU 2000A. */ iauPnm06a(tta, ttb, rnpb); /* Greenwich apparent sidereal time. */ gst = iauGst06(uta, utb, tta, ttb, rnpb); return gst; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gst06.c0000644000113000011300000001656013027221062014277 0ustar bellsbells#include "sofa.h" double iauGst06(double uta, double utb, double tta, double ttb, double rnpb[3][3]) /* ** - - - - - - - - - ** i a u G s t 0 6 ** - - - - - - - - - ** ** Greenwich apparent sidereal time, IAU 2006, given the NPB matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** tta,ttb double TT as a 2-part Julian Date (Notes 1,2) ** rnpb double[3][3] nutation x precession x bias matrix ** ** Returned (function value): ** double Greenwich apparent sidereal time (radians) ** ** Notes: ** ** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both ** Julian Dates, apportioned in any convenient way between the ** argument pairs. For example, JD=2450123.7 could be expressed in ** any of these ways, among others: ** ** Part A Part B ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable (in the case of UT; the TT is not at all critical ** in this respect). The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** rotation angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation ** and TT to predict the effects of precession-nutation. If UT1 is ** used for both purposes, errors of order 100 microarcseconds ** result. ** ** 3) Although the function uses the IAU 2006 series for s+XY/2, it is ** otherwise independent of the precession-nutation model and can in ** practice be used with any equinox-based NPB matrix. ** ** 4) The result is returned in the range 0 to 2pi. ** ** Called: ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** iauAnp normalize angle into range 0 to 2pi ** iauEra00 Earth rotation angle, IAU 2000 ** iauEors equation of the origins, given NPB matrix and s ** ** Reference: ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double x, y, s, era, eors, gst; /* Extract CIP coordinates. */ iauBpn2xy(rnpb, &x, &y); /* The CIO locator, s. */ s = iauS06(tta, ttb, x, y); /* Greenwich apparent sidereal time. */ era = iauEra00(uta, utb); eors = iauEors(rnpb, s); gst = iauAnp(era - eors); return gst; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/gst94.c0000644000113000011300000001567313027221062014312 0ustar bellsbells#include "sofa.h" double iauGst94(double uta, double utb) /* ** - - - - - - - - - ** i a u G s t 9 4 ** - - - - - - - - - ** ** Greenwich apparent sidereal time (consistent with IAU 1982/94 ** resolutions). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich apparent sidereal time (radians) ** ** Notes: ** ** 1) The UT1 date uta+utb is a Julian Date, apportioned in any ** convenient way between the argument pair. For example, ** JD=2450123.7 could be expressed in any of these ways, among ** others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** Rotation Angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) The result is compatible with the IAU 1982 and 1994 resolutions, ** except that accuracy has been compromised for the sake of ** convenience in that UT is used instead of TDB (or TT) to compute ** the equation of the equinoxes. ** ** 3) This GAST must be used only in conjunction with contemporaneous ** IAU standards such as 1976 precession, 1980 obliquity and 1982 ** nutation. It is not compatible with the IAU 2000 resolutions. ** ** 4) The result is returned in the range 0 to 2pi. ** ** Called: ** iauGmst82 Greenwich mean sidereal time, IAU 1982 ** iauEqeq94 equation of the equinoxes, IAU 1994 ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** IAU Resolution C7, Recommendation 3 (1994) ** ** This revision: 2008 May 16 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double gmst82, eqeq94, gst; gmst82 = iauGmst82(uta, utb); eqeq94 = iauEqeq94(uta, utb); gst = iauAnp(gmst82 + eqeq94); return gst; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/h2fk5.c0000644000113000011300000001667313027221062014260 0ustar bellsbells#include "sofa.h" void iauH2fk5(double rh, double dh, double drh, double ddh, double pxh, double rvh, double *r5, double *d5, double *dr5, double *dd5, double *px5, double *rv5) /* ** - - - - - - - - - ** i a u H 2 f k 5 ** - - - - - - - - - ** ** Transform Hipparcos star data into the FK5 (J2000.0) system. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given (all Hipparcos, epoch J2000.0): ** rh double RA (radians) ** dh double Dec (radians) ** drh double proper motion in RA (dRA/dt, rad/Jyear) ** ddh double proper motion in Dec (dDec/dt, rad/Jyear) ** pxh double parallax (arcsec) ** rvh double radial velocity (km/s, positive = receding) ** ** Returned (all FK5, equinox J2000.0, epoch J2000.0): ** r5 double RA (radians) ** d5 double Dec (radians) ** dr5 double proper motion in RA (dRA/dt, rad/Jyear) ** dd5 double proper motion in Dec (dDec/dt, rad/Jyear) ** px5 double parallax (arcsec) ** rv5 double radial velocity (km/s, positive = receding) ** ** Notes: ** ** 1) This function transforms Hipparcos star positions and proper ** motions into FK5 J2000.0. ** ** 2) The proper motions in RA are dRA/dt rather than ** cos(Dec)*dRA/dt, and are per year rather than per century. ** ** 3) The FK5 to Hipparcos transformation is modeled as a pure ** rotation and spin; zonal errors in the FK5 catalog are not ** taken into account. ** ** 4) See also iauFk52h, iauFk5hz, iauHfk5z. ** ** Called: ** iauStarpv star catalog data to space motion pv-vector ** iauFk5hip FK5 to Hipparcos rotation and spin ** iauRv2m r-vector to r-matrix ** iauRxp product of r-matrix and p-vector ** iauTrxp product of transpose of r-matrix and p-vector ** iauPxp vector product of two p-vectors ** iauPmp p-vector minus p-vector ** iauPvstar space motion pv-vector to star catalog data ** ** Reference: ** ** F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int i; double pvh[2][3], r5h[3][3], s5h[3], sh[3], wxp[3], vv[3], pv5[2][3]; /* Hipparcos barycentric position/velocity pv-vector (normalized). */ iauStarpv(rh, dh, drh, ddh, pxh, rvh, pvh); /* FK5 to Hipparcos orientation matrix and spin vector. */ iauFk5hip(r5h, s5h); /* Make spin units per day instead of per year. */ for ( i = 0; i < 3; s5h[i++] /= 365.25 ); /* Orient the spin into the Hipparcos system. */ iauRxp(r5h, s5h, sh); /* De-orient the Hipparcos position into the FK5 system. */ iauTrxp(r5h, pvh[0], pv5[0]); /* Apply spin to the position giving an extra space motion component. */ iauPxp(pvh[0], sh, wxp); /* Subtract this component from the Hipparcos space motion. */ iauPmp(pvh[1], wxp, vv); /* De-orient the Hipparcos space motion into the FK5 system. */ iauTrxp(r5h, vv, pv5[1]); /* FK5 pv-vector to spherical. */ iauPvstar(pv5, r5, d5, dr5, dd5, px5, rv5); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/hfk5z.c0000644000113000011300000002075413027221062014363 0ustar bellsbells#include "sofa.h" void iauHfk5z(double rh, double dh, double date1, double date2, double *r5, double *d5, double *dr5, double *dd5) /* ** - - - - - - - - - ** i a u H f k 5 z ** - - - - - - - - - ** ** Transform a Hipparcos star position into FK5 J2000.0, assuming ** zero Hipparcos proper motion. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rh double Hipparcos RA (radians) ** dh double Hipparcos Dec (radians) ** date1,date2 double TDB date (Note 1) ** ** Returned (all FK5, equinox J2000.0, date date1+date2): ** r5 double RA (radians) ** d5 double Dec (radians) ** dr5 double FK5 RA proper motion (rad/year, Note 4) ** dd5 double Dec proper motion (rad/year, Note 4) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 3) The FK5 to Hipparcos transformation is modeled as a pure rotation ** and spin; zonal errors in the FK5 catalogue are not taken into ** account. ** ** 4) It was the intention that Hipparcos should be a close ** approximation to an inertial frame, so that distant objects have ** zero proper motion; such objects have (in general) non-zero ** proper motion in FK5, and this function returns those fictitious ** proper motions. ** ** 5) The position returned by this function is in the FK5 J2000.0 ** reference system but at date date1+date2. ** ** 6) See also iauFk52h, iauH2fk5, iauFk5zhz. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauFk5hip FK5 to Hipparcos rotation and spin ** iauRxp product of r-matrix and p-vector ** iauSxp multiply p-vector by scalar ** iauRxr product of two r-matrices ** iauTrxp product of transpose of r-matrix and p-vector ** iauPxp vector product of two p-vectors ** iauPv2s pv-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, ph[3], r5h[3][3], s5h[3], sh[3], vst[3], rst[3][3], r5ht[3][3], pv5e[2][3], vv[3], w, r, v; /* Time interval from fundamental epoch J2000.0 to given date (JY). */ t = ((date1 - DJ00) + date2) / DJY; /* Hipparcos barycentric position vector (normalized). */ iauS2c(rh, dh, ph); /* FK5 to Hipparcos orientation matrix and spin vector. */ iauFk5hip(r5h, s5h); /* Rotate the spin into the Hipparcos system. */ iauRxp(r5h, s5h, sh); /* Accumulated Hipparcos wrt FK5 spin over that interval. */ iauSxp(t, s5h, vst); /* Express the accumulated spin as a rotation matrix. */ iauRv2m(vst, rst); /* Rotation matrix: accumulated spin, then FK5 to Hipparcos. */ iauRxr(r5h, rst, r5ht); /* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */ iauTrxp(r5ht, ph, pv5e[0]); /* Apply spin to the position giving a space motion. */ iauPxp(sh, ph, vv); /* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */ iauTrxp(r5ht, vv, pv5e[1]); /* FK5 position/velocity pv-vector to spherical. */ iauPv2s(pv5e, &w, d5, &r, dr5, dd5, &v); *r5 = iauAnp(w); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/icrs2g.c0000644000113000011300000002027713027221062014525 0ustar bellsbells#include "sofa.h" void iauIcrs2g ( double dr, double dd, double *dl, double *db ) /* ** - - - - - - - - - - ** i a u I c r s 2 g ** - - - - - - - - - - ** ** Transformation from ICRS to Galactic Coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support routine. ** ** Given: ** dr double ICRS right ascension (radians) ** dd double ICRS declination (radians) ** ** Returned: ** dl double galactic longitude (radians) ** db double galactic latitude (radians) ** ** Notes: ** ** 1) The IAU 1958 system of Galactic coordinates was defined with ** respect to the now obsolete reference system FK4 B1950.0. When ** interpreting the system in a modern context, several factors have ** to be taken into account: ** ** . The inclusion in FK4 positions of the E-terms of aberration. ** ** . The distortion of the FK4 proper motion system by differential ** Galactic rotation. ** ** . The use of the B1950.0 equinox rather than the now-standard ** J2000.0. ** ** . The frame bias between ICRS and the J2000.0 mean place system. ** ** The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation ** matrix that transforms directly between ICRS and Galactic ** coordinates with the above factors taken into account. The ** matrix is derived from three angles, namely the ICRS coordinates ** of the Galactic pole and the longitude of the ascending node of ** the galactic equator on the ICRS equator. They are given in ** degrees to five decimal places and for canonical purposes are ** regarded as exact. In the Hipparcos Catalogue the matrix ** elements are given to 10 decimal places (about 20 microarcsec). ** In the present SOFA function the matrix elements have been ** recomputed from the canonical three angles and are given to 30 ** decimal places. ** ** 2) The inverse transformation is performed by the function iauG2icrs. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** iauS2c spherical coordinates to unit vector ** iauRxp product of r-matrix and p-vector ** iauC2s p-vector to spherical ** ** Reference: ** Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho ** catalogues. Astrometric and photometric star catalogues ** derived from the ESA Hipparcos Space Astrometry Mission. ESA ** Publications Division, Noordwijk, Netherlands. ** ** This revision: 2015 January 20 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double v1[3], v2[3]; /* ** L2,B2 system of galactic coordinates in the form presented in the ** Hipparcos Catalogue. In degrees: ** ** P = 192.85948 right ascension of the Galactic north pole in ICRS ** Q = 27.12825 declination of the Galactic north pole in ICRS ** R = 32.93192 longitude of the ascending node of the Galactic ** plane on the ICRS equator ** ** ICRS to galactic rotation matrix, obtained by computing ** R_3(-R) R_1(pi/2-Q) R_3(pi/2+P) to the full precision shown: */ double r[3][3] = { { -0.054875560416215368492398900454, -0.873437090234885048760383168409, -0.483835015548713226831774175116 }, { +0.494109427875583673525222371358, -0.444829629960011178146614061616, +0.746982244497218890527388004556 }, { -0.867666149019004701181616534570, -0.198076373431201528180486091412, +0.455983776175066922272100478348 } }; /* Spherical to Cartesian. */ iauS2c(dr, dd, v1); /* ICRS to Galactic. */ iauRxp(r, v1, v2); /* Cartesian to spherical. */ iauC2s(v2, dl, db); /* Express in conventional ranges. */ *dl = iauAnp(*dl); *db = iauAnpm(*db); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ir.c0000644000113000011300000001155213027221062013742 0ustar bellsbells#include "sofa.h" void iauIr(double r[3][3]) /* ** - - - - - - ** i a u I r ** - - - - - - ** ** Initialize an r-matrix to the identity matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Returned: ** r double[3][3] r-matrix ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { r[0][0] = 1.0; r[0][1] = 0.0; r[0][2] = 0.0; r[1][0] = 0.0; r[1][1] = 1.0; r[1][2] = 0.0; r[2][0] = 0.0; r[2][1] = 0.0; r[2][2] = 1.0; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/jd2cal.c0000644000113000011300000001611413027221062014466 0ustar bellsbells#include "sofa.h" int iauJd2cal(double dj1, double dj2, int *iy, int *im, int *id, double *fd) /* ** - - - - - - - - - - ** i a u J d 2 c a l ** - - - - - - - - - - ** ** Julian Date to Gregorian year, month, day, and fraction of a day. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** dj1,dj2 double Julian Date (Notes 1, 2) ** ** Returned (arguments): ** iy int year ** im int month ** id int day ** fd double fraction of day ** ** Returned (function value): ** int status: ** 0 = OK ** -1 = unacceptable date (Note 3) ** ** Notes: ** ** 1) The earliest valid date is -68569.5 (-4900 March 1). The ** largest value accepted is 1e9. ** ** 2) The Julian Date is apportioned in any convenient way between ** the arguments dj1 and dj2. For example, JD=2450123.7 could ** be expressed in any of these ways, among others: ** ** dj1 dj2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** 3) In early eras the conversion is from the "proleptic Gregorian ** calendar"; no account is taken of the date(s) of adoption of ** the Gregorian calendar, nor is the AD/BC numbering convention ** observed. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 12.92 (p604). ** ** This revision: 2016 December 2 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Minimum and maximum allowed JD */ const double DJMIN = -68569.5; const double DJMAX = 1e9; long jd, l, n, i, k; double dj, d1, d2, f1, f2, f, d; /* Verify date is acceptable. */ dj = dj1 + dj2; if (dj < DJMIN || dj > DJMAX) return -1; /* Copy the date, big then small, and re-align to midnight. */ if (dj1 >= dj2) { d1 = dj1; d2 = dj2; } else { d1 = dj2; d2 = dj1; } d2 -= 0.5; /* Separate day and fraction. */ f1 = fmod(d1, 1.0); f2 = fmod(d2, 1.0); f = fmod(f1 + f2, 1.0); if (f < 0.0) f += 1.0; d = dnint(d1-f1) + dnint(d2-f2) + dnint(f1+f2-f); jd = (long) dnint(d) + 1L; /* Express day in Gregorian calendar. */ l = jd + 68569L; n = (4L * l) / 146097L; l -= (146097L * n + 3L) / 4L; i = (4000L * (l + 1L)) / 1461001L; l -= (1461L * i) / 4L - 31L; k = (80L * l) / 2447L; *id = (int) (l - (2447L * k) / 80L); l = k / 11L; *im = (int) (k + 2L - 12L * l); *iy = (int) (100L * (n - 49L) + i + l); *fd = f; return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/jdcalf.c0000644000113000011300000001635113027221062014555 0ustar bellsbells#include "sofa.h" int iauJdcalf(int ndp, double dj1, double dj2, int iymdf[4]) /* ** - - - - - - - - - - ** i a u J d c a l f ** - - - - - - - - - - ** ** Julian Date to Gregorian Calendar, expressed in a form convenient ** for formatting messages: rounded to a specified precision. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ndp int number of decimal places of days in fraction ** dj1,dj2 double dj1+dj2 = Julian Date (Note 1) ** ** Returned: ** iymdf int[4] year, month, day, fraction in Gregorian ** calendar ** ** Returned (function value): ** int status: ** -1 = date out of range ** 0 = OK ** +1 = NDP not 0-9 (interpreted as 0) ** ** Notes: ** ** 1) The Julian Date is apportioned in any convenient way between ** the arguments dj1 and dj2. For example, JD=2450123.7 could ** be expressed in any of these ways, among others: ** ** dj1 dj2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** 2) In early eras the conversion is from the "Proleptic Gregorian ** Calendar"; no account is taken of the date(s) of adoption of ** the Gregorian Calendar, nor is the AD/BC numbering convention ** observed. ** ** 3) Refer to the function iauJd2cal. ** ** 4) NDP should be 4 or less if internal overflows are to be ** avoided on machines which use 16-bit integers. ** ** Called: ** iauJd2cal JD to Gregorian calendar ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 12.92 (p604). ** ** This revision: 2016 December 2 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int j, js; double denom, d1, d2, f1, f2, f; /* Denominator of fraction (e.g. 100 for 2 decimal places). */ if ((ndp >= 0) && (ndp <= 9)) { j = 0; denom = pow(10.0, ndp); } else { j = 1; denom = 1.0; } /* Copy the date, big then small, and realign to midnight. */ if (dj1 >= dj2) { d1 = dj1; d2 = dj2; } else { d1 = dj2; d2 = dj1; } d2 -= 0.5; /* Separate days and fractions. */ f1 = fmod(d1, 1.0); f2 = fmod(d2, 1.0); d1 = dnint(d1-f1); d2 = dnint(d2-f2); /* Round the total fraction to the specified number of places. */ f = dnint((f1+f2)*denom) / denom; /* Re-assemble the rounded date and re-align to noon. */ d2 += f + 0.5; /* Convert to Gregorian calendar. */ js = iauJd2cal(d1, d2, &iymdf[0], &iymdf[1], &iymdf[2], &f); if (js == 0) { iymdf[3] = (int) (f * denom); } else { j = js; } /* Return the status. */ return j; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ld.c0000644000113000011300000001675713027221062013743 0ustar bellsbells#include "sofa.h" void iauLd(double bm, double p[3], double q[3], double e[3], double em, double dlim, double p1[3]) /* ** - - - - - - ** i a u L d ** - - - - - - ** ** Apply light deflection by a solar-system body, as part of ** transforming coordinate direction into natural direction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** bm double mass of the gravitating body (solar masses) ** p double[3] direction from observer to source (unit vector) ** q double[3] direction from body to source (unit vector) ** e double[3] direction from body to observer (unit vector) ** em double distance from body to observer (au) ** dlim double deflection limiter (Note 4) ** ** Returned: ** p1 double[3] observer to deflected source (unit vector) ** ** Notes: ** ** 1) The algorithm is based on Expr. (70) in Klioner (2003) and ** Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann ** 2013), with some rearrangement to minimize the effects of machine ** precision. ** ** 2) The mass parameter bm can, as required, be adjusted in order to ** allow for such effects as quadrupole field. ** ** 3) The barycentric position of the deflecting body should ideally ** correspond to the time of closest approach of the light ray to ** the body. ** ** 4) The deflection limiter parameter dlim is phi^2/2, where phi is ** the angular separation (in radians) between source and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. ** ** 5) The returned vector p1 is not normalized, but the consequential ** departure from unit magnitude is always negligible. ** ** 6) The arguments p and p1 can be the same array. ** ** 7) To accumulate total light deflection taking into account the ** contributions from several bodies, call the present function for ** each body in succession, in decreasing order of distance from the ** observer. ** ** 8) For efficiency, validation is omitted. The supplied vectors must ** be of unit magnitude, and the deflection limiter non-zero and ** positive. ** ** References: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013). ** ** Klioner, Sergei A., "A practical relativistic model for micro- ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). ** ** Called: ** iauPdp scalar product of two p-vectors ** iauPxp vector product of two p-vectors ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int i; double qpe[3], qdqpe, w, eq[3], peq[3]; /* q . (q + e). */ for (i = 0; i < 3; i++) { qpe[i] = q[i] + e[i]; } qdqpe = iauPdp(q, qpe); /* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */ w = bm * SRS / em / gmax(qdqpe,dlim); /* p x (e x q). */ iauPxp(e, q, eq); iauPxp(p, eq, peq); /* Apply the deflection. */ for (i = 0; i < 3; i++) { p1[i] = p[i] + w*peq[i]; } /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ldn.c0000644000113000011300000002117713027221062014111 0ustar bellsbells#include "sofa.h" void iauLdn(int n, iauLDBODY b[], double ob[3], double sc[3], double sn[3]) /*+ ** - - - - - - - ** i a u L d n ** - - - - - - - ** ** For a star, apply light deflection by multiple solar-system bodies, ** as part of transforming coordinate direction into natural direction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** n int number of bodies (note 1) ** b iauLDBODY[n] data for each of the n bodies (Notes 1,2): ** bm double mass of the body (solar masses, Note 3) ** dl double deflection limiter (Note 4) ** pv [2][3] barycentric PV of the body (au, au/day) ** ob double[3] barycentric position of the observer (au) ** sc double[3] observer to star coord direction (unit vector) ** ** Returned: ** sn double[3] observer to deflected star (unit vector) ** ** 1) The array b contains n entries, one for each body to be ** considered. If n = 0, no gravitational light deflection will be ** applied, not even for the Sun. ** ** 2) The array b should include an entry for the Sun as well as for ** any planet or other body to be taken into account. The entries ** should be in the order in which the light passes the body. ** ** 3) In the entry in the b array for body i, the mass parameter ** b[i].bm can, as required, be adjusted in order to allow for such ** effects as quadrupole field. ** ** 4) The deflection limiter parameter b[i].dl is phi^2/2, where phi is ** the angular separation (in radians) between star and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. Example values suitable for a terrestrial ** observer, together with masses, are as follows: ** ** body i b[i].bm b[i].dl ** ** Sun 1.0 6e-6 ** Jupiter 0.00095435 3e-9 ** Saturn 0.00028574 3e-10 ** ** 5) For cases where the starlight passes the body before reaching the ** observer, the body is placed back along its barycentric track by ** the light time from that point to the observer. For cases where ** the body is "behind" the observer no such shift is applied. If ** a different treatment is preferred, the user has the option of ** instead using the iauLd function. Similarly, iauLd can be used ** for cases where the source is nearby, not a star. ** ** 6) The returned vector sn is not normalized, but the consequential ** departure from unit magnitude is always negligible. ** ** 7) The arguments sc and sn can be the same array. ** ** 8) For efficiency, validation is omitted. The supplied masses must ** be greater than zero, the position and velocity vectors must be ** right, and the deflection limiter greater than zero. ** ** Reference: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013), Section 7.2.4. ** ** Called: ** iauCp copy p-vector ** iauPdp scalar product of two p-vectors ** iauPmp p-vector minus p-vector ** iauPpsp p-vector plus scaled p-vector ** iauPn decompose p-vector into modulus and direction ** iauLd light deflection by a solar-system body ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Light time for 1 AU (days) */ const double CR = AULT/DAYSEC; int i; double v[3], dt, ev[3], em, e[3]; /* Star direction prior to deflection. */ iauCp(sc, sn); /* Body by body. */ for ( i = 0; i < n; i++ ) { /* Body to observer vector at epoch of observation (au). */ iauPmp ( ob, b[i].pv[0], v ); /* Minus the time since the light passed the body (days). */ dt = iauPdp(sn,v) * CR; /* Neutralize if the star is "behind" the observer. */ dt = gmin(dt, 0.0); /* Backtrack the body to the time the light was passing the body. */ iauPpsp(v, -dt, b[i].pv[1], ev); /* Body to observer vector as magnitude and direction. */ iauPn(ev, &em, e); /* Apply light deflection for this body. */ iauLd ( b[i].bm, sn, sn, e, em, b[i].dl, sn ); /* Next body. */ } /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ldsun.c0000644000113000011300000001353713027221062014462 0ustar bellsbells#include "sofa.h" void iauLdsun(double p[3], double e[3], double em, double p1[3]) /* ** - - - - - - - - - ** i a u L d s u n ** - - - - - - - - - ** ** Deflection of starlight by the Sun. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** p double[3] direction from observer to star (unit vector) ** e double[3] direction from Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** ** Returned: ** p1 double[3] observer to deflected star (unit vector) ** ** Notes: ** ** 1) The source is presumed to be sufficiently distant that its ** directions seen from the Sun and the observer are essentially ** the same. ** ** 2) The deflection is restrained when the angle between the star and ** the center of the Sun is less than a threshold value, falling to ** zero deflection for zero separation. The chosen threshold value ** is within the solar limb for all solar-system applications, and ** is about 5 arcminutes for the case of a terrestrial observer. ** ** 3) The arguments p and p1 can be the same array. ** ** Called: ** iauLd light deflection by a solar-system body ** ** This revision: 2016 June 16 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double em2, dlim; /* Deflection limiter (smaller for distant observers). */ em2 = em*em; if ( em2 < 1.0 ) em2 = 1.0; dlim = 1e-6 / (em2 > 1.0 ? em2 : 1.0); /* Apply the deflection. */ iauLd(1.0, p, p, e, em, dlim, p1); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/lteceq.c0000644000113000011300000001554713027221062014615 0ustar bellsbells#include "sofa.h" void iauLteceq(double epj, double dl, double db, double *dr, double *dd) /* ** - - - - - - - - - - ** i a u L t e c e q ** - - - - - - - - - - ** ** Transformation from ecliptic coordinates (mean equinox and ecliptic ** of date) to ICRS RA,Dec, using a long-term precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** dl,db double ecliptic longitude and latitude (radians) ** ** Returned: ** dr,dd double ICRS right ascension and declination (radians) ** ** 1) No assumptions are made about whether the coordinates represent ** starlight and embody astrometric effects such as parallax or ** aberration. ** ** 2) The transformation is approximately that from ecliptic longitude ** and latitude (mean equinox and ecliptic of date) to mean J2000.0 ** right ascension and declination, with only frame bias (always ** less than 25 mas) to disturb this classical picture. ** ** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauLtecm J2000.0 to ecliptic rotation matrix, long term ** iauTrxp product of transpose of r-matrix and p-vector ** iauC2s unit vector to spherical coordinates ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** ** This revision: 2016 February 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rm[3][3], v1[3], v2[3], a, b; /* Spherical to Cartesian. */ iauS2c(dl, db, v1); /* Rotation matrix, ICRS equatorial to ecliptic. */ iauLtecm(epj, rm); /* The transformation from ecliptic to ICRS. */ iauTrxp(rm, v1, v2); /* Cartesian to spherical. */ iauC2s(v2, &a, &b); /* Express in conventional ranges. */ *dr = iauAnp(a); *dd = iauAnpm(b); /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ltecm.c0000644000113000011300000001662013027221062014435 0ustar bellsbells#include "sofa.h" void iauLtecm(double epj, double rm[3][3]) /* ** - - - - - - - - - ** i a u L t e c m ** - - - - - - - - - ** ** ICRS equatorial to ecliptic rotation matrix, long-term. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** ** Returned: ** rm double[3][3] ICRS to ecliptic rotation matrix ** ** Notes: ** ** 1) The matrix is in the sense ** ** E_ep = rm x P_ICRS, ** ** where P_ICRS is a vector with respect to ICRS right ascension ** and declination axes and E_ep is the same vector with respect to ** the (inertial) ecliptic and equinox of epoch epj. ** ** 2) P_ICRS is a free vector, merely a direction, typically of unit ** magnitude, and not bound to any particular spatial origin, such ** as the Earth, Sun or SSB. No assumptions are made about whether ** it represents starlight and embodies astrometric effects such as ** parallax or aberration. The transformation is approximately that ** between mean J2000.0 right ascension and declination and ecliptic ** longitude and latitude, with only frame bias (always less than ** 25 mas) to disturb this classical picture. ** ** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** Called: ** iauLtpequ equator pole, long term ** iauLtpecl ecliptic pole, long term ** iauPxp vector product ** iauPn normalize vector ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** ** This revision: 2015 December 6 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) */ const double dx = -0.016617 * DAS2R, de = -0.0068192 * DAS2R, dr = -0.0146 * DAS2R; double p[3], z[3], w[3], s, x[3], y[3]; /* Equator pole. */ iauLtpequ(epj, p); /* Ecliptic pole (bottom row of equatorial to ecliptic matrix). */ iauLtpecl(epj, z); /* Equinox (top row of matrix). */ iauPxp(p, z, w); iauPn(w, &s, x); /* Middle row of matrix. */ iauPxp(z, x, y); /* Combine with frame bias. */ rm[0][0] = x[0] - x[1]*dr + x[2]*dx; rm[0][1] = x[0]*dr + x[1] + x[2]*de; rm[0][2] = - x[0]*dx - x[1]*de + x[2]; rm[1][0] = y[0] - y[1]*dr + y[2]*dx; rm[1][1] = y[0]*dr + y[1] + y[2]*de; rm[1][2] = - y[0]*dx - y[1]*de + y[2]; rm[2][0] = z[0] - z[1]*dr + z[2]*dx; rm[2][1] = z[0]*dr + z[1] + z[2]*de; rm[2][2] = - z[0]*dx - z[1]*de + z[2]; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/lteqec.c0000644000113000011300000001555413027221062014613 0ustar bellsbells#include "sofa.h" void iauLteqec(double epj, double dr, double dd, double *dl, double *db) /* ** - - - - - - - - - - ** i a u L t e q e c ** - - - - - - - - - - ** ** Transformation from ICRS equatorial coordinates to ecliptic ** coordinates (mean equinox and ecliptic of date) using a long-term ** precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** dr,dd double ICRS right ascension and declination (radians) ** ** Returned: ** dl,db double ecliptic longitude and latitude (radians) ** ** 1) No assumptions are made about whether the coordinates represent ** starlight and embody astrometric effects such as parallax or ** aberration. ** ** 2) The transformation is approximately that from mean J2000.0 right ** ascension and declination to ecliptic longitude and latitude ** (mean equinox and ecliptic of date), with only frame bias (always ** less than 25 mas) to disturb this classical picture. ** ** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauLtecm J2000.0 to ecliptic rotation matrix, long term ** iauRxp product of r-matrix and p-vector ** iauC2s unit vector to spherical coordinates ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** ** This revision: 2016 February 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rm[3][3], v1[3], v2[3], a, b; /* Spherical to Cartesian. */ iauS2c(dr, dd, v1); /* Rotation matrix, ICRS equatorial to ecliptic. */ iauLtecm(epj, rm); /* The transformation from ICRS to ecliptic. */ iauRxp(rm, v1, v2); /* Cartesian to spherical. */ iauC2s(v2, &a, &b); /* Express in conventional ranges. */ *dl = iauAnp(a); *db = iauAnpm(b); /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ltpb.c0000644000113000011300000001466613027221062014302 0ustar bellsbells#include "sofa.h" void iauLtpb(double epj, double rpb[3][3]) /* ** - - - - - - - - ** i a u L t p b ** - - - - - - - - ** ** Long-term precession matrix, including ICRS frame bias. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** ** Returned: ** rpb double[3][3] precession-bias matrix, J2000.0 to date ** ** Notes: ** ** 1) The matrix is in the sense ** ** P_date = rpb x P_ICRS, ** ** where P_ICRS is a vector in the Geocentric Celestial Reference ** System, and P_date is the vector with respect to the Celestial ** Intermediate Reference System at that date but with nutation ** neglected. ** ** 2) A first order frame bias formulation is used, of sub- ** microarcsecond accuracy compared with a full 3D rotation. ** ** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** ** This revision: 2015 December 6 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) */ const double dx = -0.016617 * DAS2R, de = -0.0068192 * DAS2R, dr = -0.0146 * DAS2R; int i; double rp[3][3]; /* Precession matrix. */ iauLtp(epj, rp); /* Apply the bias. */ for ( i = 0; i < 3; i++ ) { rpb[i][0] = rp[i][0] - rp[i][1]*dr + rp[i][2]*dx; rpb[i][1] = rp[i][0]*dr + rp[i][1] + rp[i][2]*de; rpb[i][2] = -rp[i][0]*dx - rp[i][1]*de + rp[i][2]; } /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ltp.c0000644000113000011300000001454513027221062014134 0ustar bellsbells#include "sofa.h" void iauLtp(double epj, double rp[3][3]) /* ** - - - - - - - ** i a u L t p ** - - - - - - - ** ** Long-term precession matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** ** Returned: ** rp double[3][3] precession matrix, J2000.0 to date ** ** Notes: ** ** 1) The matrix is in the sense ** ** P_date = rp x P_J2000, ** ** where P_J2000 is a vector with respect to the J2000.0 mean ** equator and equinox and P_date is the same vector with respect to ** the equator and equinox of epoch epj. ** ** 2) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** Called: ** iauLtpequ equator pole, long term ** iauLtpecl ecliptic pole, long term ** iauPxp vector product ** iauPn normalize vector ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** ** This revision: 2015 December 6 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int i; double peqr[3], pecl[3], v[3], w, eqx[3]; /* Equator pole (bottom row of matrix). */ iauLtpequ(epj, peqr); /* Ecliptic pole. */ iauLtpecl(epj, pecl); /* Equinox (top row of matrix). */ iauPxp(peqr, pecl, v); iauPn(v, &w, eqx); /* Middle row of matrix. */ iauPxp(peqr, eqx, v); /* Assemble the matrix. */ for ( i = 0; i < 3; i++ ) { rp[0][i] = eqx[i]; rp[1][i] = v[i]; rp[2][i] = peqr[i]; } /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ltpecl.c0000644000113000011300000001666213027221062014622 0ustar bellsbells#include "sofa.h" void iauLtpecl(double epj, double vec[3]) /* ** - - - - - - - - - - ** i a u L t p e c l ** - - - - - - - - - - ** ** Long-term precession of the ecliptic. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** ** Returned: ** vec double[3] ecliptic pole unit vector ** ** Notes: ** ** 1) The returned vector is with respect to the J2000.0 mean equator ** and equinox. ** ** 2) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** ** This revision: 2016 February 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Obliquity at J2000.0 (radians). */ static const double eps0 = 84381.406 * DAS2R; /* Polynomial coefficients */ enum { NPOL = 4 }; static const double pqpol[2][NPOL] = { { 5851.607687, -0.1189000, -0.00028913, 0.000000101}, {-1600.886300, 1.1689818, -0.00000020, -0.000000437} }; /* Periodic coefficients */ static const double pqper[][5] = { { 708.15,-5486.751211,-684.661560, 667.666730,-5523.863691}, {2309.00, -17.127623,2446.283880,-2354.886252, -549.747450}, {1620.00, -617.517403, 399.671049, -428.152441, -310.998056}, { 492.20, 413.442940,-356.652376, 376.202861, 421.535876}, {1183.00, 78.614193,-186.387003, 184.778874, -36.776172}, { 622.00, -180.732815,-316.800070, 335.321713, -145.278396}, { 882.00, -87.676083, 198.296701, -185.138669, -34.744450}, { 547.00, 46.140315, 101.135679, -120.972830, 22.885731} }; static const int NPER = (int) ( sizeof pqper / 5 / sizeof (double) ); /* Miscellaneous */ int i; double t, p, q, w, a, s, c; /* Centuries since J2000. */ t = ( epj - 2000.0 ) / 100.0; /* Initialize P_A and Q_A accumulators. */ p = 0.0; q = 0.0; /* Periodic terms. */ w = D2PI*t; for ( i = 0; i < NPER; i++ ) { a = w/pqper[i][0]; s = sin(a); c = cos(a); p += c*pqper[i][1] + s*pqper[i][3]; q += c*pqper[i][2] + s*pqper[i][4]; } /* Polynomial terms. */ w = 1.0; for ( i = 0; i < NPOL; i++ ) { p += pqpol[0][i]*w; q += pqpol[1][i]*w; w *= t; } /* P_A and Q_A (radians). */ p *= DAS2R; q *= DAS2R; /* Form the ecliptic pole vector. */ w = 1.0 - p*p - q*q; w = w < 0.0 ? 0.0 : sqrt(w); s = sin(eps0); c = cos(eps0); vec[0] = p; vec[1] = - q*c - w*s; vec[2] = - q*s + w*c; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ltpequ.c0000644000113000011300000001731113027221062014641 0ustar bellsbells#include "sofa.h" void iauLtpequ(double epj, double veq[3]) /* ** - - - - - - - - - - ** i a u L t p e q u ** - - - - - - - - - - ** ** Long-term precession of the equator. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** ** Returned: ** veq double[3] equator pole unit vector ** ** Notes: ** ** 1) The returned vector is with respect to the J2000.0 mean equator ** and equinox. ** ** 2) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** ** This revision: 2016 February 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Polynomial coefficients */ enum { NPOL = 4 }; static const double xypol[2][NPOL] = { { 5453.282155, 0.4252841, -0.00037173, -0.000000152}, {-73750.930350, -0.7675452, -0.00018725, 0.000000231} }; /* Periodic coefficients */ static const double xyper[][5] = { { 256.75, -819.940624,75004.344875,81491.287984, 1558.515853}, { 708.15,-8444.676815, 624.033993, 787.163481, 7774.939698}, { 274.20, 2600.009459, 1251.136893, 1251.296102,-2219.534038}, { 241.45, 2755.175630,-1102.212834,-1257.950837,-2523.969396}, {2309.00, -167.659835,-2660.664980,-2966.799730, 247.850422}, { 492.20, 871.855056, 699.291817, 639.744522, -846.485643}, { 396.10, 44.769698, 153.167220, 131.600209,-1393.124055}, { 288.90, -512.313065, -950.865637, -445.040117, 368.526116}, { 231.10, -819.415595, 499.754645, 584.522874, 749.045012}, {1610.00, -538.071099, -145.188210, -89.756563, 444.704518}, { 620.00, -189.793622, 558.116553, 524.429630, 235.934465}, { 157.87, -402.922932, -23.923029, -13.549067, 374.049623}, { 220.30, 179.516345, -165.405086, -210.157124, -171.330180}, {1200.00, -9.814756, 9.344131, -44.919798, -22.899655} }; static const int NPER = (int) ( sizeof xyper / 5 / sizeof (double) ); /* Miscellaneous */ int i; double t, x, y, w, a, s, c; /* Centuries since J2000. */ t = ( epj - 2000.0 ) / 100.0; /* Initialize X and Y accumulators. */ x = 0.0; y = 0.0; /* Periodic terms. */ w = D2PI * t; for ( i = 0; i < NPER; i++ ) { a = w / xyper[i][0]; s = sin(a); c = cos(a); x += c*xyper[i][1] + s*xyper[i][3]; y += c*xyper[i][2] + s*xyper[i][4]; } /* Polynomial terms. */ w = 1.0; for ( i = 0; i < NPOL; i++ ) { x += xypol[0][i]*w; y += xypol[1][i]*w; w *= t; } /* X and Y (direction cosines). */ x *= DAS2R; y *= DAS2R; /* Form the equator pole vector. */ veq[0] = x; veq[1] = y; w = 1.0 - x*x - y*y; veq[2] = w < 0.0 ? 0.0 : sqrt(w); /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/num00a.c0000644000113000011300000001511013027221062014422 0ustar bellsbells#include "sofa.h" void iauNum00a(double date1, double date2, double rmatn[3][3]) /* ** - - - - - - - - - - ** i a u N u m 0 0 a ** - - - - - - - - - - ** ** Form the matrix of nutation for a given date, IAU 2000A model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rmatn double[3][3] nutation matrix ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(true) = rmatn * V(mean), where ** the p-vector V(true) is with respect to the true equatorial triad ** of date and the p-vector V(mean) is with respect to the mean ** equatorial triad of date. ** ** 3) A faster, but slightly less accurate result (about 1 mas), can be ** obtained by using instead the iauNum00b function. ** ** Called: ** iauPn00a bias/precession/nutation, IAU 2000A ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222-3 (p114). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dpsi, deps, epsa, rb[3][3], rp[3][3], rbp[3][3], rbpn[3][3]; /* Obtain the required matrix (discarding other results). */ iauPn00a(date1, date2, &dpsi, &deps, &epsa, rb, rp, rbp, rmatn, rbpn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/num00b.c0000644000113000011300000001507113027221062014431 0ustar bellsbells#include "sofa.h" void iauNum00b(double date1, double date2, double rmatn[3][3]) /* ** - - - - - - - - - - ** i a u N u m 0 0 b ** - - - - - - - - - - ** ** Form the matrix of nutation for a given date, IAU 2000B model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rmatn double[3][3] nutation matrix ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(true) = rmatn * V(mean), where ** the p-vector V(true) is with respect to the true equatorial triad ** of date and the p-vector V(mean) is with respect to the mean ** equatorial triad of date. ** ** 3) The present function is faster, but slightly less accurate (about ** 1 mas), than the iauNum00a function. ** ** Called: ** iauPn00b bias/precession/nutation, IAU 2000B ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222-3 (p114). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dpsi, deps, epsa, rb[3][3], rp[3][3], rbp[3][3], rbpn[3][3]; /* Obtain the required matrix (discarding other results). */ iauPn00b(date1, date2, &dpsi, &deps, &epsa, rb, rp, rbp, rmatn, rbpn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/num06a.c0000644000113000011300000001500413027221062014432 0ustar bellsbells#include "sofa.h" void iauNum06a(double date1, double date2, double rmatn[3][3]) /* ** - - - - - - - - - - ** i a u N u m 0 6 a ** - - - - - - - - - - ** ** Form the matrix of nutation for a given date, IAU 2006/2000A model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rmatn double[3][3] nutation matrix ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(true) = rmatn * V(mean), where ** the p-vector V(true) is with respect to the true equatorial triad ** of date and the p-vector V(mean) is with respect to the mean ** equatorial triad of date. ** ** Called: ** iauObl06 mean obliquity, IAU 2006 ** iauNut06a nutation, IAU 2006/2000A ** iauNumat form nutation matrix ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222-3 (p114). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double eps, dp, de; /* Mean obliquity. */ eps = iauObl06(date1, date2); /* Nutation components. */ iauNut06a(date1, date2, &dp, &de); /* Nutation matrix. */ iauNumat(eps, dp, de, rmatn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/numat.c0000644000113000011300000001365113027221062014456 0ustar bellsbells#include "sofa.h" void iauNumat(double epsa, double dpsi, double deps, double rmatn[3][3]) /* ** - - - - - - - - - ** i a u N u m a t ** - - - - - - - - - ** ** Form the matrix of nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epsa double mean obliquity of date (Note 1) ** dpsi,deps double nutation (Note 2) ** ** Returned: ** rmatn double[3][3] nutation matrix (Note 3) ** ** Notes: ** ** ** 1) The supplied mean obliquity epsa, must be consistent with the ** precession-nutation models from which dpsi and deps were obtained. ** ** 2) The caller is responsible for providing the nutation components; ** they are in longitude and obliquity, in radians and are with ** respect to the equinox and ecliptic of date. ** ** 3) The matrix operates in the sense V(true) = rmatn * V(mean), ** where the p-vector V(true) is with respect to the true ** equatorial triad of date and the p-vector V(mean) is with ** respect to the mean equatorial triad of date. ** ** Called: ** iauIr initialize r-matrix to identity ** iauRx rotate around X-axis ** iauRz rotate around Z-axis ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222-3 (p114). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Build the rotation matrix. */ iauIr(rmatn); iauRx(epsa, rmatn); iauRz(-dpsi, rmatn); iauRx(-(epsa + deps), rmatn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/nut00a.c0000644000113000011300000035177113027221062014451 0ustar bellsbells#include "sofa.h" void iauNut00a(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - - ** i a u N u t 0 0 a ** - - - - - - - - - - ** ** Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation ** with free core nutation omitted). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation, luni-solar + planetary (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components in longitude and obliquity are in radians ** and with respect to the equinox and ecliptic of date. The ** obliquity at J2000.0 is assumed to be the Lieske et al. (1977) ** value of 84381.448 arcsec. ** ** Both the luni-solar and planetary nutations are included. The ** latter are due to direct planetary nutations and the ** perturbations of the lunar and terrestrial orbits. ** ** 3) The function computes the MHB2000 nutation series with the ** associated corrections for planetary nutations. It is an ** implementation of the nutation part of the IAU 2000A precession- ** nutation model, formally adopted by the IAU General Assembly in ** 2000, namely MHB2000 (Mathews et al. 2002), but with the free ** core nutation (FCN - see Note 4) omitted. ** ** 4) The full MHB2000 model also contains contributions to the ** nutations in longitude and obliquity due to the free-excitation ** of the free-core-nutation during the period 1979-2000. These FCN ** terms, which are time-dependent and unpredictable, are NOT ** included in the present function and, if required, must be ** independently computed. With the FCN corrections included, the ** present function delivers a pole which is at current epochs ** accurate to a few hundred microarcseconds. The omission of FCN ** introduces further errors of about that size. ** ** 5) The present function provides classical nutation. The MHB2000 ** algorithm, from which it is adapted, deals also with (i) the ** offsets between the GCRS and mean poles and (ii) the adjustments ** in longitude and obliquity due to the changed precession rates. ** These additional functions, namely frame bias and precession ** adjustments, are supported by the SOFA functions iauBi00 and ** iauPr00. ** ** 6) The MHB2000 algorithm also provides "total" nutations, comprising ** the arithmetic sum of the frame bias, precession adjustments, ** luni-solar nutation and planetary nutation. These total ** nutations can be used in combination with an existing IAU 1976 ** precession implementation, such as iauPmat76, to deliver GCRS- ** to-true predictions of sub-mas accuracy at current dates. ** However, there are three shortcomings in the MHB2000 model that ** must be taken into account if more accurate or definitive results ** are required (see Wallace 2002): ** ** (i) The MHB2000 total nutations are simply arithmetic sums, ** yet in reality the various components are successive Euler ** rotations. This slight lack of rigor leads to cross terms ** that exceed 1 mas after a century. The rigorous procedure ** is to form the GCRS-to-true rotation matrix by applying the ** bias, precession and nutation in that order. ** ** (ii) Although the precession adjustments are stated to be with ** respect to Lieske et al. (1977), the MHB2000 model does ** not specify which set of Euler angles are to be used and ** how the adjustments are to be applied. The most literal ** and straightforward procedure is to adopt the 4-rotation ** epsilon_0, psi_A, omega_A, xi_A option, and to add DPSIPR ** to psi_A and DEPSPR to both omega_A and eps_A. ** ** (iii) The MHB2000 model predates the determination by Chapront ** et al. (2002) of a 14.6 mas displacement between the ** J2000.0 mean equinox and the origin of the ICRS frame. It ** should, however, be noted that neglecting this displacement ** when calculating star coordinates does not lead to a ** 14.6 mas change in right ascension, only a small second- ** order distortion in the pattern of the precession-nutation ** effect. ** ** For these reasons, the SOFA functions do not generate the "total ** nutations" directly, though they can of course easily be ** generated by calling iauBi00, iauPr00 and the present function ** and adding the results. ** ** 7) The MHB2000 model contains 41 instances where the same frequency ** appears multiple times, of which 38 are duplicates and three are ** triplicates. To keep the present code close to the original MHB ** algorithm, this small inefficiency has not been corrected. ** ** Called: ** iauFal03 mean anomaly of the Moon ** iauFaf03 mean argument of the latitude of the Moon ** iauFaom03 mean longitude of the Moon's ascending node ** iauFame03 mean longitude of Mercury ** iauFave03 mean longitude of Venus ** iauFae03 mean longitude of Earth ** iauFama03 mean longitude of Mars ** iauFaju03 mean longitude of Jupiter ** iauFasa03 mean longitude of Saturn ** iauFaur03 mean longitude of Uranus ** iauFapa03 general accumulated precession in longitude ** ** References: ** ** Chapront, J., Chapront-Touze, M. & Francou, G. 2002, ** Astron.Astrophys. 387, 700 ** ** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, ** Astron.Astrophys. 58, 1-16 ** ** Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. ** 107, B4. The MHB_2000 code itself was obtained on 9th September ** 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A. ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** Wallace, P.T., "Software for Implementing the IAU 2000 ** Resolutions", in IERS Workshop 5.1 (2002) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int i; double t, el, elp, f, d, om, arg, dp, de, sarg, carg, al, af, ad, aom, alme, alve, alea, alma, alju, alsa, alur, alne, apa, dpsils, depsls, dpsipl, depspl; /* Units of 0.1 microarcsecond to radians */ const double U2R = DAS2R / 1e7; /* ------------------------- */ /* Luni-Solar nutation model */ /* ------------------------- */ /* The units for the sine and cosine coefficients are */ /* 0.1 microarcsecond and the same per Julian century */ static const struct { int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */ double sp,spt,cp; /* longitude sin, t*sin, cos coefficients */ double ce,cet,se; /* obliquity cos, t*cos, sin coefficients */ } xls[] = { /* 1- 10 */ { 0, 0, 0, 0, 1, -172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0}, { 0, 0, 2,-2, 2, -13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0}, { 0, 0, 2, 0, 2,-2276413.0,-234.0,2796.0,978459.0,-485.0, 1374.0}, { 0, 0, 0, 0, 2,2074554.0, 207.0, -698.0,-897492.0,470.0, -291.0}, { 0, 1, 0, 0, 0,1475877.0,-3633.0,11817.0,73871.0,-184.0,-1924.0}, { 0, 1, 2,-2, 2,-516821.0,1226.0, -524.0,224386.0,-677.0, -174.0}, { 1, 0, 0, 0, 0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0}, { 0, 0, 2, 0, 1,-387298.0,-367.0, 380.0, 200728.0, 18.0, 318.0}, { 1, 0, 2, 0, 2,-301461.0, -36.0, 816.0, 129025.0,-63.0, 367.0}, { 0,-1, 2,-2, 2, 215829.0,-494.0, 111.0, -95929.0,299.0, 132.0}, /* 11-20 */ { 0, 0, 2,-2, 1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0}, {-1, 0, 2, 0, 2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0}, {-1, 0, 0, 2, 0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0}, { 1, 0, 0, 0, 1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0}, {-1, 0, 0, 0, 1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0}, {-1, 0, 2, 2, 2, -59641.0, -11.0, 149.0, 25543.0,-11.0, 66.0}, { 1, 0, 2, 0, 1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0}, {-2, 0, 2, 0, 1, 45893.0, 50.0, 31.0, -24236.0,-10.0, 20.0}, { 0, 0, 0, 2, 0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0}, { 0, 0, 2, 2, 2, -38571.0, -1.0, 158.0, 16452.0,-11.0, 68.0}, /* 21-30 */ { 0,-2, 2,-2, 2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0}, {-2, 0, 0, 2, 0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0}, { 2, 0, 2, 0, 2, -31046.0, -1.0, 131.0, 13238.0,-11.0, 59.0}, { 1, 0, 2,-2, 2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0}, {-1, 0, 2, 0, 1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0}, { 2, 0, 0, 0, 0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0}, { 0, 0, 2, 0, 0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0}, { 0, 1, 0, 0, 1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0}, {-1, 0, 0, 2, 1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0}, { 0, 2, 2,-2, 2, -15794.0, 72.0, -16.0, 6850.0,-42.0, -5.0}, /* 31-40 */ { 0, 0,-2, 2, 0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0}, { 1, 0, 0,-2, 1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0}, { 0,-1, 0, 0, 1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0}, {-1, 0, 2, 2, 1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0}, { 0, 2, 0, 0, 0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0}, { 1, 0, 2, 2, 2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0}, {-2, 0, 2, 0, 0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0}, { 0, 1, 2, 0, 2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0}, { 0, 0, 2, 2, 1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0}, { 0,-1, 2, 0, 2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0}, /* 41-50 */ { 0, 0, 0, 2, 1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0}, { 1, 0, 2,-2, 1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0}, { 2, 0, 2,-2, 2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0}, {-2, 0, 0, 2, 1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0}, { 2, 0, 2, 0, 1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0}, { 0,-1, 2,-2, 1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0}, { 0, 0, 0,-2, 1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0}, {-1,-1, 0, 2, 0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0}, { 2, 0, 0,-2, 1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0}, { 1, 0, 0, 2, 0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0}, /* 51-60 */ { 0, 1, 2,-2, 1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0}, { 1,-1, 0, 0, 0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0}, {-2, 0, 2, 0, 2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0}, { 3, 0, 2, 0, 2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0}, { 0,-1, 0, 2, 0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0}, { 1,-1, 2, 0, 2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0}, { 0, 0, 0, 1, 0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0}, {-1,-1, 2, 2, 2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0}, {-1, 0, 2, 0, 0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0}, { 0,-1, 2, 2, 2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0}, /* 61-70 */ {-2, 0, 0, 0, 1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0}, { 1, 1, 2, 0, 2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0}, { 2, 0, 0, 0, 1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0}, {-1, 1, 0, 1, 0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0}, { 1, 1, 0, 0, 0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0}, { 1, 0, 2, 0, 0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0}, {-1, 0, 2,-2, 1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0}, { 1, 0, 0, 0, 2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0}, {-1, 0, 0, 1, 0, 4026.0, 0.0, -353.0, -553.0, 0.0, -139.0}, { 0, 0, 2, 1, 2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0}, /* 71-80 */ {-1, 0, 2, 4, 2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0}, {-1, 1, 0, 1, 1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0}, { 0,-2, 2,-2, 1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0}, { 1, 0, 2, 2, 1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0}, {-2, 0, 2, 2, 2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0}, {-1, 0, 0, 0, 2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0}, { 1, 1, 2,-2, 2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0}, {-2, 0, 2, 4, 2, -1214.0, 0.0, 5.0, 518.0, 0.0, 2.0}, {-1, 0, 4, 0, 2, 1146.0, 0.0, -3.0, -490.0, 0.0, -1.0}, { 2, 0, 2,-2, 1, 1019.0, 0.0, -1.0, -527.0, 0.0, -1.0}, /* 81-90 */ { 2, 0, 2, 2, 2, -1100.0, 0.0, 9.0, 465.0, 0.0, 4.0}, { 1, 0, 0, 2, 1, -970.0, 0.0, 2.0, 496.0, 0.0, 1.0}, { 3, 0, 0, 0, 0, 1575.0, 0.0, -6.0, -50.0, 0.0, 0.0}, { 3, 0, 2,-2, 2, 934.0, 0.0, -3.0, -399.0, 0.0, -1.0}, { 0, 0, 4,-2, 2, 922.0, 0.0, -1.0, -395.0, 0.0, -1.0}, { 0, 1, 2, 0, 1, 815.0, 0.0, -1.0, -422.0, 0.0, -1.0}, { 0, 0,-2, 2, 1, 834.0, 0.0, 2.0, -440.0, 0.0, 1.0}, { 0, 0, 2,-2, 3, 1248.0, 0.0, 0.0, -170.0, 0.0, 1.0}, {-1, 0, 0, 4, 0, 1338.0, 0.0, -5.0, -39.0, 0.0, 0.0}, { 2, 0,-2, 0, 1, 716.0, 0.0, -2.0, -389.0, 0.0, -1.0}, /* 91-100 */ {-2, 0, 0, 4, 0, 1282.0, 0.0, -3.0, -23.0, 0.0, 1.0}, {-1,-1, 0, 2, 1, 742.0, 0.0, 1.0, -391.0, 0.0, 0.0}, {-1, 0, 0, 1, 1, 1020.0, 0.0, -25.0, -495.0, 0.0, -10.0}, { 0, 1, 0, 0, 2, 715.0, 0.0, -4.0, -326.0, 0.0, 2.0}, { 0, 0,-2, 0, 1, -666.0, 0.0, -3.0, 369.0, 0.0, -1.0}, { 0,-1, 2, 0, 1, -667.0, 0.0, 1.0, 346.0, 0.0, 1.0}, { 0, 0, 2,-1, 2, -704.0, 0.0, 0.0, 304.0, 0.0, 0.0}, { 0, 0, 2, 4, 2, -694.0, 0.0, 5.0, 294.0, 0.0, 2.0}, {-2,-1, 0, 2, 0, -1014.0, 0.0, -1.0, 4.0, 0.0, -1.0}, { 1, 1, 0,-2, 1, -585.0, 0.0, -2.0, 316.0, 0.0, -1.0}, /* 101-110 */ {-1, 1, 0, 2, 0, -949.0, 0.0, 1.0, 8.0, 0.0, -1.0}, {-1, 1, 0, 1, 2, -595.0, 0.0, 0.0, 258.0, 0.0, 0.0}, { 1,-1, 0, 0, 1, 528.0, 0.0, 0.0, -279.0, 0.0, 0.0}, { 1,-1, 2, 2, 2, -590.0, 0.0, 4.0, 252.0, 0.0, 2.0}, {-1, 1, 2, 2, 2, 570.0, 0.0, -2.0, -244.0, 0.0, -1.0}, { 3, 0, 2, 0, 1, -502.0, 0.0, 3.0, 250.0, 0.0, 2.0}, { 0, 1,-2, 2, 0, -875.0, 0.0, 1.0, 29.0, 0.0, 0.0}, {-1, 0, 0,-2, 1, -492.0, 0.0, -3.0, 275.0, 0.0, -1.0}, { 0, 1, 2, 2, 2, 535.0, 0.0, -2.0, -228.0, 0.0, -1.0}, {-1,-1, 2, 2, 1, -467.0, 0.0, 1.0, 240.0, 0.0, 1.0}, /* 111-120 */ { 0,-1, 0, 0, 2, 591.0, 0.0, 0.0, -253.0, 0.0, 0.0}, { 1, 0, 2,-4, 1, -453.0, 0.0, -1.0, 244.0, 0.0, -1.0}, {-1, 0,-2, 2, 0, 766.0, 0.0, 1.0, 9.0, 0.0, 0.0}, { 0,-1, 2, 2, 1, -446.0, 0.0, 2.0, 225.0, 0.0, 1.0}, { 2,-1, 2, 0, 2, -488.0, 0.0, 2.0, 207.0, 0.0, 1.0}, { 0, 0, 0, 2, 2, -468.0, 0.0, 0.0, 201.0, 0.0, 0.0}, { 1,-1, 2, 0, 1, -421.0, 0.0, 1.0, 216.0, 0.0, 1.0}, {-1, 1, 2, 0, 2, 463.0, 0.0, 0.0, -200.0, 0.0, 0.0}, { 0, 1, 0, 2, 0, -673.0, 0.0, 2.0, 14.0, 0.0, 0.0}, { 0,-1,-2, 2, 0, 658.0, 0.0, 0.0, -2.0, 0.0, 0.0}, /* 121-130 */ { 0, 3, 2,-2, 2, -438.0, 0.0, 0.0, 188.0, 0.0, 0.0}, { 0, 0, 0, 1, 1, -390.0, 0.0, 0.0, 205.0, 0.0, 0.0}, {-1, 0, 2, 2, 0, 639.0, -11.0, -2.0, -19.0, 0.0, 0.0}, { 2, 1, 2, 0, 2, 412.0, 0.0, -2.0, -176.0, 0.0, -1.0}, { 1, 1, 0, 0, 1, -361.0, 0.0, 0.0, 189.0, 0.0, 0.0}, { 1, 1, 2, 0, 1, 360.0, 0.0, -1.0, -185.0, 0.0, -1.0}, { 2, 0, 0, 2, 0, 588.0, 0.0, -3.0, -24.0, 0.0, 0.0}, { 1, 0,-2, 2, 0, -578.0, 0.0, 1.0, 5.0, 0.0, 0.0}, {-1, 0, 0, 2, 2, -396.0, 0.0, 0.0, 171.0, 0.0, 0.0}, { 0, 1, 0, 1, 0, 565.0, 0.0, -1.0, -6.0, 0.0, 0.0}, /* 131-140 */ { 0, 1, 0,-2, 1, -335.0, 0.0, -1.0, 184.0, 0.0, -1.0}, {-1, 0, 2,-2, 2, 357.0, 0.0, 1.0, -154.0, 0.0, 0.0}, { 0, 0, 0,-1, 1, 321.0, 0.0, 1.0, -174.0, 0.0, 0.0}, {-1, 1, 0, 0, 1, -301.0, 0.0, -1.0, 162.0, 0.0, 0.0}, { 1, 0, 2,-1, 2, -334.0, 0.0, 0.0, 144.0, 0.0, 0.0}, { 1,-1, 0, 2, 0, 493.0, 0.0, -2.0, -15.0, 0.0, 0.0}, { 0, 0, 0, 4, 0, 494.0, 0.0, -2.0, -19.0, 0.0, 0.0}, { 1, 0, 2, 1, 2, 337.0, 0.0, -1.0, -143.0, 0.0, -1.0}, { 0, 0, 2, 1, 1, 280.0, 0.0, -1.0, -144.0, 0.0, 0.0}, { 1, 0, 0,-2, 2, 309.0, 0.0, 1.0, -134.0, 0.0, 0.0}, /* 141-150 */ {-1, 0, 2, 4, 1, -263.0, 0.0, 2.0, 131.0, 0.0, 1.0}, { 1, 0,-2, 0, 1, 253.0, 0.0, 1.0, -138.0, 0.0, 0.0}, { 1, 1, 2,-2, 1, 245.0, 0.0, 0.0, -128.0, 0.0, 0.0}, { 0, 0, 2, 2, 0, 416.0, 0.0, -2.0, -17.0, 0.0, 0.0}, {-1, 0, 2,-1, 1, -229.0, 0.0, 0.0, 128.0, 0.0, 0.0}, {-2, 0, 2, 2, 1, 231.0, 0.0, 0.0, -120.0, 0.0, 0.0}, { 4, 0, 2, 0, 2, -259.0, 0.0, 2.0, 109.0, 0.0, 1.0}, { 2,-1, 0, 0, 0, 375.0, 0.0, -1.0, -8.0, 0.0, 0.0}, { 2, 1, 2,-2, 2, 252.0, 0.0, 0.0, -108.0, 0.0, 0.0}, { 0, 1, 2, 1, 2, -245.0, 0.0, 1.0, 104.0, 0.0, 0.0}, /* 151-160 */ { 1, 0, 4,-2, 2, 243.0, 0.0, -1.0, -104.0, 0.0, 0.0}, {-1,-1, 0, 0, 1, 208.0, 0.0, 1.0, -112.0, 0.0, 0.0}, { 0, 1, 0, 2, 1, 199.0, 0.0, 0.0, -102.0, 0.0, 0.0}, {-2, 0, 2, 4, 1, -208.0, 0.0, 1.0, 105.0, 0.0, 0.0}, { 2, 0, 2, 0, 0, 335.0, 0.0, -2.0, -14.0, 0.0, 0.0}, { 1, 0, 0, 1, 0, -325.0, 0.0, 1.0, 7.0, 0.0, 0.0}, {-1, 0, 0, 4, 1, -187.0, 0.0, 0.0, 96.0, 0.0, 0.0}, {-1, 0, 4, 0, 1, 197.0, 0.0, -1.0, -100.0, 0.0, 0.0}, { 2, 0, 2, 2, 1, -192.0, 0.0, 2.0, 94.0, 0.0, 1.0}, { 0, 0, 2,-3, 2, -188.0, 0.0, 0.0, 83.0, 0.0, 0.0}, /* 161-170 */ {-1,-2, 0, 2, 0, 276.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 2, 1, 0, 0, 0, -286.0, 0.0, 1.0, 6.0, 0.0, 0.0}, { 0, 0, 4, 0, 2, 186.0, 0.0, -1.0, -79.0, 0.0, 0.0}, { 0, 0, 0, 0, 3, -219.0, 0.0, 0.0, 43.0, 0.0, 0.0}, { 0, 3, 0, 0, 0, 276.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 0, 0, 2,-4, 1, -153.0, 0.0, -1.0, 84.0, 0.0, 0.0}, { 0,-1, 0, 2, 1, -156.0, 0.0, 0.0, 81.0, 0.0, 0.0}, { 0, 0, 0, 4, 1, -154.0, 0.0, 1.0, 78.0, 0.0, 0.0}, {-1,-1, 2, 4, 2, -174.0, 0.0, 1.0, 75.0, 0.0, 0.0}, { 1, 0, 2, 4, 2, -163.0, 0.0, 2.0, 69.0, 0.0, 1.0}, /* 171-180 */ {-2, 2, 0, 2, 0, -228.0, 0.0, 0.0, 1.0, 0.0, 0.0}, {-2,-1, 2, 0, 1, 91.0, 0.0, -4.0, -54.0, 0.0, -2.0}, {-2, 0, 0, 2, 2, 175.0, 0.0, 0.0, -75.0, 0.0, 0.0}, {-1,-1, 2, 0, 2, -159.0, 0.0, 0.0, 69.0, 0.0, 0.0}, { 0, 0, 4,-2, 1, 141.0, 0.0, 0.0, -72.0, 0.0, 0.0}, { 3, 0, 2,-2, 1, 147.0, 0.0, 0.0, -75.0, 0.0, 0.0}, {-2,-1, 0, 2, 1, -132.0, 0.0, 0.0, 69.0, 0.0, 0.0}, { 1, 0, 0,-1, 1, 159.0, 0.0, -28.0, -54.0, 0.0, 11.0}, { 0,-2, 0, 2, 0, 213.0, 0.0, 0.0, -4.0, 0.0, 0.0}, {-2, 0, 0, 4, 1, 123.0, 0.0, 0.0, -64.0, 0.0, 0.0}, /* 181-190 */ {-3, 0, 0, 0, 1, -118.0, 0.0, -1.0, 66.0, 0.0, 0.0}, { 1, 1, 2, 2, 2, 144.0, 0.0, -1.0, -61.0, 0.0, 0.0}, { 0, 0, 2, 4, 1, -121.0, 0.0, 1.0, 60.0, 0.0, 0.0}, { 3, 0, 2, 2, 2, -134.0, 0.0, 1.0, 56.0, 0.0, 1.0}, {-1, 1, 2,-2, 1, -105.0, 0.0, 0.0, 57.0, 0.0, 0.0}, { 2, 0, 0,-4, 1, -102.0, 0.0, 0.0, 56.0, 0.0, 0.0}, { 0, 0, 0,-2, 2, 120.0, 0.0, 0.0, -52.0, 0.0, 0.0}, { 2, 0, 2,-4, 1, 101.0, 0.0, 0.0, -54.0, 0.0, 0.0}, {-1, 1, 0, 2, 1, -113.0, 0.0, 0.0, 59.0, 0.0, 0.0}, { 0, 0, 2,-1, 1, -106.0, 0.0, 0.0, 61.0, 0.0, 0.0}, /* 191-200 */ { 0,-2, 2, 2, 2, -129.0, 0.0, 1.0, 55.0, 0.0, 0.0}, { 2, 0, 0, 2, 1, -114.0, 0.0, 0.0, 57.0, 0.0, 0.0}, { 4, 0, 2,-2, 2, 113.0, 0.0, -1.0, -49.0, 0.0, 0.0}, { 2, 0, 0,-2, 2, -102.0, 0.0, 0.0, 44.0, 0.0, 0.0}, { 0, 2, 0, 0, 1, -94.0, 0.0, 0.0, 51.0, 0.0, 0.0}, { 1, 0, 0,-4, 1, -100.0, 0.0, -1.0, 56.0, 0.0, 0.0}, { 0, 2, 2,-2, 1, 87.0, 0.0, 0.0, -47.0, 0.0, 0.0}, {-3, 0, 0, 4, 0, 161.0, 0.0, 0.0, -1.0, 0.0, 0.0}, {-1, 1, 2, 0, 1, 96.0, 0.0, 0.0, -50.0, 0.0, 0.0}, {-1,-1, 0, 4, 0, 151.0, 0.0, -1.0, -5.0, 0.0, 0.0}, /* 201-210 */ {-1,-2, 2, 2, 2, -104.0, 0.0, 0.0, 44.0, 0.0, 0.0}, {-2,-1, 2, 4, 2, -110.0, 0.0, 0.0, 48.0, 0.0, 0.0}, { 1,-1, 2, 2, 1, -100.0, 0.0, 1.0, 50.0, 0.0, 0.0}, {-2, 1, 0, 2, 0, 92.0, 0.0, -5.0, 12.0, 0.0, -2.0}, {-2, 1, 2, 0, 1, 82.0, 0.0, 0.0, -45.0, 0.0, 0.0}, { 2, 1, 0,-2, 1, 82.0, 0.0, 0.0, -45.0, 0.0, 0.0}, {-3, 0, 2, 0, 1, -78.0, 0.0, 0.0, 41.0, 0.0, 0.0}, {-2, 0, 2,-2, 1, -77.0, 0.0, 0.0, 43.0, 0.0, 0.0}, {-1, 1, 0, 2, 2, 2.0, 0.0, 0.0, 54.0, 0.0, 0.0}, { 0,-1, 2,-1, 2, 94.0, 0.0, 0.0, -40.0, 0.0, 0.0}, /* 211-220 */ {-1, 0, 4,-2, 2, -93.0, 0.0, 0.0, 40.0, 0.0, 0.0}, { 0,-2, 2, 0, 2, -83.0, 0.0, 10.0, 40.0, 0.0, -2.0}, {-1, 0, 2, 1, 2, 83.0, 0.0, 0.0, -36.0, 0.0, 0.0}, { 2, 0, 0, 0, 2, -91.0, 0.0, 0.0, 39.0, 0.0, 0.0}, { 0, 0, 2, 0, 3, 128.0, 0.0, 0.0, -1.0, 0.0, 0.0}, {-2, 0, 4, 0, 2, -79.0, 0.0, 0.0, 34.0, 0.0, 0.0}, {-1, 0,-2, 0, 1, -83.0, 0.0, 0.0, 47.0, 0.0, 0.0}, {-1, 1, 2, 2, 1, 84.0, 0.0, 0.0, -44.0, 0.0, 0.0}, { 3, 0, 0, 0, 1, 83.0, 0.0, 0.0, -43.0, 0.0, 0.0}, {-1, 0, 2, 3, 2, 91.0, 0.0, 0.0, -39.0, 0.0, 0.0}, /* 221-230 */ { 2,-1, 2, 0, 1, -77.0, 0.0, 0.0, 39.0, 0.0, 0.0}, { 0, 1, 2, 2, 1, 84.0, 0.0, 0.0, -43.0, 0.0, 0.0}, { 0,-1, 2, 4, 2, -92.0, 0.0, 1.0, 39.0, 0.0, 0.0}, { 2,-1, 2, 2, 2, -92.0, 0.0, 1.0, 39.0, 0.0, 0.0}, { 0, 2,-2, 2, 0, -94.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1,-1, 2,-1, 1, 68.0, 0.0, 0.0, -36.0, 0.0, 0.0}, { 0,-2, 0, 0, 1, -61.0, 0.0, 0.0, 32.0, 0.0, 0.0}, { 1, 0, 2,-4, 2, 71.0, 0.0, 0.0, -31.0, 0.0, 0.0}, { 1,-1, 0,-2, 1, 62.0, 0.0, 0.0, -34.0, 0.0, 0.0}, {-1,-1, 2, 0, 1, -63.0, 0.0, 0.0, 33.0, 0.0, 0.0}, /* 231-240 */ { 1,-1, 2,-2, 2, -73.0, 0.0, 0.0, 32.0, 0.0, 0.0}, {-2,-1, 0, 4, 0, 115.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-1, 0, 0, 3, 0, -103.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-2,-1, 2, 2, 2, 63.0, 0.0, 0.0, -28.0, 0.0, 0.0}, { 0, 2, 2, 0, 2, 74.0, 0.0, 0.0, -32.0, 0.0, 0.0}, { 1, 1, 0, 2, 0, -103.0, 0.0, -3.0, 3.0, 0.0, -1.0}, { 2, 0, 2,-1, 2, -69.0, 0.0, 0.0, 30.0, 0.0, 0.0}, { 1, 0, 2, 1, 1, 57.0, 0.0, 0.0, -29.0, 0.0, 0.0}, { 4, 0, 0, 0, 0, 94.0, 0.0, 0.0, -4.0, 0.0, 0.0}, { 2, 1, 2, 0, 1, 64.0, 0.0, 0.0, -33.0, 0.0, 0.0}, /* 241-250 */ { 3,-1, 2, 0, 2, -63.0, 0.0, 0.0, 26.0, 0.0, 0.0}, {-2, 2, 0, 2, 1, -38.0, 0.0, 0.0, 20.0, 0.0, 0.0}, { 1, 0, 2,-3, 1, -43.0, 0.0, 0.0, 24.0, 0.0, 0.0}, { 1, 1, 2,-4, 1, -45.0, 0.0, 0.0, 23.0, 0.0, 0.0}, {-1,-1, 2,-2, 1, 47.0, 0.0, 0.0, -24.0, 0.0, 0.0}, { 0,-1, 0,-1, 1, -48.0, 0.0, 0.0, 25.0, 0.0, 0.0}, { 0,-1, 0,-2, 1, 45.0, 0.0, 0.0, -26.0, 0.0, 0.0}, {-2, 0, 0, 0, 2, 56.0, 0.0, 0.0, -25.0, 0.0, 0.0}, {-2, 0,-2, 2, 0, 88.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-1, 0,-2, 4, 0, -75.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 251-260 */ { 1,-2, 0, 0, 0, 85.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 1, 0, 1, 1, 49.0, 0.0, 0.0, -26.0, 0.0, 0.0}, {-1, 2, 0, 2, 0, -74.0, 0.0, -3.0, -1.0, 0.0, -1.0}, { 1,-1, 2,-2, 1, -39.0, 0.0, 0.0, 21.0, 0.0, 0.0}, { 1, 2, 2,-2, 2, 45.0, 0.0, 0.0, -20.0, 0.0, 0.0}, { 2,-1, 2,-2, 2, 51.0, 0.0, 0.0, -22.0, 0.0, 0.0}, { 1, 0, 2,-1, 1, -40.0, 0.0, 0.0, 21.0, 0.0, 0.0}, { 2, 1, 2,-2, 1, 41.0, 0.0, 0.0, -21.0, 0.0, 0.0}, {-2, 0, 0,-2, 1, -42.0, 0.0, 0.0, 24.0, 0.0, 0.0}, { 1,-2, 2, 0, 2, -51.0, 0.0, 0.0, 22.0, 0.0, 0.0}, /* 261-270 */ { 0, 1, 2, 1, 1, -42.0, 0.0, 0.0, 22.0, 0.0, 0.0}, { 1, 0, 4,-2, 1, 39.0, 0.0, 0.0, -21.0, 0.0, 0.0}, {-2, 0, 4, 2, 2, 46.0, 0.0, 0.0, -18.0, 0.0, 0.0}, { 1, 1, 2, 1, 2, -53.0, 0.0, 0.0, 22.0, 0.0, 0.0}, { 1, 0, 0, 4, 0, 82.0, 0.0, 0.0, -4.0, 0.0, 0.0}, { 1, 0, 2, 2, 0, 81.0, 0.0, -1.0, -4.0, 0.0, 0.0}, { 2, 0, 2, 1, 2, 47.0, 0.0, 0.0, -19.0, 0.0, 0.0}, { 3, 1, 2, 0, 2, 53.0, 0.0, 0.0, -23.0, 0.0, 0.0}, { 4, 0, 2, 0, 1, -45.0, 0.0, 0.0, 22.0, 0.0, 0.0}, {-2,-1, 2, 0, 0, -44.0, 0.0, 0.0, -2.0, 0.0, 0.0}, /* 271-280 */ { 0, 1,-2, 2, 1, -33.0, 0.0, 0.0, 16.0, 0.0, 0.0}, { 1, 0,-2, 1, 0, -61.0, 0.0, 0.0, 1.0, 0.0, 0.0}, { 0,-1,-2, 2, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0}, { 2,-1, 0,-2, 1, -38.0, 0.0, 0.0, 19.0, 0.0, 0.0}, {-1, 0, 2,-1, 2, -33.0, 0.0, 0.0, 21.0, 0.0, 0.0}, { 1, 0, 2,-3, 2, -60.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 1, 2,-2, 3, 48.0, 0.0, 0.0, -10.0, 0.0, 0.0}, { 0, 0, 2,-3, 1, 27.0, 0.0, 0.0, -14.0, 0.0, 0.0}, {-1, 0,-2, 2, 1, 38.0, 0.0, 0.0, -20.0, 0.0, 0.0}, { 0, 0, 2,-4, 2, 31.0, 0.0, 0.0, -13.0, 0.0, 0.0}, /* 281-290 */ {-2, 1, 0, 0, 1, -29.0, 0.0, 0.0, 15.0, 0.0, 0.0}, {-1, 0, 0,-1, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0}, { 2, 0, 2,-4, 2, -32.0, 0.0, 0.0, 15.0, 0.0, 0.0}, { 0, 0, 4,-4, 4, 45.0, 0.0, 0.0, -8.0, 0.0, 0.0}, { 0, 0, 4,-4, 2, -44.0, 0.0, 0.0, 19.0, 0.0, 0.0}, {-1,-2, 0, 2, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0}, {-2, 0, 0, 3, 0, -51.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 0,-2, 2, 1, -36.0, 0.0, 0.0, 20.0, 0.0, 0.0}, {-3, 0, 2, 2, 2, 44.0, 0.0, 0.0, -19.0, 0.0, 0.0}, {-3, 0, 2, 2, 1, 26.0, 0.0, 0.0, -14.0, 0.0, 0.0}, /* 291-300 */ {-2, 0, 2, 2, 0, -60.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 2,-1, 0, 0, 1, 35.0, 0.0, 0.0, -18.0, 0.0, 0.0}, {-2, 1, 2, 2, 2, -27.0, 0.0, 0.0, 11.0, 0.0, 0.0}, { 1, 1, 0, 1, 0, 47.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 0, 1, 4,-2, 2, 36.0, 0.0, 0.0, -15.0, 0.0, 0.0}, {-1, 1, 0,-2, 1, -36.0, 0.0, 0.0, 20.0, 0.0, 0.0}, { 0, 0, 0,-4, 1, -35.0, 0.0, 0.0, 19.0, 0.0, 0.0}, { 1,-1, 0, 2, 1, -37.0, 0.0, 0.0, 19.0, 0.0, 0.0}, { 1, 1, 0, 2, 1, 32.0, 0.0, 0.0, -16.0, 0.0, 0.0}, {-1, 2, 2, 2, 2, 35.0, 0.0, 0.0, -14.0, 0.0, 0.0}, /* 301-310 */ { 3, 1, 2,-2, 2, 32.0, 0.0, 0.0, -13.0, 0.0, 0.0}, { 0,-1, 0, 4, 0, 65.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 2,-1, 0, 2, 0, 47.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 0, 0, 4, 0, 1, 32.0, 0.0, 0.0, -16.0, 0.0, 0.0}, { 2, 0, 4,-2, 2, 37.0, 0.0, 0.0, -16.0, 0.0, 0.0}, {-1,-1, 2, 4, 1, -30.0, 0.0, 0.0, 15.0, 0.0, 0.0}, { 1, 0, 0, 4, 1, -32.0, 0.0, 0.0, 16.0, 0.0, 0.0}, { 1,-2, 2, 2, 2, -31.0, 0.0, 0.0, 13.0, 0.0, 0.0}, { 0, 0, 2, 3, 2, 37.0, 0.0, 0.0, -16.0, 0.0, 0.0}, {-1, 1, 2, 4, 2, 31.0, 0.0, 0.0, -13.0, 0.0, 0.0}, /* 311-320 */ { 3, 0, 0, 2, 0, 49.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-1, 0, 4, 2, 2, 32.0, 0.0, 0.0, -13.0, 0.0, 0.0}, { 1, 1, 2, 2, 1, 23.0, 0.0, 0.0, -12.0, 0.0, 0.0}, {-2, 0, 2, 6, 2, -43.0, 0.0, 0.0, 18.0, 0.0, 0.0}, { 2, 1, 2, 2, 2, 26.0, 0.0, 0.0, -11.0, 0.0, 0.0}, {-1, 0, 2, 6, 2, -32.0, 0.0, 0.0, 14.0, 0.0, 0.0}, { 1, 0, 2, 4, 1, -29.0, 0.0, 0.0, 14.0, 0.0, 0.0}, { 2, 0, 2, 4, 2, -27.0, 0.0, 0.0, 12.0, 0.0, 0.0}, { 1, 1,-2, 1, 0, 30.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-3, 1, 2, 1, 2, -11.0, 0.0, 0.0, 5.0, 0.0, 0.0}, /* 321-330 */ { 2, 0,-2, 0, 2, -21.0, 0.0, 0.0, 10.0, 0.0, 0.0}, {-1, 0, 0, 1, 2, -34.0, 0.0, 0.0, 15.0, 0.0, 0.0}, {-4, 0, 2, 2, 1, -10.0, 0.0, 0.0, 6.0, 0.0, 0.0}, {-1,-1, 0, 1, 0, -36.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 0,-2, 2, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0}, { 1, 0, 0,-1, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0}, { 0,-1, 2,-2, 3, -21.0, 0.0, 0.0, 5.0, 0.0, 0.0}, {-2, 1, 2, 0, 0, -29.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 0, 0, 2,-2, 4, -15.0, 0.0, 0.0, 3.0, 0.0, 0.0}, {-2,-2, 0, 2, 0, -20.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 331-340 */ {-2, 0,-2, 4, 0, 28.0, 0.0, 0.0, 0.0, 0.0, -2.0}, { 0,-2,-2, 2, 0, 17.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 2, 0,-2, 1, -22.0, 0.0, 0.0, 12.0, 0.0, 0.0}, { 3, 0, 0,-4, 1, -14.0, 0.0, 0.0, 7.0, 0.0, 0.0}, {-1, 1, 2,-2, 2, 24.0, 0.0, 0.0, -11.0, 0.0, 0.0}, { 1,-1, 2,-4, 1, 11.0, 0.0, 0.0, -6.0, 0.0, 0.0}, { 1, 1, 0,-2, 2, 14.0, 0.0, 0.0, -6.0, 0.0, 0.0}, {-3, 0, 2, 0, 0, 24.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-3, 0, 2, 0, 2, 18.0, 0.0, 0.0, -8.0, 0.0, 0.0}, {-2, 0, 0, 1, 0, -38.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 341-350 */ { 0, 0,-2, 1, 0, -31.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-3, 0, 0, 2, 1, -16.0, 0.0, 0.0, 8.0, 0.0, 0.0}, {-1,-1,-2, 2, 0, 29.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 1, 2,-4, 1, -18.0, 0.0, 0.0, 10.0, 0.0, 0.0}, { 2, 1, 0,-4, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0}, { 0, 2, 0,-2, 1, -17.0, 0.0, 0.0, 10.0, 0.0, 0.0}, { 1, 0, 0,-3, 1, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0}, {-2, 0, 2,-2, 2, 16.0, 0.0, 0.0, -6.0, 0.0, 0.0}, {-2,-1, 0, 0, 1, 22.0, 0.0, 0.0, -12.0, 0.0, 0.0}, {-4, 0, 0, 2, 0, 20.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 351-360 */ { 1, 1, 0,-4, 1, -13.0, 0.0, 0.0, 6.0, 0.0, 0.0}, {-1, 0, 2,-4, 1, -17.0, 0.0, 0.0, 9.0, 0.0, 0.0}, { 0, 0, 4,-4, 1, -14.0, 0.0, 0.0, 8.0, 0.0, 0.0}, { 0, 3, 2,-2, 2, 0.0, 0.0, 0.0, -7.0, 0.0, 0.0}, {-3,-1, 0, 4, 0, 14.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-3, 0, 0, 4, 1, 19.0, 0.0, 0.0, -10.0, 0.0, 0.0}, { 1,-1,-2, 2, 0, -34.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1,-1, 0, 2, 2, -20.0, 0.0, 0.0, 8.0, 0.0, 0.0}, { 1,-2, 0, 0, 1, 9.0, 0.0, 0.0, -5.0, 0.0, 0.0}, { 1,-1, 0, 0, 2, -18.0, 0.0, 0.0, 7.0, 0.0, 0.0}, /* 361-370 */ { 0, 0, 0, 1, 2, 13.0, 0.0, 0.0, -6.0, 0.0, 0.0}, {-1,-1, 2, 0, 0, 17.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1,-2, 2,-2, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0}, { 0,-1, 2,-1, 1, 15.0, 0.0, 0.0, -8.0, 0.0, 0.0}, {-1, 0, 2, 0, 3, -11.0, 0.0, 0.0, 3.0, 0.0, 0.0}, { 1, 1, 0, 0, 2, 13.0, 0.0, 0.0, -5.0, 0.0, 0.0}, {-1, 1, 2, 0, 0, -18.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 2, 0, 0, 0, -35.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1, 2, 2, 0, 2, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0}, {-1, 0, 4,-2, 1, -19.0, 0.0, 0.0, 10.0, 0.0, 0.0}, /* 371-380 */ { 3, 0, 2,-4, 2, -26.0, 0.0, 0.0, 11.0, 0.0, 0.0}, { 1, 2, 2,-2, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0}, { 1, 0, 4,-4, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0}, {-2,-1, 0, 4, 1, 10.0, 0.0, 0.0, -6.0, 0.0, 0.0}, { 0,-1, 0, 2, 2, -21.0, 0.0, 0.0, 9.0, 0.0, 0.0}, {-2, 1, 0, 4, 0, -15.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2,-1, 2, 2, 1, 9.0, 0.0, 0.0, -5.0, 0.0, 0.0}, { 2, 0,-2, 2, 0, -29.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 0, 0, 1, 1, -19.0, 0.0, 0.0, 10.0, 0.0, 0.0}, { 0, 1, 0, 2, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0}, /* 381-390 */ { 1,-1, 2,-1, 2, 22.0, 0.0, 0.0, -9.0, 0.0, 0.0}, {-2, 0, 4, 0, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0}, { 2, 1, 0, 0, 1, -20.0, 0.0, 0.0, 11.0, 0.0, 0.0}, { 0, 1, 2, 0, 0, -20.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0,-1, 4,-2, 2, -17.0, 0.0, 0.0, 7.0, 0.0, 0.0}, { 0, 0, 4,-2, 4, 15.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 0, 2, 2, 0, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0}, {-3, 0, 0, 6, 0, 14.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1,-1, 0, 4, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0}, { 1,-2, 0, 2, 0, 25.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 391-400 */ {-1, 0, 0, 4, 2, -13.0, 0.0, 0.0, 6.0, 0.0, 0.0}, {-1,-2, 2, 2, 1, -14.0, 0.0, 0.0, 8.0, 0.0, 0.0}, {-1, 0, 0,-2, 2, 13.0, 0.0, 0.0, -5.0, 0.0, 0.0}, { 1, 0,-2,-2, 1, -17.0, 0.0, 0.0, 9.0, 0.0, 0.0}, { 0, 0,-2,-2, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0}, {-2, 0,-2, 0, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0}, { 0, 0, 0, 3, 1, 10.0, 0.0, 0.0, -6.0, 0.0, 0.0}, { 0, 0, 0, 3, 0, -15.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1, 1, 0, 4, 0, -22.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1,-1, 2, 2, 0, 28.0, 0.0, 0.0, -1.0, 0.0, 0.0}, /* 401-410 */ {-2, 0, 2, 3, 2, 15.0, 0.0, 0.0, -7.0, 0.0, 0.0}, { 1, 0, 0, 2, 2, 23.0, 0.0, 0.0, -10.0, 0.0, 0.0}, { 0,-1, 2, 1, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0}, { 3,-1, 0, 0, 0, 29.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 2, 0, 0, 1, 0, -25.0, 0.0, 0.0, 1.0, 0.0, 0.0}, { 1,-1, 2, 0, 0, 22.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 0, 2, 1, 0, -18.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 0, 2, 0, 3, 15.0, 0.0, 0.0, 3.0, 0.0, 0.0}, { 3, 1, 0, 0, 0, -23.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 3,-1, 2,-2, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0}, /* 411-420 */ { 2, 0, 2,-1, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0}, { 1, 1, 2, 0, 0, -19.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 0, 4,-1, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0}, { 1, 2, 2, 0, 2, 21.0, 0.0, 0.0, -9.0, 0.0, 0.0}, {-2, 0, 0, 6, 0, 23.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 0,-1, 0, 4, 1, -16.0, 0.0, 0.0, 8.0, 0.0, 0.0}, {-2,-1, 2, 4, 1, -19.0, 0.0, 0.0, 9.0, 0.0, 0.0}, { 0,-2, 2, 2, 1, -22.0, 0.0, 0.0, 10.0, 0.0, 0.0}, { 0,-1, 2, 2, 0, 27.0, 0.0, 0.0, -1.0, 0.0, 0.0}, {-1, 0, 2, 3, 1, 16.0, 0.0, 0.0, -8.0, 0.0, 0.0}, /* 421-430 */ {-2, 1, 2, 4, 2, 19.0, 0.0, 0.0, -8.0, 0.0, 0.0}, { 2, 0, 0, 2, 2, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0}, { 2,-2, 2, 0, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0}, {-1, 1, 2, 3, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0}, { 3, 0, 2,-1, 2, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0}, { 4, 0, 2,-2, 1, 18.0, 0.0, 0.0, -9.0, 0.0, 0.0}, {-1, 0, 0, 6, 0, 16.0, 0.0, 0.0, -1.0, 0.0, 0.0}, {-1,-2, 2, 4, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0}, {-3, 0, 2, 6, 2, -23.0, 0.0, 0.0, 9.0, 0.0, 0.0}, {-1, 0, 2, 4, 0, 16.0, 0.0, 0.0, -1.0, 0.0, 0.0}, /* 431-440 */ { 3, 0, 0, 2, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0}, { 3,-1, 2, 0, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0}, { 3, 0, 2, 0, 0, 30.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 1, 0, 4, 0, 2, 24.0, 0.0, 0.0, -10.0, 0.0, 0.0}, { 5, 0, 2,-2, 2, 10.0, 0.0, 0.0, -4.0, 0.0, 0.0}, { 0,-1, 2, 4, 1, -16.0, 0.0, 0.0, 7.0, 0.0, 0.0}, { 2,-1, 2, 2, 1, -16.0, 0.0, 0.0, 7.0, 0.0, 0.0}, { 0, 1, 2, 4, 2, 17.0, 0.0, 0.0, -7.0, 0.0, 0.0}, { 1,-1, 2, 4, 2, -24.0, 0.0, 0.0, 10.0, 0.0, 0.0}, { 3,-1, 2, 2, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0}, /* 441-450 */ { 3, 0, 2, 2, 1, -24.0, 0.0, 0.0, 11.0, 0.0, 0.0}, { 5, 0, 2, 0, 2, -23.0, 0.0, 0.0, 9.0, 0.0, 0.0}, { 0, 0, 2, 6, 2, -13.0, 0.0, 0.0, 5.0, 0.0, 0.0}, { 4, 0, 2, 2, 2, -15.0, 0.0, 0.0, 7.0, 0.0, 0.0}, { 0,-1, 1,-1, 1, 0.0, 0.0,-1988.0, 0.0, 0.0,-1679.0}, {-1, 0, 1, 0, 3, 0.0, 0.0, -63.0, 0.0, 0.0, -27.0}, { 0,-2, 2,-2, 3, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 0,-1, 0, 1, 0.0, 0.0, 5.0, 0.0, 0.0, 4.0}, { 2,-2, 0,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, {-1, 0, 1, 0, 2, 0.0, 0.0, 364.0, 0.0, 0.0, 176.0}, /* 451-460 */ {-1, 0, 1, 0, 1, 0.0, 0.0,-1044.0, 0.0, 0.0, -891.0}, {-1,-1, 2,-1, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, {-2, 2, 0, 2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-1, 0, 1, 0, 0, 0.0, 0.0, 330.0, 0.0, 0.0, 0.0}, {-4, 1, 2, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-3, 0, 2, 1, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-2,-1, 2, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, { 1, 0,-2, 1, 1, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 2,-1,-2, 0, 1, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, {-4, 0, 2, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 461-470 */ {-3, 1, 0, 3, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1, 0,-1, 2, 0, 0.0, 0.0, 5.0, 0.0, 0.0, 0.0}, { 0,-2, 0, 0, 2, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0}, { 0,-2, 0, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-3, 0, 0, 3, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2,-1, 0, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-1, 0,-2, 3, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-4, 0, 0, 4, 0, -12.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 2, 1,-2, 0, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 2,-1, 0,-2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, /* 471-480 */ { 0, 0, 1,-1, 0, -5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1, 2, 0, 1, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2, 1, 2, 0, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0}, { 1, 1, 0,-1, 1, 7.0, 0.0, 0.0, -4.0, 0.0, 0.0}, { 1, 0, 1,-2, 1, 0.0, 0.0, -12.0, 0.0, 0.0, -10.0}, { 0, 2, 0, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 1,-1, 2,-3, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-1, 1, 2,-1, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-2, 0, 4,-2, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0}, {-2, 0, 4,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, /* 481-490 */ {-2,-2, 0, 2, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, {-2, 0,-2, 4, 0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 2, 2,-4, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, { 1, 1, 2,-4, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0}, {-1, 2, 2,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 2, 0, 0,-3, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-1, 2, 0, 0, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0}, { 0, 0, 0,-2, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1,-1, 2,-2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-1, 1, 0, 0, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, /* 491-500 */ { 0, 0, 0,-1, 2, -8.0, 0.0, 0.0, 3.0, 0.0, 0.0}, {-2, 1, 0, 1, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1,-2, 0,-2, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 1, 0,-2, 0, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-3, 1, 0, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1, 1,-2, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1,-1, 0, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, {-3, 0, 0, 2, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-3,-1, 0, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 2, 0, 2,-6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, /* 501-510 */ { 0, 1, 2,-4, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 2, 0, 0,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, {-2, 1, 2,-2, 1, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 0,-1, 2,-4, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 0, 1, 0,-2, 2, 9.0, 0.0, 0.0, -3.0, 0.0, 0.0}, {-1, 0, 0,-2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 2, 0,-2,-2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-4, 0, 2, 0, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-1,-1, 0,-1, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 0, 0,-2, 0, 2, 9.0, 0.0, 0.0, -3.0, 0.0, 0.0}, /* 511-520 */ {-3, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1, 0,-2, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2, 0,-2, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 0, 0,-4, 2, 0, 8.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2,-1,-2, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 0, 2,-6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-1, 0, 2,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 1, 0, 0,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 2, 1, 2,-4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, { 2, 1, 2,-4, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, /* 521-530 */ { 0, 1, 4,-4, 4, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 1, 4,-4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, {-1,-1,-2, 4, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1,-3, 0, 2, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1, 0,-2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-2,-1, 0, 3, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 0,-2, 3, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2, 0, 0, 3, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0}, { 0,-1, 0, 1, 0, -13.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-3, 0, 2, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 531-540 */ { 1, 1,-2, 2, 0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1, 1, 0, 2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 1,-2, 2,-2, 1, 10.0, 0.0, 13.0, 6.0, 0.0, -5.0}, { 0, 0, 1, 0, 2, 0.0, 0.0, 30.0, 0.0, 0.0, 14.0}, { 0, 0, 1, 0, 1, 0.0, 0.0, -162.0, 0.0, 0.0, -138.0}, { 0, 0, 1, 0, 0, 0.0, 0.0, 75.0, 0.0, 0.0, 0.0}, {-1, 2, 0, 2, 1, -7.0, 0.0, 0.0, 4.0, 0.0, 0.0}, { 0, 0, 2, 0, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-2, 0, 2, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 2, 0, 0,-1, 1, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, /* 541-550 */ { 3, 0, 0,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 1, 0, 2,-2, 3, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 2, 0, 0, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 2, 0, 2,-3, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-1, 1, 4,-2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-2,-2, 0, 4, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0,-3, 0, 2, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 0,-2, 4, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1,-1, 0, 3, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2, 0, 0, 4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, /* 551-560 */ {-1, 0, 0, 3, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 2,-2, 0, 0, 0, 7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1,-1, 0, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1, 0, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0,-2, 2, 0, 1, -6.0, 0.0, -3.0, 3.0, 0.0, 1.0}, {-1, 0, 1, 2, 1, 0.0, 0.0, -3.0, 0.0, 0.0, -2.0}, {-1, 1, 0, 3, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1,-1, 2, 1, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 0,-1, 2, 0, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2, 1, 2, 2, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, /* 561-570 */ { 2,-2, 2,-2, 2, -1.0, 0.0, 3.0, 3.0, 0.0, -1.0}, { 1, 1, 0, 1, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 1, 0, 1, 0, 1, 0.0, 0.0, -13.0, 0.0, 0.0, -11.0}, { 1, 0, 1, 0, 0, 3.0, 0.0, 6.0, 0.0, 0.0, 0.0}, { 0, 2, 0, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 2,-1, 2,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 0,-1, 4,-2, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, { 0, 0, 4,-2, 3, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 1, 4,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 4, 0, 2,-4, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0}, /* 571-580 */ { 2, 2, 2,-2, 2, 8.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 2, 0, 4,-4, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-1,-2, 0, 4, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1,-3, 2, 2, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, {-3, 0, 2, 4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, {-3, 0, 2,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-1,-1, 0,-2, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0}, {-3, 0, 0, 0, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, {-3, 0,-2, 2, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 1, 0,-4, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, /* 581-590 */ {-2, 1, 0,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-4, 0, 0, 0, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0}, {-1, 0, 0,-4, 1, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0}, {-3, 0, 0,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 0, 0, 0, 3, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, {-1, 1, 0, 4, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 1,-2, 2, 0, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, { 0, 1, 0, 3, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1, 0, 2, 2, 3, 6.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 0, 0, 2, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, /* 591-600 */ {-2, 0, 2, 2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-1, 1, 2, 2, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 3, 0, 0, 0, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 2, 1, 0, 1, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 2,-1, 2,-1, 2, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 0, 0, 2, 0, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 0, 0, 3, 0, 3, 0.0, 0.0, -26.0, 0.0, 0.0, -11.0}, { 0, 0, 3, 0, 2, 0.0, 0.0, -10.0, 0.0, 0.0, -5.0}, {-1, 2, 2, 2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, {-1, 0, 4, 0, 0, -13.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 601-610 */ { 1, 2, 2, 0, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 3, 1, 2,-2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 1, 1, 4,-2, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0}, {-2,-1, 0, 6, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0,-2, 0, 4, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2, 0, 0, 6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-2,-2, 2, 4, 2, -6.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 0,-3, 2, 2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 0, 0, 0, 4, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0}, {-1,-1, 2, 3, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, /* 611-620 */ {-2, 0, 2, 4, 0, 13.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 2,-1, 0, 2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 1, 0, 0, 3, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 1, 0, 4, 1, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 0, 1, 0, 4, 0, -11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1,-1, 2, 1, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 0, 0, 2, 2, 3, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 0, 2, 2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-1, 0, 2, 2, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-2, 0, 4, 2, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, /* 621-630 */ { 2, 1, 0, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 2, 1, 0, 2, 0, -12.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 2,-1, 2, 0, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 0, 2, 1, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 1, 2, 2, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 2, 0, 2, 0, 3, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 3, 0, 2, 0, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 1, 0, 2, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, { 1, 0, 3, 0, 3, 0.0, 0.0, -5.0, 0.0, 0.0, -2.0}, { 1, 1, 2, 1, 1, -7.0, 0.0, 0.0, 4.0, 0.0, 0.0}, /* 631-640 */ { 0, 2, 2, 2, 2, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 2, 1, 2, 0, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 2, 0, 4,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 4, 1, 2,-2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, {-1,-1, 0, 6, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-3,-1, 2, 6, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, {-1, 0, 0, 6, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0}, {-3, 0, 2, 6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 1,-1, 0, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 1,-1, 0, 4, 0, 12.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 641-650 */ {-2, 0, 2, 5, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 1,-2, 2, 2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 3,-1, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1,-1, 2, 2, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 0, 2, 3, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0}, {-1, 1, 2, 4, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 0, 1, 2, 3, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, {-1, 0, 4, 2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 2, 0, 2, 1, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 5, 0, 0, 0, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 651-660 */ { 2, 1, 2, 1, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, { 1, 0, 4, 0, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 3, 1, 2, 0, 1, 7.0, 0.0, 0.0, -4.0, 0.0, 0.0}, { 3, 0, 4,-2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, {-2,-1, 2, 6, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 0, 0, 0, 6, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0,-2, 2, 4, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, {-2, 0, 2, 6, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0}, { 2, 0, 0, 4, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 2, 0, 0, 4, 0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0}, /* 661-670 */ { 2,-2, 2, 2, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 0, 0, 2, 4, 0, 7.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 1, 0, 2, 3, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0}, { 4, 0, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 2, 0, 2, 2, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0}, { 0, 0, 4, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 4,-1, 2, 0, 2, -6.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 3, 0, 2, 1, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 2, 1, 2, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 4, 1, 2, 0, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0}, /* 671-678 */ {-1,-1, 2, 6, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, {-1, 0, 2, 6, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 1,-1, 2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0}, { 1, 1, 2, 4, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0}, { 3, 1, 2, 2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0}, { 5, 0, 2, 0, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, { 2,-1, 2, 4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0}, { 2, 0, 2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0} }; /* Number of terms in the luni-solar nutation model */ const int NLS = (int) (sizeof xls / sizeof xls[0]); /* ------------------------ */ /* Planetary nutation model */ /* ------------------------ */ /* The units for the sine and cosine coefficients are */ /* 0.1 microarcsecond */ static const struct { int nl, /* coefficients of l, F, D and Omega */ nf, nd, nom, nme, /* coefficients of planetary longitudes */ nve, nea, nma, nju, nsa, nur, nne, npa; /* coefficient of general precession */ int sp,cp; /* longitude sin, cos coefficients */ int se,ce; /* obliquity sin, cos coefficients */ } xpl[] = { /* 1-10 */ { 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 0, 1440, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, -8, 16,-4,-5, 0, 0, 2, 56,-117, -42, -40}, { 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 2, 125, -43, 0, -54}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 2, 2, 0, 5, 0, 0}, { 0, 0, 0, 0, 0, 0, -4, 8,-1,-5, 0, 0, 2, 3, -7, -3, 0}, { 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1, 3, 0, 0, -2}, { 0, 1,-1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0, -114, 0, 0, 61}, {-1, 0, 0, 0, 0, 10, -3, 0, 0, 0, 0, 0, 0, -219, 89, 0, 0}, { 0, 0, 0, 0, 0, 0, 0, 0,-2, 6,-3, 0, 2, -3, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, -462,1604, 0, 0}, /* 11-20 */ { 0, 1,-1, 1, 0, 0, -5, 8,-3, 0, 0, 0, 0, 99, 0, 0, -53}, { 0, 0, 0, 0, 0, 0, -4, 8,-3, 0, 0, 0, 1, -3, 0, 0, 2}, { 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2, 0, 6, 2, 0}, { 0, 0, 0, 0, 0, -5, 6, 4, 0, 0, 0, 0, 2, 3, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 2, -12, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 1, 14,-218, 117, 8}, { 0, 1,-1, 1, 0, 0, -1, 0, 2,-5, 0, 0, 0, 31,-481, -257, -17}, { 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 0, -491, 128, 0, 0}, { 0, 1,-1, 1, 0, 0, -1, 0,-2, 5, 0, 0, 0,-3084,5123, 2735,1647}, { 0, 0, 0, 0, 0, 0, 0, 0,-2, 5, 0, 0, 1,-1444,2409,-1286,-771}, /* 21-30 */ { 0, 0, 0, 0, 0, 0, 0, 0,-2, 5, 0, 0, 2, 11, -24, -11, -9}, { 2,-1,-1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0, 26, -9, 0, 0}, { 1, 0,-2, 0, 0, 19,-21, 3, 0, 0, 0, 0, 0, 103, -60, 0, 0}, { 0, 1,-1, 1, 0, 2, -4, 0,-3, 0, 0, 0, 0, 0, -13, -7, 0}, { 1, 0,-1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, -26, -29, -16, 14}, { 0, 1,-1, 1, 0, 0, -1, 0,-4,10, 0, 0, 0, 9, -27, -14, -5}, {-2, 0, 2, 1, 0, 0, 2, 0, 0,-5, 0, 0, 0, 12, 0, 0, -6}, { 0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0, -7, 0, 0, 0}, { 0,-1, 1, 0, 0, 0, 1, 0, 1,-1, 0, 0, 0, 0, 24, 0, 0}, {-2, 0, 2, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, 284, 0, 0,-151}, /* 31-40 */ {-1, 0, 0, 0, 0, 18,-16, 0, 0, 0, 0, 0, 0, 226, 101, 0, 0}, {-2, 1, 1, 2, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -8, -2, 0}, {-1, 1,-1, 1, 0, 18,-17, 0, 0, 0, 0, 0, 0, 0, -6, -3, 0}, {-1, 0, 1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 5, 0, 0, -3}, { 0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 2, -41, 175, 76, 17}, { 0, 2,-2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0, 0, 15, 6, 0}, { 0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 1, 425, 212, -133, 269}, { 0, 1,-1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0, 1200, 598, 319,-641}, { 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 0, 235, 334, 0, 0}, { 0, 1,-1, 1, 0, 8,-14, 0, 0, 0, 0, 0, 0, 11, -12, -7, -6}, /* 41-50 */ { 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 1, 5, -6, 3, 3}, {-2, 0, 2, 1, 0, 0, 2, 0,-4, 5, 0, 0, 0, -5, 0, 0, 3}, {-2, 0, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3}, {-2, 0, 2, 0, 0, 0, 2, 0,-3, 1, 0, 0, 0, 15, 0, 0, 0}, { 0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0, 13, 0, 0, -7}, {-2, 0, 2, 0, 0, 0, 2, 0,-4, 3, 0, 0, 0, -6, -9, 0, 0}, { 0,-1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 266, -78, 0, 0}, { 0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0, -460,-435, -232, 246}, { 0, 1,-1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 15, 7, 0}, {-1, 1, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2}, /* 51-60 */ {-1, 0, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0}, {-2, 0, 2, 0, 0, 0, 2, 0,-2,-2, 0, 0, 0, 4, 0, 0, 0}, {-2, 2, 0, 2, 0, 0, -5, 9, 0, 0, 0, 0, 0, 0, 3, 0, 0}, { 0, 1,-1, 1, 0, 0, -1, 0, 0, 0,-1, 0, 0, 0, 4, 2, 0}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0}, { 0, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, -17, -19, -10, 9}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, -9, -11, 6, -5}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -6, 0, 0, 3}, {-1, 0, 1, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -16, 8, 0, 0}, { 0,-1, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0}, /* 61-70 */ { 0, 1,-1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 11, 24, 11, -5}, { 0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0, -3, -4, -2, 1}, { 0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, { 0, 1,-1, 1, 0, 0, -1, 0,-1, 2, 0, 0, 0, 0, -8, -4, 0}, { 0, 0, 0, 0, 0, 0, 0, 0, 1,-2, 0, 0, 0, 0, 3, 0, 0}, { 1, 0,-2, 0, 0, 17,-16, 0,-2, 0, 0, 0, 0, 0, 5, 0, 0}, { 0, 1,-1, 1, 0, 0, -1, 0, 1,-3, 0, 0, 0, 0, 3, 2, 0}, {-2, 0, 2, 1, 0, 0, 5, -6, 0, 0, 0, 0, 0, -6, 4, 2, 3}, { 0,-2, 2, 0, 0, 0, 9,-13, 0, 0, 0, 0, 0, -3, -5, 0, 0}, { 0, 1,-1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0, -5, 0, 0, 2}, /* 71-80 */ { 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 24, 13, -2}, { 0,-1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -42, 20, 0, 0}, { 0,-2, 2, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, -10, 233, 0, 0}, { 0,-1, 1, 1, 0, 5, -7, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1}, {-2, 0, 2, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, 78, -18, 0, 0}, { 2, 1,-3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0}, { 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, -1, 0}, { 0,-1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -4, -2, 1}, { 0, 1,-1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -8, -4, -1}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, -5, 3, 0}, /* 81-90 */ { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -7, 0, 0, 3}, { 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 2, -14, 8, 3, 6}, { 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 1, 0, 8, -4, 0}, { 0, 1,-1, 1, 0, 0, -9, 15, 0, 0, 0, 0, 0, 0, 19, 10, 0}, { 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, 45, -22, 0, 0}, { 1,-1,-1, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, -3, 0, 0, 0}, { 2, 0,-2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0}, {-2, 0, 2, 0, 0, 0, 2, 0,-5, 5, 0, 0, 0, 0, 3, 0, 0}, { 2, 0,-2, 1, 0, 0, -6, 8, 0, 0, 0, 0, 0, 3, 5, 3, -2}, { 2, 0,-2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 89, -16, -9, -48}, /* 91-100 */ {-2, 1, 1, 0, 0, 0, 1, 0,-3, 0, 0, 0, 0, 0, 3, 0, 0}, {-2, 1, 1, 1, 0, 0, 1, 0,-3, 0, 0, 0, 0, -3, 7, 4, 2}, {-2, 0, 2, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, -349, -62, 0, 0}, {-2, 0, 2, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -15, 22, 0, 0}, {-2, 0, 2, 0, 0, 0, 2, 0,-1,-5, 0, 0, 0, -3, 0, 0, 0}, {-1, 0, 1, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, -53, 0, 0, 0}, {-1, 1, 1, 1, 0,-20, 20, 0, 0, 0, 0, 0, 0, 5, 0, 0, -3}, { 1, 0,-2, 0, 0, 20,-21, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0}, { 0, 0, 0, 1, 0, 0, 8,-15, 0, 0, 0, 0, 0, 15, -7, -4, -8}, { 0, 2,-2, 1, 0, 0,-10, 15, 0, 0, 0, 0, 0, -3, 0, 0, 1}, /* 101-110 */ { 0,-1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, -21, -78, 0, 0}, { 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 20, -70, -37, -11}, { 0, 1,-1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 6, 3, 0}, { 0, 1,-1, 1, 0, 0, -1, 0,-2, 4, 0, 0, 0, 5, 3, 2, -2}, { 2, 0,-2, 1, 0, -6, 8, 0, 0, 0, 0, 0, 0, -17, -4, -2, 9}, { 0,-2, 2, 1, 0, 5, -6, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0}, { 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 0, 0, 1, 32, 15, -8, 17}, { 0, 1,-1, 1, 0, 0, -1, 0, 0,-1, 0, 0, 0, 174, 84, 45, -93}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 11, 56, 0, 0}, { 0, 1,-1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, -66, -12, -6, 35}, /* 111-120 */ { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 47, 8, 4, -25}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 8, 4, 0}, { 0, 2,-2, 1, 0, 0, -9, 13, 0, 0, 0, 0, 0, 10, -22, -12, -5}, { 0, 0, 0, 1, 0, 0, 7,-13, 0, 0, 0, 0, 0, -3, 0, 0, 2}, {-2, 0, 2, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -24, 12, 0, 0}, { 0, 0, 0, 0, 0, 0, 9,-17, 0, 0, 0, 0, 0, 5, -6, 0, 0}, { 0, 0, 0, 0, 0, 0, -9, 17, 0, 0, 0, 0, 2, 3, 0, 0, -2}, { 1, 0,-1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 4, 3, 1, -2}, { 1, 0,-1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 29, 15, 0}, { 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0, -5, -4, -2, 2}, /* 121-130 */ { 0,-1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, -3, -1, -5}, { 0,-2, 2, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0}, { 0, 0, 0, 0, 0, 3, -5, 0, 2, 0, 0, 0, 0, 10, 0, 0, 0}, {-2, 0, 2, 1, 0, 0, 2, 0,-3, 1, 0, 0, 0, 3, 0, 0, -2}, {-2, 0, 2, 1, 0, 3, -3, 0, 0, 0, 0, 0, 0, -5, 0, 0, 3}, { 0, 0, 0, 1, 0, 8,-13, 0, 0, 0, 0, 0, 0, 46, 66, 35, -25}, { 0,-1, 1, 0, 0, 8,-12, 0, 0, 0, 0, 0, 0, -14, 7, 0, 0}, { 0, 2,-2, 1, 0, -8, 11, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0}, {-1, 0, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -5, 0, 0, 0}, {-1, 0, 0, 1, 0, 18,-16, 0, 0, 0, 0, 0, 0, -68, -34, -18, 36}, /* 131-140 */ { 0, 1,-1, 1, 0, 0, -1, 0,-1, 1, 0, 0, 0, 0, 14, 7, 0}, { 0, 0, 0, 1, 0, 3, -7, 4, 0, 0, 0, 0, 0, 10, -6, -3, -5}, {-2, 1, 1, 1, 0, 0, -3, 7, 0, 0, 0, 0, 0, -5, -4, -2, 3}, { 0, 1,-1, 2, 0, 0, -1, 0,-2, 5, 0, 0, 0, -3, 5, 2, 1}, { 0, 0, 0, 1, 0, 0, 0, 0,-2, 5, 0, 0, 0, 76, 17, 9, -41}, { 0, 0, 0, 1, 0, 0, -4, 8,-3, 0, 0, 0, 0, 84, 298, 159, -45}, { 1, 0, 0, 1, 0,-10, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, { 0, 2,-2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2}, {-1, 0, 0, 1, 0, 10, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1}, { 0, 0, 0, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, -82, 292, 156, 44}, /* 141-150 */ { 0, 0, 0, 1, 0, 0, 0, 0, 2,-5, 0, 0, 0, -73, 17, 9, 39}, { 0,-1, 1, 0, 0, 0, 1, 0, 2,-5, 0, 0, 0, -9, -16, 0, 0}, { 2,-1,-1, 1, 0, 0, 3, -7, 0, 0, 0, 0, 0, 3, 0, -1, -2}, {-2, 0, 2, 0, 0, 0, 2, 0, 0,-5, 0, 0, 0, -3, 0, 0, 0}, { 0, 0, 0, 1, 0, -3, 7, -4, 0, 0, 0, 0, 0, -9, -5, -3, 5}, {-2, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -439, 0, 0, 0}, { 1, 0, 0, 1, 0,-18, 16, 0, 0, 0, 0, 0, 0, 57, -28, -15, -30}, {-2, 1, 1, 1, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -6, -3, 0}, { 0, 1,-1, 2, 0, -8, 12, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2}, { 0, 0, 0, 1, 0, -8, 13, 0, 0, 0, 0, 0, 0, -40, 57, 30, 21}, /* 151-160 */ { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, 23, 7, 3, -13}, { 0, 1,-1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 273, 80, 43,-146}, { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -449, 430, 0, 0}, { 0, 1,-1, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, -8, -47, -25, 4}, { 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 1, 6, 47, 25, -3}, {-1, 0, 1, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 23, 13, 0}, {-1, 0, 1, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, -3, 0, 0, 2}, { 0, 1,-1, 1, 0, 0, -1, 0, 0,-2, 0, 0, 0, 3, -4, -2, -2}, { 0, 1,-1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0, -48,-110, -59, 26}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 51, 114, 61, -27}, /* 161-170 */ { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, -133, 0, 0, 57}, { 0, 1,-1, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0}, { 0, 0, 0, 1, 0, -3, 5, 0, 0, 0, 0, 0, 0, -21, -6, -3, 11}, { 0, 1,-1, 2, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, -3, -1, 0}, { 0, 0, 0, 1, 0, 0, -2, 4, 0, 0, 0, 0, 0, -11, -21, -11, 6}, { 0, 2,-2, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, -18,-436, -233, 9}, { 0,-1, 1, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, 35, -7, 0, 0}, { 0, 0, 0, 1, 0, 5, -8, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0}, {-2, 0, 2, 1, 0, 6, -8, 0, 0, 0, 0, 0, 0, 11, -3, -1, -6}, { 0, 0, 0, 1, 0, 0, -8, 15, 0, 0, 0, 0, 0, -5, -3, -1, 3}, /* 171-180 */ {-2, 0, 2, 1, 0, 0, 2, 0,-3, 0, 0, 0, 0, -53, -9, -5, 28}, {-2, 0, 2, 1, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, 3, 2, 1}, { 1, 0,-1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 4, 0, 0, -2}, { 0, 0, 0, 0, 0, 0, 0, 0, 3,-5, 0, 0, 0, 0, -4, 0, 0}, { 0, 1,-1, 1, 0, 0, -1, 0,-1, 0, 0, 0, 0, -50, 194, 103, 27}, { 0, 0, 0, 0, 0, 0, 0, 0,-1, 0, 0, 0, 1, -13, 52, 28, 7}, { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -91, 248, 0, 0}, { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 6, 49, 26, -3}, { 0, 1,-1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -6, -47, -25, 3}, { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 5, 3, 0}, /* 181-190 */ { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 52, 23, 10, -23}, { 0, 1,-1, 2, 0, 0, -1, 0, 0,-1, 0, 0, 0, -3, 0, 0, 1}, { 0, 0, 0, 1, 0, 0, 0, 0, 0,-1, 0, 0, 0, 0, 5, 3, 0}, { 0,-1, 1, 0, 0, 0, 1, 0, 0,-1, 0, 0, 0, -4, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, -7, 13, 0, 0, 0, 0, 2, -4, 8, 3, 2}, { 0, 0, 0, 0, 0, 0, 7,-13, 0, 0, 0, 0, 0, 10, 0, 0, 0}, { 2, 0,-2, 1, 0, 0, -5, 6, 0, 0, 0, 0, 0, 3, 0, 0, -2}, { 0, 2,-2, 1, 0, 0, -8, 11, 0, 0, 0, 0, 0, 0, 8, 4, 0}, { 0, 2,-2, 1,-1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 4, 1}, {-2, 0, 2, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0}, /* 191-200 */ { 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, -4, 0, 0, 0}, { 0, 1,-1, 1, 0, 0, -1, 0, 0, 3, 0, 0, 0, -8, 4, 2, 4}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 8, -4, -2, -4}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 15, 7, 0}, {-2, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, -138, 0, 0, 0}, { 0, 0, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, -7, -3, 0}, { 0, 0, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -7, -3, 0}, { 2, 0,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 54, 0, 0, -29}, { 0, 1,-1, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 10, 4, 0}, { 0, 1,-1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -7, 0, 0, 3}, /* 201-210 */ { 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0, -37, 35, 19, 20}, { 0,-1, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0}, { 0,-1, 1, 0, 0, 0, 1, 0, 0,-2, 0, 0, 0, -4, 9, 0, 0}, { 0, 2,-2, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0, 8, 0, 0, -4}, { 0, 1,-1, 1, 0, 3, -6, 0, 0, 0, 0, 0, 0, -9, -14, -8, 5}, { 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 1, -3, -9, -5, 3}, { 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 0, -145, 47, 0, 0}, { 0, 1,-1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, -10, 40, 21, 5}, { 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 1, 11, -49, -26, -7}, { 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 2,-2150, 0, 0, 932}, /* 211-220 */ { 0, 2,-2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, -12, 0, 0, 5}, { 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 2, 85, 0, 0, -37}, { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 1, 4, 0, 0, -2}, { 0, 1,-1, 1, 0, 0, 1, -4, 0, 0, 0, 0, 0, 3, 0, 0, -2}, { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -86, 153, 0, 0}, { 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -6, 9, 5, 3}, { 0, 1,-1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 9, -13, -7, -5}, { 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -8, 12, 6, 4}, { 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 2, -51, 0, 0, 22}, { 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 2, -11,-268, -116, 5}, /* 221-230 */ { 0, 2,-2, 2, 0, -5, 6, 0, 0, 0, 0, 0, 0, 0, 12, 5, 0}, { 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 2, 0, 7, 3, 0}, { 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 1, 31, 6, 3, -17}, { 0, 1,-1, 1, 0, -5, 7, 0, 0, 0, 0, 0, 0, 140, 27, 14, -75}, { 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 1, 57, 11, 6, -30}, { 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0, -14, -39, 0, 0}, { 0, 1,-1, 2, 0, 0, -1, 0,-1, 0, 0, 0, 0, 0, -6, -2, 0}, { 0, 0, 0, 1, 0, 0, 0, 0,-1, 0, 0, 0, 0, 4, 15, 8, -2}, { 0,-1, 1, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 0, 4, 0, 0}, { 0, 2,-2, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0, -3, 0, 0, 1}, /* 231-240 */ { 0, 0, 0, 0, 0, 0, -6, 11, 0, 0, 0, 0, 2, 0, 11, 5, 0}, { 0, 0, 0, 0, 0, 0, 6,-11, 0, 0, 0, 0, 0, 9, 6, 0, 0}, { 0, 0, 0, 0,-1, 0, 4, 0, 0, 0, 0, 0, 2, -4, 10, 4, 2}, { 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0, 5, 3, 0, 0}, { 2, 0,-2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0, 16, 0, 0, -9}, {-2, 0, 2, 0, 0, 0, 2, 0, 0,-2, 0, 0, 0, -3, 0, 0, 0}, { 0, 2,-2, 1, 0, 0, -7, 9, 0, 0, 0, 0, 0, 0, 3, 2, -1}, { 0, 0, 0, 0, 0, 0, 0, 0, 4,-5, 0, 0, 2, 7, 0, 0, -3}, { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -25, 22, 0, 0}, { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 42, 223, 119, -22}, /* 241-250 */ { 0, 1,-1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, -27,-143, -77, 14}, { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 9, 49, 26, -5}, { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2,-1166, 0, 0, 505}, { 0, 2,-2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -5, 0, 0, 2}, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2, -6, 0, 0, 3}, { 0, 0, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, -8, 0, 1, 4}, { 0,-1, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0}, { 0, 2,-2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0, 117, 0, 0, -63}, { 0, 0, 0, 1, 0, 0, 2, -4, 0, 0, 0, 0, 0, -4, 8, 4, 2}, { 0, 2,-2, 1, 0, 0, -4, 4, 0, 0, 0, 0, 0, 3, 0, 0, -2}, /* 251-260 */ { 0, 1,-1, 2, 0, -5, 7, 0, 0, 0, 0, 0, 0, -5, 0, 0, 2}, { 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 31, 0, 0}, { 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 1, -5, 0, 1, 3}, { 0, 1,-1, 1, 0, 0, -4, 6, 0, 0, 0, 0, 0, 4, 0, 0, -2}, { 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 1, -4, 0, 0, 2}, { 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 2, -24, -13, -6, 10}, { 0,-1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0}, { 0, 0, 0, 1, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, -32, -17, 0}, { 0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 2, 8, 12, 5, -3}, { 0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 1, 3, 0, 0, -1}, /* 261-270 */ { 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0, 7, 13, 0, 0}, { 0,-1, 1, 0, 0, 0, 1, 0,-2, 0, 0, 0, 0, -3, 16, 0, 0}, { 0, 2,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 50, 0, 0, -27}, {-2, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -5, -3, 0}, { 0,-2, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0}, { 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 1, 0, 5, 3, 1}, { 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 2, 24, 5, 2, -11}, { 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 2, 5, -11, -5, -2}, { 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 1, 30, -3, -2, -16}, { 0, 1,-1, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 18, 0, 0, -9}, /* 271-280 */ { 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0, 8, 614, 0, 0}, { 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 1, 3, -3, -1, -2}, { 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 6, 17, 9, -3}, { 0, 1,-1, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0, -3, -9, -5, 2}, { 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 6, 3, -1}, { 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, -127, 21, 9, 55}, { 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, 3, 5, 0, 0}, { 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 2, -6, -10, -4, 3}, { 0,-2, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 5, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 2, 16, 9, 4, -7}, /* 281-290 */ { 0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 1, 3, 0, 0, -2}, { 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, 0, 22, 0, 0}, { 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 19, 10, 0}, { 0, 2,-2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 7, 0, 0, -4}, { 0, 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 2, 0, -5, -2, 0}, { 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0}, { 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, -9, 3, 1, 4}, { 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 2, 17, 0, 0, -7}, { 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 1, 0, -3, -2, -1}, { 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -20, 34, 0, 0}, /* 291-300 */ { 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, -10, 0, 1, 5}, { 0, 1,-1, 1, 0, 1, -3, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2}, { 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 22, -87, 0, 0}, { 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2}, { 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 2, -3, -6, -2, 1}, { 0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 2, -16, -3, -1, 7}, { 0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0}, { 0,-2, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -68, 39, 0, 0}, { 0, 2,-2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 0, 27, 0, 0, -14}, /* 301-310 */ { 0,-1, 1, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0}, { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -25, 0, 0, 0}, { 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 1, -12, -3, -2, 6}, { 0, 1,-1, 1, 0, -4, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, { 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 2, 3, 66, 29, -1}, { 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 2, 490, 0, 0,-213}, { 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, -22, 93, 49, 12}, { 0, 1,-1, 1, 0, -4, 5, 0, 0, 0, 0, 0, 0, -7, 28, 15, 4}, { 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, -3, 13, 7, 2}, { 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0, -46, 14, 0, 0}, /* 311-320 */ {-2, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0}, { 0,-1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0}, { 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, -28, 0, 0, 15}, { 0, 0, 0, 0, 0, 0, -1, 0, 5, 0, 0, 0, 2, 5, 0, 0, -2}, { 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0}, { 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 2, -11, 0, 0, 5}, { 0, 0, 0, 0, 0, 0, -7, 12, 0, 0, 0, 0, 2, 0, 3, 1, 0}, { 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1}, { 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 25, 106, 57, -13}, /* 321-330 */ { 0, 1,-1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, 21, 11, -3}, { 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1485, 0, 0, 0}, { 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -7, -32, -17, 4}, { 0, 1,-1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0}, { 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 2, -6, -3, -2, 3}, { 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 2, 30, -6, -2, -13}, { 0, 0, 0, 0, 0, 0, 1, 0,-4, 0, 0, 0, 0, -4, 4, 0, 0}, { 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -19, 0, 0, 10}, { 0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 2, 0, 4, 2, -1}, { 0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 0, 3, 0, 0}, /* 331-340 */ { 0, 2,-2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0, 4, 0, 0, -2}, { 0, 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 2, 0, -3, -1, 0}, {-2, 0, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 2, 5, 3, 1, -2}, { 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0, 11, 0, 0}, { 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 2, 118, 0, 0, -52}, { 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 1, 0, -5, -3, 0}, { 0, 0, 0, 0, 0, 0, 1, 0,-3, 0, 0, 0, 0, -28, 36, 0, 0}, { 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0}, { 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 1, 14, -59, -31, -8}, /* 341-350 */ { 0, 1,-1, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 9, 5, 1}, { 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 2, -458, 0, 0, 198}, { 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 2, 0, -45, -20, 0}, { 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 1, 9, 0, 0, -5}, { 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0}, { 0, 0, 0, 1, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -4, -2, -1}, { 0, 2,-2, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 11, 0, 0, -6}, { 0, 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 2, 6, 0, 0, -2}, { 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -16, 23, 0, 0}, { 0, 0, 0, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0}, /* 351-360 */ { 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, -5, 0, 0, 2}, { 0, 0, 0, 0, 0, 0, 1, 0,-2, 0, 0, 0, 0, -166, 269, 0, 0}, { 0, 0, 0, 1, 0, 0, 1, 0,-1, 0, 0, 0, 0, 15, 0, 0, -8}, { 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 0, 2, 10, 0, 0, -4}, { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -78, 45, 0, 0}, { 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 2, 0, -5, -2, 0}, { 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 1, 7, 0, 0, -4}, { 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, -5, 328, 0, 0}, { 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 1, 3, 0, 0, -2}, { 0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 5, 0, 0, -2}, /* 361-370 */ { 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 3, 1, 0}, { 0, 0, 0, 0, 0, 0, 1, 0, 0,-3, 0, 0, 0, -3, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 1, 0, 1,-5, 0, 0, 0, -3, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -4, -2, 0}, { 0, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0,-1223, -26, 0, 0}, { 0, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 1, 0, 7, 3, 0}, { 0, 0, 0, 0, 0, 0, 1, 0,-3, 5, 0, 0, 0, 3, 0, 0, 0}, { 0, 0, 0, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0}, { 0, 0, 0, 0, 0, 0, 1, 0, 0,-2, 0, 0, 0, -6, 20, 0, 0}, { 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -368, 0, 0, 0}, /* 371-380 */ { 0, 0, 0, 0, 0, 0, 1, 0, 0,-1, 0, 0, 0, -75, 0, 0, 0}, { 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 11, 0, 0, -6}, { 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, 3, 0, 0, -2}, { 0, 0, 0, 0, 0, -8, 14, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1}, { 0, 0, 0, 0, 0, 0, 1, 0, 2,-5, 0, 0, 0, -13, -30, 0, 0}, { 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 0, 21, 3, 0, 0}, { 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 2, -3, 0, 0, 1}, { 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2}, { 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 8, -27, 0, 0}, { 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, 0, -19, -11, 0, 0}, /* 381-390 */ { 0, 0, 0, 0, 0, 0, -3, 8,-3, 0, 0, 0, 2, -4, 0, 0, 2}, { 0, 0, 0, 0, 0, 0, 1, 0,-2, 5, 0, 0, 2, 0, 5, 2, 0}, { 0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 2, -6, 0, 0, 2}, { 0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 1, 0, 1,-2, 0, 0, 0, -1, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, -14, 0, 0, 6}, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -74, 0, 0, 32}, { 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, -3, -1, 0}, { 0, 2,-2, 1, 0, -5, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2}, /* 391-400 */ { 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 8, 11, 0, 0}, { 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 3, 2, 0}, { 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, -262, 0, 0, 114}, { 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0}, { 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 1, -7, 0, 0, 4}, { 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 2, 0, -27, -12, 0}, { 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 2, -19, -8, -4, 8}, { 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 2, 202, 0, 0, -87}, { 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 1, -8, 35, 19, 5}, { 0, 1,-1, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0}, /* 401-410 */ { 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, 16, -5, 0, 0}, { 0, 2,-2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 5, 0, 0, -3}, { 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0}, { 0, 0, 0, 0,-1, 0, 3, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, -35, -48, -21, 15}, { 0, 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 2, -3, -5, -2, 1}, { 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3}, { 0, 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 2, 3, 0, 0, -1}, { 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, -5, 0, 0}, { 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 1, 12, 55, 29, -6}, /* 411-420 */ { 0, 1,-1, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0}, { 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -598, 0, 0, 0}, { 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1, -3, -13, -7, 1}, { 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, -5, -7, -3, 2}, { 0, 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 2, 3, 0, 0, -1}, { 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 5, -7, 0, 0}, { 0, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2}, { 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 16, -6, 0, 0}, { 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 8, -3, 0, 0}, { 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 1, 8, -31, -16, -4}, /* 421-430 */ { 0, 1,-1, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0}, { 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 2, 113, 0, 0, -49}, { 0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 2, 0, -24, -10, 0}, { 0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 1, 4, 0, 0, -2}, { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 27, 0, 0, 0}, { 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1}, { 0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 2, 0, -4, -2, 0}, { 0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 1, 5, 0, 0, -2}, { 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0}, { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, -13, 0, 0, 6}, /* 431-440 */ { 0, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 2, 5, 0, 0, -2}, { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2, -18, -10, -4, 8}, { 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, -28, 0, 0}, { 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, -5, 6, 3, 2}, { 0, 0, 0, 0, 0, -9, 13, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1}, { 0, 0, 0, 0, 0, 0, -1, 5, 0, 0, 0, 0, 2, -5, -9, -4, 2}, { 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 2, 17, 0, 0, -7}, { 0, 0, 0, 0, 0, 0, 2, 0,-4, 0, 0, 0, 0, 11, 4, 0, 0}, { 0, 0, 0, 0, 0, 0, -2, 7, 0, 0, 0, 0, 2, 0, -6, -2, 0}, { 0, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 83, 15, 0, 0}, /* 441-450 */ { 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2}, { 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 2, 0,-114, -49, 0}, { 0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 2, 117, 0, 0, -51}, { 0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 1, -5, 19, 10, 2}, { 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0}, { 0, 0, 0, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 2}, { 0, 0, 0, 0, 0, 0, -3, 9, 0, 0, 0, 0, 2, 0, -3, -1, 0}, { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 2, 0, -6, -2, 0}, { 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 393, 3, 0, 0}, /* 451-460 */ { 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 1, -4, 21, 11, 2}, { 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 2, -6, 0, -1, 3}, { 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 0, 2, -3, 8, 4, 1}, { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2, 18, -29, -13, -8}, { 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 1, 8, 34, 18, -4}, { 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0}, { 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 1, 3, 12, 6, -1}, { 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 2, 54, -15, -7, -24}, { 0, 0, 0, 0, 0, 0, 2, 0, 0,-3, 0, 0, 0, 0, 3, 0, 0}, /* 461-470 */ { 0, 0, 0, 0, 0, 0, -5, 13, 0, 0, 0, 0, 2, 3, 0, 0, -1}, { 0, 0, 0, 0, 0, 0, 2, 0,-1, 0, 0, 0, 0, 0, 35, 0, 0}, { 0, 0, 0, 0, 0, 0, 2, 0,-1, 0, 0, 0, 2, -154, -30, -13, 67}, { 0, 0, 0, 0, 0, 0, 2, 0, 0,-2, 0, 0, 0, 15, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 2, 0, 0,-2, 0, 0, 1, 0, 4, 2, 0}, { 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 9, 0, 0}, { 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 2, 80, -71, -31, -35}, { 0, 0, 0, 0, 0, 0, 2, 0, 0,-1, 0, 0, 2, 0, -20, -9, 0}, { 0, 0, 0, 0, 0, 0, -6, 15, 0, 0, 0, 0, 2, 11, 5, 2, -5}, { 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 0, 2, 61, -96, -42, -27}, /* 471-480 */ { 0, 0, 0, 0, 0, -3, 9, -4, 0, 0, 0, 0, 2, 14, 9, 4, -6}, { 0, 0, 0, 0, 0, 0, 2, 0, 2,-5, 0, 0, 2, -11, -6, -3, 5}, { 0, 0, 0, 0, 0, 0, -2, 8,-1,-5, 0, 0, 2, 0, -3, -1, 0}, { 0, 0, 0, 0, 0, 0, 6, -8, 3, 0, 0, 0, 2, 123,-415, -180, -53}, { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35}, { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 7, -32, -17, -4}, { 0, 1,-1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -9, -5, 0}, { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -4, 2, 0}, { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -89, 0, 0, 38}, /* 481-490 */ { 0, 0, 0, 0, 0, 0, -6, 16,-4,-5, 0, 0, 2, 0, -86, -19, -6}, { 0, 0, 0, 0, 0, 0, -2, 8,-3, 0, 0, 0, 2, 0, 0, -19, 6}, { 0, 0, 0, 0, 0, 0, -2, 8,-3, 0, 0, 0, 2, -123,-416, -180, 53}, { 0, 0, 0, 0, 0, 0, 6, -8, 1, 5, 0, 0, 2, 0, -3, -1, 0}, { 0, 0, 0, 0, 0, 0, 2, 0,-2, 5, 0, 0, 2, 12, -6, -3, -5}, { 0, 0, 0, 0, 0, 3, -5, 4, 0, 0, 0, 0, 2, -13, 9, 4, 6}, { 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, 0, -15, -7, 0}, { 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 1, 3, 0, 0, -1}, { 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, -62, -97, -42, 27}, { 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 2, -11, 5, 2, 5}, /* 491-500 */ { 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, -19, -8, 0}, { 0, 0, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 2, -3, 0, 0, 1}, { 0, 2,-2, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 4, 2, 0}, { 0, 1,-1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0}, { 0, 2,-2, 1, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 4, 2, 0}, { 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, -85, -70, -31, 37}, { 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 163, -12, -5, -72}, { 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 0, 2, -63, -16, -7, 28}, { 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, -21, -32, -14, 9}, { 0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 2, 0, -3, -1, 0}, /* 501-510 */ { 0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 1, 3, 0, 0, -2}, { 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0}, { 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 2, 3, 10, 4, -1}, { 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 3, 0, 0, -1}, { 0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 2, 0, -7, -3, 0}, { 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 2, 0, -4, -2, 0}, { 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 6, 19, 0, 0}, { 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2, 5,-173, -75, -2}, { 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 2, 0, -7, -3, 0}, { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 2, 7, -12, -5, -3}, /* 511-520 */ { 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 1, -3, 0, 0, 2}, { 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 2, 3, -4, -2, -1}, { 0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 2, 74, 0, 0, -32}, { 0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 1, -3, 12, 6, 2}, { 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 2, 26, -14, -6, -11}, { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2, 19, 0, 0, -8}, { 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 1, 6, 24, 13, -3}, { 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0}, { 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 1, 0, -10, -5, 0}, { 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2, 11, -3, -1, -5}, /* 521-530 */ { 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 3, 0, 1, -1}, { 0, 0, 0, 0, 0, 0, -3, 0, 5, 0, 0, 0, 2, 3, 0, 0, -1}, { 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0}, { 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 5, -23, -12, -3}, { 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, -339, 0, 0, 147}, { 0, 0, 0, 0, 0, -9, 12, 0, 0, 0, 0, 0, 2, 0, -10, -5, 0}, { 0, 0, 0, 0, 0, 0, 3, 0,-4, 0, 0, 0, 0, 5, 0, 0, 0}, { 0, 2,-2, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, { 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 2, 0, -4, -2, 0}, { 0, 0, 0, 0, 0, 0, 3, 0,-3, 0, 0, 0, 0, 18, -3, 0, 0}, /* 531-540 */ { 0, 0, 0, 0, 0, 0, 3, 0,-3, 0, 0, 0, 2, 9, -11, -5, -4}, { 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 0, 2, -8, 0, 0, 4}, { 0, 0, 0, 0, 0, -6, 7, 0, 0, 0, 0, 0, 1, 3, 0, 0, -1}, { 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0}, { 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 2, 6, -9, -4, -2}, { 0, 0, 0, 0, 0, 0, 3, 0,-2, 0, 0, 0, 0, -4, -12, 0, 0}, { 0, 0, 0, 0, 0, 0, 3, 0,-2, 0, 0, 0, 2, 67, -91, -39, -29}, { 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 2, 30, -18, -8, -13}, { 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, { 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 2, 0,-114, -50, 0}, /* 541-550 */ { 0, 0, 0, 0, 0, 0, 3, 0,-1, 0, 0, 0, 2, 0, 0, 0, 23}, { 0, 0, 0, 0, 0, 0, 3, 0,-1, 0, 0, 0, 2, 517, 16, 7,-224}, { 0, 0, 0, 0, 0, 0, 3, 0, 0,-2, 0, 0, 2, 0, -7, -3, 0}, { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2, 143, -3, -1, -62}, { 0, 0, 0, 0, 0, 0, 3, 0, 0,-1, 0, 0, 2, 29, 0, 0, -13}, { 0, 2,-2, 1, 0, 0, 1, 0,-1, 0, 0, 0, 0, -4, 0, 0, 2}, { 0, 0, 0, 0, 0, -8, 16, 0, 0, 0, 0, 0, 2, -6, 0, 0, 3}, { 0, 0, 0, 0, 0, 0, 3, 0, 2,-5, 0, 0, 2, 5, 12, 5, -2}, { 0, 0, 0, 0, 0, 0, 7, -8, 3, 0, 0, 0, 2, -25, 0, 0, 11}, { 0, 0, 0, 0, 0, 0, -5, 16,-4,-5, 0, 0, 2, -3, 0, 0, 1}, /* 551-560 */ { 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0}, { 0, 0, 0, 0, 0, 0, -1, 8,-3, 0, 0, 0, 2, -22, 12, 5, 10}, { 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, 50, 0, 0, -22}, { 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 1, 0, 7, 4, 0}, { 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0}, { 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, -4, 4, 2, 2}, { 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2, -5, -11, -5, 2}, { 0, 0, 0, 0, 0, -3, 8, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0}, { 0, 0, 0, 0, 0, -5, 5, 0, 0, 0, 0, 0, 1, 4, 17, 9, -2}, { 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0}, /* 561-570 */ { 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 1, 0, -4, -2, 0}, { 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 2, -8, 0, 0, 4}, { 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0}, { 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 4, -15, -8, -2}, { 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 370, -8, 0,-160}, { 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, 0, 0, -3, 0}, { 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, 0, 3, 1, 0}, { 0, 0, 0, 0, 0, 0, 6, -5, 0, 0, 0, 0, 2, -6, 3, 1, 3}, { 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0}, { 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 2, -10, 0, 0, 4}, /* 571-580 */ { 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 2, 0, 9, 4, 0}, { 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 4, 17, 7, -2}, { 0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 2, 34, 0, 0, -15}, { 0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 1, 0, 5, 3, 0}, { 0, 0, 0, 0, 0, 0, 4, 0,-4, 0, 0, 0, 2, -5, 0, 0, 2}, { 0, 0, 0, 0, 0, 0, 4, 0,-3, 0, 0, 0, 2, -37, -7, -3, 16}, { 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 1, 3, 13, 7, -2}, { 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0}, { 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0}, { 0, 0, 0, 0, 0, 0, 4, 0,-2, 0, 0, 0, 2, -184, -3, -1, 80}, /* 581-590 */ { 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 2, -3, 0, 0, 1}, { 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0}, { 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 1, 0, -10, -6, -1}, { 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2, 31, -6, 0, -13}, { 0, 0, 0, 0, 0, 0, 4, 0,-1, 0, 0, 0, 2, -3, -32, -14, 1}, { 0, 0, 0, 0, 0, 0, 4, 0, 0,-2, 0, 0, 2, -7, 0, 0, 3}, { 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 2, 0, -8, -4, 0}, { 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0}, { 0, 0, 0, 0, 0, 8, -9, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0}, { 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0}, /* 591-600 */ { 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 19, -23, -10, 2}, { 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -10}, { 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 3, 2, 0}, { 0, 0, 0, 0, 0, -7, 7, 0, 0, 0, 0, 0, 1, 0, 9, 5, -1}, { 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0}, { 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 1, 0, -7, -4, 0}, { 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2, 8, -4, 0, -4}, { 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0}, { 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0}, { 0, 0, 0, 0, 0, 0, 5, 0,-4, 0, 0, 0, 2, -3, 0, 0, 1}, /* 601-610 */ { 0, 0, 0, 0, 0, 0, 5, 0,-3, 0, 0, 0, 2, -9, 0, 1, 4}, { 0, 0, 0, 0, 0, 0, 5, 0,-2, 0, 0, 0, 2, 3, 12, 5, -1}, { 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 17, -3, -1, 0}, { 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 1, 0, 7, 4, 0}, { 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0}, { 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 1, 0, -5, -3, 0}, { 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 2, 14, -3, 0, -1}, { 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0}, { 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 0, 0, -5}, { 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 5, 3, 0}, /* 611-620 */ { 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0}, { 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0}, { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, 9, 4, 3}, { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4}, { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 4, 2, 0}, { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 6, 0, 0, -3}, { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 3, 1, 0}, { 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 5, 0, 0, -2}, /* 621-630 */ { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, -1}, { 1, 0,-2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 0}, { 1, 0,-2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0}, { 1, 0,-2, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 7, 0, 0, 0}, { 1, 0,-2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0}, {-1, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0}, {-1, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 6, 0, 0, 0}, {-1, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -4, 0, 0}, { 1, 0,-2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -4, 0, 0}, {-2, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 5, 0, 0, 0}, /* 631-640 */ {-1, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, -3, 0, 0, 0}, {-1, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 4, 0, 0, 0}, {-1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0}, {-1, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0}, { 1,-1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0}, {-1, 0, 2, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 13, 0, 0, 0}, {-2, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 21, 11, 0, 0}, { 1, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -5, 0, 0}, {-1, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -5, -2, 0}, { 1, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0}, /* 641-650 */ {-1, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -5, 0, 0}, {-1, 0, 2, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 2}, { 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 20, 10, 0, 0}, {-1, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -34, 0, 0, 0}, {-1, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0}, { 1, 0,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 3, 0, 0, -2}, { 1, 2,-2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1}, { 1, 2,-2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -6, 0, 0, 3}, { 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0}, { 1, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 3, 0, 0, 0}, /* 651-660 */ { 0, 0,-2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0}, { 0, 0,-2, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 4, 0, 0, 0}, { 0, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, { 0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 6, 0, 0, -3}, { 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -8, 0, 0, 3}, { 0, 2, 0, 2, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0}, { 0, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 0}, { 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0}, { 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 126, -63, -27, -55}, {-1, 2, 0, 2, 0, 10, -3, 0, 0, 0, 0, 0, 0, -5, 0, 1, 2}, /* 661-670 */ { 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -3, 28, 15, 2}, { 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 1, -2}, { 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 9, 4, 1}, { 0, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 9, 4, -1}, {-1, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, -126, -63, -27, 55}, { 2, 2,-2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0, 3, 0, 0, -1}, { 1, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 21, -11, -6, -11}, { 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0}, {-1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -21, -11, -6, 11}, {-2, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 1}, /* 671-680 */ { 0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0}, { 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4}, { 0, 2, 0, 2, 0, 0, 1, 0,-1, 0, 0, 0, 0, -6, 0, 0, 3}, { 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1}, {-1, 2, 2, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 3, 0, 0, -1}, { 1, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1}, {-1, 2, 2, 2, 0, 0, 2, 0,-3, 0, 0, 0, 0, -5, 0, 0, 2}, { 2, 2, 0, 2, 0, 0, 2, 0,-3, 0, 0, 0, 0, 24, -12, -5, -11}, { 1, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 3, 1, 0}, { 1, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 3, 1, 0}, /* 681-687 */ { 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0}, { 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, -24, -12, -5, 10}, { 2, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 4, 0, -1, -2}, {-1, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, 13, 0, 0, -6}, {-1, 2, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 7, 0, 0, -3}, { 1, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1}, { 0, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, 3, 0, 0, -1} }; /* Number of terms in the planetary nutation model */ const int NPL = (int) (sizeof xpl / sizeof xpl[0]); /*--------------------------------------------------------------------*/ /* Interval between fundamental date J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* ------------------- */ /* LUNI-SOLAR NUTATION */ /* ------------------- */ /* Fundamental (Delaunay) arguments */ /* Mean anomaly of the Moon (IERS 2003). */ el = iauFal03(t); /* Mean anomaly of the Sun (MHB2000). */ elp = fmod(1287104.79305 + t * (129596581.0481 + t * (-0.5532 + t * (0.000136 + t * (-0.00001149)))), TURNAS) * DAS2R; /* Mean longitude of the Moon minus that of the ascending node */ /* (IERS 2003. */ f = iauFaf03(t); /* Mean elongation of the Moon from the Sun (MHB2000). */ d = fmod(1072260.70369 + t * (1602961601.2090 + t * (-6.3706 + t * (0.006593 + t * (-0.00003169)))), TURNAS) * DAS2R; /* Mean longitude of the ascending node of the Moon (IERS 2003). */ om = iauFaom03(t); /* Initialize the nutation values. */ dp = 0.0; de = 0.0; /* Summation of luni-solar nutation series (in reverse order). */ for (i = NLS-1; i >= 0; i--) { /* Argument and functions. */ arg = fmod((double)xls[i].nl * el + (double)xls[i].nlp * elp + (double)xls[i].nf * f + (double)xls[i].nd * d + (double)xls[i].nom * om, D2PI); sarg = sin(arg); carg = cos(arg); /* Term. */ dp += (xls[i].sp + xls[i].spt * t) * sarg + xls[i].cp * carg; de += (xls[i].ce + xls[i].cet * t) * carg + xls[i].se * sarg; } /* Convert from 0.1 microarcsec units to radians. */ dpsils = dp * U2R; depsls = de * U2R; /* ------------------ */ /* PLANETARY NUTATION */ /* ------------------ */ /* n.b. The MHB2000 code computes the luni-solar and planetary nutation */ /* in different functions, using slightly different Delaunay */ /* arguments in the two cases. This behaviour is faithfully */ /* reproduced here. Use of the IERS 2003 expressions for both */ /* cases leads to negligible changes, well below */ /* 0.1 microarcsecond. */ /* Mean anomaly of the Moon (MHB2000). */ al = fmod(2.35555598 + 8328.6914269554 * t, D2PI); /* Mean longitude of the Moon minus that of the ascending node */ /*(MHB2000). */ af = fmod(1.627905234 + 8433.466158131 * t, D2PI); /* Mean elongation of the Moon from the Sun (MHB2000). */ ad = fmod(5.198466741 + 7771.3771468121 * t, D2PI); /* Mean longitude of the ascending node of the Moon (MHB2000). */ aom = fmod(2.18243920 - 33.757045 * t, D2PI); /* General accumulated precession in longitude (IERS 2003). */ apa = iauFapa03(t); /* Planetary longitudes, Mercury through Uranus (IERS 2003). */ alme = iauFame03(t); alve = iauFave03(t); alea = iauFae03(t); alma = iauFama03(t); alju = iauFaju03(t); alsa = iauFasa03(t); alur = iauFaur03(t); /* Neptune longitude (MHB2000). */ alne = fmod(5.321159000 + 3.8127774000 * t, D2PI); /* Initialize the nutation values. */ dp = 0.0; de = 0.0; /* Summation of planetary nutation series (in reverse order). */ for (i = NPL-1; i >= 0; i--) { /* Argument and functions. */ arg = fmod((double)xpl[i].nl * al + (double)xpl[i].nf * af + (double)xpl[i].nd * ad + (double)xpl[i].nom * aom + (double)xpl[i].nme * alme + (double)xpl[i].nve * alve + (double)xpl[i].nea * alea + (double)xpl[i].nma * alma + (double)xpl[i].nju * alju + (double)xpl[i].nsa * alsa + (double)xpl[i].nur * alur + (double)xpl[i].nne * alne + (double)xpl[i].npa * apa, D2PI); sarg = sin(arg); carg = cos(arg); /* Term. */ dp += (double)xpl[i].sp * sarg + (double)xpl[i].cp * carg; de += (double)xpl[i].se * sarg + (double)xpl[i].ce * carg; } /* Convert from 0.1 microarcsec units to radians. */ dpsipl = dp * U2R; depspl = de * U2R; /* ------- */ /* RESULTS */ /* ------- */ /* Add luni-solar and planetary components. */ *dpsi = dpsils + dpsipl; *deps = depsls + depspl; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/nut00b.c0000644000113000011300000004511413027221062014441 0ustar bellsbells#include "sofa.h" void iauNut00b(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - - ** i a u N u t 0 0 b ** - - - - - - - - - - ** ** Nutation, IAU 2000B model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation, luni-solar + planetary (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components in longitude and obliquity are in radians ** and with respect to the equinox and ecliptic of date. The ** obliquity at J2000.0 is assumed to be the Lieske et al. (1977) ** value of 84381.448 arcsec. (The errors that result from using ** this function with the IAU 2006 value of 84381.406 arcsec can be ** neglected.) ** ** The nutation model consists only of luni-solar terms, but ** includes also a fixed offset which compensates for certain long- ** period planetary terms (Note 7). ** ** 3) This function is an implementation of the IAU 2000B abridged ** nutation model formally adopted by the IAU General Assembly in ** 2000. The function computes the MHB_2000_SHORT luni-solar ** nutation series (Luzum 2001), but without the associated ** corrections for the precession rate adjustments and the offset ** between the GCRS and J2000.0 mean poles. ** ** 4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400 ** terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only ** 77 terms, plus additional simplifications, yet still delivers ** results of 1 mas accuracy at present epochs. This combination of ** accuracy and size makes the IAU 2000B abridged nutation model ** suitable for most practical applications. ** ** The function delivers a pole accurate to 1 mas from 1900 to 2100 ** (usually better than 1 mas, very occasionally just outside ** 1 mas). The full IAU 2000A model, which is implemented in the ** function iauNut00a (q.v.), delivers considerably greater accuracy ** at current dates; however, to realize this improved accuracy, ** corrections for the essentially unpredictable free-core-nutation ** (FCN) must also be included. ** ** 5) The present function provides classical nutation. The ** MHB_2000_SHORT algorithm, from which it is adapted, deals also ** with (i) the offsets between the GCRS and mean poles and (ii) the ** adjustments in longitude and obliquity due to the changed ** precession rates. These additional functions, namely frame bias ** and precession adjustments, are supported by the SOFA functions ** iauBi00 and iauPr00. ** ** 6) The MHB_2000_SHORT algorithm also provides "total" nutations, ** comprising the arithmetic sum of the frame bias, precession ** adjustments, and nutation (luni-solar + planetary). These total ** nutations can be used in combination with an existing IAU 1976 ** precession implementation, such as iauPmat76, to deliver GCRS- ** to-true predictions of mas accuracy at current epochs. However, ** for symmetry with the iauNut00a function (q.v. for the reasons), ** the SOFA functions do not generate the "total nutations" ** directly. Should they be required, they could of course easily ** be generated by calling iauBi00, iauPr00 and the present function ** and adding the results. ** ** 7) The IAU 2000B model includes "planetary bias" terms that are ** fixed in size but compensate for long-period nutations. The ** amplitudes quoted in McCarthy & Luzum (2003), namely ** Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for ** the "total nutations" method described in Note 6. The Luzum ** (2001) values used in this SOFA implementation, namely -0.135 mas ** and +0.388 mas, are optimized for the "rigorous" method, where ** frame bias, precession and nutation are applied separately and in ** that order. During the interval 1995-2050, the SOFA ** implementation delivers a maximum error of 1.001 mas (not ** including FCN). ** ** References: ** ** Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions ** for the precession quantities based upon the IAU /1976/ system of ** astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977) ** ** Luzum, B., private communication, 2001 (Fortran code ** MHB_2000_SHORT) ** ** McCarthy, D.D. & Luzum, B.J., "An abridged model of the ** precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron. ** 85, 37-49 (2003) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, el, elp, f, d, om, arg, dp, de, sarg, carg, dpsils, depsls, dpsipl, depspl; int i; /* Units of 0.1 microarcsecond to radians */ static const double U2R = DAS2R / 1e7; /* ---------------------------------------- */ /* Fixed offsets in lieu of planetary terms */ /* ---------------------------------------- */ static const double DPPLAN = -0.135 * DMAS2R; static const double DEPLAN = 0.388 * DMAS2R; /* --------------------------------------------------- */ /* Luni-solar nutation: argument and term coefficients */ /* --------------------------------------------------- */ /* The units for the sine and cosine coefficients are */ /* 0.1 microarcsec and the same per Julian century */ static const struct { int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */ double ps,pst,pc; /* longitude sin, t*sin, cos coefficients */ double ec,ect,es; /* obliquity cos, t*cos, sin coefficients */ } x[] = { /* 1-10 */ { 0, 0, 0, 0,1, -172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0}, { 0, 0, 2,-2,2, -13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0}, { 0, 0, 2, 0,2,-2276413.0,-234.0, 2796.0, 978459.0,-485.0,1374.0}, { 0, 0, 0, 0,2,2074554.0, 207.0, -698.0,-897492.0, 470.0,-291.0}, { 0, 1, 0, 0,0,1475877.0,-3633.0,11817.0, 73871.0,-184.0,-1924.0}, { 0, 1, 2,-2,2,-516821.0, 1226.0, -524.0, 224386.0,-677.0,-174.0}, { 1, 0, 0, 0,0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0}, { 0, 0, 2, 0,1,-387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0}, { 1, 0, 2, 0,2,-301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0}, { 0,-1, 2,-2,2, 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0}, /* 11-20 */ { 0, 0, 2,-2,1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0}, {-1, 0, 2, 0,2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0}, {-1, 0, 0, 2,0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0}, { 1, 0, 0, 0,1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0}, {-1, 0, 0, 0,1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0}, {-1, 0, 2, 2,2, -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0}, { 1, 0, 2, 0,1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0}, {-2, 0, 2, 0,1, 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0}, { 0, 0, 0, 2,0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0}, { 0, 0, 2, 2,2, -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0}, /* 21-30 */ { 0,-2, 2,-2,2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0}, {-2, 0, 0, 2,0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0}, { 2, 0, 2, 0,2, -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0}, { 1, 0, 2,-2,2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0}, {-1, 0, 2, 0,1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0}, { 2, 0, 0, 0,0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0}, { 0, 0, 2, 0,0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0}, { 0, 1, 0, 0,1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0}, {-1, 0, 0, 2,1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0}, { 0, 2, 2,-2,2, -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0}, /* 31-40 */ { 0, 0,-2, 2,0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0}, { 1, 0, 0,-2,1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0}, { 0,-1, 0, 0,1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0}, {-1, 0, 2, 2,1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0}, { 0, 2, 0, 0,0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0}, { 1, 0, 2, 2,2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0}, {-2, 0, 2, 0,0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0}, { 0, 1, 2, 0,2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0}, { 0, 0, 2, 2,1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0}, { 0,-1, 2, 0,2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0}, /* 41-50 */ { 0, 0, 0, 2,1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0}, { 1, 0, 2,-2,1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0}, { 2, 0, 2,-2,2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0}, {-2, 0, 0, 2,1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0}, { 2, 0, 2, 0,1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0}, { 0,-1, 2,-2,1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0}, { 0, 0, 0,-2,1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0}, {-1,-1, 0, 2,0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0}, { 2, 0, 0,-2,1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0}, { 1, 0, 0, 2,0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0}, /* 51-60 */ { 0, 1, 2,-2,1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0}, { 1,-1, 0, 0,0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0}, {-2, 0, 2, 0,2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0}, { 3, 0, 2, 0,2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0}, { 0,-1, 0, 2,0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0}, { 1,-1, 2, 0,2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0}, { 0, 0, 0, 1,0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0}, {-1,-1, 2, 2,2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0}, {-1, 0, 2, 0,0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0}, { 0,-1, 2, 2,2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0}, /* 61-70 */ {-2, 0, 0, 0,1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0}, { 1, 1, 2, 0,2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0}, { 2, 0, 0, 0,1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0}, {-1, 1, 0, 1,0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0}, { 1, 1, 0, 0,0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0}, { 1, 0, 2, 0,0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0}, {-1, 0, 2,-2,1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0}, { 1, 0, 0, 0,2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0}, {-1, 0, 0, 1,0, 4026.0, 0.0, -353.0, -553.0, 0.0,-139.0}, { 0, 0, 2, 1,2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0}, /* 71-77 */ {-1, 0, 2, 4,2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0}, {-1, 1, 0, 1,1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0}, { 0,-2, 2,-2,1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0}, { 1, 0, 2, 2,1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0}, {-2, 0, 2, 2,2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0}, {-1, 0, 0, 0,2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0}, { 1, 1, 2,-2,2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0} }; /* Number of terms in the series */ const int NLS = (int) (sizeof x / sizeof x[0]); /*--------------------------------------------------------------------*/ /* Interval between fundamental epoch J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* --------------------*/ /* LUNI-SOLAR NUTATION */ /* --------------------*/ /* Fundamental (Delaunay) arguments from Simon et al. (1994) */ /* Mean anomaly of the Moon. */ el = fmod(485868.249036 + (1717915923.2178) * t, TURNAS) * DAS2R; /* Mean anomaly of the Sun. */ elp = fmod(1287104.79305 + (129596581.0481) * t, TURNAS) * DAS2R; /* Mean argument of the latitude of the Moon. */ f = fmod(335779.526232 + (1739527262.8478) * t, TURNAS) * DAS2R; /* Mean elongation of the Moon from the Sun. */ d = fmod(1072260.70369 + (1602961601.2090) * t, TURNAS) * DAS2R; /* Mean longitude of the ascending node of the Moon. */ om = fmod(450160.398036 + (-6962890.5431) * t, TURNAS) * DAS2R; /* Initialize the nutation values. */ dp = 0.0; de = 0.0; /* Summation of luni-solar nutation series (smallest terms first). */ for (i = NLS-1; i >= 0; i--) { /* Argument and functions. */ arg = fmod( (double)x[i].nl * el + (double)x[i].nlp * elp + (double)x[i].nf * f + (double)x[i].nd * d + (double)x[i].nom * om, D2PI ); sarg = sin(arg); carg = cos(arg); /* Term. */ dp += (x[i].ps + x[i].pst * t) * sarg + x[i].pc * carg; de += (x[i].ec + x[i].ect * t) * carg + x[i].es * sarg; } /* Convert from 0.1 microarcsec units to radians. */ dpsils = dp * U2R; depsls = de * U2R; /* ------------------------------*/ /* IN LIEU OF PLANETARY NUTATION */ /* ------------------------------*/ /* Fixed offset to correct for missing terms in truncated series. */ dpsipl = DPPLAN; depspl = DEPLAN; /* --------*/ /* RESULTS */ /* --------*/ /* Add luni-solar and planetary components. */ *dpsi = dpsils + dpsipl; *deps = depsls + depspl; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/nut06a.c0000644000113000011300000001721713027221062014451 0ustar bellsbells#include "sofa.h" void iauNut06a(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - - ** i a u N u t 0 6 a ** - - - - - - - - - - ** ** IAU 2000A nutation with adjustments to match the IAU 2006 ** precession. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation, luni-solar + planetary (Note 2) ** ** Status: canonical model. ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components in longitude and obliquity are in radians ** and with respect to the mean equinox and ecliptic of date, ** IAU 2006 precession model (Hilton et al. 2006, Capitaine et al. ** 2005). ** ** 3) The function first computes the IAU 2000A nutation, then applies ** adjustments for (i) the consequences of the change in obliquity ** from the IAU 1980 ecliptic to the IAU 2006 ecliptic and (ii) the ** secular variation in the Earth's dynamical form factor J2. ** ** 4) The present function provides classical nutation, complementing ** the IAU 2000 frame bias and IAU 2006 precession. It delivers a ** pole which is at current epochs accurate to a few tens of ** microarcseconds, apart from the free core nutation. ** ** Called: ** iauNut00a nutation, IAU 2000A ** ** References: ** ** Chapront, J., Chapront-Touze, M. & Francou, G. 2002, ** Astron.Astrophys. 387, 700 ** ** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, ** Astron.Astrophys. 58, 1-16 ** ** Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. ** 107, B4. The MHB_2000 code itself was obtained on 9th September ** 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A. ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** Wallace, P.T., "Software for Implementing the IAU 2000 ** Resolutions", in IERS Workshop 5.1 (2002) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, fj2, dp, de; /* Interval between fundamental date J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Factor correcting for secular variation of J2. */ fj2 = -2.7774e-6 * t; /* Obtain IAU 2000A nutation. */ iauNut00a(date1, date2, &dp, &de); /* Apply P03 adjustments (Wallace & Capitaine, 2006, Eqs.5). */ *dpsi = dp + dp * (0.4697e-6 + fj2); *deps = de + de * fj2; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/nut80.c0000644000113000011300000003764713027221062014323 0ustar bellsbells#include "sofa.h" void iauNut80(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - ** i a u N u t 8 0 ** - - - - - - - - - ** ** Nutation, IAU 1980 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi double nutation in longitude (radians) ** deps double nutation in obliquity (radians) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components are with respect to the ecliptic of ** date. ** ** Called: ** iauAnpm normalize angle into range +/- pi ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222 (p111). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, el, elp, f, d, om, dp, de, arg, s, c; int j; /* Units of 0.1 milliarcsecond to radians */ const double U2R = DAS2R / 1e4; /* ------------------------------------------------ */ /* Table of multiples of arguments and coefficients */ /* ------------------------------------------------ */ /* The units for the sine and cosine coefficients are 0.1 mas and */ /* the same per Julian century */ static const struct { int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */ double sp,spt; /* longitude sine, 1 and t coefficients */ double ce,cet; /* obliquity cosine, 1 and t coefficients */ } x[] = { /* 1-10 */ { 0, 0, 0, 0, 1, -171996.0, -174.2, 92025.0, 8.9 }, { 0, 0, 0, 0, 2, 2062.0, 0.2, -895.0, 0.5 }, { -2, 0, 2, 0, 1, 46.0, 0.0, -24.0, 0.0 }, { 2, 0, -2, 0, 0, 11.0, 0.0, 0.0, 0.0 }, { -2, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 }, { 1, -1, 0, -1, 0, -3.0, 0.0, 0.0, 0.0 }, { 0, -2, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 }, { 2, 0, -2, 0, 1, 1.0, 0.0, 0.0, 0.0 }, { 0, 0, 2, -2, 2, -13187.0, -1.6, 5736.0, -3.1 }, { 0, 1, 0, 0, 0, 1426.0, -3.4, 54.0, -0.1 }, /* 11-20 */ { 0, 1, 2, -2, 2, -517.0, 1.2, 224.0, -0.6 }, { 0, -1, 2, -2, 2, 217.0, -0.5, -95.0, 0.3 }, { 0, 0, 2, -2, 1, 129.0, 0.1, -70.0, 0.0 }, { 2, 0, 0, -2, 0, 48.0, 0.0, 1.0, 0.0 }, { 0, 0, 2, -2, 0, -22.0, 0.0, 0.0, 0.0 }, { 0, 2, 0, 0, 0, 17.0, -0.1, 0.0, 0.0 }, { 0, 1, 0, 0, 1, -15.0, 0.0, 9.0, 0.0 }, { 0, 2, 2, -2, 2, -16.0, 0.1, 7.0, 0.0 }, { 0, -1, 0, 0, 1, -12.0, 0.0, 6.0, 0.0 }, { -2, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 }, /* 21-30 */ { 0, -1, 2, -2, 1, -5.0, 0.0, 3.0, 0.0 }, { 2, 0, 0, -2, 1, 4.0, 0.0, -2.0, 0.0 }, { 0, 1, 2, -2, 1, 4.0, 0.0, -2.0, 0.0 }, { 1, 0, 0, -1, 0, -4.0, 0.0, 0.0, 0.0 }, { 2, 1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 }, { 0, 0, -2, 2, 1, 1.0, 0.0, 0.0, 0.0 }, { 0, 1, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 }, { 0, 1, 0, 0, 2, 1.0, 0.0, 0.0, 0.0 }, { -1, 0, 0, 1, 1, 1.0, 0.0, 0.0, 0.0 }, { 0, 1, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 }, /* 31-40 */ { 0, 0, 2, 0, 2, -2274.0, -0.2, 977.0, -0.5 }, { 1, 0, 0, 0, 0, 712.0, 0.1, -7.0, 0.0 }, { 0, 0, 2, 0, 1, -386.0, -0.4, 200.0, 0.0 }, { 1, 0, 2, 0, 2, -301.0, 0.0, 129.0, -0.1 }, { 1, 0, 0, -2, 0, -158.0, 0.0, -1.0, 0.0 }, { -1, 0, 2, 0, 2, 123.0, 0.0, -53.0, 0.0 }, { 0, 0, 0, 2, 0, 63.0, 0.0, -2.0, 0.0 }, { 1, 0, 0, 0, 1, 63.0, 0.1, -33.0, 0.0 }, { -1, 0, 0, 0, 1, -58.0, -0.1, 32.0, 0.0 }, { -1, 0, 2, 2, 2, -59.0, 0.0, 26.0, 0.0 }, /* 41-50 */ { 1, 0, 2, 0, 1, -51.0, 0.0, 27.0, 0.0 }, { 0, 0, 2, 2, 2, -38.0, 0.0, 16.0, 0.0 }, { 2, 0, 0, 0, 0, 29.0, 0.0, -1.0, 0.0 }, { 1, 0, 2, -2, 2, 29.0, 0.0, -12.0, 0.0 }, { 2, 0, 2, 0, 2, -31.0, 0.0, 13.0, 0.0 }, { 0, 0, 2, 0, 0, 26.0, 0.0, -1.0, 0.0 }, { -1, 0, 2, 0, 1, 21.0, 0.0, -10.0, 0.0 }, { -1, 0, 0, 2, 1, 16.0, 0.0, -8.0, 0.0 }, { 1, 0, 0, -2, 1, -13.0, 0.0, 7.0, 0.0 }, { -1, 0, 2, 2, 1, -10.0, 0.0, 5.0, 0.0 }, /* 51-60 */ { 1, 1, 0, -2, 0, -7.0, 0.0, 0.0, 0.0 }, { 0, 1, 2, 0, 2, 7.0, 0.0, -3.0, 0.0 }, { 0, -1, 2, 0, 2, -7.0, 0.0, 3.0, 0.0 }, { 1, 0, 2, 2, 2, -8.0, 0.0, 3.0, 0.0 }, { 1, 0, 0, 2, 0, 6.0, 0.0, 0.0, 0.0 }, { 2, 0, 2, -2, 2, 6.0, 0.0, -3.0, 0.0 }, { 0, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 }, { 0, 0, 2, 2, 1, -7.0, 0.0, 3.0, 0.0 }, { 1, 0, 2, -2, 1, 6.0, 0.0, -3.0, 0.0 }, { 0, 0, 0, -2, 1, -5.0, 0.0, 3.0, 0.0 }, /* 61-70 */ { 1, -1, 0, 0, 0, 5.0, 0.0, 0.0, 0.0 }, { 2, 0, 2, 0, 1, -5.0, 0.0, 3.0, 0.0 }, { 0, 1, 0, -2, 0, -4.0, 0.0, 0.0, 0.0 }, { 1, 0, -2, 0, 0, 4.0, 0.0, 0.0, 0.0 }, { 0, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0 }, { 1, 1, 0, 0, 0, -3.0, 0.0, 0.0, 0.0 }, { 1, 0, 2, 0, 0, 3.0, 0.0, 0.0, 0.0 }, { 1, -1, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 }, { -1, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 }, { -2, 0, 0, 0, 1, -2.0, 0.0, 1.0, 0.0 }, /* 71-80 */ { 3, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 }, { 0, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 }, { 1, 1, 2, 0, 2, 2.0, 0.0, -1.0, 0.0 }, { -1, 0, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 }, { 2, 0, 0, 0, 1, 2.0, 0.0, -1.0, 0.0 }, { 1, 0, 0, 0, 2, -2.0, 0.0, 1.0, 0.0 }, { 3, 0, 0, 0, 0, 2.0, 0.0, 0.0, 0.0 }, { 0, 0, 2, 1, 2, 2.0, 0.0, -1.0, 0.0 }, { -1, 0, 0, 0, 2, 1.0, 0.0, -1.0, 0.0 }, { 1, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 }, /* 81-90 */ { -2, 0, 2, 2, 2, 1.0, 0.0, -1.0, 0.0 }, { -1, 0, 2, 4, 2, -2.0, 0.0, 1.0, 0.0 }, { 2, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 }, { 1, 1, 2, -2, 2, 1.0, 0.0, -1.0, 0.0 }, { 1, 0, 2, 2, 1, -1.0, 0.0, 1.0, 0.0 }, { -2, 0, 2, 4, 2, -1.0, 0.0, 1.0, 0.0 }, { -1, 0, 4, 0, 2, 1.0, 0.0, 0.0, 0.0 }, { 1, -1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 }, { 2, 0, 2, -2, 1, 1.0, 0.0, -1.0, 0.0 }, { 2, 0, 2, 2, 2, -1.0, 0.0, 0.0, 0.0 }, /* 91-100 */ { 1, 0, 0, 2, 1, -1.0, 0.0, 0.0, 0.0 }, { 0, 0, 4, -2, 2, 1.0, 0.0, 0.0, 0.0 }, { 3, 0, 2, -2, 2, 1.0, 0.0, 0.0, 0.0 }, { 1, 0, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 }, { 0, 1, 2, 0, 1, 1.0, 0.0, 0.0, 0.0 }, { -1, -1, 0, 2, 1, 1.0, 0.0, 0.0, 0.0 }, { 0, 0, -2, 0, 1, -1.0, 0.0, 0.0, 0.0 }, { 0, 0, 2, -1, 2, -1.0, 0.0, 0.0, 0.0 }, { 0, 1, 0, 2, 0, -1.0, 0.0, 0.0, 0.0 }, { 1, 0, -2, -2, 0, -1.0, 0.0, 0.0, 0.0 }, /* 101-106 */ { 0, -1, 2, 0, 1, -1.0, 0.0, 0.0, 0.0 }, { 1, 1, 0, -2, 1, -1.0, 0.0, 0.0, 0.0 }, { 1, 0, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 }, { 2, 0, 0, 2, 0, 1.0, 0.0, 0.0, 0.0 }, { 0, 0, 2, 4, 2, -1.0, 0.0, 0.0, 0.0 }, { 0, 1, 0, 1, 0, 1.0, 0.0, 0.0, 0.0 } }; /* Number of terms in the series */ const int NT = (int) (sizeof x / sizeof x[0]); /*--------------------------------------------------------------------*/ /* Interval between fundamental epoch J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* --------------------- */ /* Fundamental arguments */ /* --------------------- */ /* Mean longitude of Moon minus mean longitude of Moon's perigee. */ el = iauAnpm( (485866.733 + (715922.633 + (31.310 + 0.064 * t) * t) * t) * DAS2R + fmod(1325.0 * t, 1.0) * D2PI); /* Mean longitude of Sun minus mean longitude of Sun's perigee. */ elp = iauAnpm( (1287099.804 + (1292581.224 + (-0.577 - 0.012 * t) * t) * t) * DAS2R + fmod(99.0 * t, 1.0) * D2PI); /* Mean longitude of Moon minus mean longitude of Moon's node. */ f = iauAnpm( (335778.877 + (295263.137 + (-13.257 + 0.011 * t) * t) * t) * DAS2R + fmod(1342.0 * t, 1.0) * D2PI); /* Mean elongation of Moon from Sun. */ d = iauAnpm( (1072261.307 + (1105601.328 + (-6.891 + 0.019 * t) * t) * t) * DAS2R + fmod(1236.0 * t, 1.0) * D2PI); /* Longitude of the mean ascending node of the lunar orbit on the */ /* ecliptic, measured from the mean equinox of date. */ om = iauAnpm( (450160.280 + (-482890.539 + (7.455 + 0.008 * t) * t) * t) * DAS2R + fmod(-5.0 * t, 1.0) * D2PI); /* --------------- */ /* Nutation series */ /* --------------- */ /* Initialize nutation components. */ dp = 0.0; de = 0.0; /* Sum the nutation terms, ending with the biggest. */ for (j = NT-1; j >= 0; j--) { /* Form argument for current term. */ arg = (double)x[j].nl * el + (double)x[j].nlp * elp + (double)x[j].nf * f + (double)x[j].nd * d + (double)x[j].nom * om; /* Accumulate current nutation term. */ s = x[j].sp + x[j].spt * t; c = x[j].ce + x[j].cet * t; if (s != 0.0) dp += s * sin(arg); if (c != 0.0) de += c * cos(arg); } /* Convert results from 0.1 mas units to radians. */ *dpsi = dp * U2R; *deps = de * U2R; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/nutm80.c0000644000113000011300000001451113027221062014461 0ustar bellsbells#include "sofa.h" void iauNutm80(double date1, double date2, double rmatn[3][3]) /* ** - - - - - - - - - - ** i a u N u t m 8 0 ** - - - - - - - - - - ** ** Form the matrix of nutation for a given date, IAU 1980 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TDB date (Note 1) ** ** Returned: ** rmatn double[3][3] nutation matrix ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(true) = rmatn * V(mean), ** where the p-vector V(true) is with respect to the true ** equatorial triad of date and the p-vector V(mean) is with ** respect to the mean equatorial triad of date. ** ** Called: ** iauNut80 nutation, IAU 1980 ** iauObl80 mean obliquity, IAU 1980 ** iauNumat form nutation matrix ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dpsi, deps, epsa; /* Nutation components and mean obliquity. */ iauNut80(date1, date2, &dpsi, &deps); epsa = iauObl80(date1, date2); /* Build the rotation matrix. */ iauNumat(epsa, dpsi, deps, rmatn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/obl06.c0000644000113000011300000001441613027221062014254 0ustar bellsbells#include "sofa.h" double iauObl06(double date1, double date2) /* ** - - - - - - - - - ** i a u O b l 0 6 ** - - - - - - - - - ** ** Mean obliquity of the ecliptic, IAU 2006 precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double obliquity of the ecliptic (radians, Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result is the angle between the ecliptic and mean equator of ** date date1+date2. ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, eps0; /* Interval between fundamental date J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Mean obliquity. */ eps0 = (84381.406 + (-46.836769 + ( -0.0001831 + ( 0.00200340 + ( -0.000000576 + ( -0.0000000434) * t) * t) * t) * t) * t) * DAS2R; return eps0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/obl80.c0000644000113000011300000001447313027221062014261 0ustar bellsbells#include "sofa.h" double iauObl80(double date1, double date2) /* ** - - - - - - - - - ** i a u O b l 8 0 ** - - - - - - - - - ** ** Mean obliquity of the ecliptic, IAU 1980 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double obliquity of the ecliptic (radians, Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result is the angle between the ecliptic and mean equator of ** date date1+date2. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Expression 3.222-1 (p114). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, eps0; /* Interval between fundamental epoch J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Mean obliquity of date. */ eps0 = DAS2R * (84381.448 + (-46.8150 + (-0.00059 + ( 0.001813) * t) * t) * t); return eps0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/p06e.c0000644000113000011300000003233013027221062014077 0ustar bellsbells#include "sofa.h" void iauP06e(double date1, double date2, double *eps0, double *psia, double *oma, double *bpa, double *bqa, double *pia, double *bpia, double *epsa, double *chia, double *za, double *zetaa, double *thetaa, double *pa, double *gam, double *phi, double *psi) /* ** - - - - - - - - ** i a u P 0 6 e ** - - - - - - - - ** ** Precession angles, IAU 2006, equinox based. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical models. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (see Note 2): ** eps0 double epsilon_0 ** psia double psi_A ** oma double omega_A ** bpa double P_A ** bqa double Q_A ** pia double pi_A ** bpia double Pi_A ** epsa double obliquity epsilon_A ** chia double chi_A ** za double z_A ** zetaa double zeta_A ** thetaa double theta_A ** pa double p_A ** gam double F-W angle gamma_J2000 ** phi double F-W angle phi_J2000 ** psi double F-W angle psi_J2000 ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) This function returns the set of equinox based angles for the ** Capitaine et al. "P03" precession theory, adopted by the IAU in ** 2006. The angles are set out in Table 1 of Hilton et al. (2006): ** ** eps0 epsilon_0 obliquity at J2000.0 ** psia psi_A luni-solar precession ** oma omega_A inclination of equator wrt J2000.0 ecliptic ** bpa P_A ecliptic pole x, J2000.0 ecliptic triad ** bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad ** pia pi_A angle between moving and J2000.0 ecliptics ** bpia Pi_A longitude of ascending node of the ecliptic ** epsa epsilon_A obliquity of the ecliptic ** chia chi_A planetary precession ** za z_A equatorial precession: -3rd 323 Euler angle ** zetaa zeta_A equatorial precession: -1st 323 Euler angle ** thetaa theta_A equatorial precession: 2nd 323 Euler angle ** pa p_A general precession ** gam gamma_J2000 J2000.0 RA difference of ecliptic poles ** phi phi_J2000 J2000.0 codeclination of ecliptic pole ** psi psi_J2000 longitude difference of equator poles, J2000.0 ** ** The returned values are all radians. ** ** 3) Hilton et al. (2006) Table 1 also contains angles that depend on ** models distinct from the P03 precession theory itself, namely the ** IAU 2000A frame bias and nutation. The quoted polynomials are ** used in other SOFA functions: ** ** . iauXy06 contains the polynomial parts of the X and Y series. ** ** . iauS06 contains the polynomial part of the s+XY/2 series. ** ** . iauPfw06 implements the series for the Fukushima-Williams ** angles that are with respect to the GCRS pole (i.e. the variants ** that include frame bias). ** ** 4) The IAU resolution stipulated that the choice of parameterization ** was left to the user, and so an IAU compliant precession ** implementation can be constructed using various combinations of ** the angles returned by the present function. ** ** 5) The parameterization used by SOFA is the version of the Fukushima- ** Williams angles that refers directly to the GCRS pole. These ** angles may be calculated by calling the function iauPfw06. SOFA ** also supports the direct computation of the CIP GCRS X,Y by ** series, available by calling iauXy06. ** ** 6) The agreement between the different parameterizations is at the ** 1 microarcsecond level in the present era. ** ** 7) When constructing a precession formulation that refers to the GCRS ** pole rather than the dynamical pole, it may (depending on the ** choice of angles) be necessary to introduce the frame bias ** explicitly. ** ** 8) It is permissible to re-use the same variable in the returned ** arguments. The quantities are stored in the stated order. ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** ** Called: ** iauObl06 mean obliquity, IAU 2006 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t; /* Interval between fundamental date J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Obliquity at J2000.0. */ *eps0 = 84381.406 * DAS2R; /* Luni-solar precession. */ *psia = ( 5038.481507 + ( -1.0790069 + ( -0.00114045 + ( 0.000132851 + ( -0.0000000951 ) * t) * t) * t) * t) * t * DAS2R; /* Inclination of mean equator with respect to the J2000.0 ecliptic. */ *oma = *eps0 + ( -0.025754 + ( 0.0512623 + ( -0.00772503 + ( -0.000000467 + ( 0.0000003337 ) * t) * t) * t) * t) * t * DAS2R; /* Ecliptic pole x, J2000.0 ecliptic triad. */ *bpa = ( 4.199094 + ( 0.1939873 + ( -0.00022466 + ( -0.000000912 + ( 0.0000000120 ) * t) * t) * t) * t) * t * DAS2R; /* Ecliptic pole -y, J2000.0 ecliptic triad. */ *bqa = ( -46.811015 + ( 0.0510283 + ( 0.00052413 + ( -0.000000646 + ( -0.0000000172 ) * t) * t) * t) * t) * t * DAS2R; /* Angle between moving and J2000.0 ecliptics. */ *pia = ( 46.998973 + ( -0.0334926 + ( -0.00012559 + ( 0.000000113 + ( -0.0000000022 ) * t) * t) * t) * t) * t * DAS2R; /* Longitude of ascending node of the moving ecliptic. */ *bpia = ( 629546.7936 + ( -867.95758 + ( 0.157992 + ( -0.0005371 + ( -0.00004797 + ( 0.000000072 ) * t) * t) * t) * t) * t) * DAS2R; /* Mean obliquity of the ecliptic. */ *epsa = iauObl06(date1, date2); /* Planetary precession. */ *chia = ( 10.556403 + ( -2.3814292 + ( -0.00121197 + ( 0.000170663 + ( -0.0000000560 ) * t) * t) * t) * t) * t * DAS2R; /* Equatorial precession: minus the third of the 323 Euler angles. */ *za = ( -2.650545 + ( 2306.077181 + ( 1.0927348 + ( 0.01826837 + ( -0.000028596 + ( -0.0000002904 ) * t) * t) * t) * t) * t) * DAS2R; /* Equatorial precession: minus the first of the 323 Euler angles. */ *zetaa = ( 2.650545 + ( 2306.083227 + ( 0.2988499 + ( 0.01801828 + ( -0.000005971 + ( -0.0000003173 ) * t) * t) * t) * t) * t) * DAS2R; /* Equatorial precession: second of the 323 Euler angles. */ *thetaa = ( 2004.191903 + ( -0.4294934 + ( -0.04182264 + ( -0.000007089 + ( -0.0000001274 ) * t) * t) * t) * t) * t * DAS2R; /* General precession. */ *pa = ( 5028.796195 + ( 1.1054348 + ( 0.00007964 + ( -0.000023857 + ( 0.0000000383 ) * t) * t) * t) * t) * t * DAS2R; /* Fukushima-Williams angles for precession. */ *gam = ( 10.556403 + ( 0.4932044 + ( -0.00031238 + ( -0.000002788 + ( 0.0000000260 ) * t) * t) * t) * t) * t * DAS2R; *phi = *eps0 + ( -46.811015 + ( 0.0511269 + ( 0.00053289 + ( -0.000000440 + ( -0.0000000176 ) * t) * t) * t) * t) * t * DAS2R; *psi = ( 5038.481507 + ( 1.5584176 + ( -0.00018522 + ( -0.000026452 + ( -0.0000000148 ) * t) * t) * t) * t) * t * DAS2R; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/p2pv.c0000644000113000011300000001164513027221062014222 0ustar bellsbells#include "sofa.h" void iauP2pv(double p[3], double pv[2][3]) /* ** - - - - - - - - ** i a u P 2 p v ** - - - - - - - - ** ** Extend a p-vector to a pv-vector by appending a zero velocity. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector ** ** Returned: ** pv double[2][3] pv-vector ** ** Called: ** iauCp copy p-vector ** iauZp zero p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauCp(p, pv[0]); iauZp(pv[1]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/p2s.c0000644000113000011300000001223413027221062014032 0ustar bellsbells#include "sofa.h" void iauP2s(double p[3], double *theta, double *phi, double *r) /* ** - - - - - - - ** i a u P 2 s ** - - - - - - - ** ** P-vector to spherical polar coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector ** ** Returned: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** r double radial distance ** ** Notes: ** ** 1) If P is null, zero theta, phi and r are returned. ** ** 2) At either pole, zero theta is returned. ** ** Called: ** iauC2s p-vector to spherical ** iauPm modulus of p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauC2s(p, theta, phi); *r = iauPm(p); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pap.c0000644000113000011300000001516013027221062014107 0ustar bellsbells#include "sofa.h" double iauPap(double a[3], double b[3]) /* ** - - - - - - - ** i a u P a p ** - - - - - - - ** ** Position-angle from two p-vectors. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] direction of reference point ** b double[3] direction of point whose PA is required ** ** Returned (function value): ** double position angle of b with respect to a (radians) ** ** Notes: ** ** 1) The result is the position angle, in radians, of direction b with ** respect to direction a. It is in the range -pi to +pi. The ** sense is such that if b is a small distance "north" of a the ** position angle is approximately zero, and if b is a small ** distance "east" of a the position angle is approximately +pi/2. ** ** 2) The vectors a and b need not be of unit length. ** ** 3) Zero is returned if the two directions are the same or if either ** vector is null. ** ** 4) If vector a is at a pole, the result is ill-defined. ** ** Called: ** iauPn decompose p-vector into modulus and direction ** iauPm modulus of p-vector ** iauPxp vector product of two p-vectors ** iauPmp p-vector minus p-vector ** iauPdp scalar product of two p-vectors ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double am, au[3], bm, st, ct, xa, ya, za, eta[3], xi[3], a2b[3], pa; /* Modulus and direction of the a vector. */ iauPn(a, &am, au); /* Modulus of the b vector. */ bm = iauPm(b); /* Deal with the case of a null vector. */ if ((am == 0.0) || (bm == 0.0)) { st = 0.0; ct = 1.0; } else { /* The "north" axis tangential from a (arbitrary length). */ xa = a[0]; ya = a[1]; za = a[2]; eta[0] = -xa * za; eta[1] = -ya * za; eta[2] = xa*xa + ya*ya; /* The "east" axis tangential from a (same length). */ iauPxp(eta, au, xi); /* The vector from a to b. */ iauPmp(b, a, a2b); /* Resolve into components along the north and east axes. */ st = iauPdp(a2b, xi); ct = iauPdp(a2b, eta); /* Deal with degenerate cases. */ if ((st == 0.0) && (ct == 0.0)) ct = 1.0; } /* Position angle. */ pa = atan2(st, ct); return pa; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pas.c0000644000113000011300000001300613027221062014107 0ustar bellsbells#include "sofa.h" double iauPas(double al, double ap, double bl, double bp) /* ** - - - - - - - ** i a u P a s ** - - - - - - - ** ** Position-angle from spherical coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** al double longitude of point A (e.g. RA) in radians ** ap double latitude of point A (e.g. Dec) in radians ** bl double longitude of point B ** bp double latitude of point B ** ** Returned (function value): ** double position angle of B with respect to A ** ** Notes: ** ** 1) The result is the bearing (position angle), in radians, of point ** B with respect to point A. It is in the range -pi to +pi. The ** sense is such that if B is a small distance "east" of point A, ** the bearing is approximately +pi/2. ** ** 2) Zero is returned if the two points are coincident. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dl, x, y, pa; dl = bl - al; y = sin(dl) * cos(bp); x = sin(bp) * cos(ap) - cos(bp) * sin(ap) * cos(dl); pa = ((x != 0.0) || (y != 0.0)) ? atan2(y, x) : 0.0; return pa; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pb06.c0000644000113000011300000001676513027221062014112 0ustar bellsbells#include "sofa.h" void iauPb06(double date1, double date2, double *bzeta, double *bz, double *btheta) /* ** - - - - - - - - ** i a u P b 0 6 ** - - - - - - - - ** ** This function forms three Euler angles which implement general ** precession from epoch J2000.0, using the IAU 2006 model. Frame ** bias (the offset between ICRS and mean J2000.0) is included. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** bzeta double 1st rotation: radians cw around z ** bz double 3rd rotation: radians cw around z ** btheta double 2nd rotation: radians ccw around y ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The traditional accumulated precession angles zeta_A, z_A, ** theta_A cannot be obtained in the usual way, namely through ** polynomial expressions, because of the frame bias. The latter ** means that two of the angles undergo rapid changes near this ** date. They are instead the results of decomposing the ** precession-bias matrix obtained by using the Fukushima-Williams ** method, which does not suffer from the problem. The ** decomposition returns values which can be used in the ** conventional formulation and which include frame bias. ** ** 3) The three angles are returned in the conventional order, which ** is not the same as the order of the corresponding Euler ** rotations. The precession-bias matrix is ** R_3(-z) x R_2(+theta) x R_3(-zeta). ** ** 4) Should zeta_A, z_A, theta_A angles be required that do not ** contain frame bias, they are available by calling the SOFA ** function iauP06e. ** ** Called: ** iauPmat06 PB matrix, IAU 2006 ** iauRz rotate around Z-axis ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double r[3][3], r31, r32; /* Precession matrix via Fukushima-Williams angles. */ iauPmat06(date1, date2, r); /* Solve for z. */ *bz = atan2(r[1][2], r[0][2]); /* Remove it from the matrix. */ iauRz(*bz, r); /* Solve for the remaining two angles. */ *bzeta = atan2 (r[1][0], r[1][1]); r31 = r[2][0]; r32 = r[2][1]; *btheta = atan2(-dsign(sqrt(r31 * r31 + r32 * r32), r[0][2]), r[2][2]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pdp.c0000644000113000011300000001162013027221062014107 0ustar bellsbells#include "sofa.h" double iauPdp(double a[3], double b[3]) /* ** - - - - - - - ** i a u P d p ** - - - - - - - ** ** p-vector inner (=scalar=dot) product. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector ** b double[3] second p-vector ** ** Returned (function value): ** double a . b ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double w; w = a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; return w; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pfw06.c0000644000113000011300000001743413027221062014277 0ustar bellsbells#include "sofa.h" void iauPfw06(double date1, double date2, double *gamb, double *phib, double *psib, double *epsa) /* ** - - - - - - - - - ** i a u P f w 0 6 ** - - - - - - - - - ** ** Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** gamb double F-W angle gamma_bar (radians) ** phib double F-W angle phi_bar (radians) ** psib double F-W angle psi_bar (radians) ** epsa double F-W angle epsilon_A (radians) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) Naming the following points: ** ** e = J2000.0 ecliptic pole, ** p = GCRS pole, ** E = mean ecliptic pole of date, ** and P = mean pole of date, ** ** the four Fukushima-Williams angles are as follows: ** ** gamb = gamma_bar = epE ** phib = phi_bar = pE ** psib = psi_bar = pEP ** epsa = epsilon_A = EP ** ** 3) The matrix representing the combined effects of frame bias and ** precession is: ** ** PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb) ** ** 4) The matrix representing the combined effects of frame bias, ** precession and nutation is simply: ** ** NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb) ** ** where dP and dE are the nutation components with respect to the ** ecliptic of date. ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** ** Called: ** iauObl06 mean obliquity, IAU 2006 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t; /* Interval between fundamental date J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* P03 bias+precession angles. */ *gamb = ( -0.052928 + ( 10.556378 + ( 0.4932044 + ( -0.00031238 + ( -0.000002788 + ( 0.0000000260 ) * t) * t) * t) * t) * t) * DAS2R; *phib = ( 84381.412819 + ( -46.811016 + ( 0.0511268 + ( 0.00053289 + ( -0.000000440 + ( -0.0000000176 ) * t) * t) * t) * t) * t) * DAS2R; *psib = ( -0.041775 + ( 5038.481484 + ( 1.5584175 + ( -0.00018522 + ( -0.000026452 + ( -0.0000000148 ) * t) * t) * t) * t) * t) * DAS2R; *epsa = iauObl06(date1, date2); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/plan94.c0000644000113000011300000005521413027221062014442 0ustar bellsbells#include "sofa.h" int iauPlan94(double date1, double date2, int np, double pv[2][3]) /* ** - - - - - - - - - - ** i a u P l a n 9 4 ** - - - - - - - - - - ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Approximate heliocentric position and velocity of a nominated major ** planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or ** Neptune (but not the Earth itself). ** ** Given: ** date1 double TDB date part A (Note 1) ** date2 double TDB date part B (Note 1) ** np int planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars, ** 5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune) ** ** Returned (argument): ** pv double[2][3] planet p,v (heliocentric, J2000.0, AU,AU/d) ** ** Returned (function value): ** int status: -1 = illegal NP (outside 1-8) ** 0 = OK ** +1 = warning: year outside 1000-3000 ** +2 = warning: failed to converge ** ** Notes: ** ** 1) The date date1+date2 is in the TDB time scale (in practice TT can ** be used) and is a Julian Date, apportioned in any convenient way ** between the two arguments. For example, JD(TDB)=2450123.7 could ** be expressed in any of these ways, among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. The limited ** accuracy of the present algorithm is such that any of the methods ** is satisfactory. ** ** 2) If an np value outside the range 1-8 is supplied, an error status ** (function value -1) is returned and the pv vector set to zeroes. ** ** 3) For np=3 the result is for the Earth-Moon Barycenter. To obtain ** the heliocentric position and velocity of the Earth, use instead ** the SOFA function iauEpv00. ** ** 4) On successful return, the array pv contains the following: ** ** pv[0][0] x } ** pv[0][1] y } heliocentric position, AU ** pv[0][2] z } ** ** pv[1][0] xdot } ** pv[1][1] ydot } heliocentric velocity, AU/d ** pv[1][2] zdot } ** ** The reference frame is equatorial and is with respect to the ** mean equator and equinox of epoch J2000.0. ** ** 5) The algorithm is due to J.L. Simon, P. Bretagnon, J. Chapront, ** M. Chapront-Touze, G. Francou and J. Laskar (Bureau des ** Longitudes, Paris, France). From comparisons with JPL ** ephemeris DE102, they quote the following maximum errors ** over the interval 1800-2050: ** ** L (arcsec) B (arcsec) R (km) ** ** Mercury 4 1 300 ** Venus 5 1 800 ** EMB 6 1 1000 ** Mars 17 1 7700 ** Jupiter 71 5 76000 ** Saturn 81 13 267000 ** Uranus 86 7 712000 ** Neptune 11 1 253000 ** ** Over the interval 1000-3000, they report that the accuracy is no ** worse than 1.5 times that over 1800-2050. Outside 1000-3000 the ** accuracy declines. ** ** Comparisons of the present function with the JPL DE200 ephemeris ** give the following RMS errors over the interval 1960-2025: ** ** position (km) velocity (m/s) ** ** Mercury 334 0.437 ** Venus 1060 0.855 ** EMB 2010 0.815 ** Mars 7690 1.98 ** Jupiter 71700 7.70 ** Saturn 199000 19.4 ** Uranus 564000 16.4 ** Neptune 158000 14.4 ** ** Comparisons against DE200 over the interval 1800-2100 gave the ** following maximum absolute differences. (The results using ** DE406 were essentially the same.) ** ** L (arcsec) B (arcsec) R (km) Rdot (m/s) ** ** Mercury 7 1 500 0.7 ** Venus 7 1 1100 0.9 ** EMB 9 1 1300 1.0 ** Mars 26 1 9000 2.5 ** Jupiter 78 6 82000 8.2 ** Saturn 87 14 263000 24.6 ** Uranus 86 7 661000 27.4 ** Neptune 11 2 248000 21.4 ** ** 6) The present SOFA re-implementation of the original Simon et al. ** Fortran code differs from the original in the following respects: ** ** * C instead of Fortran. ** ** * The date is supplied in two parts. ** ** * The result is returned only in equatorial Cartesian form; ** the ecliptic longitude, latitude and radius vector are not ** returned. ** ** * The result is in the J2000.0 equatorial frame, not ecliptic. ** ** * More is done in-line: there are fewer calls to subroutines. ** ** * Different error/warning status values are used. ** ** * A different Kepler's-equation-solver is used (avoiding ** use of double precision complex). ** ** * Polynomials in t are nested to minimize rounding errors. ** ** * Explicit double constants are used to avoid mixed-mode ** expressions. ** ** None of the above changes affects the result significantly. ** ** 7) The returned status indicates the most serious condition ** encountered during execution of the function. Illegal np is ** considered the most serious, overriding failure to converge, ** which in turn takes precedence over the remote date warning. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: Simon, J.L, Bretagnon, P., Chapront, J., ** Chapront-Touze, M., Francou, G., and Laskar, J., ** Astron. Astrophys. 282, 663 (1994). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Gaussian constant */ static const double GK = 0.017202098950; /* Sin and cos of J2000.0 mean obliquity (IAU 1976) */ static const double SINEPS = 0.3977771559319137; static const double COSEPS = 0.9174820620691818; /* Maximum number of iterations allowed to solve Kepler's equation */ static const int KMAX = 10; int jstat, i, k; double t, da, dl, de, dp, di, dom, dmu, arga, argl, am, ae, dae, ae2, at, r, v, si2, xq, xp, tl, xsw, xcw, xm2, xf, ci2, xms, xmc, xpxq2, x, y, z; /* Planetary inverse masses */ static const double amas[] = { 6023600.0, /* Mercury */ 408523.5, /* Venus */ 328900.5, /* EMB */ 3098710.0, /* Mars */ 1047.355, /* Jupiter */ 3498.5, /* Saturn */ 22869.0, /* Uranus */ 19314.0 }; /* Neptune */ /* ** Tables giving the mean Keplerian elements, limited to t^2 terms: ** ** a semi-major axis (AU) ** dlm mean longitude (degree and arcsecond) ** e eccentricity ** pi longitude of the perihelion (degree and arcsecond) ** dinc inclination (degree and arcsecond) ** omega longitude of the ascending node (degree and arcsecond) */ static const double a[][3] = { { 0.3870983098, 0.0, 0.0 }, /* Mercury */ { 0.7233298200, 0.0, 0.0 }, /* Venus */ { 1.0000010178, 0.0, 0.0 }, /* EMB */ { 1.5236793419, 3e-10, 0.0 }, /* Mars */ { 5.2026032092, 19132e-10, -39e-10 }, /* Jupiter */ { 9.5549091915, -0.0000213896, 444e-10 }, /* Saturn */ { 19.2184460618, -3716e-10, 979e-10 }, /* Uranus */ { 30.1103868694, -16635e-10, 686e-10 } /* Neptune */ }; static const double dlm[][3] = { { 252.25090552, 5381016286.88982, -1.92789 }, { 181.97980085, 2106641364.33548, 0.59381 }, { 100.46645683, 1295977422.83429, -2.04411 }, { 355.43299958, 689050774.93988, 0.94264 }, { 34.35151874, 109256603.77991, -30.60378 }, { 50.07744430, 43996098.55732, 75.61614 }, { 314.05500511, 15424811.93933, -1.75083 }, { 304.34866548, 7865503.20744, 0.21103 } }; static const double e[][3] = { { 0.2056317526, 0.0002040653, -28349e-10 }, { 0.0067719164, -0.0004776521, 98127e-10 }, { 0.0167086342, -0.0004203654, -0.0000126734 }, { 0.0934006477, 0.0009048438, -80641e-10 }, { 0.0484979255, 0.0016322542, -0.0000471366 }, { 0.0555481426, -0.0034664062, -0.0000643639 }, { 0.0463812221, -0.0002729293, 0.0000078913 }, { 0.0094557470, 0.0000603263, 0.0 } }; static const double pi[][3] = { { 77.45611904, 5719.11590, -4.83016 }, { 131.56370300, 175.48640, -498.48184 }, { 102.93734808, 11612.35290, 53.27577 }, { 336.06023395, 15980.45908, -62.32800 }, { 14.33120687, 7758.75163, 259.95938 }, { 93.05723748, 20395.49439, 190.25952 }, { 173.00529106, 3215.56238, -34.09288 }, { 48.12027554, 1050.71912, 27.39717 } }; static const double dinc[][3] = { { 7.00498625, -214.25629, 0.28977 }, { 3.39466189, -30.84437, -11.67836 }, { 0.0, 469.97289, -3.35053 }, { 1.84972648, -293.31722, -8.11830 }, { 1.30326698, -71.55890, 11.95297 }, { 2.48887878, 91.85195, -17.66225 }, { 0.77319689, -60.72723, 1.25759 }, { 1.76995259, 8.12333, 0.08135 } }; static const double omega[][3] = { { 48.33089304, -4515.21727, -31.79892 }, { 76.67992019, -10008.48154, -51.32614 }, { 174.87317577, -8679.27034, 15.34191 }, { 49.55809321, -10620.90088, -230.57416 }, { 100.46440702, 6362.03561, 326.52178 }, { 113.66550252, -9240.19942, -66.23743 }, { 74.00595701, 2669.15033, 145.93964 }, { 131.78405702, -221.94322, -0.78728 } }; /* Tables for trigonometric terms to be added to the mean elements of */ /* the semi-major axes */ static const double kp[][9] = { { 69613, 75645, 88306, 59899, 15746, 71087, 142173, 3086, 0 }, { 21863, 32794, 26934, 10931, 26250, 43725, 53867, 28939, 0 }, { 16002, 21863, 32004, 10931, 14529, 16368, 15318, 32794, 0 }, { 6345, 7818, 15636, 7077, 8184, 14163, 1107, 4872, 0 }, { 1760, 1454, 1167, 880, 287, 2640, 19, 2047, 1454 }, { 574, 0, 880, 287, 19, 1760, 1167, 306, 574 }, { 204, 0, 177, 1265, 4, 385, 200, 208, 204 }, { 0, 102, 106, 4, 98, 1367, 487, 204, 0 } }; static const double ca[][9] = { { 4, -13, 11, -9, -9, -3, -1, 4, 0 }, { -156, 59, -42, 6, 19, -20, -10, -12, 0 }, { 64, -152, 62, -8, 32, -41, 19, -11, 0 }, { 124, 621, -145, 208, 54, -57, 30, 15, 0 }, { -23437, -2634, 6601, 6259, -1507,-1821, 2620, -2115, -1489 }, { 62911,-119919, 79336,17814,-24241,12068, 8306, -4893, 8902 }, { 389061,-262125,-44088, 8387,-22976,-2093, -615, -9720, 6633 }, { -412235,-157046,-31430,37817, -9740, -13, -7449, 9644, 0 } }; static const double sa[][9] = { { -29, -1, 9, 6, -6, 5, 4, 0, 0 }, { -48, -125, -26, -37, 18, -13, -20, -2, 0 }, { -150, -46, 68, 54, 14, 24, -28, 22, 0 }, { -621, 532, -694, -20, 192, -94, 71, -73, 0 }, { -14614,-19828, -5869, 1881, -4372, -2255, 782, 930, 913 }, { 139737, 0, 24667, 51123, -5102, 7429, -4095, -1976, -9566 }, { -138081, 0, 37205,-49039,-41901,-33872,-27037,-12474, 18797 }, { 0, 28492,133236, 69654, 52322,-49577,-26430, -3593, 0 } }; /* Tables giving the trigonometric terms to be added to the mean */ /* elements of the mean longitudes */ static const double kq[][10] = { { 3086,15746,69613,59899,75645,88306, 12661, 2658, 0, 0 }, { 21863,32794,10931, 73, 4387,26934, 1473, 2157, 0, 0 }, { 10,16002,21863,10931, 1473,32004, 4387, 73, 0, 0 }, { 10, 6345, 7818, 1107,15636, 7077, 8184, 532, 10, 0 }, { 19, 1760, 1454, 287, 1167, 880, 574, 2640, 19, 1454 }, { 19, 574, 287, 306, 1760, 12, 31, 38, 19, 574 }, { 4, 204, 177, 8, 31, 200, 1265, 102, 4, 204 }, { 4, 102, 106, 8, 98, 1367, 487, 204, 4, 102 } }; static const double cl[][10] = { { 21, -95, -157, 41, -5, 42, 23, 30, 0, 0 }, { -160, -313, -235, 60, -74, -76, -27, 34, 0, 0 }, { -325, -322, -79, 232, -52, 97, 55, -41, 0, 0 }, { 2268, -979, 802, 602, -668, -33, 345, 201, -55, 0 }, { 7610, -4997,-7689,-5841,-2617, 1115,-748,-607, 6074, 354 }, { -18549, 30125,20012, -730, 824, 23,1289,-352, -14767, -2062 }, { -135245,-14594, 4197,-4030,-5630,-2898,2540,-306, 2939, 1986 }, { 89948, 2103, 8963, 2695, 3682, 1648, 866,-154, -1963, -283 } }; static const double sl[][10] = { { -342, 136, -23, 62, 66, -52, -33, 17, 0, 0 }, { 524, -149, -35, 117, 151, 122, -71, -62, 0, 0 }, { -105, -137, 258, 35, -116, -88,-112, -80, 0, 0 }, { 854, -205, -936, -240, 140, -341, -97, -232, 536, 0 }, { -56980, 8016, 1012, 1448,-3024,-3710, 318, 503, 3767, 577 }, { 138606,-13478,-4964, 1441,-1319,-1482, 427, 1236, -9167, -1918 }, { 71234,-41116, 5334,-4935,-1848, 66, 434, -1748, 3780, -701 }, { -47645, 11647, 2166, 3194, 679, 0,-244, -419, -2531, 48 } }; /*--------------------------------------------------------------------*/ /* Validate the planet number. */ if ((np < 1) || (np > 8)) { jstat = -1; /* Reset the result in case of failure. */ for (k = 0; k < 2; k++) { for (i = 0; i < 3; i++) { pv[k][i] = 0.0; } } } else { /* Decrement the planet number to start at zero. */ np--; /* Time: Julian millennia since J2000.0. */ t = ((date1 - DJ00) + date2) / DJM; /* OK status unless remote date. */ jstat = fabs(t) <= 1.0 ? 0 : 1; /* Compute the mean elements. */ da = a[np][0] + (a[np][1] + a[np][2] * t) * t; dl = (3600.0 * dlm[np][0] + (dlm[np][1] + dlm[np][2] * t) * t) * DAS2R; de = e[np][0] + ( e[np][1] + e[np][2] * t) * t; dp = iauAnpm((3600.0 * pi[np][0] + (pi[np][1] + pi[np][2] * t) * t) * DAS2R); di = (3600.0 * dinc[np][0] + (dinc[np][1] + dinc[np][2] * t) * t) * DAS2R; dom = iauAnpm((3600.0 * omega[np][0] + (omega[np][1] + omega[np][2] * t) * t) * DAS2R); /* Apply the trigonometric terms. */ dmu = 0.35953620 * t; for (k = 0; k < 8; k++) { arga = kp[np][k] * dmu; argl = kq[np][k] * dmu; da += (ca[np][k] * cos(arga) + sa[np][k] * sin(arga)) * 1e-7; dl += (cl[np][k] * cos(argl) + sl[np][k] * sin(argl)) * 1e-7; } arga = kp[np][8] * dmu; da += t * (ca[np][8] * cos(arga) + sa[np][8] * sin(arga)) * 1e-7; for (k = 8; k < 10; k++) { argl = kq[np][k] * dmu; dl += t * (cl[np][k] * cos(argl) + sl[np][k] * sin(argl)) * 1e-7; } dl = fmod(dl, D2PI); /* Iterative soln. of Kepler's equation to get eccentric anomaly. */ am = dl - dp; ae = am + de * sin(am); k = 0; dae = 1.0; while (k < KMAX && fabs(dae) > 1e-12) { dae = (am - ae + de * sin(ae)) / (1.0 - de * cos(ae)); ae += dae; k++; if (k == KMAX-1) jstat = 2; } /* True anomaly. */ ae2 = ae / 2.0; at = 2.0 * atan2(sqrt((1.0 + de) / (1.0 - de)) * sin(ae2), cos(ae2)); /* Distance (AU) and speed (radians per day). */ r = da * (1.0 - de * cos(ae)); v = GK * sqrt((1.0 + 1.0 / amas[np]) / (da * da * da)); si2 = sin(di / 2.0); xq = si2 * cos(dom); xp = si2 * sin(dom); tl = at + dp; xsw = sin(tl); xcw = cos(tl); xm2 = 2.0 * (xp * xcw - xq * xsw); xf = da / sqrt(1 - de * de); ci2 = cos(di / 2.0); xms = (de * sin(dp) + xsw) * xf; xmc = (de * cos(dp) + xcw) * xf; xpxq2 = 2 * xp * xq; /* Position (J2000.0 ecliptic x,y,z in AU). */ x = r * (xcw - xm2 * xp); y = r * (xsw + xm2 * xq); z = r * (-xm2 * ci2); /* Rotate to equatorial. */ pv[0][0] = x; pv[0][1] = y * COSEPS - z * SINEPS; pv[0][2] = y * SINEPS + z * COSEPS; /* Velocity (J2000.0 ecliptic xdot,ydot,zdot in AU/d). */ x = v * (( -1.0 + 2.0 * xp * xp) * xms + xpxq2 * xmc); y = v * (( 1.0 - 2.0 * xq * xq) * xmc - xpxq2 * xms); z = v * (2.0 * ci2 * (xp * xms + xq * xmc)); /* Rotate to equatorial. */ pv[1][0] = x; pv[1][1] = y * COSEPS - z * SINEPS; pv[1][2] = y * SINEPS + z * COSEPS; } /* Return the status. */ return jstat; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pmat00.c0000644000113000011300000001466313027221062014437 0ustar bellsbells#include "sofa.h" void iauPmat00(double date1, double date2, double rbp[3][3]) /* ** - - - - - - - - - - ** i a u P m a t 0 0 ** - - - - - - - - - - ** ** Precession matrix (including frame bias) from GCRS to a specified ** date, IAU 2000 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rbp double[3][3] bias-precession matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rbp * V(GCRS), where ** the p-vector V(GCRS) is with respect to the Geocentric Celestial ** Reference System (IAU, 2000) and the p-vector V(date) is with ** respect to the mean equatorial triad of the given date. ** ** Called: ** iauBp00 frame bias and precession matrices, IAU 2000 ** ** Reference: ** ** IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. ** 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. ** (2000) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rb[3][3], rp[3][3]; /* Obtain the required matrix (discarding others). */ iauBp00(date1, date2, rb, rp, rbp); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pmat06.c0000644000113000011300000001503313027221063014436 0ustar bellsbells#include "sofa.h" void iauPmat06(double date1, double date2, double rbp[3][3]) /* ** - - - - - - - - - - ** i a u P m a t 0 6 ** - - - - - - - - - - ** ** Precession matrix (including frame bias) from GCRS to a specified ** date, IAU 2006 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rbp double[3][3] bias-precession matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rbp * V(GCRS), where ** the p-vector V(GCRS) is with respect to the Geocentric Celestial ** Reference System (IAU, 2000) and the p-vector V(date) is with ** respect to the mean equatorial triad of the given date. ** ** Called: ** iauPfw06 bias-precession F-W angles, IAU 2006 ** iauFw2m F-W angles to r-matrix ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double gamb, phib, psib, epsa; /* Bias-precession Fukushima-Williams angles. */ iauPfw06(date1, date2, &gamb, &phib, &psib, &epsa); /* Form the matrix. */ iauFw2m(gamb, phib, psib, epsa, rbp); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pmat76.c0000644000113000011300000001657413027221063014460 0ustar bellsbells#include "sofa.h" void iauPmat76(double date1, double date2, double rmatp[3][3]) /* ** - - - - - - - - - - ** i a u P m a t 7 6 ** - - - - - - - - - - ** ** Precession matrix from J2000.0 to a specified date, IAU 1976 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double ending date, TT (Note 1) ** ** Returned: ** rmatp double[3][3] precession matrix, J2000.0 -> date1+date2 ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = RMATP * V(J2000), ** where the p-vector V(J2000) is with respect to the mean ** equatorial triad of epoch J2000.0 and the p-vector V(date) ** is with respect to the mean equatorial triad of the given ** date. ** ** 3) Though the matrix method itself is rigorous, the precession ** angles are expressed through canonical polynomials which are ** valid only for a limited time span. In addition, the IAU 1976 ** precession rate is known to be imperfect. The absolute accuracy ** of the present formulation is better than 0.1 arcsec from ** 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD, ** and remains below 3 arcsec for the whole of the period ** 500BC to 3000AD. The errors exceed 10 arcsec outside the ** range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to ** 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD. ** ** Called: ** iauPrec76 accumulated precession angles, IAU 1976 ** iauIr initialize r-matrix to identity ** iauRz rotate around Z-axis ** iauRy rotate around Y-axis ** iauCr copy r-matrix ** ** References: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282. ** equations (6) & (7), p283. ** ** Kaplan,G.H., 1981. USNO circular no. 163, pA2. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double zeta, z, theta, wmat[3][3]; /* Precession Euler angles, J2000.0 to specified date. */ iauPrec76(DJ00, 0.0, date1, date2, &zeta, &z, &theta); /* Form the rotation matrix. */ iauIr( wmat); iauRz( -zeta, wmat); iauRy( theta, wmat); iauRz( -z, wmat); iauCr( wmat, rmatp); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pm.c0000644000113000011300000001142713027221063013746 0ustar bellsbells#include "sofa.h" double iauPm(double p[3]) /* ** - - - - - - ** i a u P m ** - - - - - - ** ** Modulus of p-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector ** ** Returned (function value): ** double modulus ** ** This revision: 2013 August 7 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { return sqrt( p[0]*p[0] + p[1]*p[1] + p[2]*p[2] ); /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pmp.c0000644000113000011300000001174213027221063014126 0ustar bellsbells#include "sofa.h" void iauPmp(double a[3], double b[3], double amb[3]) /* ** - - - - - - - ** i a u P m p ** - - - - - - - ** ** P-vector subtraction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector ** b double[3] second p-vector ** ** Returned: ** amb double[3] a - b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { amb[0] = a[0] - b[0]; amb[1] = a[1] - b[1]; amb[2] = a[2] - b[2]; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pmpx.c0000644000113000011300000001561713027221063014323 0ustar bellsbells#include "sofa.h" void iauPmpx(double rc, double dc, double pr, double pd, double px, double rv, double pmt, double pob[3], double pco[3]) /* ** - - - - - - - - ** i a u P m p x ** - - - - - - - - ** ** Proper motion and parallax. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc,dc double ICRS RA,Dec at catalog epoch (radians) ** pr double RA proper motion (radians/year; Note 1) ** pd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, +ve if receding) ** pmt double proper motion time interval (SSB, Julian years) ** pob double[3] SSB to observer vector (au) ** ** Returned: ** pco double[3] coordinate direction (BCRS unit vector) ** ** Notes: ** ** 1) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 2) The proper motion time interval is for when the starlight ** reaches the solar system barycenter. ** ** 3) To avoid the need for iteration, the Roemer effect (i.e. the ** small annual modulation of the proper motion coming from the ** changing light time) is applied approximately, using the ** direction of the star at the catalog epoch. ** ** References: ** ** 1984 Astronomical Almanac, pp B39-B41. ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013), Section 7.2. ** ** Called: ** iauPdp scalar product of two p-vectors ** iauPn decompose p-vector into modulus and direction ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Km/s to au/year */ const double VF = DAYSEC*DJM/DAU; /* Light time for 1 au, Julian years */ const double AULTY = AULT/DAYSEC/DJY; int i; double sr, cr, sd, cd, x, y, z, p[3], dt, pxr, w, pdz, pm[3]; /* Spherical coordinates to unit vector (and useful functions). */ sr = sin(rc); cr = cos(rc); sd = sin(dc); cd = cos(dc); p[0] = x = cr*cd; p[1] = y = sr*cd; p[2] = z = sd; /* Proper motion time interval (y) including Roemer effect. */ dt = pmt + iauPdp(p,pob)*AULTY; /* Space motion (radians per year). */ pxr = px * DAS2R; w = VF * rv * pxr; pdz = pd * z; pm[0] = - pr*y - pdz*cr + w*x; pm[1] = pr*x - pdz*sr + w*y; pm[2] = pd*cd + w*z; /* Coordinate direction of star (unit vector, BCRS). */ for (i = 0; i < 3; i++) { p[i] += dt*pm[i] - pxr*pob[i]; } iauPn(p, &w, pco); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pmsafe.c0000644000113000011300000002375513027221063014614 0ustar bellsbells#include "sofa.h" int iauPmsafe(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2) /* ** - - - - - - - - - - ** i a u P m s a f e ** - - - - - - - - - - ** ** Star proper motion: update star catalog data for space motion, with ** special handling to handle the zero parallax case. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ra1 double right ascension (radians), before ** dec1 double declination (radians), before ** pmr1 double RA proper motion (radians/year), before ** pmd1 double Dec proper motion (radians/year), before ** px1 double parallax (arcseconds), before ** rv1 double radial velocity (km/s, +ve = receding), before ** ep1a double "before" epoch, part A (Note 1) ** ep1b double "before" epoch, part B (Note 1) ** ep2a double "after" epoch, part A (Note 1) ** ep2b double "after" epoch, part B (Note 1) ** ** Returned: ** ra2 double right ascension (radians), after ** dec2 double declination (radians), after ** pmr2 double RA proper motion (radians/year), after ** pmd2 double Dec proper motion (radians/year), after ** px2 double parallax (arcseconds), after ** rv2 double radial velocity (km/s, +ve = receding), after ** ** Returned (function value): ** int status: ** -1 = system error (should not occur) ** 0 = no warnings or errors ** 1 = distance overridden (Note 6) ** 2 = excessive velocity (Note 7) ** 4 = solution didn't converge (Note 8) ** else = binary logical OR of the above warnings ** ** Notes: ** ** 1) The starting and ending TDB epochs ep1a+ep1b and ep2a+ep2b are ** Julian Dates, apportioned in any convenient way between the two ** parts (A and B). For example, JD(TDB)=2450123.7 could be ** expressed in any of these ways, among others: ** ** epNa epNb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. ** ** 2) In accordance with normal star-catalog conventions, the object's ** right ascension and declination are freed from the effects of ** secular aberration. The frame, which is aligned to the catalog ** equator and equinox, is Lorentzian and centered on the SSB. ** ** The proper motions are the rate of change of the right ascension ** and declination at the catalog epoch and are in radians per TDB ** Julian year. ** ** The parallax and radial velocity are in the same frame. ** ** 3) Care is needed with units. The star coordinates are in radians ** and the proper motions in radians per Julian year, but the ** parallax is in arcseconds. ** ** 4) The RA proper motion is in terms of coordinate angle, not true ** angle. If the catalog uses arcseconds for both RA and Dec proper ** motions, the RA proper motion will need to be divided by cos(Dec) ** before use. ** ** 5) Straight-line motion at constant speed, in the inertial frame, is ** assumed. ** ** 6) An extremely small (or zero or negative) parallax is overridden ** to ensure that the object is at a finite but very large distance, ** but not so large that the proper motion is equivalent to a large ** but safe speed (about 0.1c using the chosen constant). A warning ** status of 1 is added to the status if this action has been taken. ** ** 7) If the space velocity is a significant fraction of c (see the ** constant VMAX in the function iauStarpv), it is arbitrarily set ** to zero. When this action occurs, 2 is added to the status. ** ** 8) The relativistic adjustment carried out in the iauStarpv function ** involves an iterative calculation. If the process fails to ** converge within a set number of iterations, 4 is added to the ** status. ** ** Called: ** iauSeps angle between two points ** iauStarpm update star catalog data for space motion ** ** This revision: 2014 July 1 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Minimum allowed parallax (arcsec) */ const double PXMIN = 5e-7; /* Factor giving maximum allowed transverse speed of about 1% c */ const double F = 326.0; int jpx, j; double pm, px1a; /* Proper motion in one year (radians). */ pm = iauSeps(ra1, dec1, ra1+pmr1, dec1+pmd1); /* Override the parallax to reduce the chances of a warning status. */ jpx = 0; px1a = px1; pm *= F; if (px1a < pm) {jpx = 1; px1a = pm;} if (px1a < PXMIN) {jpx = 1; px1a = PXMIN;} /* Carry out the transformation using the modified parallax. */ j = iauStarpm(ra1, dec1, pmr1, pmd1, px1a, rv1, ep1a, ep1b, ep2a, ep2b, ra2, dec2, pmr2, pmd2, px2, rv2); /* Revise and return the status. */ if ( !(j%2) ) j += jpx; return j; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pn00a.c0000644000113000011300000002120113027221063014237 0ustar bellsbells#include "sofa.h" void iauPn00a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - - ** i a u P n 0 0 a ** - - - - - - - - - ** ** Precession-nutation, IAU 2000A model: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based ** use indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation (Note 2) ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components (luni-solar + planetary, IAU 2000A) in ** longitude and obliquity are in radians and with respect to the ** equinox and ecliptic of date. Free core nutation is omitted; ** for the utmost accuracy, use the iauPn00 function, where the ** nutation components are caller-specified. For faster but ** slightly less accurate results, use the iauPn00b function. ** ** 3) The mean obliquity is consistent with the IAU 2000 precession. ** ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean ** equator and equinox by applying frame bias. ** ** 5) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean equator and equinox ** of date to true equator and equinox of date by applying the ** nutation (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true equator and ** equinox of date. It is the product rn x rbp, applying frame ** bias, precession and nutation in that order. ** ** 9) The X,Y,Z coordinates of the IAU 2000A Celestial Intermediate ** Pole are elements (3,1-3) of the GCRS-to-true matrix, ** i.e. rbpn[2][0-2]. ** ** 10) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the order given. ** ** Called: ** iauNut00a nutation, IAU 2000A ** iauPn00 bias/precession/nutation results, IAU 2000 ** ** Reference: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** This revision: 2013 November 14 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Nutation. */ iauNut00a(date1, date2, dpsi, deps); /* Remaining results. */ iauPn00(date1, date2, *dpsi, *deps, epsa, rb, rp, rbp, rn, rbpn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pn00b.c0000644000113000011300000002117113027221063014246 0ustar bellsbells#include "sofa.h" void iauPn00b(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - - ** i a u P n 0 0 b ** - - - - - - - - - ** ** Precession-nutation, IAU 2000B model: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based ** use indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation (Note 2) ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components (luni-solar + planetary, IAU 2000B) in ** longitude and obliquity are in radians and with respect to the ** equinox and ecliptic of date. For more accurate results, but ** at the cost of increased computation, use the iauPn00a function. ** For the utmost accuracy, use the iauPn00 function, where the ** nutation components are caller-specified. ** ** 3) The mean obliquity is consistent with the IAU 2000 precession. ** ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean ** equator and equinox by applying frame bias. ** ** 5) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean equator and equinox ** of date to true equator and equinox of date by applying the ** nutation (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true equator and ** equinox of date. It is the product rn x rbp, applying frame ** bias, precession and nutation in that order. ** ** 9) The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate ** Pole are elements (3,1-3) of the GCRS-to-true matrix, ** i.e. rbpn[2][0-2]. ** ** 10) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the stated order. ** ** Called: ** iauNut00b nutation, IAU 2000B ** iauPn00 bias/precession/nutation results, IAU 2000 ** ** Reference: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003). ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** This revision: 2013 November 13 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Nutation. */ iauNut00b(date1, date2, dpsi, deps); /* Remaining results. */ iauPn00(date1, date2, *dpsi, *deps, epsa, rb, rp, rbp, rn, rbpn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pn00.c0000644000113000011300000002167213027221063014112 0ustar bellsbells#include "sofa.h" void iauPn00(double date1, double date2, double dpsi, double deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - ** i a u P n 0 0 ** - - - - - - - - ** ** Precession-nutation, IAU 2000 model: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based ** use indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** dpsi,deps double nutation (Note 2) ** ** Returned: ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Note 8) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The caller is responsible for providing the nutation components; ** they are in longitude and obliquity, in radians and are with ** respect to the equinox and ecliptic of date. For high-accuracy ** applications, free core nutation should be included as well as ** any other relevant corrections to the position of the CIP. ** ** 3) The returned mean obliquity is consistent with the IAU 2000 ** precession-nutation models. ** ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean ** equator and equinox by applying frame bias. ** ** 5) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean equator and equinox of ** date to true equator and equinox of date by applying the nutation ** (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true equator and ** equinox of date. It is the product rn x rbp, applying frame ** bias, precession and nutation in that order. ** ** 9) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the order given. ** ** Called: ** iauPr00 IAU 2000 precession adjustments ** iauObl80 mean obliquity, IAU 1980 ** iauBp00 frame bias and precession matrices, IAU 2000 ** iauCr copy r-matrix ** iauNumat form nutation matrix ** iauRxr product of two r-matrices ** ** Reference: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dpsipr, depspr, rbpw[3][3], rnw[3][3]; /* IAU 2000 precession-rate adjustments. */ iauPr00(date1, date2, &dpsipr, &depspr); /* Mean obliquity, consistent with IAU 2000 precession-nutation. */ *epsa = iauObl80(date1, date2) + depspr; /* Frame bias and precession matrices and their product. */ iauBp00(date1, date2, rb, rp, rbpw); iauCr(rbpw, rbp); /* Nutation matrix. */ iauNumat(*epsa, dpsi, deps, rnw); iauCr(rnw, rn); /* Bias-precession-nutation matrix (classical). */ iauRxr(rnw, rbpw, rbpn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pn06a.c0000644000113000011300000002013213027221063014247 0ustar bellsbells#include "sofa.h" void iauPn06a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - - ** i a u P n 0 6 a ** - - - - - - - - - ** ** Precession-nutation, IAU 2006/2000A models: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based use ** indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation (Note 2) ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components (luni-solar + planetary, IAU 2000A) in ** longitude and obliquity are in radians and with respect to the ** equinox and ecliptic of date. Free core nutation is omitted; ** for the utmost accuracy, use the iauPn06 function, where the ** nutation components are caller-specified. ** ** 3) The mean obliquity is consistent with the IAU 2006 precession. ** ** 4) The matrix rb transforms vectors from GCRS to mean J2000.0 by ** applying frame bias. ** ** 5) The matrix rp transforms vectors from mean J2000.0 to mean of ** date by applying precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean of date by ** applying frame bias then precession. It is the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean of date to true of ** date by applying the nutation (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true of date ** (CIP/equinox). It is the product rn x rbp, applying frame bias, ** precession and nutation in that order. ** ** 9) The X,Y,Z coordinates of the IAU 2006/2000A Celestial ** Intermediate Pole are elements (3,1-3) of the GCRS-to-true ** matrix, i.e. rbpn[2][0-2]. ** ** 10) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the stated order. ** ** Called: ** iauNut06a nutation, IAU 2006/2000A ** iauPn06 bias/precession/nutation results, IAU 2006 ** ** Reference: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** This revision: 2013 November 13 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Nutation. */ iauNut06a(date1, date2, dpsi, deps); /* Remaining results. */ iauPn06(date1, date2, *dpsi, *deps, epsa, rb, rp, rbp, rn, rbpn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pn06.c0000644000113000011300000002204513027221063014113 0ustar bellsbells#include "sofa.h" void iauPn06(double date1, double date2, double dpsi, double deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - ** i a u P n 0 6 ** - - - - - - - - ** ** Precession-nutation, IAU 2006 model: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based use ** indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** dpsi,deps double nutation (Note 2) ** ** Returned: ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Note 8) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The caller is responsible for providing the nutation components; ** they are in longitude and obliquity, in radians and are with ** respect to the equinox and ecliptic of date. For high-accuracy ** applications, free core nutation should be included as well as ** any other relevant corrections to the position of the CIP. ** ** 3) The returned mean obliquity is consistent with the IAU 2006 ** precession. ** ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean ** equator and equinox by applying frame bias. ** ** 5) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean equator and equinox ** of date to true equator and equinox of date by applying the ** nutation (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true equator and ** equinox of date. It is the product rn x rbp, applying frame ** bias, precession and nutation in that order. ** ** 9) The X,Y,Z coordinates of the Celestial Intermediate Pole are ** elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2]. ** ** 10) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the stated order. ** ** Called: ** iauPfw06 bias-precession F-W angles, IAU 2006 ** iauFw2m F-W angles to r-matrix ** iauCr copy r-matrix ** iauTr transpose r-matrix ** iauRxr product of two r-matrices ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** This revision: 2013 November 14 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double gamb, phib, psib, eps, r1[3][3], r2[3][3], rt[3][3]; /* Bias-precession Fukushima-Williams angles of J2000.0 = frame bias. */ iauPfw06(DJM0, DJM00, &gamb, &phib, &psib, &eps); /* B matrix. */ iauFw2m(gamb, phib, psib, eps, r1); iauCr(r1, rb); /* Bias-precession Fukushima-Williams angles of date. */ iauPfw06(date1, date2, &gamb, &phib, &psib, &eps); /* Bias-precession matrix. */ iauFw2m(gamb, phib, psib, eps, r2); iauCr(r2, rbp); /* Solve for precession matrix. */ iauTr(r1, rt); iauRxr(r2, rt, rp); /* Equinox-based bias-precession-nutation matrix. */ iauFw2m(gamb, phib, psib + dpsi, eps + deps, r1); iauCr(r1, rbpn); /* Solve for nutation matrix. */ iauTr(r2, rt); iauRxr(r1, rt, rn); /* Obliquity, mean of date. */ *epsa = eps; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pn.c0000644000113000011300000001256713027221063013755 0ustar bellsbells#include "sofa.h" void iauPn(double p[3], double *r, double u[3]) /* ** - - - - - - ** i a u P n ** - - - - - - ** ** Convert a p-vector into modulus and unit vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector ** ** Returned: ** r double modulus ** u double[3] unit vector ** ** Notes: ** ** 1) If p is null, the result is null. Otherwise the result is a unit ** vector. ** ** 2) It is permissible to re-use the same array for any of the ** arguments. ** ** Called: ** iauPm modulus of p-vector ** iauZp zero p-vector ** iauSxp multiply p-vector by scalar ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double w; /* Obtain the modulus and test for zero. */ w = iauPm(p); if (w == 0.0) { /* Null vector. */ iauZp(u); } else { /* Unit vector. */ iauSxp(1.0/w, p, u); } /* Return the modulus. */ *r = w; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pnm00a.c0000644000113000011300000001522213027221063014422 0ustar bellsbells#include "sofa.h" void iauPnm00a(double date1, double date2, double rbpn[3][3]) /* ** - - - - - - - - - - ** i a u P n m 0 0 a ** - - - - - - - - - - ** ** Form the matrix of precession-nutation for a given date (including ** frame bias), equinox-based, IAU 2000A model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rbpn double[3][3] classical NPB matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where ** the p-vector V(date) is with respect to the true equatorial triad ** of date date1+date2 and the p-vector V(GCRS) is with respect to ** the Geocentric Celestial Reference System (IAU, 2000). ** ** 3) A faster, but slightly less accurate result (about 1 mas), can be ** obtained by using instead the iauPnm00b function. ** ** Called: ** iauPn00a bias/precession/nutation, IAU 2000A ** ** Reference: ** ** IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. ** 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. ** (2000) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dpsi, deps, epsa, rb[3][3], rp[3][3], rbp[3][3], rn[3][3]; /* Obtain the required matrix (discarding other results). */ iauPn00a(date1, date2, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pnm00b.c0000644000113000011300000001521513027221063014425 0ustar bellsbells#include "sofa.h" void iauPnm00b(double date1, double date2, double rbpn[3][3]) /* ** - - - - - - - - - - ** i a u P n m 0 0 b ** - - - - - - - - - - ** ** Form the matrix of precession-nutation for a given date (including ** frame bias), equinox-based, IAU 2000B model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rbpn double[3][3] bias-precession-nutation matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where ** the p-vector V(date) is with respect to the true equatorial triad ** of date date1+date2 and the p-vector V(GCRS) is with respect to ** the Geocentric Celestial Reference System (IAU, 2000). ** ** 3) The present function is faster, but slightly less accurate (about ** 1 mas), than the iauPnm00a function. ** ** Called: ** iauPn00b bias/precession/nutation, IAU 2000B ** ** Reference: ** ** IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. ** 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. ** (2000) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dpsi, deps, epsa, rb[3][3], rp[3][3], rbp[3][3], rn[3][3]; /* Obtain the required matrix (discarding other results). */ iauPn00b(date1, date2, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pnm06a.c0000644000113000011300000001526313027221063014435 0ustar bellsbells#include "sofa.h" void iauPnm06a(double date1, double date2, double rnpb[3][3]) /* ** - - - - - - - - - - ** i a u P n m 0 6 a ** - - - - - - - - - - ** ** Form the matrix of precession-nutation for a given date (including ** frame bias), IAU 2006 precession and IAU 2000A nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rnpb double[3][3] bias-precession-nutation matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rnpb * V(GCRS), where ** the p-vector V(date) is with respect to the true equatorial triad ** of date date1+date2 and the p-vector V(GCRS) is with respect to ** the Geocentric Celestial Reference System (IAU, 2000). ** ** Called: ** iauPfw06 bias-precession F-W angles, IAU 2006 ** iauNut06a nutation, IAU 2006/2000A ** iauFw2m F-W angles to r-matrix ** ** Reference: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double gamb, phib, psib, epsa, dp, de; /* Fukushima-Williams angles for frame bias and precession. */ iauPfw06(date1, date2, &gamb, &phib, &psib, &epsa); /* Nutation components. */ iauNut06a(date1, date2, &dp, &de); /* Equinox based nutation x precession x bias matrix. */ iauFw2m(gamb, phib, psib + dp, epsa + de, rnpb); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pnm80.c0000644000113000011300000001517213027221063014275 0ustar bellsbells#include "sofa.h" void iauPnm80(double date1, double date2, double rmatpn[3][3]) /* ** - - - - - - - - - ** i a u P n m 8 0 ** - - - - - - - - - ** ** Form the matrix of precession/nutation for a given date, IAU 1976 ** precession model, IAU 1980 nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TDB date (Note 1) ** ** Returned: ** rmatpn double[3][3] combined precession/nutation matrix ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rmatpn * V(J2000), ** where the p-vector V(date) is with respect to the true equatorial ** triad of date date1+date2 and the p-vector V(J2000) is with ** respect to the mean equatorial triad of epoch J2000.0. ** ** Called: ** iauPmat76 precession matrix, IAU 1976 ** iauNutm80 nutation matrix, IAU 1980 ** iauRxr product of two r-matrices ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.3 (p145). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rmatp[3][3], rmatn[3][3]; /* Precession matrix, J2000.0 to date. */ iauPmat76(date1, date2, rmatp); /* Nutation matrix. */ iauNutm80(date1, date2, rmatn); /* Combine the matrices: PN = N x P. */ iauRxr(rmatn, rmatp, rmatpn); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pom00.c0000644000113000011300000001446513027221063014272 0ustar bellsbells#include "sofa.h" void iauPom00(double xp, double yp, double sp, double rpom[3][3]) /* ** - - - - - - - - - - ** i a u P o m 0 0 ** - - - - - - - - - - ** ** Form the matrix of polar motion for a given date, IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** xp,yp double coordinates of the pole (radians, Note 1) ** sp double the TIO locator s' (radians, Note 2) ** ** Returned: ** rpom double[3][3] polar-motion matrix (Note 3) ** ** Notes: ** ** 1) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 2) The argument sp is the TIO locator s', in radians, which ** positions the Terrestrial Intermediate Origin on the equator. It ** is obtained from polar motion observations by numerical ** integration, and so is in essence unpredictable. However, it is ** dominated by a secular drift of about 47 microarcseconds per ** century, and so can be taken into account by using s' = -47*t, ** where t is centuries since J2000.0. The function iauSp00 ** implements this approximation. ** ** 3) The matrix operates in the sense V(TRS) = rpom * V(CIP), meaning ** that it is the final rotation when computing the pointing ** direction to a celestial source. ** ** Called: ** iauIr initialize r-matrix to identity ** iauRz rotate around Z-axis ** iauRy rotate around Y-axis ** iauRx rotate around X-axis ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Construct the matrix. */ iauIr(rpom); iauRz(sp, rpom); iauRy(-xp, rpom); iauRx(-yp, rpom); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ppp.c0000644000113000011300000001173713027221063014135 0ustar bellsbells#include "sofa.h" void iauPpp(double a[3], double b[3], double apb[3]) /* ** - - - - - - - ** i a u P p p ** - - - - - - - ** ** P-vector addition. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector ** b double[3] second p-vector ** ** Returned: ** apb double[3] a + b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { apb[0] = a[0] + b[0]; apb[1] = a[1] + b[1]; apb[2] = a[2] + b[2]; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ppsp.c0000644000113000011300000001223313027221063014310 0ustar bellsbells#include "sofa.h" void iauPpsp(double a[3], double s, double b[3], double apsb[3]) /* ** - - - - - - - - ** i a u P p s p ** - - - - - - - - ** ** P-vector plus scaled p-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector ** s double scalar (multiplier for b) ** b double[3] second p-vector ** ** Returned: ** apsb double[3] a + s*b ** ** Note: ** It is permissible for any of a, b and apsb to be the same array. ** ** Called: ** iauSxp multiply p-vector by scalar ** iauPpp p-vector plus p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double sb[3]; /* s*b. */ iauSxp(s, b, sb); /* a + s*b. */ iauPpp(a, sb, apsb); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pr00.c0000644000113000011300000001720513027221063014113 0ustar bellsbells#include "sofa.h" void iauPr00(double date1, double date2, double *dpsipr, double *depspr) /* ** - - - - - - - - ** i a u P r 0 0 ** - - - - - - - - ** ** Precession-rate part of the IAU 2000 precession-nutation models ** (part of MHB2000). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsipr,depspr double precession corrections (Notes 2,3) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The precession adjustments are expressed as "nutation ** components", corrections in longitude and obliquity with respect ** to the J2000.0 equinox and ecliptic. ** ** 3) Although the precession adjustments are stated to be with respect ** to Lieske et al. (1977), the MHB2000 model does not specify which ** set of Euler angles are to be used and how the adjustments are to ** be applied. The most literal and straightforward procedure is to ** adopt the 4-rotation epsilon_0, psi_A, omega_A, xi_A option, and ** to add dpsipr to psi_A and depspr to both omega_A and eps_A. ** ** 4) This is an implementation of one aspect of the IAU 2000A nutation ** model, formally adopted by the IAU General Assembly in 2000, ** namely MHB2000 (Mathews et al. 2002). ** ** References: ** ** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B., "Expressions ** for the precession quantities based upon the IAU (1976) System of ** Astronomical Constants", Astron.Astrophys., 58, 1-16 (1977) ** ** Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation ** and precession New nutation series for nonrigid Earth and ** insights into the Earth's interior", J.Geophys.Res., 107, B4, ** 2002. The MHB2000 code itself was obtained on 9th September 2002 ** from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A. ** ** Wallace, P.T., "Software for Implementing the IAU 2000 ** Resolutions", in IERS Workshop 5.1 (2002). ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t; /* Precession and obliquity corrections (radians per century) */ static const double PRECOR = -0.29965 * DAS2R, OBLCOR = -0.02524 * DAS2R; /* Interval between fundamental epoch J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Precession rate contributions with respect to IAU 1976/80. */ *dpsipr = PRECOR * t; *depspr = OBLCOR * t; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/prec76.c0000644000113000011300000001752713027221063014447 0ustar bellsbells#include "sofa.h" void iauPrec76(double date01, double date02, double date11, double date12, double *zeta, double *z, double *theta) /* ** - - - - - - - - - - ** i a u P r e c 7 6 ** - - - - - - - - - - ** ** IAU 1976 precession model. ** ** This function forms the three Euler angles which implement general ** precession between two dates, using the IAU 1976 model (as for the ** FK5 catalog). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date01,date02 double TDB starting date (Note 1) ** date11,date12 double TDB ending date (Note 1) ** ** Returned: ** zeta double 1st rotation: radians cw around z ** z double 3rd rotation: radians cw around z ** theta double 2nd rotation: radians ccw around y ** ** Notes: ** ** 1) The dates date01+date02 and date11+date12 are Julian Dates, ** apportioned in any convenient way between the arguments daten1 ** and daten2. For example, JD(TDB)=2450123.7 could be expressed in ** any of these ways, among others: ** ** daten1 daten2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** The two dates may be expressed using different methods, but at ** the risk of losing some resolution. ** ** 2) The accumulated precession angles zeta, z, theta are expressed ** through canonical polynomials which are valid only for a limited ** time span. In addition, the IAU 1976 precession rate is known to ** be imperfect. The absolute accuracy of the present formulation ** is better than 0.1 arcsec from 1960AD to 2040AD, better than ** 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for ** the whole of the period 500BC to 3000AD. The errors exceed ** 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec ** outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to ** 8200AD. ** ** 3) The three angles are returned in the conventional order, which ** is not the same as the order of the corresponding Euler ** rotations. The precession matrix is ** R_3(-z) x R_2(+theta) x R_3(-zeta). ** ** Reference: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations ** (6) & (7), p283. ** ** This revision: 2013 November 19 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t0, t, tas2r, w; /* Interval between fundamental epoch J2000.0 and start date (JC). */ t0 = ((date01 - DJ00) + date02) / DJC; /* Interval over which precession required (JC). */ t = ((date11 - date01) + (date12 - date02)) / DJC; /* Euler angles. */ tas2r = t * DAS2R; w = 2306.2181 + (1.39656 - 0.000139 * t0) * t0; *zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r; *z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r; *theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0) + ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pv2p.c0000644000113000011300000001153613027221063014222 0ustar bellsbells#include "sofa.h" void iauPv2p(double pv[2][3], double p[3]) /* ** - - - - - - - - ** i a u P v 2 p ** - - - - - - - - ** ** Discard velocity component of a pv-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** pv double[2][3] pv-vector ** ** Returned: ** p double[3] p-vector ** ** Called: ** iauCp copy p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauCp(pv[0], p); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pv2s.c0000644000113000011300000001531513027221063014224 0ustar bellsbells#include "sofa.h" void iauPv2s(double pv[2][3], double *theta, double *phi, double *r, double *td, double *pd, double *rd) /* ** - - - - - - - - ** i a u P v 2 s ** - - - - - - - - ** ** Convert position/velocity from Cartesian to spherical coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** pv double[2][3] pv-vector ** ** Returned: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** r double radial distance ** td double rate of change of theta ** pd double rate of change of phi ** rd double rate of change of r ** ** Notes: ** ** 1) If the position part of pv is null, theta, phi, td and pd ** are indeterminate. This is handled by extrapolating the ** position through unit time by using the velocity part of ** pv. This moves the origin without changing the direction ** of the velocity component. If the position and velocity ** components of pv are both null, zeroes are returned for all ** six results. ** ** 2) If the position is a pole, theta, td and pd are indeterminate. ** In such cases zeroes are returned for all three. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double x, y, z, xd, yd, zd, rxy2, rxy, r2, rtrue, rw, xyp; /* Components of position/velocity vector. */ x = pv[0][0]; y = pv[0][1]; z = pv[0][2]; xd = pv[1][0]; yd = pv[1][1]; zd = pv[1][2]; /* Component of r in XY plane squared. */ rxy2 = x*x + y*y; /* Modulus squared. */ r2 = rxy2 + z*z; /* Modulus. */ rtrue = sqrt(r2); /* If null vector, move the origin along the direction of movement. */ rw = rtrue; if (rtrue == 0.0) { x = xd; y = yd; z = zd; rxy2 = x*x + y*y; r2 = rxy2 + z*z; rw = sqrt(r2); } /* Position and velocity in spherical coordinates. */ rxy = sqrt(rxy2); xyp = x*xd + y*yd; if (rxy2 != 0.0) { *theta = atan2(y, x); *phi = atan2(z, rxy); *td = (x*yd - y*xd) / rxy2; *pd = (zd*rxy2 - z*xyp) / (r2*rxy); } else { *theta = 0.0; *phi = (z != 0.0) ? atan2(z, rxy) : 0.0; *td = 0.0; *pd = 0.0; } *r = rtrue; *rd = (rw != 0.0) ? (xyp + z*zd) / rw : 0.0; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pvdpv.c0000644000113000011300000001272313027221063014471 0ustar bellsbells#include "sofa.h" void iauPvdpv(double a[2][3], double b[2][3], double adb[2]) /* ** - - - - - - - - - ** i a u P v d p v ** - - - - - - - - - ** ** Inner (=scalar=dot) product of two pv-vectors. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[2][3] first pv-vector ** b double[2][3] second pv-vector ** ** Returned: ** adb double[2] a . b (see note) ** ** Note: ** ** If the position and velocity components of the two pv-vectors are ** ( ap, av ) and ( bp, bv ), the result, a . b, is the pair of ** numbers ( ap . bp , ap . bv + av . bp ). The two numbers are the ** dot-product of the two p-vectors and its derivative. ** ** Called: ** iauPdp scalar product of two p-vectors ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double adbd, addb; /* a . b = constant part of result. */ adb[0] = iauPdp(a[0], b[0]); /* a . bdot */ adbd = iauPdp(a[0], b[1]); /* adot . b */ addb = iauPdp(a[1], b[0]); /* Velocity part of result. */ adb[1] = adbd + addb; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pvm.c0000644000113000011300000001172113027221063014131 0ustar bellsbells#include "sofa.h" void iauPvm(double pv[2][3], double *r, double *s) /* ** - - - - - - - ** i a u P v m ** - - - - - - - ** ** Modulus of pv-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** pv double[2][3] pv-vector ** ** Returned: ** r double modulus of position component ** s double modulus of velocity component ** ** Called: ** iauPm modulus of p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Distance. */ *r = iauPm(pv[0]); /* Speed. */ *s = iauPm(pv[1]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pvmpv.c0000644000113000011300000001207613027221063014503 0ustar bellsbells#include "sofa.h" void iauPvmpv(double a[2][3], double b[2][3], double amb[2][3]) /* ** - - - - - - - - - ** i a u P v m p v ** - - - - - - - - - ** ** Subtract one pv-vector from another. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[2][3] first pv-vector ** b double[2][3] second pv-vector ** ** Returned: ** amb double[2][3] a - b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** ** Called: ** iauPmp p-vector minus p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauPmp(a[0], b[0], amb[0]); iauPmp(a[1], b[1], amb[1]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pvppv.c0000644000113000011300000001207113027221063014501 0ustar bellsbells#include "sofa.h" void iauPvppv(double a[2][3], double b[2][3], double apb[2][3]) /* ** - - - - - - - - - ** i a u P v p p v ** - - - - - - - - - ** ** Add one pv-vector to another. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[2][3] first pv-vector ** b double[2][3] second pv-vector ** ** Returned: ** apb double[2][3] a + b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** ** Called: ** iauPpp p-vector plus p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauPpp(a[0], b[0], apb[0]); iauPpp(a[1], b[1], apb[1]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pvstar.c0000644000113000011300000002360713027221063014654 0ustar bellsbells#include "sofa.h" int iauPvstar(double pv[2][3], double *ra, double *dec, double *pmr, double *pmd, double *px, double *rv) /* ** - - - - - - - - - - ** i a u P v s t a r ** - - - - - - - - - - ** ** Convert star position+velocity vector to catalog coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given (Note 1): ** pv double[2][3] pv-vector (AU, AU/day) ** ** Returned (Note 2): ** ra double right ascension (radians) ** dec double declination (radians) ** pmr double RA proper motion (radians/year) ** pmd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, positive = receding) ** ** Returned (function value): ** int status: ** 0 = OK ** -1 = superluminal speed (Note 5) ** -2 = null position vector ** ** Notes: ** ** 1) The specified pv-vector is the coordinate direction (and its rate ** of change) for the date at which the light leaving the star ** reached the solar-system barycenter. ** ** 2) The star data returned by this function are "observables" for an ** imaginary observer at the solar-system barycenter. Proper motion ** and radial velocity are, strictly, in terms of barycentric ** coordinate time, TCB. For most practical applications, it is ** permissible to neglect the distinction between TCB and ordinary ** "proper" time on Earth (TT/TAI). The result will, as a rule, be ** limited by the intrinsic accuracy of the proper-motion and ** radial-velocity data; moreover, the supplied pv-vector is likely ** to be merely an intermediate result (for example generated by the ** function iauStarpv), so that a change of time unit will cancel ** out overall. ** ** In accordance with normal star-catalog conventions, the object's ** right ascension and declination are freed from the effects of ** secular aberration. The frame, which is aligned to the catalog ** equator and equinox, is Lorentzian and centered on the SSB. ** ** Summarizing, the specified pv-vector is for most stars almost ** identical to the result of applying the standard geometrical ** "space motion" transformation to the catalog data. The ** differences, which are the subject of the Stumpff paper cited ** below, are: ** ** (i) In stars with significant radial velocity and proper motion, ** the constantly changing light-time distorts the apparent proper ** motion. Note that this is a classical, not a relativistic, ** effect. ** ** (ii) The transformation complies with special relativity. ** ** 3) Care is needed with units. The star coordinates are in radians ** and the proper motions in radians per Julian year, but the ** parallax is in arcseconds; the radial velocity is in km/s, but ** the pv-vector result is in AU and AU/day. ** ** 4) The proper motions are the rate of change of the right ascension ** and declination at the catalog epoch and are in radians per Julian ** year. The RA proper motion is in terms of coordinate angle, not ** true angle, and will thus be numerically larger at high ** declinations. ** ** 5) Straight-line motion at constant speed in the inertial frame is ** assumed. If the speed is greater than or equal to the speed of ** light, the function aborts with an error status. ** ** 6) The inverse transformation is performed by the function iauStarpv. ** ** Called: ** iauPn decompose p-vector into modulus and direction ** iauPdp scalar product of two p-vectors ** iauSxp multiply p-vector by scalar ** iauPmp p-vector minus p-vector ** iauPm modulus of p-vector ** iauPpp p-vector plus p-vector ** iauPv2s pv-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double r, x[3], vr, ur[3], vt, ut[3], bett, betr, d, w, del, usr[3], ust[3], a, rad, decd, rd; /* Isolate the radial component of the velocity (AU/day, inertial). */ iauPn(pv[0], &r, x); vr = iauPdp(x, pv[1]); iauSxp(vr, x, ur); /* Isolate the transverse component of the velocity (AU/day, inertial). */ iauPmp(pv[1], ur, ut); vt = iauPm(ut); /* Special-relativity dimensionless parameters. */ bett = vt / DC; betr = vr / DC; /* The inertial-to-observed correction terms. */ d = 1.0 + betr; w = 1.0 - betr*betr - bett*bett; if (d == 0.0 || w < 0) return -1; del = sqrt(w) - 1.0; /* Apply relativistic correction factor to radial velocity component. */ w = (betr != 0) ? (betr - del) / (betr * d) : 1.0; iauSxp(w, ur, usr); /* Apply relativistic correction factor to tangential velocity */ /* component. */ iauSxp(1.0/d, ut, ust); /* Combine the two to obtain the observed velocity vector (AU/day). */ iauPpp(usr, ust, pv[1]); /* Cartesian to spherical. */ iauPv2s(pv, &a, dec, &r, &rad, &decd, &rd); if (r == 0.0) return -2; /* Return RA in range 0 to 2pi. */ *ra = iauAnp(a); /* Return proper motions in radians per year. */ *pmr = rad * DJY; *pmd = decd * DJY; /* Return parallax in arcsec. */ *px = DR2AS / r; /* Return radial velocity in km/s. */ *rv = 1e-3 * rd * DAU / DAYSEC; /* OK status. */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pvtob.c0000644000113000011300000001704113027221063014462 0ustar bellsbells#include "sofa.h" void iauPvtob(double elong, double phi, double hm, double xp, double yp, double sp, double theta, double pv[2][3]) /* ** - - - - - - - - - ** i a u P v t o b ** - - - - - - - - - ** ** Position and velocity of a terrestrial observing station. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** elong double longitude (radians, east +ve, Note 1) ** phi double latitude (geodetic, radians, Note 1) ** hm double height above ref. ellipsoid (geodetic, m) ** xp,yp double coordinates of the pole (radians, Note 2) ** sp double the TIO locator s' (radians, Note 2) ** theta double Earth rotation angle (radians, Note 3) ** ** Returned: ** pv double[2][3] position/velocity vector (m, m/s, CIRS) ** ** Notes: ** ** 1) The terrestrial coordinates are with respect to the WGS84 ** reference ellipsoid. ** ** 2) xp and yp are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions), measured along the ** meridians 0 and 90 deg west respectively. sp is the TIO locator ** s', in radians, which positions the Terrestrial Intermediate ** Origin on the equator. For many applications, xp, yp and ** (especially) sp can be set to zero. ** ** 3) If theta is Greenwich apparent sidereal time instead of Earth ** rotation angle, the result is with respect to the true equator ** and equinox of date, i.e. with the x-axis at the equinox rather ** than the celestial intermediate origin. ** ** 4) The velocity units are meters per UT1 second, not per SI second. ** This is unlikely to have any practical consequences in the modern ** era. ** ** 5) No validation is performed on the arguments. Error cases that ** could lead to arithmetic exceptions are trapped by the iauGd2gc ** function, and the result set to zeros. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013), Section 7.4.3.3. ** ** Called: ** iauGd2gc geodetic to geocentric transformation ** iauPom00 polar motion matrix ** iauTrxp product of transpose of r-matrix and p-vector ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Earth rotation rate in radians per UT1 second */ const double OM = 1.00273781191135448 * D2PI / DAYSEC; double xyzm[3], rpm[3][3], xyz[3], x, y, z, s, c; /* Geodetic to geocentric transformation (WGS84). */ (void) iauGd2gc(1, elong, phi, hm, xyzm); /* Polar motion and TIO position. */ iauPom00(xp, yp, sp, rpm); iauTrxp(rpm, xyzm, xyz); x = xyz[0]; y = xyz[1]; z = xyz[2]; /* Functions of ERA. */ s = sin(theta); c = cos(theta); /* Position. */ pv[0][0] = c*x - s*y; pv[0][1] = s*x + c*y; pv[0][2] = z; /* Velocity. */ pv[1][0] = OM * ( -s*x - c*y ); pv[1][1] = OM * ( c*x - s*y ); pv[1][2] = 0.0; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pvu.c0000644000113000011300000001237513027221063014147 0ustar bellsbells#include "sofa.h" void iauPvu(double dt, double pv[2][3], double upv[2][3]) /* ** - - - - - - - ** i a u P v u ** - - - - - - - ** ** Update a pv-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** dt double time interval ** pv double[2][3] pv-vector ** ** Returned: ** upv double[2][3] p updated, v unchanged ** ** Notes: ** ** 1) "Update" means "refer the position component of the vector ** to a new date dt time units from the existing date". ** ** 2) The time units of dt must match those of the velocity. ** ** 3) It is permissible for pv and upv to be the same array. ** ** Called: ** iauPpsp p-vector plus scaled p-vector ** iauCp copy p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauPpsp(pv[0], dt, pv[1], upv[0]); iauCp(pv[1], upv[1]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pvup.c0000644000113000011300000001224013027221063014316 0ustar bellsbells#include "sofa.h" void iauPvup(double dt, double pv[2][3], double p[3]) /* ** - - - - - - - - ** i a u P v u p ** - - - - - - - - ** ** Update a pv-vector, discarding the velocity component. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** dt double time interval ** pv double[2][3] pv-vector ** ** Returned: ** p double[3] p-vector ** ** Notes: ** ** 1) "Update" means "refer the position component of the vector to a ** new date dt time units from the existing date". ** ** 2) The time units of dt must match those of the velocity. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { p[0] = pv[0][0] + dt * pv[1][0]; p[1] = pv[0][1] + dt * pv[1][1]; p[2] = pv[0][2] + dt * pv[1][2]; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pvxpv.c0000644000113000011300000001332213027221063014511 0ustar bellsbells#include "sofa.h" void iauPvxpv(double a[2][3], double b[2][3], double axb[2][3]) /* ** - - - - - - - - - ** i a u P v x p v ** - - - - - - - - - ** ** Outer (=vector=cross) product of two pv-vectors. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[2][3] first pv-vector ** b double[2][3] second pv-vector ** ** Returned: ** axb double[2][3] a x b ** ** Notes: ** ** 1) If the position and velocity components of the two pv-vectors are ** ( ap, av ) and ( bp, bv ), the result, a x b, is the pair of ** vectors ( ap x bp, ap x bv + av x bp ). The two vectors are the ** cross-product of the two p-vectors and its derivative. ** ** 2) It is permissible to re-use the same array for any of the ** arguments. ** ** Called: ** iauCpv copy pv-vector ** iauPxp vector product of two p-vectors ** iauPpp p-vector plus p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double wa[2][3], wb[2][3], axbd[3], adxb[3]; /* Make copies of the inputs. */ iauCpv(a, wa); iauCpv(b, wb); /* a x b = position part of result. */ iauPxp(wa[0], wb[0], axb[0]); /* a x bdot + adot x b = velocity part of result. */ iauPxp(wa[0], wb[1], axbd); iauPxp(wa[1], wb[0], adxb); iauPpp(axbd, adxb, axb[1]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/pxp.c0000644000113000011300000001216213027221063014136 0ustar bellsbells#include "sofa.h" void iauPxp(double a[3], double b[3], double axb[3]) /* ** - - - - - - - ** i a u P x p ** - - - - - - - ** ** p-vector outer (=vector=cross) product. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector ** b double[3] second p-vector ** ** Returned: ** axb double[3] a x b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double xa, ya, za, xb, yb, zb; xa = a[0]; ya = a[1]; za = a[2]; xb = b[0]; yb = b[1]; zb = b[2]; axb[0] = ya*zb - za*yb; axb[1] = za*xb - xa*zb; axb[2] = xa*yb - ya*xb; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/refco.c0000644000113000011300000002662013027221063014431 0ustar bellsbells#include "sofa.h" void iauRefco(double phpa, double tc, double rh, double wl, double *refa, double *refb) /* ** - - - - - - - - - ** i a u R e f c o ** - - - - - - - - - ** ** Determine the constants A and B in the atmospheric refraction model ** dZ = A tan Z + B tan^3 Z. ** ** Z is the "observed" zenith distance (i.e. affected by refraction) ** and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo) ** zenith distance. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** phpa double pressure at the observer (hPa = millibar) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers) ** ** Returned: ** refa double* tan Z coefficient (radians) ** refb double* tan^3 Z coefficient (radians) ** ** Notes: ** ** 1) The model balances speed and accuracy to give good results in ** applications where performance at low altitudes is not paramount. ** Performance is maintained across a range of conditions, and ** applies to both optical/IR and radio. ** ** 2) The model omits the effects of (i) height above sea level (apart ** from the reduced pressure itself), (ii) latitude (i.e. the ** flattening of the Earth), (iii) variations in tropospheric lapse ** rate and (iv) dispersive effects in the radio. ** ** The model was tested using the following range of conditions: ** ** lapse rates 0.0055, 0.0065, 0.0075 deg/meter ** latitudes 0, 25, 50, 75 degrees ** heights 0, 2500, 5000 meters ASL ** pressures mean for height -10% to +5% in steps of 5% ** temperatures -10 deg to +20 deg with respect to 280 deg at SL ** relative humidity 0, 0.5, 1 ** wavelengths 0.4, 0.6, ... 2 micron, + radio ** zenith distances 15, 45, 75 degrees ** ** The accuracy with respect to raytracing through a model ** atmosphere was as follows: ** ** worst RMS ** ** optical/IR 62 mas 8 mas ** radio 319 mas 49 mas ** ** For this particular set of conditions: ** ** lapse rate 0.0065 K/meter ** latitude 50 degrees ** sea level ** pressure 1005 mb ** temperature 280.15 K ** humidity 80% ** wavelength 5740 Angstroms ** ** the results were as follows: ** ** ZD raytrace iauRefco Saastamoinen ** ** 10 10.27 10.27 10.27 ** 20 21.19 21.20 21.19 ** 30 33.61 33.61 33.60 ** 40 48.82 48.83 48.81 ** 45 58.16 58.18 58.16 ** 50 69.28 69.30 69.27 ** 55 82.97 82.99 82.95 ** 60 100.51 100.54 100.50 ** 65 124.23 124.26 124.20 ** 70 158.63 158.68 158.61 ** 72 177.32 177.37 177.31 ** 74 200.35 200.38 200.32 ** 76 229.45 229.43 229.42 ** 78 267.44 267.29 267.41 ** 80 319.13 318.55 319.10 ** ** deg arcsec arcsec arcsec ** ** The values for Saastamoinen's formula (which includes terms ** up to tan^5) are taken from Hohenkerk and Sinclair (1985). ** ** 3) A wl value in the range 0-100 selects the optical/IR case and is ** wavelength in micrometers. Any value outside this range selects ** the radio case. ** ** 4) Outlandish input parameters are silently limited to ** mathematically safe values. Zero pressure is permissible, and ** causes zeroes to be returned. ** ** 5) The algorithm draws on several sources, as follows: ** ** a) The formula for the saturation vapour pressure of water as ** a function of temperature and temperature is taken from ** Equations (A4.5-A4.7) of Gill (1982). ** ** b) The formula for the water vapour pressure, given the ** saturation pressure and the relative humidity, is from ** Crane (1976), Equation (2.5.5). ** ** c) The refractivity of air is a function of temperature, ** total pressure, water-vapour pressure and, in the case ** of optical/IR, wavelength. The formulae for the two cases are ** developed from Hohenkerk & Sinclair (1985) and Rueger (2002). ** ** d) The formula for beta, the ratio of the scale height of the ** atmosphere to the geocentric distance of the observer, is ** an adaption of Equation (9) from Stone (1996). The ** adaptations, arrived at empirically, consist of (i) a small ** adjustment to the coefficient and (ii) a humidity term for the ** radio case only. ** ** e) The formulae for the refraction constants as a function of ** n-1 and beta are from Green (1987), Equation (4.31). ** ** References: ** ** Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral ** Atmosphere", Methods of Experimental Physics: Astrophysics 12B, ** Academic Press, 1976. ** ** Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press, ** 1982. ** ** Green, R.M., "Spherical Astronomy", Cambridge University Press, ** 1987. ** ** Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63, ** 1985. ** ** Rueger, J.M., "Refractive Index Formulae for Electronic Distance ** Measurement with Radio and Millimetre Waves", in Unisurv Report ** S-68, School of Surveying and Spatial Information Systems, ** University of New South Wales, Sydney, Australia, 2002. ** ** Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996. ** ** This revision: 2013 October 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int optic; double p, t, r, w, ps, pw, tk, wlsq, gamma, beta; /* Decide whether optical/IR or radio case: switch at 100 microns. */ optic = ( wl <= 100.0 ); /* Restrict parameters to safe values. */ t = gmax ( tc, -150.0 ); t = gmin ( t, 200.0 ); p = gmax ( phpa, 0.0 ); p = gmin ( p, 10000.0 ); r = gmax ( rh, 0.0 ); r = gmin ( r, 1.0 ); w = gmax ( wl, 0.1 ); w = gmin ( w, 1e6 ); /* Water vapour pressure at the observer. */ if ( p > 0.0 ) { ps = pow ( 10.0, ( 0.7859 + 0.03477*t ) / ( 1.0 + 0.00412*t ) ) * ( 1.0 + p * ( 4.5e-6 + 6e-10*t*t ) ); pw = r * ps / ( 1.0 - (1.0-r)*ps/p ); } else { pw = 0.0; } /* Refractive index minus 1 at the observer. */ tk = t + 273.15; if ( optic ) { wlsq = w * w; gamma = ( ( 77.53484e-6 + ( 4.39108e-7 + 3.666e-9/wlsq ) / wlsq ) * p - 11.2684e-6*pw ) / tk; } else { gamma = ( 77.6890e-6*p - ( 6.3938e-6 - 0.375463/tk ) * pw ) / tk; } /* Formula for beta from Stone, with empirical adjustments. */ beta = 4.4474e-6 * tk; if ( ! optic ) beta -= 0.0074 * pw * beta; /* Refraction constants from Green. */ *refa = gamma * ( 1.0 - beta ); *refb = - gamma * ( beta - gamma / 2.0 ); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/rm2v.c0000644000113000011300000001354513027221063014223 0ustar bellsbells#include "sofa.h" void iauRm2v(double r[3][3], double w[3]) /* ** - - - - - - - - ** i a u R m 2 v ** - - - - - - - - ** ** Express an r-matrix as an r-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] rotation matrix ** ** Returned: ** w double[3] rotation vector (Note 1) ** ** Notes: ** ** 1) A rotation matrix describes a rotation through some angle about ** some arbitrary axis called the Euler axis. The "rotation vector" ** returned by this function has the same direction as the Euler axis, ** and its magnitude is the angle in radians. (The magnitude and ** direction can be separated by means of the function iauPn.) ** ** 2) If r is null, so is the result. If r is not a rotation matrix ** the result is undefined; r must be proper (i.e. have a positive ** determinant) and real orthogonal (inverse = transpose). ** ** 3) The reference frame rotates clockwise as seen looking along ** the rotation vector from the origin. ** ** This revision: 2015 January 30 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double x, y, z, s2, c2, phi, f; x = r[1][2] - r[2][1]; y = r[2][0] - r[0][2]; z = r[0][1] - r[1][0]; s2 = sqrt(x*x + y*y + z*z); if (s2 > 0) { c2 = r[0][0] + r[1][1] + r[2][2] - 1.0; phi = atan2(s2, c2); f = phi / s2; w[0] = x * f; w[1] = y * f; w[2] = z * f; } else { w[0] = 0.0; w[1] = 0.0; w[2] = 0.0; } return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/rv2m.c0000644000113000011300000001355413027221063014223 0ustar bellsbells#include "sofa.h" void iauRv2m(double w[3], double r[3][3]) /* ** - - - - - - - - ** i a u R v 2 m ** - - - - - - - - ** ** Form the r-matrix corresponding to a given r-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** w double[3] rotation vector (Note 1) ** ** Returned: ** r double[3][3] rotation matrix ** ** Notes: ** ** 1) A rotation matrix describes a rotation through some angle about ** some arbitrary axis called the Euler axis. The "rotation vector" ** supplied to This function has the same direction as the Euler ** axis, and its magnitude is the angle in radians. ** ** 2) If w is null, the unit matrix is returned. ** ** 3) The reference frame rotates clockwise as seen looking along the ** rotation vector from the origin. ** ** This revision: 2015 January 30 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double x, y, z, phi, s, c, f; /* Euler angle (magnitude of rotation vector) and functions. */ x = w[0]; y = w[1]; z = w[2]; phi = sqrt(x*x + y*y + z*z); s = sin(phi); c = cos(phi); f = 1.0 - c; /* Euler axis (direction of rotation vector), perhaps null. */ if (phi > 0.0) { x /= phi; y /= phi; z /= phi; } /* Form the rotation matrix. */ r[0][0] = x*x*f + c; r[0][1] = x*y*f + z*s; r[0][2] = x*z*f - y*s; r[1][0] = y*x*f - z*s; r[1][1] = y*y*f + c; r[1][2] = y*z*f + x*s; r[2][0] = z*x*f + y*s; r[2][1] = z*y*f - x*s; r[2][2] = z*z*f + c; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/rx.c0000644000113000011300000001325713027221063013766 0ustar bellsbells#include "sofa.h" void iauRx(double phi, double r[3][3]) /* ** - - - - - - ** i a u R x ** - - - - - - ** ** Rotate an r-matrix about the x-axis. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** phi double angle (radians) ** ** Given and returned: ** r double[3][3] r-matrix, rotated ** ** Notes: ** ** 1) Calling this function with positive phi incorporates in the ** supplied r-matrix r an additional rotation, about the x-axis, ** anticlockwise as seen looking towards the origin from positive x. ** ** 2) The additional rotation can be represented by this matrix: ** ** ( 1 0 0 ) ** ( ) ** ( 0 + cos(phi) + sin(phi) ) ** ( ) ** ( 0 - sin(phi) + cos(phi) ) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double s, c, a10, a11, a12, a20, a21, a22; s = sin(phi); c = cos(phi); a10 = c*r[1][0] + s*r[2][0]; a11 = c*r[1][1] + s*r[2][1]; a12 = c*r[1][2] + s*r[2][2]; a20 = - s*r[1][0] + c*r[2][0]; a21 = - s*r[1][1] + c*r[2][1]; a22 = - s*r[1][2] + c*r[2][2]; r[1][0] = a10; r[1][1] = a11; r[1][2] = a12; r[2][0] = a20; r[2][1] = a21; r[2][2] = a22; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/rxp.c0000644000113000011300000001226213027221063014141 0ustar bellsbells#include "sofa.h" void iauRxp(double r[3][3], double p[3], double rp[3]) /* ** - - - - - - - ** i a u R x p ** - - - - - - - ** ** Multiply a p-vector by an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix ** p double[3] p-vector ** ** Returned: ** rp double[3] r * p ** ** Note: ** It is permissible for p and rp to be the same array. ** ** Called: ** iauCp copy p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double w, wrp[3]; int i, j; /* Matrix r * vector p. */ for (j = 0; j < 3; j++) { w = 0.0; for (i = 0; i < 3; i++) { w += r[j][i] * p[i]; } wrp[j] = w; } /* Return the result. */ iauCp(wrp, rp); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/rxpv.c0000644000113000011300000001203013027221063014320 0ustar bellsbells#include "sofa.h" void iauRxpv(double r[3][3], double pv[2][3], double rpv[2][3]) /* ** - - - - - - - - ** i a u R x p v ** - - - - - - - - ** ** Multiply a pv-vector by an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix ** pv double[2][3] pv-vector ** ** Returned: ** rpv double[2][3] r * pv ** ** Note: ** It is permissible for pv and rpv to be the same array. ** ** Called: ** iauRxp product of r-matrix and p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauRxp(r, pv[0], rpv[0]); iauRxp(r, pv[1], rpv[1]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/rxr.c0000644000113000011300000001233113027221063014140 0ustar bellsbells#include "sofa.h" void iauRxr(double a[3][3], double b[3][3], double atb[3][3]) /* ** - - - - - - - ** i a u R x r ** - - - - - - - ** ** Multiply two r-matrices. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3][3] first r-matrix ** b double[3][3] second r-matrix ** ** Returned: ** atb double[3][3] a * b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** ** Called: ** iauCr copy r-matrix ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int i, j, k; double w, wm[3][3]; for (i = 0; i < 3; i++) { for (j = 0; j < 3; j++) { w = 0.0; for (k = 0; k < 3; k++) { w += a[i][k] * b[k][j]; } wm[i][j] = w; } } iauCr(wm, atb); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ry.c0000644000113000011300000001333013027221063013757 0ustar bellsbells#include "sofa.h" void iauRy(double theta, double r[3][3]) /* ** - - - - - - ** i a u R y ** - - - - - - ** ** Rotate an r-matrix about the y-axis. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** theta double angle (radians) ** ** Given and returned: ** r double[3][3] r-matrix, rotated ** ** Notes: ** ** 1) Calling this function with positive theta incorporates in the ** supplied r-matrix r an additional rotation, about the y-axis, ** anticlockwise as seen looking towards the origin from positive y. ** ** 2) The additional rotation can be represented by this matrix: ** ** ( + cos(theta) 0 - sin(theta) ) ** ( ) ** ( 0 1 0 ) ** ( ) ** ( + sin(theta) 0 + cos(theta) ) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double s, c, a00, a01, a02, a20, a21, a22; s = sin(theta); c = cos(theta); a00 = c*r[0][0] - s*r[2][0]; a01 = c*r[0][1] - s*r[2][1]; a02 = c*r[0][2] - s*r[2][2]; a20 = s*r[0][0] + c*r[2][0]; a21 = s*r[0][1] + c*r[2][1]; a22 = s*r[0][2] + c*r[2][2]; r[0][0] = a00; r[0][1] = a01; r[0][2] = a02; r[2][0] = a20; r[2][1] = a21; r[2][2] = a22; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/rz.c0000644000113000011300000001327113027221063013764 0ustar bellsbells#include "sofa.h" void iauRz(double psi, double r[3][3]) /* ** - - - - - - ** i a u R z ** - - - - - - ** ** Rotate an r-matrix about the z-axis. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** psi double angle (radians) ** ** Given and returned: ** r double[3][3] r-matrix, rotated ** ** Notes: ** ** 1) Calling this function with positive psi incorporates in the ** supplied r-matrix r an additional rotation, about the z-axis, ** anticlockwise as seen looking towards the origin from positive z. ** ** 2) The additional rotation can be represented by this matrix: ** ** ( + cos(psi) + sin(psi) 0 ) ** ( ) ** ( - sin(psi) + cos(psi) 0 ) ** ( ) ** ( 0 0 1 ) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double s, c, a00, a01, a02, a10, a11, a12; s = sin(psi); c = cos(psi); a00 = c*r[0][0] + s*r[1][0]; a01 = c*r[0][1] + s*r[1][1]; a02 = c*r[0][2] + s*r[1][2]; a10 = - s*r[0][0] + c*r[1][0]; a11 = - s*r[0][1] + c*r[1][1]; a12 = - s*r[0][2] + c*r[1][2]; r[0][0] = a00; r[0][1] = a01; r[0][2] = a02; r[1][0] = a10; r[1][1] = a11; r[1][2] = a12; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/s00a.c0000644000113000011300000001714513027221063014100 0ustar bellsbells#include "sofa.h" double iauS00a(double date1, double date2) /* ** - - - - - - - - ** i a u S 0 0 a ** - - - - - - - - ** ** The CIO locator s, positioning the Celestial Intermediate Origin on ** the equator of the Celestial Intermediate Pole, using the IAU 2000A ** precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double the CIO locator s in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The CIO locator s is the difference between the right ascensions ** of the same point in two systems. The two systems are the GCRS ** and the CIP,CIO, and the point is the ascending node of the ** CIP equator. The CIO locator s remains a small fraction of ** 1 arcsecond throughout 1900-2100. ** ** 3) The series used to compute s is in fact for s+XY/2, where X and Y ** are the x and y components of the CIP unit vector; this series ** is more compact than a direct series for s would be. The present ** function uses the full IAU 2000A nutation model when predicting ** the CIP position. Faster results, with no significant loss of ** accuracy, can be obtained via the function iauS00b, which uses ** instead the IAU 2000B truncated model. ** ** Called: ** iauPnm00a classical NPB matrix, IAU 2000A ** iauBnp2xy extract CIP X,Y from the BPN matrix ** iauS00 the CIO locator s, given X,Y, IAU 2000A ** ** References: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rbpn[3][3], x, y, s; /* Bias-precession-nutation-matrix, IAU 2000A. */ iauPnm00a(date1, date2, rbpn); /* Extract the CIP coordinates. */ iauBpn2xy(rbpn, &x, &y); /* Compute the CIO locator s, given the CIP coordinates. */ s = iauS00(date1, date2, x, y); return s; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/s00b.c0000644000113000011300000001713413027221063014077 0ustar bellsbells#include "sofa.h" double iauS00b(double date1, double date2) /* ** - - - - - - - - ** i a u S 0 0 b ** - - - - - - - - ** ** The CIO locator s, positioning the Celestial Intermediate Origin on ** the equator of the Celestial Intermediate Pole, using the IAU 2000B ** precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double the CIO locator s in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The CIO locator s is the difference between the right ascensions ** of the same point in two systems. The two systems are the GCRS ** and the CIP,CIO, and the point is the ascending node of the ** CIP equator. The CIO locator s remains a small fraction of ** 1 arcsecond throughout 1900-2100. ** ** 3) The series used to compute s is in fact for s+XY/2, where X and Y ** are the x and y components of the CIP unit vector; this series ** is more compact than a direct series for s would be. The present ** function uses the IAU 2000B truncated nutation model when ** predicting the CIP position. The function iauS00a uses instead ** the full IAU 2000A model, but with no significant increase in ** accuracy and at some cost in speed. ** ** Called: ** iauPnm00b classical NPB matrix, IAU 2000B ** iauBnp2xy extract CIP X,Y from the BPN matrix ** iauS00 the CIO locator s, given X,Y, IAU 2000A ** ** References: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rbpn[3][3], x, y, s; /* Bias-precession-nutation-matrix, IAU 2000B. */ iauPnm00b(date1, date2, rbpn); /* Extract the CIP coordinates. */ iauBpn2xy(rbpn, &x, &y); /* Compute the CIO locator s, given the CIP coordinates. */ s = iauS00(date1, date2, x, y); return s; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/s00.c0000644000113000011300000003626413027221063013742 0ustar bellsbells#include "sofa.h" double iauS00(double date1, double date2, double x, double y) /* ** - - - - - - - ** i a u S 0 0 ** - - - - - - - ** ** The CIO locator s, positioning the Celestial Intermediate Origin on ** the equator of the Celestial Intermediate Pole, given the CIP's X,Y ** coordinates. Compatible with IAU 2000A precession-nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** x,y double CIP coordinates (Note 3) ** ** Returned (function value): ** double the CIO locator s in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The CIO locator s is the difference between the right ascensions ** of the same point in two systems: the two systems are the GCRS ** and the CIP,CIO, and the point is the ascending node of the ** CIP equator. The quantity s remains below 0.1 arcsecond ** throughout 1900-2100. ** ** 3) The series used to compute s is in fact for s+XY/2, where X and Y ** are the x and y components of the CIP unit vector; this series ** is more compact than a direct series for s would be. This ** function requires X,Y to be supplied by the caller, who is ** responsible for providing values that are consistent with the ** supplied date. ** ** 4) The model is consistent with the IAU 2000A precession-nutation. ** ** Called: ** iauFal03 mean anomaly of the Moon ** iauFalp03 mean anomaly of the Sun ** iauFaf03 mean argument of the latitude of the Moon ** iauFad03 mean elongation of the Moon from the Sun ** iauFaom03 mean longitude of the Moon's ascending node ** iauFave03 mean longitude of Venus ** iauFae03 mean longitude of Earth ** iauFapa03 general accumulated precession in longitude ** ** References: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Time since J2000.0, in Julian centuries */ double t; /* Miscellaneous */ int i, j; double a, w0, w1, w2, w3, w4, w5; /* Fundamental arguments */ double fa[8]; /* Returned value */ double s; /* --------------------- */ /* The series for s+XY/2 */ /* --------------------- */ typedef struct { int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */ double s, c; /* sine and cosine coefficients */ } TERM; /* Polynomial coefficients */ static const double sp[] = { /* 1-6 */ 94.00e-6, 3808.35e-6, -119.94e-6, -72574.09e-6, 27.70e-6, 15.61e-6 }; /* Terms of order t^0 */ static const TERM s0[] = { /* 1-10 */ {{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 }, {{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6 }, {{ 0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6 }, {{ 0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6 }, {{ 0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6 }, {{ 0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6 }, {{ 0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6 }, {{ 0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6 }, /* 11-20 */ {{ 1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6 }, {{ 1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6 }, {{ 0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6 }, {{ 0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6 }, {{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6 }, {{ 1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6 }, {{ 1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6 }, /* 21-30 */ {{ 0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6 }, {{ 0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6 }, {{ 0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6 }, {{ 0, 0, 0, 0, 0, 8,-13, -1}, 0.10e-6, -0.05e-6 }, {{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6 }, {{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6 }, {{ 1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6 }, {{ 1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 }, {{ 0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6 }, /* 31-33 */ {{ 0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6 }, {{ 1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6 }, {{ 1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6 } }; /* Terms of order t^1 */ static const TERM s1[] ={ /* 1-3 */ {{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 }, {{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.71e-6, -0.03e-6 }, {{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 } }; /* Terms of order t^2 */ static const TERM s2[] ={ /* 1-10 */ {{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.53e-6, -0.17e-6 }, {{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 }, {{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 }, {{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 }, {{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 }, {{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 }, {{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 }, {{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 }, /* 11-20 */ {{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 }, {{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 }, {{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 }, {{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 }, {{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 }, {{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 }, {{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 }, {{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 }, {{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 }, {{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 }, /* 21-25 */ {{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 }, {{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 }, {{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 }, {{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 } }; /* Terms of order t^3 */ static const TERM s3[] ={ /* 1-4 */ {{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.51e-6 }, {{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.39e-6 }, {{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.24e-6 }, {{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.22e-6 } }; /* Terms of order t^4 */ static const TERM s4[] ={ /* 1-1 */ {{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 } }; /* Number of terms in the series */ const int NS0 = (int) (sizeof s0 / sizeof (TERM)); const int NS1 = (int) (sizeof s1 / sizeof (TERM)); const int NS2 = (int) (sizeof s2 / sizeof (TERM)); const int NS3 = (int) (sizeof s3 / sizeof (TERM)); const int NS4 = (int) (sizeof s4 / sizeof (TERM)); /*--------------------------------------------------------------------*/ /* Interval between fundamental epoch J2000.0 and current date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Fundamental Arguments (from IERS Conventions 2003) */ /* Mean anomaly of the Moon. */ fa[0] = iauFal03(t); /* Mean anomaly of the Sun. */ fa[1] = iauFalp03(t); /* Mean longitude of the Moon minus that of the ascending node. */ fa[2] = iauFaf03(t); /* Mean elongation of the Moon from the Sun. */ fa[3] = iauFad03(t); /* Mean longitude of the ascending node of the Moon. */ fa[4] = iauFaom03(t); /* Mean longitude of Venus. */ fa[5] = iauFave03(t); /* Mean longitude of Earth. */ fa[6] = iauFae03(t); /* General precession in longitude. */ fa[7] = iauFapa03(t); /* Evaluate s. */ w0 = sp[0]; w1 = sp[1]; w2 = sp[2]; w3 = sp[3]; w4 = sp[4]; w5 = sp[5]; for (i = NS0-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)s0[i].nfa[j] * fa[j]; } w0 += s0[i].s * sin(a) + s0[i].c * cos(a); } for (i = NS1-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)s1[i].nfa[j] * fa[j]; } w1 += s1[i].s * sin(a) + s1[i].c * cos(a); } for (i = NS2-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)s2[i].nfa[j] * fa[j]; } w2 += s2[i].s * sin(a) + s2[i].c * cos(a); } for (i = NS3-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)s3[i].nfa[j] * fa[j]; } w3 += s3[i].s * sin(a) + s3[i].c * cos(a); } for (i = NS4-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)s4[i].nfa[j] * fa[j]; } w4 += s4[i].s * sin(a) + s4[i].c * cos(a); } s = (w0 + (w1 + (w2 + (w3 + (w4 + w5 * t) * t) * t) * t) * t) * DAS2R - x*y/2.0; return s; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/s06a.c0000644000113000011300000001716713027221063014112 0ustar bellsbells#include "sofa.h" double iauS06a(double date1, double date2) /* ** - - - - - - - - ** i a u S 0 6 a ** - - - - - - - - ** ** The CIO locator s, positioning the Celestial Intermediate Origin on ** the equator of the Celestial Intermediate Pole, using the IAU 2006 ** precession and IAU 2000A nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double the CIO locator s in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The CIO locator s is the difference between the right ascensions ** of the same point in two systems. The two systems are the GCRS ** and the CIP,CIO, and the point is the ascending node of the ** CIP equator. The CIO locator s remains a small fraction of ** 1 arcsecond throughout 1900-2100. ** ** 3) The series used to compute s is in fact for s+XY/2, where X and Y ** are the x and y components of the CIP unit vector; this series is ** more compact than a direct series for s would be. The present ** function uses the full IAU 2000A nutation model when predicting ** the CIP position. ** ** Called: ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** ** References: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rnpb[3][3], x, y, s; /* Bias-precession-nutation-matrix, IAU 20006/2000A. */ iauPnm06a(date1, date2, rnpb); /* Extract the CIP coordinates. */ iauBpn2xy(rnpb, &x, &y); /* Compute the CIO locator s, given the CIP coordinates. */ s = iauS06(date1, date2, x, y); return s; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/s06.c0000644000113000011300000003612213027221063013741 0ustar bellsbells#include "sofa.h" double iauS06(double date1, double date2, double x, double y) /* ** - - - - - - - ** i a u S 0 6 ** - - - - - - - ** ** The CIO locator s, positioning the Celestial Intermediate Origin on ** the equator of the Celestial Intermediate Pole, given the CIP's X,Y ** coordinates. Compatible with IAU 2006/2000A precession-nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** x,y double CIP coordinates (Note 3) ** ** Returned (function value): ** double the CIO locator s in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The CIO locator s is the difference between the right ascensions ** of the same point in two systems: the two systems are the GCRS ** and the CIP,CIO, and the point is the ascending node of the ** CIP equator. The quantity s remains below 0.1 arcsecond ** throughout 1900-2100. ** ** 3) The series used to compute s is in fact for s+XY/2, where X and Y ** are the x and y components of the CIP unit vector; this series ** is more compact than a direct series for s would be. This ** function requires X,Y to be supplied by the caller, who is ** responsible for providing values that are consistent with the ** supplied date. ** ** 4) The model is consistent with the "P03" precession (Capitaine et ** al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the ** IAU 2000A nutation (with P03 adjustments). ** ** Called: ** iauFal03 mean anomaly of the Moon ** iauFalp03 mean anomaly of the Sun ** iauFaf03 mean argument of the latitude of the Moon ** iauFad03 mean elongation of the Moon from the Sun ** iauFaom03 mean longitude of the Moon's ascending node ** iauFave03 mean longitude of Venus ** iauFae03 mean longitude of Earth ** iauFapa03 general accumulated precession in longitude ** ** References: ** ** Capitaine, N., Wallace, P.T. & Chapront, J., 2003, Astron. ** Astrophys. 432, 355 ** ** McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Time since J2000.0, in Julian centuries */ double t; /* Miscellaneous */ int i, j; double a, w0, w1, w2, w3, w4, w5; /* Fundamental arguments */ double fa[8]; /* Returned value */ double s; /* --------------------- */ /* The series for s+XY/2 */ /* --------------------- */ typedef struct { int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */ double s, c; /* sine and cosine coefficients */ } TERM; /* Polynomial coefficients */ static const double sp[] = { /* 1-6 */ 94.00e-6, 3808.65e-6, -122.68e-6, -72574.11e-6, 27.98e-6, 15.62e-6 }; /* Terms of order t^0 */ static const TERM s0[] = { /* 1-10 */ {{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 }, {{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6 }, {{ 0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6 }, {{ 0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6 }, {{ 0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6 }, {{ 0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6 }, {{ 0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6 }, {{ 0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6 }, /* 11-20 */ {{ 1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6 }, {{ 1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6 }, {{ 0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6 }, {{ 0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6 }, {{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6 }, {{ 1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6 }, {{ 1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6 }, /* 21-30 */ {{ 0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6 }, {{ 0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6 }, {{ 0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6 }, {{ 0, 0, 0, 0, 0, 8,-13, -1}, 0.10e-6, -0.05e-6 }, {{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6 }, {{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6 }, {{ 1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6 }, {{ 1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 }, {{ 0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6 }, /* 31-33 */ {{ 0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6 }, {{ 1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6 }, {{ 1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6 } }; /* Terms of order t^1 */ static const TERM s1[] = { /* 1 - 3 */ {{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 }, {{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.73e-6, -0.03e-6 }, {{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 } }; /* Terms of order t^2 */ static const TERM s2[] = { /* 1-10 */ {{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.52e-6, -0.17e-6 }, {{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 }, {{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 }, {{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 }, {{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 }, {{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 }, {{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 }, {{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 }, {{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 }, /* 11-20 */ {{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 }, {{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 }, {{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 }, {{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 }, {{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 }, {{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 }, {{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 }, {{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 }, {{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 }, {{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 }, /* 21-25 */ {{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 }, {{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 }, {{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 }, {{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 }, {{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 } }; /* Terms of order t^3 */ static const TERM s3[] = { /* 1-4 */ {{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.42e-6 }, {{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.46e-6 }, {{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.25e-6 }, {{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.23e-6 } }; /* Terms of order t^4 */ static const TERM s4[] = { /* 1-1 */ {{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 } }; /* Number of terms in the series */ static const int NS0 = (int) (sizeof s0 / sizeof (TERM)); static const int NS1 = (int) (sizeof s1 / sizeof (TERM)); static const int NS2 = (int) (sizeof s2 / sizeof (TERM)); static const int NS3 = (int) (sizeof s3 / sizeof (TERM)); static const int NS4 = (int) (sizeof s4 / sizeof (TERM)); /*--------------------------------------------------------------------*/ /* Interval between fundamental epoch J2000.0 and current date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Fundamental Arguments (from IERS Conventions 2003) */ /* Mean anomaly of the Moon. */ fa[0] = iauFal03(t); /* Mean anomaly of the Sun. */ fa[1] = iauFalp03(t); /* Mean longitude of the Moon minus that of the ascending node. */ fa[2] = iauFaf03(t); /* Mean elongation of the Moon from the Sun. */ fa[3] = iauFad03(t); /* Mean longitude of the ascending node of the Moon. */ fa[4] = iauFaom03(t); /* Mean longitude of Venus. */ fa[5] = iauFave03(t); /* Mean longitude of Earth. */ fa[6] = iauFae03(t); /* General precession in longitude. */ fa[7] = iauFapa03(t); /* Evaluate s. */ w0 = sp[0]; w1 = sp[1]; w2 = sp[2]; w3 = sp[3]; w4 = sp[4]; w5 = sp[5]; for (i = NS0-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)s0[i].nfa[j] * fa[j]; } w0 += s0[i].s * sin(a) + s0[i].c * cos(a); } for (i = NS1-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)s1[i].nfa[j] * fa[j]; } w1 += s1[i].s * sin(a) + s1[i].c * cos(a); } for (i = NS2-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)s2[i].nfa[j] * fa[j]; } w2 += s2[i].s * sin(a) + s2[i].c * cos(a); } for (i = NS3-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)s3[i].nfa[j] * fa[j]; } w3 += s3[i].s * sin(a) + s3[i].c * cos(a); } for (i = NS4-1; i >= 0; i--) { a = 0.0; for (j = 0; j < 8; j++) { a += (double)s4[i].nfa[j] * fa[j]; } w4 += s4[i].s * sin(a) + s4[i].c * cos(a); } s = (w0 + (w1 + (w2 + (w3 + (w4 + w5 * t) * t) * t) * t) * t) * DAS2R - x*y/2.0; return s; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/s2c.c0000644000113000011300000001172113027221063014016 0ustar bellsbells#include "sofa.h" void iauS2c(double theta, double phi, double c[3]) /* ** - - - - - - - ** i a u S 2 c ** - - - - - - - ** ** Convert spherical coordinates to Cartesian. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** ** Returned: ** c double[3] direction cosines ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double cp; cp = cos(phi); c[0] = cos(theta) * cp; c[1] = sin(theta) * cp; c[2] = sin(phi); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/s2p.c0000644000113000011300000001213113027221063014027 0ustar bellsbells#include "sofa.h" void iauS2p(double theta, double phi, double r, double p[3]) /* ** - - - - - - - ** i a u S 2 p ** - - - - - - - ** ** Convert spherical polar coordinates to p-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** r double radial distance ** ** Returned: ** p double[3] Cartesian coordinates ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauSxp multiply p-vector by scalar ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double u[3]; iauS2c(theta, phi, u); iauSxp(r, u, p); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/s2pv.c0000644000113000011300000001300413027221063014215 0ustar bellsbells#include "sofa.h" void iauS2pv(double theta, double phi, double r, double td, double pd, double rd, double pv[2][3]) /* ** - - - - - - - - ** i a u S 2 p v ** - - - - - - - - ** ** Convert position/velocity from spherical to Cartesian coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** r double radial distance ** td double rate of change of theta ** pd double rate of change of phi ** rd double rate of change of r ** ** Returned: ** pv double[2][3] pv-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double st, ct, sp, cp, rcp, x, y, rpd, w; st = sin(theta); ct = cos(theta); sp = sin(phi); cp = cos(phi); rcp = r * cp; x = rcp * ct; y = rcp * st; rpd = r * pd; w = rpd*sp - cp*rd; pv[0][0] = x; pv[0][1] = y; pv[0][2] = r * sp; pv[1][0] = -y*td - w*ct; pv[1][1] = x*td - w*st; pv[1][2] = rpd*cp + sp*rd; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/s2xpv.c0000644000113000011300000001224213027221063014410 0ustar bellsbells#include "sofa.h" void iauS2xpv(double s1, double s2, double pv[2][3], double spv[2][3]) /* ** - - - - - - - - - ** i a u S 2 x p v ** - - - - - - - - - ** ** Multiply a pv-vector by two scalars. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** s1 double scalar to multiply position component by ** s2 double scalar to multiply velocity component by ** pv double[2][3] pv-vector ** ** Returned: ** spv double[2][3] pv-vector: p scaled by s1, v scaled by s2 ** ** Note: ** It is permissible for pv and spv to be the same array. ** ** Called: ** iauSxp multiply p-vector by scalar ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauSxp(s1, pv[0], spv[0]); iauSxp(s2, pv[1], spv[1]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/sepp.c0000644000113000011300000001336513027221063014304 0ustar bellsbells#include "sofa.h" double iauSepp(double a[3], double b[3]) /* ** - - - - - - - - ** i a u S e p p ** - - - - - - - - ** ** Angular separation between two p-vectors. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector (not necessarily unit length) ** b double[3] second p-vector (not necessarily unit length) ** ** Returned (function value): ** double angular separation (radians, always positive) ** ** Notes: ** ** 1) If either vector is null, a zero result is returned. ** ** 2) The angular separation is most simply formulated in terms of ** scalar product. However, this gives poor accuracy for angles ** near zero and pi. The present algorithm uses both cross product ** and dot product, to deliver full accuracy whatever the size of ** the angle. ** ** Called: ** iauPxp vector product of two p-vectors ** iauPm modulus of p-vector ** iauPdp scalar product of two p-vectors ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double axb[3], ss, cs, s; /* Sine of angle between the vectors, multiplied by the two moduli. */ iauPxp(a, b, axb); ss = iauPm(axb); /* Cosine of the angle, multiplied by the two moduli. */ cs = iauPdp(a, b); /* The angle. */ s = ((ss != 0.0) || (cs != 0.0)) ? atan2(ss, cs) : 0.0; return s; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/seps.c0000644000113000011300000001246013027221063014302 0ustar bellsbells#include "sofa.h" double iauSeps(double al, double ap, double bl, double bp) /* ** - - - - - - - - ** i a u S e p s ** - - - - - - - - ** ** Angular separation between two sets of spherical coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** al double first longitude (radians) ** ap double first latitude (radians) ** bl double second longitude (radians) ** bp double second latitude (radians) ** ** Returned (function value): ** double angular separation (radians) ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauSepp angular separation between two p-vectors ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double ac[3], bc[3], s; /* Spherical to Cartesian. */ iauS2c(al, ap, ac); iauS2c(bl, bp, bc); /* Angle between the vectors. */ s = iauSepp(ac, bc); return s; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/sp00.c0000644000113000011300000001463513027221063014120 0ustar bellsbells#include "sofa.h" double iauSp00(double date1, double date2) /* ** - - - - - - - - ** i a u S p 0 0 ** - - - - - - - - ** ** The TIO locator s', positioning the Terrestrial Intermediate Origin ** on the equator of the Celestial Intermediate Pole. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double the TIO locator s' in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The TIO locator s' is obtained from polar motion observations by ** numerical integration, and so is in essence unpredictable. ** However, it is dominated by a secular drift of about ** 47 microarcseconds per century, which is the approximation ** evaluated by the present function. ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double t, sp; /* Interval between fundamental epoch J2000.0 and current date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Approximate s'. */ sp = -47e-6 * t * DAS2R; return sp; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/starpm.c0000644000113000011300000002466513027221063014650 0ustar bellsbells#include "sofa.h" int iauStarpm(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2) /* ** - - - - - - - - - - ** i a u S t a r p m ** - - - - - - - - - - ** ** Star proper motion: update star catalog data for space motion. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ra1 double right ascension (radians), before ** dec1 double declination (radians), before ** pmr1 double RA proper motion (radians/year), before ** pmd1 double Dec proper motion (radians/year), before ** px1 double parallax (arcseconds), before ** rv1 double radial velocity (km/s, +ve = receding), before ** ep1a double "before" epoch, part A (Note 1) ** ep1b double "before" epoch, part B (Note 1) ** ep2a double "after" epoch, part A (Note 1) ** ep2b double "after" epoch, part B (Note 1) ** ** Returned: ** ra2 double right ascension (radians), after ** dec2 double declination (radians), after ** pmr2 double RA proper motion (radians/year), after ** pmd2 double Dec proper motion (radians/year), after ** px2 double parallax (arcseconds), after ** rv2 double radial velocity (km/s, +ve = receding), after ** ** Returned (function value): ** int status: ** -1 = system error (should not occur) ** 0 = no warnings or errors ** 1 = distance overridden (Note 6) ** 2 = excessive velocity (Note 7) ** 4 = solution didn't converge (Note 8) ** else = binary logical OR of the above warnings ** ** Notes: ** ** 1) The starting and ending TDB dates ep1a+ep1b and ep2a+ep2b are ** Julian Dates, apportioned in any convenient way between the two ** parts (A and B). For example, JD(TDB)=2450123.7 could be ** expressed in any of these ways, among others: ** ** epna epnb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) In accordance with normal star-catalog conventions, the object's ** right ascension and declination are freed from the effects of ** secular aberration. The frame, which is aligned to the catalog ** equator and equinox, is Lorentzian and centered on the SSB. ** ** The proper motions are the rate of change of the right ascension ** and declination at the catalog epoch and are in radians per TDB ** Julian year. ** ** The parallax and radial velocity are in the same frame. ** ** 3) Care is needed with units. The star coordinates are in radians ** and the proper motions in radians per Julian year, but the ** parallax is in arcseconds. ** ** 4) The RA proper motion is in terms of coordinate angle, not true ** angle. If the catalog uses arcseconds for both RA and Dec proper ** motions, the RA proper motion will need to be divided by cos(Dec) ** before use. ** ** 5) Straight-line motion at constant speed, in the inertial frame, ** is assumed. ** ** 6) An extremely small (or zero or negative) parallax is interpreted ** to mean that the object is on the "celestial sphere", the radius ** of which is an arbitrary (large) value (see the iauStarpv ** function for the value used). When the distance is overridden in ** this way, the status, initially zero, has 1 added to it. ** ** 7) If the space velocity is a significant fraction of c (see the ** constant VMAX in the function iauStarpv), it is arbitrarily set ** to zero. When this action occurs, 2 is added to the status. ** ** 8) The relativistic adjustment carried out in the iauStarpv function ** involves an iterative calculation. If the process fails to ** converge within a set number of iterations, 4 is added to the ** status. ** ** Called: ** iauStarpv star catalog data to space motion pv-vector ** iauPvu update a pv-vector ** iauPdp scalar product of two p-vectors ** iauPvstar space motion pv-vector to star catalog data ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double pv1[2][3], tl1, dt, pv[2][3], r2, rdv, v2, c2mv2, tl2, pv2[2][3]; int j1, j2, j; /* RA,Dec etc. at the "before" epoch to space motion pv-vector. */ j1 = iauStarpv(ra1, dec1, pmr1, pmd1, px1, rv1, pv1); /* Light time when observed (days). */ tl1 = iauPm(pv1[0]) / DC; /* Time interval, "before" to "after" (days). */ dt = (ep2a - ep1a) + (ep2b - ep1b); /* Move star along track from the "before" observed position to the */ /* "after" geometric position. */ iauPvu(dt + tl1, pv1, pv); /* From this geometric position, deduce the observed light time (days) */ /* at the "after" epoch (with theoretically unneccessary error check). */ r2 = iauPdp(pv[0], pv[0]); rdv = iauPdp(pv[0], pv[1]); v2 = iauPdp(pv[1], pv[1]); c2mv2 = DC*DC - v2; if (c2mv2 <= 0) return -1; tl2 = (-rdv + sqrt(rdv*rdv + c2mv2*r2)) / c2mv2; /* Move the position along track from the observed place at the */ /* "before" epoch to the observed place at the "after" epoch. */ iauPvu(dt + (tl1 - tl2), pv1, pv2); /* Space motion pv-vector to RA,Dec etc. at the "after" epoch. */ j2 = iauPvstar(pv2, ra2, dec2, pmr2, pmd2, px2, rv2); /* Final status. */ j = (j2 == 0) ? j1 : -1; return j; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/starpv.c0000644000113000011300000002727113027221063014655 0ustar bellsbells#include "sofa.h" int iauStarpv(double ra, double dec, double pmr, double pmd, double px, double rv, double pv[2][3]) /* ** - - - - - - - - - - ** i a u S t a r p v ** - - - - - - - - - - ** ** Convert star catalog coordinates to position+velocity vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given (Note 1): ** ra double right ascension (radians) ** dec double declination (radians) ** pmr double RA proper motion (radians/year) ** pmd double Dec proper motion (radians/year) ** px double parallax (arcseconds) ** rv double radial velocity (km/s, positive = receding) ** ** Returned (Note 2): ** pv double[2][3] pv-vector (AU, AU/day) ** ** Returned (function value): ** int status: ** 0 = no warnings ** 1 = distance overridden (Note 6) ** 2 = excessive speed (Note 7) ** 4 = solution didn't converge (Note 8) ** else = binary logical OR of the above ** ** Notes: ** ** 1) The star data accepted by this function are "observables" for an ** imaginary observer at the solar-system barycenter. Proper motion ** and radial velocity are, strictly, in terms of barycentric ** coordinate time, TCB. For most practical applications, it is ** permissible to neglect the distinction between TCB and ordinary ** "proper" time on Earth (TT/TAI). The result will, as a rule, be ** limited by the intrinsic accuracy of the proper-motion and ** radial-velocity data; moreover, the pv-vector is likely to be ** merely an intermediate result, so that a change of time unit ** would cancel out overall. ** ** In accordance with normal star-catalog conventions, the object's ** right ascension and declination are freed from the effects of ** secular aberration. The frame, which is aligned to the catalog ** equator and equinox, is Lorentzian and centered on the SSB. ** ** 2) The resulting position and velocity pv-vector is with respect to ** the same frame and, like the catalog coordinates, is freed from ** the effects of secular aberration. Should the "coordinate ** direction", where the object was located at the catalog epoch, be ** required, it may be obtained by calculating the magnitude of the ** position vector pv[0][0-2] dividing by the speed of light in ** AU/day to give the light-time, and then multiplying the space ** velocity pv[1][0-2] by this light-time and adding the result to ** pv[0][0-2]. ** ** Summarizing, the pv-vector returned is for most stars almost ** identical to the result of applying the standard geometrical ** "space motion" transformation. The differences, which are the ** subject of the Stumpff paper referenced below, are: ** ** (i) In stars with significant radial velocity and proper motion, ** the constantly changing light-time distorts the apparent proper ** motion. Note that this is a classical, not a relativistic, ** effect. ** ** (ii) The transformation complies with special relativity. ** ** 3) Care is needed with units. The star coordinates are in radians ** and the proper motions in radians per Julian year, but the ** parallax is in arcseconds; the radial velocity is in km/s, but ** the pv-vector result is in AU and AU/day. ** ** 4) The RA proper motion is in terms of coordinate angle, not true ** angle. If the catalog uses arcseconds for both RA and Dec proper ** motions, the RA proper motion will need to be divided by cos(Dec) ** before use. ** ** 5) Straight-line motion at constant speed, in the inertial frame, ** is assumed. ** ** 6) An extremely small (or zero or negative) parallax is interpreted ** to mean that the object is on the "celestial sphere", the radius ** of which is an arbitrary (large) value (see the constant PXMIN). ** When the distance is overridden in this way, the status, ** initially zero, has 1 added to it. ** ** 7) If the space velocity is a significant fraction of c (see the ** constant VMAX), it is arbitrarily set to zero. When this action ** occurs, 2 is added to the status. ** ** 8) The relativistic adjustment involves an iterative calculation. ** If the process fails to converge within a set number (IMAX) of ** iterations, 4 is added to the status. ** ** 9) The inverse transformation is performed by the function ** iauPvstar. ** ** Called: ** iauS2pv spherical coordinates to pv-vector ** iauPm modulus of p-vector ** iauZp zero p-vector ** iauPn decompose p-vector into modulus and direction ** iauPdp scalar product of two p-vectors ** iauSxp multiply p-vector by scalar ** iauPmp p-vector minus p-vector ** iauPpp p-vector plus p-vector ** ** Reference: ** ** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240. ** ** This revision: 2016 December 8 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Smallest allowed parallax */ static const double PXMIN = 1e-7; /* Largest allowed speed (fraction of c) */ static const double VMAX = 0.5; /* Maximum number of iterations for relativistic solution */ static const int IMAX = 100; int i, iwarn; double w, r, rd, rad, decd, v, x[3], usr[3], ust[3], vsr, vst, betst, betsr, bett, betr, dd, ddel, ur[3], ut[3], d = 0.0, del = 0.0, /* to prevent */ odd = 0.0, oddel = 0.0, /* compiler */ od = 0.0, odel = 0.0; /* warnings */ /* Distance (AU). */ if (px >= PXMIN) { w = px; iwarn = 0; } else { w = PXMIN; iwarn = 1; } r = DR2AS / w; /* Radial velocity (AU/day). */ rd = DAYSEC * rv * 1e3 / DAU; /* Proper motion (radian/day). */ rad = pmr / DJY; decd = pmd / DJY; /* To pv-vector (AU,AU/day). */ iauS2pv(ra, dec, r, rad, decd, rd, pv); /* If excessive velocity, arbitrarily set it to zero. */ v = iauPm(pv[1]); if (v / DC > VMAX) { iauZp(pv[1]); iwarn += 2; } /* Isolate the radial component of the velocity (AU/day). */ iauPn(pv[0], &w, x); vsr = iauPdp(x, pv[1]); iauSxp(vsr, x, usr); /* Isolate the transverse component of the velocity (AU/day). */ iauPmp(pv[1], usr, ust); vst = iauPm(ust); /* Special-relativity dimensionless parameters. */ betsr = vsr / DC; betst = vst / DC; /* Determine the inertial-to-observed relativistic correction terms. */ bett = betst; betr = betsr; for (i = 0; i < IMAX; i++) { d = 1.0 + betr; w = betr*betr + bett*bett; del = - w / (sqrt(1.0 - w) + 1.0); betr = d * betsr + del; bett = d * betst; if (i > 0) { dd = fabs(d - od); ddel = fabs(del - odel); if ((i > 1) && (dd >= odd) && (ddel >= oddel)) break; odd = dd; oddel = ddel; } od = d; odel = del; } if (i >= IMAX) iwarn += 4; /* Replace observed radial velocity with inertial value. */ w = (betsr != 0.0) ? d + del / betsr : 1.0; iauSxp(w, usr, ur); /* Replace observed tangential velocity with inertial value. */ iauSxp(d, ust, ut); /* Combine the two to obtain the inertial space velocity. */ iauPpp(ur, ut, pv[1]); /* Return the status. */ return iwarn; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/sxp.c0000644000113000011300000001165613027221063014150 0ustar bellsbells#include "sofa.h" void iauSxp(double s, double p[3], double sp[3]) /* ** - - - - - - - ** i a u S x p ** - - - - - - - ** ** Multiply a p-vector by a scalar. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** s double scalar ** p double[3] p-vector ** ** Returned: ** sp double[3] s * p ** ** Note: ** It is permissible for p and sp to be the same array. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { sp[0] = s * p[0]; sp[1] = s * p[1]; sp[2] = s * p[2]; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/sxpv.c0000644000113000011300000001175513027221063014336 0ustar bellsbells#include "sofa.h" void iauSxpv(double s, double pv[2][3], double spv[2][3]) /* ** - - - - - - - - ** i a u S x p v ** - - - - - - - - ** ** Multiply a pv-vector by a scalar. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** s double scalar ** pv double[2][3] pv-vector ** ** Returned: ** spv double[2][3] s * pv ** ** Note: ** It is permissible for pv and spv to be the same array ** ** Called: ** iauS2xpv multiply pv-vector by two scalars ** ** This revision: 2013 August 7 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauS2xpv(s, s, pv, spv); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/taitt.c0000644000113000011300000001331113027221063014451 0ustar bellsbells#include "sofa.h" int iauTaitt(double tai1, double tai2, double *tt1, double *tt2) /* ** - - - - - - - - - ** i a u T a i t t ** - - - - - - - - - ** ** Time scale transformation: International Atomic Time, TAI, to ** Terrestrial Time, TT. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tai1,tai2 double TAI as a 2-part Julian Date ** ** Returned: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Note: ** ** tai1+tai2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tai1 is the Julian ** Day Number and tai2 is the fraction of a day. The returned ** tt1,tt2 follow suit. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* TT minus TAI (days). */ static const double dtat = TTMTAI/DAYSEC; /* Result, safeguarding precision. */ if ( tai1 > tai2 ) { *tt1 = tai1; *tt2 = tai2 + dtat; } else { *tt1 = tai1 + dtat; *tt2 = tai2; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/taiut1.c0000644000113000011300000001340113027221063014533 0ustar bellsbells#include "sofa.h" int iauTaiut1(double tai1, double tai2, double dta, double *ut11, double *ut12) /* ** - - - - - - - - - - ** i a u T a i u t 1 ** - - - - - - - - - - ** ** Time scale transformation: International Atomic Time, TAI, to ** Universal Time, UT1. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tai1,tai2 double TAI as a 2-part Julian Date ** dta double UT1-TAI in seconds ** ** Returned: ** ut11,ut12 double UT1 as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tai1+tai2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tai1 is the Julian ** Day Number and tai2 is the fraction of a day. The returned ** UT11,UT12 follow suit. ** ** 2) The argument dta, i.e. UT1-TAI, is an observed quantity, and is ** available from IERS tabulations. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. ** */ { double dtad; /* Result, safeguarding precision. */ dtad = dta / DAYSEC; if ( tai1 > tai2 ) { *ut11 = tai1; *ut12 = tai2 + dtad; } else { *ut11 = tai1 + dtad; *ut12 = tai2; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/taiutc.c0000644000113000011300000001647613027221063014634 0ustar bellsbells#include "sofa.h" int iauTaiutc(double tai1, double tai2, double *utc1, double *utc2) /* ** - - - - - - - - - - ** i a u T a i u t c ** - - - - - - - - - - ** ** Time scale transformation: International Atomic Time, TAI, to ** Coordinated Universal Time, UTC. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tai1,tai2 double TAI as a 2-part Julian Date (Note 1) ** ** Returned: ** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-3) ** ** Returned (function value): ** int status: +1 = dubious year (Note 4) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) tai1+tai2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tai1 is the Julian ** Day Number and tai2 is the fraction of a day. The returned utc1 ** and utc2 form an analogous pair, except that a special convention ** is used, to deal with the problem of leap seconds - see the next ** note. ** ** 2) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The convention in the present ** function is that the JD day represents UTC days whether the ** length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era ** there were smaller jumps (in either direction) each time the ** linear UTC(TAI) expression was changed, and these "mini-leaps" ** are also included in the SOFA convention. ** ** 3) The function iauD2dtf can be used to transform the UTC quasi-JD ** into calendar date and clock time, including UTC leap second ** handling. ** ** 4) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** Called: ** iauUtctai UTC to TAI ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** This revision: 2013 September 12 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int big1; int i, j; double a1, a2, u1, u2, g1, g2; /* Put the two parts of the TAI into big-first order. */ big1 = ( tai1 >= tai2 ); if ( big1 ) { a1 = tai1; a2 = tai2; } else { a1 = tai2; a2 = tai1; } /* Initial guess for UTC. */ u1 = a1; u2 = a2; /* Iterate (though in most cases just once is enough). */ for ( i = 0; i < 3; i++ ) { /* Guessed UTC to TAI. */ j = iauUtctai(u1, u2, &g1, &g2); if ( j < 0 ) return j; /* Adjust guessed UTC. */ u2 += a1 - g1; u2 += a2 - g2; } /* Return the UTC result, preserving the TAI order. */ if ( big1 ) { *utc1 = u1; *utc2 = u2; } else { *utc1 = u2; *utc2 = u1; } /* Status. */ return j; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/tcbtdb.c0000644000113000011300000001547713027221063014605 0ustar bellsbells#include "sofa.h" int iauTcbtdb(double tcb1, double tcb2, double *tdb1, double *tdb2) /* ** - - - - - - - - - - ** i a u T c b t d b ** - - - - - - - - - - ** ** Time scale transformation: Barycentric Coordinate Time, TCB, to ** Barycentric Dynamical Time, TDB. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tcb1,tcb2 double TCB as a 2-part Julian Date ** ** Returned: ** tdb1,tdb2 double TDB as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tcb1+tcb2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tcb1 is the Julian ** Day Number and tcb2 is the fraction of a day. The returned ** tdb1,tdb2 follow suit. ** ** 2) The 2006 IAU General Assembly introduced a conventional linear ** transformation between TDB and TCB. This transformation ** compensates for the drift between TCB and terrestrial time TT, ** and keeps TDB approximately centered on TT. Because the ** relationship between TT and TCB depends on the adopted solar ** system ephemeris, the degree of alignment between TDB and TT over ** long intervals will vary according to which ephemeris is used. ** Former definitions of TDB attempted to avoid this problem by ** stipulating that TDB and TT should differ only by periodic ** effects. This is a good description of the nature of the ** relationship but eluded precise mathematical formulation. The ** conventional linear relationship adopted in 2006 sidestepped ** these difficulties whilst delivering a TDB that in practice was ** consistent with values before that date. ** ** 3) TDB is essentially the same as Teph, the time argument for the ** JPL solar system ephemerides. ** ** Reference: ** ** IAU 2006 Resolution B3 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* 1977 Jan 1 00:00:32.184 TT, as two-part JD */ static const double t77td = DJM0 + DJM77; static const double t77tf = TTMTAI/DAYSEC; /* TDB (days) at TAI 1977 Jan 1.0 */ static const double tdb0 = TDB0/DAYSEC; double d; /* Result, safeguarding precision. */ if ( tcb1 > tcb2 ) { d = tcb1 - t77td; *tdb1 = tcb1; *tdb2 = tcb2 + tdb0 - ( d + ( tcb2 - t77tf ) ) * ELB; } else { d = tcb2 - t77td; *tdb1 = tcb1 + tdb0 - ( d + ( tcb1 - t77tf ) ) * ELB; *tdb2 = tcb2; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/tcgtt.c0000644000113000011300000001331113027221063014451 0ustar bellsbells#include "sofa.h" int iauTcgtt(double tcg1, double tcg2, double *tt1, double *tt2) /* ** - - - - - - - - - ** i a u T c g t t ** - - - - - - - - - ** ** Time scale transformation: Geocentric Coordinate Time, TCG, to ** Terrestrial Time, TT. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tcg1,tcg2 double TCG as a 2-part Julian Date ** ** Returned: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Note: ** ** tcg1+tcg2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tcg1 is the Julian ** Day Number and tcg22 is the fraction of a day. The returned ** tt1,tt2 follow suit. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),. ** IERS Technical Note No. 32, BKG (2004) ** ** IAU 2000 Resolution B1.9 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* 1977 Jan 1 00:00:32.184 TT, as MJD */ static const double t77t = DJM77 + TTMTAI/DAYSEC; /* Result, safeguarding precision. */ if ( tcg1 > tcg2 ) { *tt1 = tcg1; *tt2 = tcg2 - ( ( tcg1 - DJM0 ) + ( tcg2 - t77t ) ) * ELG; } else { *tt1 = tcg1 - ( ( tcg2 - DJM0 ) + ( tcg1 - t77t ) ) * ELG; *tt2 = tcg2; } /* OK status. */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/tdbtcb.c0000644000113000011300000001567113027221063014601 0ustar bellsbells#include "sofa.h" int iauTdbtcb(double tdb1, double tdb2, double *tcb1, double *tcb2) /* ** - - - - - - - - - - ** i a u T d b t c b ** - - - - - - - - - - ** ** Time scale transformation: Barycentric Dynamical Time, TDB, to ** Barycentric Coordinate Time, TCB. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tdb1,tdb2 double TDB as a 2-part Julian Date ** ** Returned: ** tcb1,tcb2 double TCB as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tdb1+tdb2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tdb1 is the Julian ** Day Number and tdb2 is the fraction of a day. The returned ** tcb1,tcb2 follow suit. ** ** 2) The 2006 IAU General Assembly introduced a conventional linear ** transformation between TDB and TCB. This transformation ** compensates for the drift between TCB and terrestrial time TT, ** and keeps TDB approximately centered on TT. Because the ** relationship between TT and TCB depends on the adopted solar ** system ephemeris, the degree of alignment between TDB and TT over ** long intervals will vary according to which ephemeris is used. ** Former definitions of TDB attempted to avoid this problem by ** stipulating that TDB and TT should differ only by periodic ** effects. This is a good description of the nature of the ** relationship but eluded precise mathematical formulation. The ** conventional linear relationship adopted in 2006 sidestepped ** these difficulties whilst delivering a TDB that in practice was ** consistent with values before that date. ** ** 3) TDB is essentially the same as Teph, the time argument for the ** JPL solar system ephemerides. ** ** Reference: ** ** IAU 2006 Resolution B3 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* 1977 Jan 1 00:00:32.184 TT, as two-part JD */ static const double t77td = DJM0 + DJM77; static const double t77tf = TTMTAI/DAYSEC; /* TDB (days) at TAI 1977 Jan 1.0 */ static const double tdb0 = TDB0/DAYSEC; /* TDB to TCB rate */ static const double elbb = ELB/(1.0-ELB); double d, f; /* Result, preserving date format but safeguarding precision. */ if ( tdb1 > tdb2 ) { d = t77td - tdb1; f = tdb2 - tdb0; *tcb1 = tdb1; *tcb2 = f - ( d - ( f - t77tf ) ) * elbb; } else { d = t77td - tdb2; f = tdb1 - tdb0; *tcb1 = f + ( d - ( f - t77tf ) ) * elbb; *tcb2 = tdb2; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/tdbtt.c0000644000113000011300000001430513027221063014451 0ustar bellsbells#include "sofa.h" int iauTdbtt(double tdb1, double tdb2, double dtr, double *tt1, double *tt2 ) /* ** - - - - - - - - - ** i a u T d b t t ** - - - - - - - - - ** ** Time scale transformation: Barycentric Dynamical Time, TDB, to ** Terrestrial Time, TT. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tdb1,tdb2 double TDB as a 2-part Julian Date ** dtr double TDB-TT in seconds ** ** Returned: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tdb1+tdb2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tdb1 is the Julian ** Day Number and tdb2 is the fraction of a day. The returned ** tt1,tt2 follow suit. ** ** 2) The argument dtr represents the quasi-periodic component of the ** GR transformation between TT and TCB. It is dependent upon the ** adopted solar-system ephemeris, and can be obtained by numerical ** integration, by interrogating a precomputed time ephemeris or by ** evaluating a model such as that implemented in the SOFA function ** iauDtdb. The quantity is dominated by an annual term of 1.7 ms ** amplitude. ** ** 3) TDB is essentially the same as Teph, the time argument for the ** JPL solar system ephemerides. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** IAU 2006 Resolution 3 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. ** */ { double dtrd; /* Result, safeguarding precision. */ dtrd = dtr / DAYSEC; if ( tdb1 > tdb2 ) { *tt1 = tdb1; *tt2 = tdb2 - dtrd; } else { *tt1 = tdb1 - dtrd; *tt2 = tdb2; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/tf2a.c0000644000113000011300000001365613027221063014174 0ustar bellsbells#include "sofa.h" #include int iauTf2a(char s, int ihour, int imin, double sec, double *rad) /* ** - - - - - - - - ** i a u T f 2 a ** - - - - - - - - ** ** Convert hours, minutes, seconds to radians. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** s char sign: '-' = negative, otherwise positive ** ihour int hours ** imin int minutes ** sec double seconds ** ** Returned: ** rad double angle in radians ** ** Returned (function value): ** int status: 0 = OK ** 1 = ihour outside range 0-23 ** 2 = imin outside range 0-59 ** 3 = sec outside range 0-59.999... ** ** Notes: ** ** 1) The result is computed even if any of the range checks fail. ** ** 2) Negative ihour, imin and/or sec produce a warning status, but ** the absolute value is used in the conversion. ** ** 3) If there are multiple errors, the status value reflects only the ** first, the smallest taking precedence. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Compute the interval. */ *rad = ( s == '-' ? -1.0 : 1.0 ) * ( 60.0 * ( 60.0 * ( (double) abs(ihour) ) + ( (double) abs(imin) ) ) + fabs(sec) ) * DS2R; /* Validate arguments and return status. */ if ( ihour < 0 || ihour > 23 ) return 1; if ( imin < 0 || imin > 59 ) return 2; if ( sec < 0.0 || sec >= 60.0 ) return 3; return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/tf2d.c0000644000113000011300000001366213027221063014174 0ustar bellsbells#include "sofa.h" #include int iauTf2d(char s, int ihour, int imin, double sec, double *days) /* ** - - - - - - - - ** i a u T f 2 d ** - - - - - - - - ** ** Convert hours, minutes, seconds to days. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** s char sign: '-' = negative, otherwise positive ** ihour int hours ** imin int minutes ** sec double seconds ** ** Returned: ** days double interval in days ** ** Returned (function value): ** int status: 0 = OK ** 1 = ihour outside range 0-23 ** 2 = imin outside range 0-59 ** 3 = sec outside range 0-59.999... ** ** Notes: ** ** 1) The result is computed even if any of the range checks fail. ** ** 2) Negative ihour, imin and/or sec produce a warning status, but ** the absolute value is used in the conversion. ** ** 3) If there are multiple errors, the status value reflects only the ** first, the smallest taking precedence. ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Compute the interval. */ *days = ( s == '-' ? -1.0 : 1.0 ) * ( 60.0 * ( 60.0 * ( (double) abs(ihour) ) + ( (double) abs(imin) ) ) + fabs(sec) ) / DAYSEC; /* Validate arguments and return status. */ if ( ihour < 0 || ihour > 23 ) return 1; if ( imin < 0 || imin > 59 ) return 2; if ( sec < 0.0 || sec >= 60.0 ) return 3; return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/tr.c0000644000113000011300000001202013027221063013745 0ustar bellsbells#include "sofa.h" void iauTr(double r[3][3], double rt[3][3]) /* ** - - - - - - ** i a u T r ** - - - - - - ** ** Transpose an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix ** ** Returned: ** rt double[3][3] transpose ** ** Note: ** It is permissible for r and rt to be the same array. ** ** Called: ** iauCr copy r-matrix ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double wm[3][3]; int i, j; for (i = 0; i < 3; i++) { for (j = 0; j < 3; j++) { wm[i][j] = r[j][i]; } } iauCr(wm, rt); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/trxp.c0000644000113000011300000001221613027221063014324 0ustar bellsbells#include "sofa.h" void iauTrxp(double r[3][3], double p[3], double trp[3]) /* ** - - - - - - - - ** i a u T r x p ** - - - - - - - - ** ** Multiply a p-vector by the transpose of an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix ** p double[3] p-vector ** ** Returned: ** trp double[3] r * p ** ** Note: ** It is permissible for p and trp to be the same array. ** ** Called: ** iauTr transpose r-matrix ** iauRxp product of r-matrix and p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double tr[3][3]; /* Transpose of matrix r. */ iauTr(r, tr); /* Matrix tr * vector p -> vector trp. */ iauRxp(tr, p, trp); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/trxpv.c0000644000113000011300000001225313027221063014513 0ustar bellsbells#include "sofa.h" void iauTrxpv(double r[3][3], double pv[2][3], double trpv[2][3]) /* ** - - - - - - - - - ** i a u T r x p v ** - - - - - - - - - ** ** Multiply a pv-vector by the transpose of an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix ** pv double[2][3] pv-vector ** ** Returned: ** trpv double[2][3] r * pv ** ** Note: ** It is permissible for pv and trpv to be the same array. ** ** Called: ** iauTr transpose r-matrix ** iauRxpv product of r-matrix and pv-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double tr[3][3]; /* Transpose of matrix r. */ iauTr(r, tr); /* Matrix tr * vector pv -> vector trpv. */ iauRxpv(tr, pv, trpv); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/t_sofa_c.c0000644000113000011300000070417013027221063015113 0ustar bellsbells#include #include static int verbose = 0; /* ** - - - - - - - - - ** t _ s o f a _ c ** - - - - - - - - - ** ** Validate the SOFA C functions. ** ** Each SOFA function is at least called and a usually quite basic test ** is performed. Successful completion is signalled by a confirming ** message. Failure of a given function or group of functions results ** in error messages. ** ** All messages go to stdout. ** ** This revision: 2016 December 22 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ static void viv(int ival, int ivalok, const char *func, const char *test, int *status) /* ** - - - - ** v i v ** - - - - ** ** Validate an integer result. ** ** Internal function used by t_sofa_c program. ** ** Given: ** ival int value computed by function under test ** ivalok int correct value ** func char[] name of function under test ** test char[] name of individual test ** ** Given and returned: ** status int set to TRUE if test fails ** ** This revision: 2013 August 7 */ { if (ival != ivalok) { *status = 1; printf("%s failed: %s want %d got %d\n", func, test, ivalok, ival); } else if (verbose) { printf("%s passed: %s want %d got %d\n", func, test, ivalok, ival); } } static void vvd(double val, double valok, double dval, const char *func, const char *test, int *status) /* ** - - - - ** v v d ** - - - - ** ** Validate a double result. ** ** Internal function used by t_sofa_c program. ** ** Given: ** val double value computed by function under test ** valok double expected value ** dval double maximum allowable error ** func char[] name of function under test ** test char[] name of individual test ** ** Given and returned: ** status int set to TRUE if test fails ** ** This revision: 2016 April 21 */ { double a, f; /* absolute and fractional error */ a = val - valok; if (a != 0.0 && fabs(a) > fabs(dval)) { f = fabs(valok / a); *status = 1; printf("%s failed: %s want %.20g got %.20g (1/%.3g)\n", func, test, valok, val, f); } else if (verbose) { printf("%s passed: %s want %.20g got %.20g\n", func, test, valok, val); } } static void t_a2af(int *status) /* ** - - - - - - - ** t _ a 2 a f ** - - - - - - - ** ** Test iauA2af function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauA2af, viv ** ** This revision: 2013 August 7 */ { int idmsf[4]; char s; iauA2af(4, 2.345, &s, idmsf); viv(s, '+', "iauA2af", "s", status); viv(idmsf[0], 134, "iauA2af", "0", status); viv(idmsf[1], 21, "iauA2af", "1", status); viv(idmsf[2], 30, "iauA2af", "2", status); viv(idmsf[3], 9706, "iauA2af", "3", status); } static void t_a2tf(int *status) /* ** - - - - - - - ** t _ a 2 t f ** - - - - - - - ** ** Test iauA2tf function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauA2tf, viv ** ** This revision: 2013 August 7 */ { int ihmsf[4]; char s; iauA2tf(4, -3.01234, &s, ihmsf); viv((int)s, '-', "iauA2tf", "s", status); viv(ihmsf[0], 11, "iauA2tf", "0", status); viv(ihmsf[1], 30, "iauA2tf", "1", status); viv(ihmsf[2], 22, "iauA2tf", "2", status); viv(ihmsf[3], 6484, "iauA2tf", "3", status); } static void t_ab(int *status) /* ** - - - - - ** t _ a b ** - - - - - ** ** Test iauAb function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAb, vvd ** ** This revision: 2013 October 1 */ { double pnat[3], v[3], s, bm1, ppr[3]; pnat[0] = -0.76321968546737951; pnat[1] = -0.60869453983060384; pnat[2] = -0.21676408580639883; v[0] = 2.1044018893653786e-5; v[1] = -8.9108923304429319e-5; v[2] = -3.8633714797716569e-5; s = 0.99980921395708788; bm1 = 0.99999999506209258; iauAb(pnat, v, s, bm1, ppr); vvd(ppr[0], -0.7631631094219556269, 1e-12, "iauAb", "1", status); vvd(ppr[1], -0.6087553082505590832, 1e-12, "iauAb", "2", status); vvd(ppr[2], -0.2167926269368471279, 1e-12, "iauAb", "3", status); } static void t_af2a(int *status) /* ** - - - - - - - ** t _ a f 2 a ** - - - - - - - ** ** Test iauAf2a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAf2a, viv ** ** This revision: 2013 August 7 */ { double a; int j; j = iauAf2a('-', 45, 13, 27.2, &a); vvd(a, -0.7893115794313644842, 1e-12, "iauAf2a", "a", status); viv(j, 0, "iauAf2a", "j", status); } static void t_anp(int *status) /* ** - - - - - - ** t _ a n p ** - - - - - - ** ** Test iauAnp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAnp, vvd ** ** This revision: 2013 August 7 */ { vvd(iauAnp(-0.1), 6.183185307179586477, 1e-12, "iauAnp", "", status); } static void t_anpm(int *status) /* ** - - - - - - - ** t _ a n p m ** - - - - - - - ** ** Test iauAnpm function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAnpm, vvd ** ** This revision: 2013 August 7 */ { vvd(iauAnpm(-4.0), 2.283185307179586477, 1e-12, "iauAnpm", "", status); } static void t_apcg(int *status) /* ** - - - - - - - ** t _ a p c g ** - - - - - - - ** ** Test iauApcg function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApcg, vvd ** ** This revision: 2013 October 3 */ { double date1, date2, ebpv[2][3], ehp[3]; iauASTROM astrom; date1 = 2456165.5; date2 = 0.401182685; ebpv[0][0] = 0.901310875; ebpv[0][1] = -0.417402664; ebpv[0][2] = -0.180982288; ebpv[1][0] = 0.00742727954; ebpv[1][1] = 0.0140507459; ebpv[1][2] = 0.00609045792; ehp[0] = 0.903358544; ehp[1] = -0.415395237; ehp[2] = -0.180084014; iauApcg(date1, date2, ebpv, ehp, &astrom); vvd(astrom.pmt, 12.65133794027378508, 1e-11, "iauApcg", "pmt", status); vvd(astrom.eb[0], 0.901310875, 1e-12, "iauApcg", "eb(1)", status); vvd(astrom.eb[1], -0.417402664, 1e-12, "iauApcg", "eb(2)", status); vvd(astrom.eb[2], -0.180982288, 1e-12, "iauApcg", "eb(3)", status); vvd(astrom.eh[0], 0.8940025429324143045, 1e-12, "iauApcg", "eh(1)", status); vvd(astrom.eh[1], -0.4110930268679817955, 1e-12, "iauApcg", "eh(2)", status); vvd(astrom.eh[2], -0.1782189004872870264, 1e-12, "iauApcg", "eh(3)", status); vvd(astrom.em, 1.010465295811013146, 1e-12, "iauApcg", "em", status); vvd(astrom.v[0], 0.4289638897813379954e-4, 1e-16, "iauApcg", "v(1_", status); vvd(astrom.v[1], 0.8115034021720941898e-4, 1e-16, "iauApcg", "v(2)", status); vvd(astrom.v[2], 0.3517555123437237778e-4, 1e-16, "iauApcg", "v(3)", status); vvd(astrom.bm1, 0.9999999951686013336, 1e-12, "iauApcg", "bm1", status); vvd(astrom.bpn[0][0], 1.0, 0.0, "iauApcg", "bpn(1,1)", status); vvd(astrom.bpn[1][0], 0.0, 0.0, "iauApcg", "bpn(2,1)", status); vvd(astrom.bpn[2][0], 0.0, 0.0, "iauApcg", "bpn(3,1)", status); vvd(astrom.bpn[0][1], 0.0, 0.0, "iauApcg", "bpn(1,2)", status); vvd(astrom.bpn[1][1], 1.0, 0.0, "iauApcg", "bpn(2,2)", status); vvd(astrom.bpn[2][1], 0.0, 0.0, "iauApcg", "bpn(3,2)", status); vvd(astrom.bpn[0][2], 0.0, 0.0, "iauApcg", "bpn(1,3)", status); vvd(astrom.bpn[1][2], 0.0, 0.0, "iauApcg", "bpn(2,3)", status); vvd(astrom.bpn[2][2], 1.0, 0.0, "iauApcg", "bpn(3,3)", status); } static void t_apcg13(int *status) /* ** - - - - - - - - - ** t _ a p c g 1 3 ** - - - - - - - - - ** ** Test iauApcg13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApcg13, vvd ** ** This revision: 2013 October 3 */ { double date1, date2; iauASTROM astrom; date1 = 2456165.5; date2 = 0.401182685; iauApcg13(date1, date2, &astrom); vvd(astrom.pmt, 12.65133794027378508, 1e-11, "iauApcg13", "pmt", status); vvd(astrom.eb[0], 0.9013108747340644755, 1e-12, "iauApcg13", "eb(1)", status); vvd(astrom.eb[1], -0.4174026640406119957, 1e-12, "iauApcg13", "eb(2)", status); vvd(astrom.eb[2], -0.1809822877867817771, 1e-12, "iauApcg13", "eb(3)", status); vvd(astrom.eh[0], 0.8940025429255499549, 1e-12, "iauApcg13", "eh(1)", status); vvd(astrom.eh[1], -0.4110930268331896318, 1e-12, "iauApcg13", "eh(2)", status); vvd(astrom.eh[2], -0.1782189006019749850, 1e-12, "iauApcg13", "eh(3)", status); vvd(astrom.em, 1.010465295964664178, 1e-12, "iauApcg13", "em", status); vvd(astrom.v[0], 0.4289638897157027528e-4, 1e-16, "iauApcg13", "v(1)", status); vvd(astrom.v[1], 0.8115034002544663526e-4, 1e-16, "iauApcg13", "v(2)", status); vvd(astrom.v[2], 0.3517555122593144633e-4, 1e-16, "iauApcg13", "v(3)", status); vvd(astrom.bm1, 0.9999999951686013498, 1e-12, "iauApcg13", "bm1", status); vvd(astrom.bpn[0][0], 1.0, 0.0, "iauApcg13", "bpn(1,1)", status); vvd(astrom.bpn[1][0], 0.0, 0.0, "iauApcg13", "bpn(2,1)", status); vvd(astrom.bpn[2][0], 0.0, 0.0, "iauApcg13", "bpn(3,1)", status); vvd(astrom.bpn[0][1], 0.0, 0.0, "iauApcg13", "bpn(1,2)", status); vvd(astrom.bpn[1][1], 1.0, 0.0, "iauApcg13", "bpn(2,2)", status); vvd(astrom.bpn[2][1], 0.0, 0.0, "iauApcg13", "bpn(3,2)", status); vvd(astrom.bpn[0][2], 0.0, 0.0, "iauApcg13", "bpn(1,3)", status); vvd(astrom.bpn[1][2], 0.0, 0.0, "iauApcg13", "bpn(2,3)", status); vvd(astrom.bpn[2][2], 1.0, 0.0, "iauApcg13", "bpn(3,3)", status); } static void t_apci(int *status) /* ** - - - - - - - ** t _ a p c i ** - - - - - - - ** ** Test iauApci function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApci, vvd ** ** This revision: 2013 October 3 */ { double date1, date2, ebpv[2][3], ehp[3], x, y, s; iauASTROM astrom; date1 = 2456165.5; date2 = 0.401182685; ebpv[0][0] = 0.901310875; ebpv[0][1] = -0.417402664; ebpv[0][2] = -0.180982288; ebpv[1][0] = 0.00742727954; ebpv[1][1] = 0.0140507459; ebpv[1][2] = 0.00609045792; ehp[0] = 0.903358544; ehp[1] = -0.415395237; ehp[2] = -0.180084014; x = 0.0013122272; y = -2.92808623e-5; s = 3.05749468e-8; iauApci(date1, date2, ebpv, ehp, x, y, s, &astrom); vvd(astrom.pmt, 12.65133794027378508, 1e-11, "iauApci", "pmt", status); vvd(astrom.eb[0], 0.901310875, 1e-12, "iauApci", "eb(1)", status); vvd(astrom.eb[1], -0.417402664, 1e-12, "iauApci", "eb(2)", status); vvd(astrom.eb[2], -0.180982288, 1e-12, "iauApci", "eb(3)", status); vvd(astrom.eh[0], 0.8940025429324143045, 1e-12, "iauApci", "eh(1)", status); vvd(astrom.eh[1], -0.4110930268679817955, 1e-12, "iauApci", "eh(2)", status); vvd(astrom.eh[2], -0.1782189004872870264, 1e-12, "iauApci", "eh(3)", status); vvd(astrom.em, 1.010465295811013146, 1e-12, "iauApci", "em", status); vvd(astrom.v[0], 0.4289638897813379954e-4, 1e-16, "iauApci", "v(1)", status); vvd(astrom.v[1], 0.8115034021720941898e-4, 1e-16, "iauApci", "v(2)", status); vvd(astrom.v[2], 0.3517555123437237778e-4, 1e-16, "iauApci", "v(3)", status); vvd(astrom.bm1, 0.9999999951686013336, 1e-12, "iauApci", "bm1", status); vvd(astrom.bpn[0][0], 0.9999991390295159156, 1e-12, "iauApci", "bpn(1,1)", status); vvd(astrom.bpn[1][0], 0.4978650072505016932e-7, 1e-12, "iauApci", "bpn(2,1)", status); vvd(astrom.bpn[2][0], 0.1312227200000000000e-2, 1e-12, "iauApci", "bpn(3,1)", status); vvd(astrom.bpn[0][1], -0.1136336653771609630e-7, 1e-12, "iauApci", "bpn(1,2)", status); vvd(astrom.bpn[1][1], 0.9999999995713154868, 1e-12, "iauApci", "bpn(2,2)", status); vvd(astrom.bpn[2][1], -0.2928086230000000000e-4, 1e-12, "iauApci", "bpn(3,2)", status); vvd(astrom.bpn[0][2], -0.1312227200895260194e-2, 1e-12, "iauApci", "bpn(1,3)", status); vvd(astrom.bpn[1][2], 0.2928082217872315680e-4, 1e-12, "iauApci", "bpn(2,3)", status); vvd(astrom.bpn[2][2], 0.9999991386008323373, 1e-12, "iauApci", "bpn(3,3)", status); } static void t_apci13(int *status) /* ** - - - - - - - - - ** t _ a p c i 1 3 ** - - - - - - - - - ** ** Test iauApci13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApci13, vvd ** ** This revision: 2013 October 3 */ { double date1, date2, eo; iauASTROM astrom; date1 = 2456165.5; date2 = 0.401182685; iauApci13(date1, date2, &astrom, &eo); vvd(astrom.pmt, 12.65133794027378508, 1e-11, "iauApci13", "pmt", status); vvd(astrom.eb[0], 0.9013108747340644755, 1e-12, "iauApci13", "eb(1)", status); vvd(astrom.eb[1], -0.4174026640406119957, 1e-12, "iauApci13", "eb(2)", status); vvd(astrom.eb[2], -0.1809822877867817771, 1e-12, "iauApci13", "eb(3)", status); vvd(astrom.eh[0], 0.8940025429255499549, 1e-12, "iauApci13", "eh(1)", status); vvd(astrom.eh[1], -0.4110930268331896318, 1e-12, "iauApci13", "eh(2)", status); vvd(astrom.eh[2], -0.1782189006019749850, 1e-12, "iauApci13", "eh(3)", status); vvd(astrom.em, 1.010465295964664178, 1e-12, "iauApci13", "em", status); vvd(astrom.v[0], 0.4289638897157027528e-4, 1e-16, "iauApci13", "v(1)", status); vvd(astrom.v[1], 0.8115034002544663526e-4, 1e-16, "iauApci13", "v(2)", status); vvd(astrom.v[2], 0.3517555122593144633e-4, 1e-16, "iauApci13", "v(3)", status); vvd(astrom.bm1, 0.9999999951686013498, 1e-12, "iauApci13", "bm1", status); vvd(astrom.bpn[0][0], 0.9999992060376761710, 1e-12, "iauApci13", "bpn(1,1)", status); vvd(astrom.bpn[1][0], 0.4124244860106037157e-7, 1e-12, "iauApci13", "bpn(2,1)", status); vvd(astrom.bpn[2][0], 0.1260128571051709670e-2, 1e-12, "iauApci13", "bpn(3,1)", status); vvd(astrom.bpn[0][1], -0.1282291987222130690e-7, 1e-12, "iauApci13", "bpn(1,2)", status); vvd(astrom.bpn[1][1], 0.9999999997456835325, 1e-12, "iauApci13", "bpn(2,2)", status); vvd(astrom.bpn[2][1], -0.2255288829420524935e-4, 1e-12, "iauApci13", "bpn(3,2)", status); vvd(astrom.bpn[0][2], -0.1260128571661374559e-2, 1e-12, "iauApci13", "bpn(1,3)", status); vvd(astrom.bpn[1][2], 0.2255285422953395494e-4, 1e-12, "iauApci13", "bpn(2,3)", status); vvd(astrom.bpn[2][2], 0.9999992057833604343, 1e-12, "iauApci13", "bpn(3,3)", status); vvd(eo, -0.2900618712657375647e-2, 1e-12, "iauApci13", "eo", status); } static void t_apco(int *status) /* ** - - - - - - - ** t _ a p c o ** - - - - - - - ** ** Test iauApco function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApco, vvd ** ** This revision: 2013 October 3 */ { double date1, date2, ebpv[2][3], ehp[3], x, y, s, theta, elong, phi, hm, xp, yp, sp, refa, refb; iauASTROM astrom; date1 = 2456384.5; date2 = 0.970031644; ebpv[0][0] = -0.974170438; ebpv[0][1] = -0.211520082; ebpv[0][2] = -0.0917583024; ebpv[1][0] = 0.00364365824; ebpv[1][1] = -0.0154287319; ebpv[1][2] = -0.00668922024; ehp[0] = -0.973458265; ehp[1] = -0.209215307; ehp[2] = -0.0906996477; x = 0.0013122272; y = -2.92808623e-5; s = 3.05749468e-8; theta = 3.14540971; elong = -0.527800806; phi = -1.2345856; hm = 2738.0; xp = 2.47230737e-7; yp = 1.82640464e-6; sp = -3.01974337e-11; refa = 0.000201418779; refb = -2.36140831e-7; iauApco(date1, date2, ebpv, ehp, x, y, s, theta, elong, phi, hm, xp, yp, sp, refa, refb, &astrom); vvd(astrom.pmt, 13.25248468622587269, 1e-11, "iauApco", "pmt", status); vvd(astrom.eb[0], -0.9741827110630897003, 1e-12, "iauApco", "eb(1)", status); vvd(astrom.eb[1], -0.2115130190135014340, 1e-12, "iauApco", "eb(2)", status); vvd(astrom.eb[2], -0.09179840186968295686, 1e-12, "iauApco", "eb(3)", status); vvd(astrom.eh[0], -0.9736425571689670428, 1e-12, "iauApco", "eh(1)", status); vvd(astrom.eh[1], -0.2092452125848862201, 1e-12, "iauApco", "eh(2)", status); vvd(astrom.eh[2], -0.09075578152261439954, 1e-12, "iauApco", "eh(3)", status); vvd(astrom.em, 0.9998233241710617934, 1e-12, "iauApco", "em", status); vvd(astrom.v[0], 0.2078704985147609823e-4, 1e-16, "iauApco", "v(1)", status); vvd(astrom.v[1], -0.8955360074407552709e-4, 1e-16, "iauApco", "v(2)", status); vvd(astrom.v[2], -0.3863338980073114703e-4, 1e-16, "iauApco", "v(3)", status); vvd(astrom.bm1, 0.9999999950277561600, 1e-12, "iauApco", "bm1", status); vvd(astrom.bpn[0][0], 0.9999991390295159156, 1e-12, "iauApco", "bpn(1,1)", status); vvd(astrom.bpn[1][0], 0.4978650072505016932e-7, 1e-12, "iauApco", "bpn(2,1)", status); vvd(astrom.bpn[2][0], 0.1312227200000000000e-2, 1e-12, "iauApco", "bpn(3,1)", status); vvd(astrom.bpn[0][1], -0.1136336653771609630e-7, 1e-12, "iauApco", "bpn(1,2)", status); vvd(astrom.bpn[1][1], 0.9999999995713154868, 1e-12, "iauApco", "bpn(2,2)", status); vvd(astrom.bpn[2][1], -0.2928086230000000000e-4, 1e-12, "iauApco", "bpn(3,2)", status); vvd(astrom.bpn[0][2], -0.1312227200895260194e-2, 1e-12, "iauApco", "bpn(1,3)", status); vvd(astrom.bpn[1][2], 0.2928082217872315680e-4, 1e-12, "iauApco", "bpn(2,3)", status); vvd(astrom.bpn[2][2], 0.9999991386008323373, 1e-12, "iauApco", "bpn(3,3)", status); vvd(astrom.along, -0.5278008060301974337, 1e-12, "iauApco", "along", status); vvd(astrom.xpl, 0.1133427418174939329e-5, 1e-17, "iauApco", "xpl", status); vvd(astrom.ypl, 0.1453347595745898629e-5, 1e-17, "iauApco", "ypl", status); vvd(astrom.sphi, -0.9440115679003211329, 1e-12, "iauApco", "sphi", status); vvd(astrom.cphi, 0.3299123514971474711, 1e-12, "iauApco", "cphi", status); vvd(astrom.diurab, 0, 0, "iauApco", "diurab", status); vvd(astrom.eral, 2.617608903969802566, 1e-12, "iauApco", "eral", status); vvd(astrom.refa, 0.2014187790000000000e-3, 1e-15, "iauApco", "refa", status); vvd(astrom.refb, -0.2361408310000000000e-6, 1e-18, "iauApco", "refb", status); } static void t_apco13(int *status) /* ** - - - - - - - - - ** t _ a p c o 1 3 ** - - - - - - - - - ** ** Test iauApco13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApco13, vvd, viv ** ** This revision: 2013 October 4 */ { double utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, eo; iauASTROM astrom; int j; utc1 = 2456384.5; utc2 = 0.969254051; dut1 = 0.1550675; elong = -0.527800806; phi = -1.2345856; hm = 2738.0; xp = 2.47230737e-7; yp = 1.82640464e-6; phpa = 731.0; tc = 12.8; rh = 0.59; wl = 0.55; j = iauApco13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom, &eo); vvd(astrom.pmt, 13.25248468622475727, 1e-11, "iauApco13", "pmt", status); vvd(astrom.eb[0], -0.9741827107321449445, 1e-12, "iauApco13", "eb(1)", status); vvd(astrom.eb[1], -0.2115130190489386190, 1e-12, "iauApco13", "eb(2)", status); vvd(astrom.eb[2], -0.09179840189515518726, 1e-12, "iauApco13", "eb(3)", status); vvd(astrom.eh[0], -0.9736425572586866640, 1e-12, "iauApco13", "eh(1)", status); vvd(astrom.eh[1], -0.2092452121602867431, 1e-12, "iauApco13", "eh(2)", status); vvd(astrom.eh[2], -0.09075578153903832650, 1e-12, "iauApco13", "eh(3)", status); vvd(astrom.em, 0.9998233240914558422, 1e-12, "iauApco13", "em", status); vvd(astrom.v[0], 0.2078704986751370303e-4, 1e-16, "iauApco13", "v(1)", status); vvd(astrom.v[1], -0.8955360100494469232e-4, 1e-16, "iauApco13", "v(2)", status); vvd(astrom.v[2], -0.3863338978840051024e-4, 1e-16, "iauApco13", "v(3)", status); vvd(astrom.bm1, 0.9999999950277561368, 1e-12, "iauApco13", "bm1", status); vvd(astrom.bpn[0][0], 0.9999991390295147999, 1e-12, "iauApco13", "bpn(1,1)", status); vvd(astrom.bpn[1][0], 0.4978650075315529277e-7, 1e-12, "iauApco13", "bpn(2,1)", status); vvd(astrom.bpn[2][0], 0.001312227200850293372, 1e-12, "iauApco13", "bpn(3,1)", status); vvd(astrom.bpn[0][1], -0.1136336652812486604e-7, 1e-12, "iauApco13", "bpn(1,2)", status); vvd(astrom.bpn[1][1], 0.9999999995713154865, 1e-12, "iauApco13", "bpn(2,2)", status); vvd(astrom.bpn[2][1], -0.2928086230975367296e-4, 1e-12, "iauApco13", "bpn(3,2)", status); vvd(astrom.bpn[0][2], -0.001312227201745553566, 1e-12, "iauApco13", "bpn(1,3)", status); vvd(astrom.bpn[1][2], 0.2928082218847679162e-4, 1e-12, "iauApco13", "bpn(2,3)", status); vvd(astrom.bpn[2][2], 0.9999991386008312212, 1e-12, "iauApco13", "bpn(3,3)", status); vvd(astrom.along, -0.5278008060301974337, 1e-12, "iauApco13", "along", status); vvd(astrom.xpl, 0.1133427418174939329e-5, 1e-17, "iauApco13", "xpl", status); vvd(astrom.ypl, 0.1453347595745898629e-5, 1e-17, "iauApco13", "ypl", status); vvd(astrom.sphi, -0.9440115679003211329, 1e-12, "iauApco13", "sphi", status); vvd(astrom.cphi, 0.3299123514971474711, 1e-12, "iauApco13", "cphi", status); vvd(astrom.diurab, 0, 0, "iauApco13", "diurab", status); vvd(astrom.eral, 2.617608909189066140, 1e-12, "iauApco13", "eral", status); vvd(astrom.refa, 0.2014187785940396921e-3, 1e-15, "iauApco13", "refa", status); vvd(astrom.refb, -0.2361408314943696227e-6, 1e-18, "iauApco13", "refb", status); vvd(eo, -0.003020548354802412839, 1e-14, "iauApco13", "eo", status); viv(j, 0, "iauApco13", "j", status); } static void t_apcs(int *status) /* ** - - - - - - - ** t _ a p c s ** - - - - - - - ** ** Test iauApcs function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApcs, vvd ** ** This revision: 2013 October 3 */ { double date1, date2, pv[2][3], ebpv[2][3], ehp[3]; iauASTROM astrom; date1 = 2456384.5; date2 = 0.970031644; pv[0][0] = -1836024.09; pv[0][1] = 1056607.72; pv[0][2] = -5998795.26; pv[1][0] = -77.0361767; pv[1][1] = -133.310856; pv[1][2] = 0.0971855934; ebpv[0][0] = -0.974170438; ebpv[0][1] = -0.211520082; ebpv[0][2] = -0.0917583024; ebpv[1][0] = 0.00364365824; ebpv[1][1] = -0.0154287319; ebpv[1][2] = -0.00668922024; ehp[0] = -0.973458265; ehp[1] = -0.209215307; ehp[2] = -0.0906996477; iauApcs(date1, date2, pv, ebpv, ehp, &astrom); vvd(astrom.pmt, 13.25248468622587269, 1e-11, "iauApcs", "pmt", status); vvd(astrom.eb[0], -0.9741827110630456169, 1e-12, "iauApcs", "eb(1)", status); vvd(astrom.eb[1], -0.2115130190136085494, 1e-12, "iauApcs", "eb(2)", status); vvd(astrom.eb[2], -0.09179840186973175487, 1e-12, "iauApcs", "eb(3)", status); vvd(astrom.eh[0], -0.9736425571689386099, 1e-12, "iauApcs", "eh(1)", status); vvd(astrom.eh[1], -0.2092452125849967195, 1e-12, "iauApcs", "eh(2)", status); vvd(astrom.eh[2], -0.09075578152266466572, 1e-12, "iauApcs", "eh(3)", status); vvd(astrom.em, 0.9998233241710457140, 1e-12, "iauApcs", "em", status); vvd(astrom.v[0], 0.2078704985513566571e-4, 1e-16, "iauApcs", "v(1)", status); vvd(astrom.v[1], -0.8955360074245006073e-4, 1e-16, "iauApcs", "v(2)", status); vvd(astrom.v[2], -0.3863338980073572719e-4, 1e-16, "iauApcs", "v(3)", status); vvd(astrom.bm1, 0.9999999950277561601, 1e-12, "iauApcs", "bm1", status); vvd(astrom.bpn[0][0], 1, 0, "iauApcs", "bpn(1,1)", status); vvd(astrom.bpn[1][0], 0, 0, "iauApcs", "bpn(2,1)", status); vvd(astrom.bpn[2][0], 0, 0, "iauApcs", "bpn(3,1)", status); vvd(astrom.bpn[0][1], 0, 0, "iauApcs", "bpn(1,2)", status); vvd(astrom.bpn[1][1], 1, 0, "iauApcs", "bpn(2,2)", status); vvd(astrom.bpn[2][1], 0, 0, "iauApcs", "bpn(3,2)", status); vvd(astrom.bpn[0][2], 0, 0, "iauApcs", "bpn(1,3)", status); vvd(astrom.bpn[1][2], 0, 0, "iauApcs", "bpn(2,3)", status); vvd(astrom.bpn[2][2], 1, 0, "iauApcs", "bpn(3,3)", status); } static void t_apcs13(int *status) /* ** - - - - - - - - - ** t _ a p c s 1 3 ** - - - - - - - - - ** ** Test iauApcs13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApcs13, vvd ** ** This revision: 2013 October 3 */ { double date1, date2, pv[2][3]; iauASTROM astrom; date1 = 2456165.5; date2 = 0.401182685; pv[0][0] = -6241497.16; pv[0][1] = 401346.896; pv[0][2] = -1251136.04; pv[1][0] = -29.264597; pv[1][1] = -455.021831; pv[1][2] = 0.0266151194; iauApcs13(date1, date2, pv, &astrom); vvd(astrom.pmt, 12.65133794027378508, 1e-11, "iauApcs13", "pmt", status); vvd(astrom.eb[0], 0.9012691529023298391, 1e-12, "iauApcs13", "eb(1)", status); vvd(astrom.eb[1], -0.4173999812023068781, 1e-12, "iauApcs13", "eb(2)", status); vvd(astrom.eb[2], -0.1809906511146821008, 1e-12, "iauApcs13", "eb(3)", status); vvd(astrom.eh[0], 0.8939939101759726824, 1e-12, "iauApcs13", "eh(1)", status); vvd(astrom.eh[1], -0.4111053891734599955, 1e-12, "iauApcs13", "eh(2)", status); vvd(astrom.eh[2], -0.1782336880637689334, 1e-12, "iauApcs13", "eh(3)", status); vvd(astrom.em, 1.010428384373318379, 1e-12, "iauApcs13", "em", status); vvd(astrom.v[0], 0.4279877278327626511e-4, 1e-16, "iauApcs13", "v(1)", status); vvd(astrom.v[1], 0.7963255057040027770e-4, 1e-16, "iauApcs13", "v(2)", status); vvd(astrom.v[2], 0.3517564000441374759e-4, 1e-16, "iauApcs13", "v(3)", status); vvd(astrom.bm1, 0.9999999952947981330, 1e-12, "iauApcs13", "bm1", status); vvd(astrom.bpn[0][0], 1, 0, "iauApcs13", "bpn(1,1)", status); vvd(astrom.bpn[1][0], 0, 0, "iauApcs13", "bpn(2,1)", status); vvd(astrom.bpn[2][0], 0, 0, "iauApcs13", "bpn(3,1)", status); vvd(astrom.bpn[0][1], 0, 0, "iauApcs13", "bpn(1,2)", status); vvd(astrom.bpn[1][1], 1, 0, "iauApcs13", "bpn(2,2)", status); vvd(astrom.bpn[2][1], 0, 0, "iauApcs13", "bpn(3,2)", status); vvd(astrom.bpn[0][2], 0, 0, "iauApcs13", "bpn(1,3)", status); vvd(astrom.bpn[1][2], 0, 0, "iauApcs13", "bpn(2,3)", status); vvd(astrom.bpn[2][2], 1, 0, "iauApcs13", "bpn(3,3)", status); } static void t_aper(int *status) /* ** - - - - - - - ** t _ a p e r ** - - - - - - - * ** Test iauAper function. * ** Returned: ** status int FALSE = success, TRUE = fail * ** Called: iauAper, vvd * ** This revision: 2013 October 3 */ { double theta; iauASTROM astrom; astrom.along = 1.234; theta = 5.678; iauAper(theta, &astrom); vvd(astrom.eral, 6.912000000000000000, 1e-12, "iauAper", "pmt", status); } static void t_aper13(int *status) /* ** - - - - - - - - - ** t _ a p e r 1 3 ** - - - - - - - - - ** ** Test iauAper13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAper13, vvd ** ** This revision: 2013 October 3 */ { double ut11, ut12; iauASTROM astrom; astrom.along = 1.234; ut11 = 2456165.5; ut12 = 0.401182685; iauAper13(ut11, ut12, &astrom); vvd(astrom.eral, 3.316236661789694933, 1e-12, "iauAper13", "pmt", status); } static void t_apio(int *status) /* ** - - - - - - - ** t _ a p i o ** - - - - - - - ** ** Test iauApio function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApio, vvd ** ** This revision: 2013 October 3 */ { double sp, theta, elong, phi, hm, xp, yp, refa, refb; iauASTROM astrom; sp = -3.01974337e-11; theta = 3.14540971; elong = -0.527800806; phi = -1.2345856; hm = 2738.0; xp = 2.47230737e-7; yp = 1.82640464e-6; refa = 0.000201418779; refb = -2.36140831e-7; iauApio(sp, theta, elong, phi, hm, xp, yp, refa, refb, &astrom); vvd(astrom.along, -0.5278008060301974337, 1e-12, "iauApio", "along", status); vvd(astrom.xpl, 0.1133427418174939329e-5, 1e-17, "iauApio", "xpl", status); vvd(astrom.ypl, 0.1453347595745898629e-5, 1e-17, "iauApio", "ypl", status); vvd(astrom.sphi, -0.9440115679003211329, 1e-12, "iauApio", "sphi", status); vvd(astrom.cphi, 0.3299123514971474711, 1e-12, "iauApio", "cphi", status); vvd(astrom.diurab, 0.5135843661699913529e-6, 1e-12, "iauApio", "diurab", status); vvd(astrom.eral, 2.617608903969802566, 1e-12, "iauApio", "eral", status); vvd(astrom.refa, 0.2014187790000000000e-3, 1e-15, "iauApio", "refa", status); vvd(astrom.refb, -0.2361408310000000000e-6, 1e-18, "iauApio", "refb", status); } static void t_apio13(int *status) /* ** - - - - - - - - - ** t _ a p i o 1 3 ** - - - - - - - - - ** ** Test iauApio13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApio13, vvd, viv ** ** This revision: 2013 October 4 */ { double utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl; int j; iauASTROM astrom; utc1 = 2456384.5; utc2 = 0.969254051; dut1 = 0.1550675; elong = -0.527800806; phi = -1.2345856; hm = 2738.0; xp = 2.47230737e-7; yp = 1.82640464e-6; phpa = 731.0; tc = 12.8; rh = 0.59; wl = 0.55; j = iauApio13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom); vvd(astrom.along, -0.5278008060301974337, 1e-12, "iauApio13", "along", status); vvd(astrom.xpl, 0.1133427418174939329e-5, 1e-17, "iauApio13", "xpl", status); vvd(astrom.ypl, 0.1453347595745898629e-5, 1e-17, "iauApio13", "ypl", status); vvd(astrom.sphi, -0.9440115679003211329, 1e-12, "iauApio13", "sphi", status); vvd(astrom.cphi, 0.3299123514971474711, 1e-12, "iauApio13", "cphi", status); vvd(astrom.diurab, 0.5135843661699913529e-6, 1e-12, "iauApio13", "diurab", status); vvd(astrom.eral, 2.617608909189066140, 1e-12, "iauApio13", "eral", status); vvd(astrom.refa, 0.2014187785940396921e-3, 1e-15, "iauApio13", "refa", status); vvd(astrom.refb, -0.2361408314943696227e-6, 1e-18, "iauApio13", "refb", status); viv(j, 0, "iauApio13", "j", status); } static void t_atci13(int *status) /* ** - - - - - - - - - ** t _ a t c i 1 3 ** - - - - - - - - - ** ** Test iauAtci13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAtci13, vvd ** ** This revision: 2013 October 3 */ { double rc, dc, pr, pd, px, rv, date1, date2, ri, di, eo; rc = 2.71; dc = 0.174; pr = 1e-5; pd = 5e-6; px = 0.1; rv = 55.0; date1 = 2456165.5; date2 = 0.401182685; iauAtci13(rc, dc, pr, pd, px, rv, date1, date2, &ri, &di, &eo); vvd(ri, 2.710121572969038991, 1e-12, "iauAtci13", "ri", status); vvd(di, 0.1729371367218230438, 1e-12, "iauAtci13", "di", status); vvd(eo, -0.002900618712657375647, 1e-14, "iauAtci13", "eo", status); } static void t_atciq(int *status) /* ** - - - - - - - - ** t _ a t c i q ** - - - - - - - - ** ** Test iauAtciq function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApci13, iauAtciq, vvd ** ** This revision: 2013 October 3 */ { double date1, date2, eo, rc, dc, pr, pd, px, rv, ri, di; iauASTROM astrom; date1 = 2456165.5; date2 = 0.401182685; iauApci13(date1, date2, &astrom, &eo); rc = 2.71; dc = 0.174; pr = 1e-5; pd = 5e-6; px = 0.1; rv = 55.0; iauAtciq(rc, dc, pr, pd, px, rv, &astrom, &ri, &di); vvd(ri, 2.710121572969038991, 1e-12, "iauAtciq", "ri", status); vvd(di, 0.1729371367218230438, 1e-12, "iauAtciq", "di", status); } static void t_atciqn(int *status) /* ** - - - - - - - - - ** t _ a t c i q n ** - - - - - - - - - ** ** Test iauAtciqn function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApci13, iauAtciqn, vvd ** ** This revision: 2013 October 3 */ { iauLDBODY b[3]; double date1, date2, eo, rc, dc, pr, pd, px, rv, ri, di; iauASTROM astrom; date1 = 2456165.5; date2 = 0.401182685; iauApci13(date1, date2, &astrom, &eo); rc = 2.71; dc = 0.174; pr = 1e-5; pd = 5e-6; px = 0.1; rv = 55.0; b[0].bm = 0.00028574; b[0].dl = 3e-10; b[0].pv[0][0] = -7.81014427; b[0].pv[0][1] = -5.60956681; b[0].pv[0][2] = -1.98079819; b[0].pv[1][0] = 0.0030723249; b[0].pv[1][1] = -0.00406995477; b[0].pv[1][2] = -0.00181335842; b[1].bm = 0.00095435; b[1].dl = 3e-9; b[1].pv[0][0] = 0.738098796; b[1].pv[0][1] = 4.63658692; b[1].pv[0][2] = 1.9693136; b[1].pv[1][0] = -0.00755816922; b[1].pv[1][1] = 0.00126913722; b[1].pv[1][2] = 0.000727999001; b[2].bm = 1.0; b[2].dl = 6e-6; b[2].pv[0][0] = -0.000712174377; b[2].pv[0][1] = -0.00230478303; b[2].pv[0][2] = -0.00105865966; b[2].pv[1][0] = 6.29235213e-6; b[2].pv[1][1] = -3.30888387e-7; b[2].pv[1][2] = -2.96486623e-7; iauAtciqn ( rc, dc, pr, pd, px, rv, &astrom, 3, b, &ri, &di); vvd(ri, 2.710122008105325582, 1e-12, "iauAtciqn", "ri", status); vvd(di, 0.1729371916491459122, 1e-12, "iauAtciqn", "di", status); } static void t_atciqz(int *status) /* ** - - - - - - - - - ** t _ a t c i q z ** - - - - - - - - - ** ** Test iauAtciqz function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApci13, iauAtciqz, vvd ** ** This revision: 2013 October 3 */ { double date1, date2, eo, rc, dc, ri, di; iauASTROM astrom; date1 = 2456165.5; date2 = 0.401182685; iauApci13(date1, date2, &astrom, &eo); rc = 2.71; dc = 0.174; iauAtciqz(rc, dc, &astrom, &ri, &di); vvd(ri, 2.709994899247599271, 1e-12, "iauAtciqz", "ri", status); vvd(di, 0.1728740720983623469, 1e-12, "iauAtciqz", "di", status); } static void t_atco13(int *status) /* ** - - - - - - - - - ** t _ a t c o 1 3 ** - - - - - - - - - ** ** Test iauAtco13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAtco13, vvd, viv ** ** This revision: 2013 October 4 */ { double rc, dc, pr, pd, px, rv, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, aob, zob, hob, dob, rob, eo; int j; rc = 2.71; dc = 0.174; pr = 1e-5; pd = 5e-6; px = 0.1; rv = 55.0; utc1 = 2456384.5; utc2 = 0.969254051; dut1 = 0.1550675; elong = -0.527800806; phi = -1.2345856; hm = 2738.0; xp = 2.47230737e-7; yp = 1.82640464e-6; phpa = 731.0; tc = 12.8; rh = 0.59; wl = 0.55; j = iauAtco13(rc, dc, pr, pd, px, rv, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &aob, &zob, &hob, &dob, &rob, &eo); vvd(aob, 0.09251774485358230653, 1e-12, "iauAtco13", "aob", status); vvd(zob, 1.407661405256767021, 1e-12, "iauAtco13", "zob", status); vvd(hob, -0.09265154431403157925, 1e-12, "iauAtco13", "hob", status); vvd(dob, 0.1716626560075591655, 1e-12, "iauAtco13", "dob", status); vvd(rob, 2.710260453503097719, 1e-12, "iauAtco13", "rob", status); vvd(eo, -0.003020548354802412839, 1e-14, "iauAtco13", "eo", status); viv(j, 0, "iauAtco13", "j", status); } static void t_atic13(int *status) /* ** - - - - - - - - - ** t _ a t i c 1 3 ** - - - - - - - - - ** ** Test iauAtic13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAtic13, vvd ** ** This revision: 2013 October 3 */ { double ri, di, date1, date2, rc, dc, eo; ri = 2.710121572969038991; di = 0.1729371367218230438; date1 = 2456165.5; date2 = 0.401182685; iauAtic13(ri, di, date1, date2, &rc, &dc, &eo); vvd(rc, 2.710126504531374930, 1e-12, "iauAtic13", "rc", status); vvd(dc, 0.1740632537628342320, 1e-12, "iauAtic13", "dc", status); vvd(eo, -0.002900618712657375647, 1e-14, "iauAtic13", "eo", status); } static void t_aticq(int *status) /* ** - - - - - - - - ** t _ a t i c q ** - - - - - - - - ** ** Test iauAticq function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApci13, iauAticq, vvd ** ** This revision: 2013 October 3 */ { double date1, date2, eo, ri, di, rc, dc; iauASTROM astrom; date1 = 2456165.5; date2 = 0.401182685; iauApci13(date1, date2, &astrom, &eo); ri = 2.710121572969038991; di = 0.1729371367218230438; iauAticq(ri, di, &astrom, &rc, &dc); vvd(rc, 2.710126504531374930, 1e-12, "iauAticq", "rc", status); vvd(dc, 0.1740632537628342320, 1e-12, "iauAticq", "dc", status); } static void t_aticqn(int *status) /* ** - - - - - - - - - ** t _ a t i c q n ** - - - - - - - - - ** ** Test iauAticqn function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApci13, iauAticqn, vvd ** ** This revision: 2013 October 3 */ { double date1, date2, eo, ri, di, rc, dc; iauLDBODY b[3]; iauASTROM astrom; date1 = 2456165.5; date2 = 0.401182685; iauApci13(date1, date2, &astrom, &eo); ri = 2.709994899247599271; di = 0.1728740720983623469; b[0].bm = 0.00028574; b[0].dl = 3e-10; b[0].pv[0][0] = -7.81014427; b[0].pv[0][1] = -5.60956681; b[0].pv[0][2] = -1.98079819; b[0].pv[1][0] = 0.0030723249; b[0].pv[1][1] = -0.00406995477; b[0].pv[1][2] = -0.00181335842; b[1].bm = 0.00095435; b[1].dl = 3e-9; b[1].pv[0][0] = 0.738098796; b[1].pv[0][1] = 4.63658692; b[1].pv[0][2] = 1.9693136; b[1].pv[1][0] = -0.00755816922; b[1].pv[1][1] = 0.00126913722; b[1].pv[1][2] = 0.000727999001; b[2].bm = 1.0; b[2].dl = 6e-6; b[2].pv[0][0] = -0.000712174377; b[2].pv[0][1] = -0.00230478303; b[2].pv[0][2] = -0.00105865966; b[2].pv[1][0] = 6.29235213e-6; b[2].pv[1][1] = -3.30888387e-7; b[2].pv[1][2] = -2.96486623e-7; iauAticqn(ri, di, &astrom, 3, b, &rc, &dc); vvd(rc, 2.709999575032685412, 1e-12, "iauAtciqn", "rc", status); vvd(dc, 0.1739999656317778034, 1e-12, "iauAtciqn", "dc", status); } static void t_atio13(int *status) /* ** - - - - - - - - - ** t _ a t i o 1 3 ** - - - - - - - - - ** ** Test iauAtio13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAtio13, vvd, viv ** ** This revision: 2013 October 3 */ { double ri, di, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, aob, zob, hob, dob, rob; int j; ri = 2.710121572969038991; di = 0.1729371367218230438; utc1 = 2456384.5; utc2 = 0.969254051; dut1 = 0.1550675; elong = -0.527800806; phi = -1.2345856; hm = 2738.0; xp = 2.47230737e-7; yp = 1.82640464e-6; phpa = 731.0; tc = 12.8; rh = 0.59; wl = 0.55; j = iauAtio13(ri, di, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &aob, &zob, &hob, &dob, &rob); vvd(aob, 0.09233952224794989993, 1e-12, "iauAtio13", "aob", status); vvd(zob, 1.407758704513722461, 1e-12, "iauAtio13", "zob", status); vvd(hob, -0.09247619879782006106, 1e-12, "iauAtio13", "hob", status); vvd(dob, 0.1717653435758265198, 1e-12, "iauAtio13", "dob", status); vvd(rob, 2.710085107986886201, 1e-12, "iauAtio13", "rob", status); viv(j, 0, "iauAtio13", "j", status); } static void t_atioq(int *status) /* ** - - - - - - - - ** t _ a t i o q ** - - - - - - - - ** ** Test iauAtioq function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauApio13, iauAtioq, vvd, viv ** ** This revision: 2013 October 4 */ { double utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, ri, di, aob, zob, hob, dob, rob; iauASTROM astrom; utc1 = 2456384.5; utc2 = 0.969254051; dut1 = 0.1550675; elong = -0.527800806; phi = -1.2345856; hm = 2738.0; xp = 2.47230737e-7; yp = 1.82640464e-6; phpa = 731.0; tc = 12.8; rh = 0.59; wl = 0.55; (void) iauApio13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom); ri = 2.710121572969038991; di = 0.1729371367218230438; iauAtioq(ri, di, &astrom, &aob, &zob, &hob, &dob, &rob); vvd(aob, 0.09233952224794989993, 1e-12, "iauAtioq", "aob", status); vvd(zob, 1.407758704513722461, 1e-12, "iauAtioq", "zob", status); vvd(hob, -0.09247619879782006106, 1e-12, "iauAtioq", "hob", status); vvd(dob, 0.1717653435758265198, 1e-12, "iauAtioq", "dob", status); vvd(rob, 2.710085107986886201, 1e-12, "iauAtioq", "rob", status); } static void t_atoc13(int *status) /* ** - - - - - - - - - ** t _ a t o c 1 3 ** - - - - - - - - - ** ** Test iauAtoc13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAtoc13, vvd, viv ** ** This revision: 2013 October 3 */ { double utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, ob1, ob2, rc, dc; int j; utc1 = 2456384.5; utc2 = 0.969254051; dut1 = 0.1550675; elong = -0.527800806; phi = -1.2345856; hm = 2738.0; xp = 2.47230737e-7; yp = 1.82640464e-6; phpa = 731.0; tc = 12.8; rh = 0.59; wl = 0.55; ob1 = 2.710085107986886201; ob2 = 0.1717653435758265198; j = iauAtoc13 ( "R", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &rc, &dc); vvd(rc, 2.709956744661000609, 1e-12, "iauAtoc13", "R/rc", status); vvd(dc, 0.1741696500895398562, 1e-12, "iauAtoc13", "R/dc", status); viv(j, 0, "iauAtoc13", "R/j", status); ob1 = -0.09247619879782006106; ob2 = 0.1717653435758265198; j = iauAtoc13 ( "H", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &rc, &dc); vvd(rc, 2.709956744661000609, 1e-12, "iauAtoc13", "H/rc", status); vvd(dc, 0.1741696500895398562, 1e-12, "iauAtoc13", "H/dc", status); viv(j, 0, "iauAtoc13", "H/j", status); ob1 = 0.09233952224794989993; ob2 = 1.407758704513722461; j = iauAtoc13 ( "A", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &rc, &dc); vvd(rc, 2.709956744661000609, 1e-12, "iauAtoc13", "A/rc", status); vvd(dc, 0.1741696500895398565, 1e-12, "iauAtoc13", "A/dc", status); viv(j, 0, "iauAtoc13", "A/j", status); } static void t_atoi13(int *status) /* ** - - - - - - - - - ** t _ a t o i 1 3 ** - - - - - - - - - ** ** Test iauAtoi13 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauAtoi13, vvd, viv ** ** This revision: 2013 October 3 */ { double utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, ob1, ob2, ri, di; int j; utc1 = 2456384.5; utc2 = 0.969254051; dut1 = 0.1550675; elong = -0.527800806; phi = -1.2345856; hm = 2738.0; xp = 2.47230737e-7; yp = 1.82640464e-6; phpa = 731.0; tc = 12.8; rh = 0.59; wl = 0.55; ob1 = 2.710085107986886201; ob2 = 0.1717653435758265198; j = iauAtoi13 ( "R", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &ri, &di); vvd(ri, 2.710121574449135955, 1e-12, "iauAtoi13", "R/ri", status); vvd(di, 0.1729371839114567725, 1e-12, "iauAtoi13", "R/di", status); viv(j, 0, "iauAtoi13", "R/J", status); ob1 = -0.09247619879782006106; ob2 = 0.1717653435758265198; j = iauAtoi13 ( "H", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &ri, &di); vvd(ri, 2.710121574449135955, 1e-12, "iauAtoi13", "H/ri", status); vvd(di, 0.1729371839114567725, 1e-12, "iauAtoi13", "H/di", status); viv(j, 0, "iauAtoi13", "H/J", status); ob1 = 0.09233952224794989993; ob2 = 1.407758704513722461; j = iauAtoi13 ( "A", ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &ri, &di); vvd(ri, 2.710121574449135955, 1e-12, "iauAtoi13", "A/ri", status); vvd(di, 0.1729371839114567728, 1e-12, "iauAtoi13", "A/di", status); viv(j, 0, "iauAtoi13", "A/J", status); } static void t_atoiq(int *status) /* ** - - - - - - - - ** t _ a t o i q ** - - - - - - - - * ** Test iauAtoiq function. * ** Returned: ** status int FALSE = success, TRUE = fail * ** Called: iauApio13, iauAtoiq, vvd * ** This revision: 2013 October 4 */ { double utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, ob1, ob2, ri, di; iauASTROM astrom; utc1 = 2456384.5; utc2 = 0.969254051; dut1 = 0.1550675; elong = -0.527800806; phi = -1.2345856; hm = 2738.0; xp = 2.47230737e-7; yp = 1.82640464e-6; phpa = 731.0; tc = 12.8; rh = 0.59; wl = 0.55; (void) iauApio13(utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom); ob1 = 2.710085107986886201; ob2 = 0.1717653435758265198; iauAtoiq("R", ob1, ob2, &astrom, &ri, &di); vvd(ri, 2.710121574449135955, 1e-12, "iauAtoiq", "R/ri", status); vvd(di, 0.1729371839114567725, 1e-12, "iauAtoiq", "R/di", status); ob1 = -0.09247619879782006106; ob2 = 0.1717653435758265198; iauAtoiq("H", ob1, ob2, &astrom, &ri, &di); vvd(ri, 2.710121574449135955, 1e-12, "iauAtoiq", "H/ri", status); vvd(di, 0.1729371839114567725, 1e-12, "iauAtoiq", "H/di", status); ob1 = 0.09233952224794989993; ob2 = 1.407758704513722461; iauAtoiq("A", ob1, ob2, &astrom, &ri, &di); vvd(ri, 2.710121574449135955, 1e-12, "iauAtoiq", "A/ri", status); vvd(di, 0.1729371839114567728, 1e-12, "iauAtoiq", "A/di", status); } static void t_bi00(int *status) /* ** - - - - - - - ** t _ b i 0 0 ** - - - - - - - ** ** Test iauBi00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauBi00, vvd ** ** This revision: 2013 August 7 */ { double dpsibi, depsbi, dra; iauBi00(&dpsibi, &depsbi, &dra); vvd(dpsibi, -0.2025309152835086613e-6, 1e-12, "iauBi00", "dpsibi", status); vvd(depsbi, -0.3306041454222147847e-7, 1e-12, "iauBi00", "depsbi", status); vvd(dra, -0.7078279744199225506e-7, 1e-12, "iauBi00", "dra", status); } static void t_bp00(int *status) /* ** - - - - - - - ** t _ b p 0 0 ** - - - - - - - ** ** Test iauBp00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauBp00, vvd ** ** This revision: 2013 August 7 */ { double rb[3][3], rp[3][3], rbp[3][3]; iauBp00(2400000.5, 50123.9999, rb, rp, rbp); vvd(rb[0][0], 0.9999999999999942498, 1e-12, "iauBp00", "rb11", status); vvd(rb[0][1], -0.7078279744199196626e-7, 1e-16, "iauBp00", "rb12", status); vvd(rb[0][2], 0.8056217146976134152e-7, 1e-16, "iauBp00", "rb13", status); vvd(rb[1][0], 0.7078279477857337206e-7, 1e-16, "iauBp00", "rb21", status); vvd(rb[1][1], 0.9999999999999969484, 1e-12, "iauBp00", "rb22", status); vvd(rb[1][2], 0.3306041454222136517e-7, 1e-16, "iauBp00", "rb23", status); vvd(rb[2][0], -0.8056217380986972157e-7, 1e-16, "iauBp00", "rb31", status); vvd(rb[2][1], -0.3306040883980552500e-7, 1e-16, "iauBp00", "rb32", status); vvd(rb[2][2], 0.9999999999999962084, 1e-12, "iauBp00", "rb33", status); vvd(rp[0][0], 0.9999995504864048241, 1e-12, "iauBp00", "rp11", status); vvd(rp[0][1], 0.8696113836207084411e-3, 1e-14, "iauBp00", "rp12", status); vvd(rp[0][2], 0.3778928813389333402e-3, 1e-14, "iauBp00", "rp13", status); vvd(rp[1][0], -0.8696113818227265968e-3, 1e-14, "iauBp00", "rp21", status); vvd(rp[1][1], 0.9999996218879365258, 1e-12, "iauBp00", "rp22", status); vvd(rp[1][2], -0.1690679263009242066e-6, 1e-14, "iauBp00", "rp23", status); vvd(rp[2][0], -0.3778928854764695214e-3, 1e-14, "iauBp00", "rp31", status); vvd(rp[2][1], -0.1595521004195286491e-6, 1e-14, "iauBp00", "rp32", status); vvd(rp[2][2], 0.9999999285984682756, 1e-12, "iauBp00", "rp33", status); vvd(rbp[0][0], 0.9999995505175087260, 1e-12, "iauBp00", "rbp11", status); vvd(rbp[0][1], 0.8695405883617884705e-3, 1e-14, "iauBp00", "rbp12", status); vvd(rbp[0][2], 0.3779734722239007105e-3, 1e-14, "iauBp00", "rbp13", status); vvd(rbp[1][0], -0.8695405990410863719e-3, 1e-14, "iauBp00", "rbp21", status); vvd(rbp[1][1], 0.9999996219494925900, 1e-12, "iauBp00", "rbp22", status); vvd(rbp[1][2], -0.1360775820404982209e-6, 1e-14, "iauBp00", "rbp23", status); vvd(rbp[2][0], -0.3779734476558184991e-3, 1e-14, "iauBp00", "rbp31", status); vvd(rbp[2][1], -0.1925857585832024058e-6, 1e-14, "iauBp00", "rbp32", status); vvd(rbp[2][2], 0.9999999285680153377, 1e-12, "iauBp00", "rbp33", status); } static void t_bp06(int *status) /* ** - - - - - - - ** t _ b p 0 6 ** - - - - - - - ** ** Test iauBp06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauBp06, vvd ** ** This revision: 2013 August 7 */ { double rb[3][3], rp[3][3], rbp[3][3]; iauBp06(2400000.5, 50123.9999, rb, rp, rbp); vvd(rb[0][0], 0.9999999999999942497, 1e-12, "iauBp06", "rb11", status); vvd(rb[0][1], -0.7078368960971557145e-7, 1e-14, "iauBp06", "rb12", status); vvd(rb[0][2], 0.8056213977613185606e-7, 1e-14, "iauBp06", "rb13", status); vvd(rb[1][0], 0.7078368694637674333e-7, 1e-14, "iauBp06", "rb21", status); vvd(rb[1][1], 0.9999999999999969484, 1e-12, "iauBp06", "rb22", status); vvd(rb[1][2], 0.3305943742989134124e-7, 1e-14, "iauBp06", "rb23", status); vvd(rb[2][0], -0.8056214211620056792e-7, 1e-14, "iauBp06", "rb31", status); vvd(rb[2][1], -0.3305943172740586950e-7, 1e-14, "iauBp06", "rb32", status); vvd(rb[2][2], 0.9999999999999962084, 1e-12, "iauBp06", "rb33", status); vvd(rp[0][0], 0.9999995504864960278, 1e-12, "iauBp06", "rp11", status); vvd(rp[0][1], 0.8696112578855404832e-3, 1e-14, "iauBp06", "rp12", status); vvd(rp[0][2], 0.3778929293341390127e-3, 1e-14, "iauBp06", "rp13", status); vvd(rp[1][0], -0.8696112560510186244e-3, 1e-14, "iauBp06", "rp21", status); vvd(rp[1][1], 0.9999996218880458820, 1e-12, "iauBp06", "rp22", status); vvd(rp[1][2], -0.1691646168941896285e-6, 1e-14, "iauBp06", "rp23", status); vvd(rp[2][0], -0.3778929335557603418e-3, 1e-14, "iauBp06", "rp31", status); vvd(rp[2][1], -0.1594554040786495076e-6, 1e-14, "iauBp06", "rp32", status); vvd(rp[2][2], 0.9999999285984501222, 1e-12, "iauBp06", "rp33", status); vvd(rbp[0][0], 0.9999995505176007047, 1e-12, "iauBp06", "rbp11", status); vvd(rbp[0][1], 0.8695404617348208406e-3, 1e-14, "iauBp06", "rbp12", status); vvd(rbp[0][2], 0.3779735201865589104e-3, 1e-14, "iauBp06", "rbp13", status); vvd(rbp[1][0], -0.8695404723772031414e-3, 1e-14, "iauBp06", "rbp21", status); vvd(rbp[1][1], 0.9999996219496027161, 1e-12, "iauBp06", "rbp22", status); vvd(rbp[1][2], -0.1361752497080270143e-6, 1e-14, "iauBp06", "rbp23", status); vvd(rbp[2][0], -0.3779734957034089490e-3, 1e-14, "iauBp06", "rbp31", status); vvd(rbp[2][1], -0.1924880847894457113e-6, 1e-14, "iauBp06", "rbp32", status); vvd(rbp[2][2], 0.9999999285679971958, 1e-12, "iauBp06", "rbp33", status); } static void t_bpn2xy(int *status) /* ** - - - - - - - - - ** t _ b p n 2 x y ** - - - - - - - - - ** ** Test iauBpn2xy function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauBpn2xy, vvd ** ** This revision: 2013 August 7 */ { double rbpn[3][3], x, y; rbpn[0][0] = 9.999962358680738e-1; rbpn[0][1] = -2.516417057665452e-3; rbpn[0][2] = -1.093569785342370e-3; rbpn[1][0] = 2.516462370370876e-3; rbpn[1][1] = 9.999968329010883e-1; rbpn[1][2] = 4.006159587358310e-5; rbpn[2][0] = 1.093465510215479e-3; rbpn[2][1] = -4.281337229063151e-5; rbpn[2][2] = 9.999994012499173e-1; iauBpn2xy(rbpn, &x, &y); vvd(x, 1.093465510215479e-3, 1e-12, "iauBpn2xy", "x", status); vvd(y, -4.281337229063151e-5, 1e-12, "iauBpn2xy", "y", status); } static void t_c2i00a(int *status) /* ** - - - - - - - - - ** t _ c 2 i 0 0 a ** - - - - - - - - - ** ** Test iauC2i00a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2i00a, vvd ** ** This revision: 2013 August 7 */ { double rc2i[3][3]; iauC2i00a(2400000.5, 53736.0, rc2i); vvd(rc2i[0][0], 0.9999998323037165557, 1e-12, "iauC2i00a", "11", status); vvd(rc2i[0][1], 0.5581526348992140183e-9, 1e-12, "iauC2i00a", "12", status); vvd(rc2i[0][2], -0.5791308477073443415e-3, 1e-12, "iauC2i00a", "13", status); vvd(rc2i[1][0], -0.2384266227870752452e-7, 1e-12, "iauC2i00a", "21", status); vvd(rc2i[1][1], 0.9999999991917405258, 1e-12, "iauC2i00a", "22", status); vvd(rc2i[1][2], -0.4020594955028209745e-4, 1e-12, "iauC2i00a", "23", status); vvd(rc2i[2][0], 0.5791308472168152904e-3, 1e-12, "iauC2i00a", "31", status); vvd(rc2i[2][1], 0.4020595661591500259e-4, 1e-12, "iauC2i00a", "32", status); vvd(rc2i[2][2], 0.9999998314954572304, 1e-12, "iauC2i00a", "33", status); } static void t_c2i00b(int *status) /* ** - - - - - - - - - ** t _ c 2 i 0 0 b ** - - - - - - - - - ** ** Test iauC2i00b function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2i00b, vvd ** ** This revision: 2013 August 7 */ { double rc2i[3][3]; iauC2i00b(2400000.5, 53736.0, rc2i); vvd(rc2i[0][0], 0.9999998323040954356, 1e-12, "iauC2i00b", "11", status); vvd(rc2i[0][1], 0.5581526349131823372e-9, 1e-12, "iauC2i00b", "12", status); vvd(rc2i[0][2], -0.5791301934855394005e-3, 1e-12, "iauC2i00b", "13", status); vvd(rc2i[1][0], -0.2384239285499175543e-7, 1e-12, "iauC2i00b", "21", status); vvd(rc2i[1][1], 0.9999999991917574043, 1e-12, "iauC2i00b", "22", status); vvd(rc2i[1][2], -0.4020552974819030066e-4, 1e-12, "iauC2i00b", "23", status); vvd(rc2i[2][0], 0.5791301929950208873e-3, 1e-12, "iauC2i00b", "31", status); vvd(rc2i[2][1], 0.4020553681373720832e-4, 1e-12, "iauC2i00b", "32", status); vvd(rc2i[2][2], 0.9999998314958529887, 1e-12, "iauC2i00b", "33", status); } static void t_c2i06a(int *status) /* ** - - - - - - - - - ** t _ c 2 i 0 6 a ** - - - - - - - - - ** ** Test iauC2i06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2i06a, vvd ** ** This revision: 2013 August 7 */ { double rc2i[3][3]; iauC2i06a(2400000.5, 53736.0, rc2i); vvd(rc2i[0][0], 0.9999998323037159379, 1e-12, "iauC2i06a", "11", status); vvd(rc2i[0][1], 0.5581121329587613787e-9, 1e-12, "iauC2i06a", "12", status); vvd(rc2i[0][2], -0.5791308487740529749e-3, 1e-12, "iauC2i06a", "13", status); vvd(rc2i[1][0], -0.2384253169452306581e-7, 1e-12, "iauC2i06a", "21", status); vvd(rc2i[1][1], 0.9999999991917467827, 1e-12, "iauC2i06a", "22", status); vvd(rc2i[1][2], -0.4020579392895682558e-4, 1e-12, "iauC2i06a", "23", status); vvd(rc2i[2][0], 0.5791308482835292617e-3, 1e-12, "iauC2i06a", "31", status); vvd(rc2i[2][1], 0.4020580099454020310e-4, 1e-12, "iauC2i06a", "32", status); vvd(rc2i[2][2], 0.9999998314954628695, 1e-12, "iauC2i06a", "33", status); } static void t_c2ibpn(int *status) /* ** - - - - - - - - - ** t _ c 2 i b p n ** - - - - - - - - - ** ** Test iauC2ibpn function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2ibpn, vvd ** ** This revision: 2013 August 7 */ { double rbpn[3][3], rc2i[3][3]; rbpn[0][0] = 9.999962358680738e-1; rbpn[0][1] = -2.516417057665452e-3; rbpn[0][2] = -1.093569785342370e-3; rbpn[1][0] = 2.516462370370876e-3; rbpn[1][1] = 9.999968329010883e-1; rbpn[1][2] = 4.006159587358310e-5; rbpn[2][0] = 1.093465510215479e-3; rbpn[2][1] = -4.281337229063151e-5; rbpn[2][2] = 9.999994012499173e-1; iauC2ibpn(2400000.5, 50123.9999, rbpn, rc2i); vvd(rc2i[0][0], 0.9999994021664089977, 1e-12, "iauC2ibpn", "11", status); vvd(rc2i[0][1], -0.3869195948017503664e-8, 1e-12, "iauC2ibpn", "12", status); vvd(rc2i[0][2], -0.1093465511383285076e-2, 1e-12, "iauC2ibpn", "13", status); vvd(rc2i[1][0], 0.5068413965715446111e-7, 1e-12, "iauC2ibpn", "21", status); vvd(rc2i[1][1], 0.9999999990835075686, 1e-12, "iauC2ibpn", "22", status); vvd(rc2i[1][2], 0.4281334246452708915e-4, 1e-12, "iauC2ibpn", "23", status); vvd(rc2i[2][0], 0.1093465510215479000e-2, 1e-12, "iauC2ibpn", "31", status); vvd(rc2i[2][1], -0.4281337229063151000e-4, 1e-12, "iauC2ibpn", "32", status); vvd(rc2i[2][2], 0.9999994012499173103, 1e-12, "iauC2ibpn", "33", status); } static void t_c2ixy(int *status) /* ** - - - - - - - - ** t _ c 2 i x y ** - - - - - - - - ** ** Test iauC2ixy function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2ixy, vvd ** ** This revision: 2013 August 7 */ { double x, y, rc2i[3][3]; x = 0.5791308486706011000e-3; y = 0.4020579816732961219e-4; iauC2ixy(2400000.5, 53736, x, y, rc2i); vvd(rc2i[0][0], 0.9999998323037157138, 1e-12, "iauC2ixy", "11", status); vvd(rc2i[0][1], 0.5581526349032241205e-9, 1e-12, "iauC2ixy", "12", status); vvd(rc2i[0][2], -0.5791308491611263745e-3, 1e-12, "iauC2ixy", "13", status); vvd(rc2i[1][0], -0.2384257057469842953e-7, 1e-12, "iauC2ixy", "21", status); vvd(rc2i[1][1], 0.9999999991917468964, 1e-12, "iauC2ixy", "22", status); vvd(rc2i[1][2], -0.4020579110172324363e-4, 1e-12, "iauC2ixy", "23", status); vvd(rc2i[2][0], 0.5791308486706011000e-3, 1e-12, "iauC2ixy", "31", status); vvd(rc2i[2][1], 0.4020579816732961219e-4, 1e-12, "iauC2ixy", "32", status); vvd(rc2i[2][2], 0.9999998314954627590, 1e-12, "iauC2ixy", "33", status); } static void t_c2ixys(int *status) /* ** - - - - - - - - - ** t _ c 2 i x y s ** - - - - - - - - - ** ** Test iauC2ixys function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2ixys, vvd ** ** This revision: 2013 August 7 */ { double x, y, s, rc2i[3][3]; x = 0.5791308486706011000e-3; y = 0.4020579816732961219e-4; s = -0.1220040848472271978e-7; iauC2ixys(x, y, s, rc2i); vvd(rc2i[0][0], 0.9999998323037157138, 1e-12, "iauC2ixys", "11", status); vvd(rc2i[0][1], 0.5581984869168499149e-9, 1e-12, "iauC2ixys", "12", status); vvd(rc2i[0][2], -0.5791308491611282180e-3, 1e-12, "iauC2ixys", "13", status); vvd(rc2i[1][0], -0.2384261642670440317e-7, 1e-12, "iauC2ixys", "21", status); vvd(rc2i[1][1], 0.9999999991917468964, 1e-12, "iauC2ixys", "22", status); vvd(rc2i[1][2], -0.4020579110169668931e-4, 1e-12, "iauC2ixys", "23", status); vvd(rc2i[2][0], 0.5791308486706011000e-3, 1e-12, "iauC2ixys", "31", status); vvd(rc2i[2][1], 0.4020579816732961219e-4, 1e-12, "iauC2ixys", "32", status); vvd(rc2i[2][2], 0.9999998314954627590, 1e-12, "iauC2ixys", "33", status); } static void t_c2s(int *status) /* ** - - - - - - ** t _ c 2 s ** - - - - - - ** ** Test iauC2s function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2s, vvd ** ** This revision: 2013 August 7 */ { double p[3], theta, phi; p[0] = 100.0; p[1] = -50.0; p[2] = 25.0; iauC2s(p, &theta, &phi); vvd(theta, -0.4636476090008061162, 1e-14, "iauC2s", "theta", status); vvd(phi, 0.2199879773954594463, 1e-14, "iauC2s", "phi", status); } static void t_c2t00a(int *status) /* ** - - - - - - - - - ** t _ c 2 t 0 0 a ** - - - - - - - - - ** ** Test iauC2t00a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2t00a, vvd ** ** This revision: 2013 August 7 */ { double tta, ttb, uta, utb, xp, yp, rc2t[3][3]; tta = 2400000.5; uta = 2400000.5; ttb = 53736.0; utb = 53736.0; xp = 2.55060238e-7; yp = 1.860359247e-6; iauC2t00a(tta, ttb, uta, utb, xp, yp, rc2t); vvd(rc2t[0][0], -0.1810332128307182668, 1e-12, "iauC2t00a", "11", status); vvd(rc2t[0][1], 0.9834769806938457836, 1e-12, "iauC2t00a", "12", status); vvd(rc2t[0][2], 0.6555535638688341725e-4, 1e-12, "iauC2t00a", "13", status); vvd(rc2t[1][0], -0.9834768134135984552, 1e-12, "iauC2t00a", "21", status); vvd(rc2t[1][1], -0.1810332203649520727, 1e-12, "iauC2t00a", "22", status); vvd(rc2t[1][2], 0.5749801116141056317e-3, 1e-12, "iauC2t00a", "23", status); vvd(rc2t[2][0], 0.5773474014081406921e-3, 1e-12, "iauC2t00a", "31", status); vvd(rc2t[2][1], 0.3961832391770163647e-4, 1e-12, "iauC2t00a", "32", status); vvd(rc2t[2][2], 0.9999998325501692289, 1e-12, "iauC2t00a", "33", status); } static void t_c2t00b(int *status) /* ** - - - - - - - - - ** t _ c 2 t 0 0 b ** - - - - - - - - - ** ** Test iauC2t00b function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2t00b, vvd ** ** This revision: 2013 August 7 */ { double tta, ttb, uta, utb, xp, yp, rc2t[3][3]; tta = 2400000.5; uta = 2400000.5; ttb = 53736.0; utb = 53736.0; xp = 2.55060238e-7; yp = 1.860359247e-6; iauC2t00b(tta, ttb, uta, utb, xp, yp, rc2t); vvd(rc2t[0][0], -0.1810332128439678965, 1e-12, "iauC2t00b", "11", status); vvd(rc2t[0][1], 0.9834769806913872359, 1e-12, "iauC2t00b", "12", status); vvd(rc2t[0][2], 0.6555565082458415611e-4, 1e-12, "iauC2t00b", "13", status); vvd(rc2t[1][0], -0.9834768134115435923, 1e-12, "iauC2t00b", "21", status); vvd(rc2t[1][1], -0.1810332203784001946, 1e-12, "iauC2t00b", "22", status); vvd(rc2t[1][2], 0.5749793922030017230e-3, 1e-12, "iauC2t00b", "23", status); vvd(rc2t[2][0], 0.5773467471863534901e-3, 1e-12, "iauC2t00b", "31", status); vvd(rc2t[2][1], 0.3961790411549945020e-4, 1e-12, "iauC2t00b", "32", status); vvd(rc2t[2][2], 0.9999998325505635738, 1e-12, "iauC2t00b", "33", status); } static void t_c2t06a(int *status) /* ** - - - - - - - - - ** t _ c 2 t 0 6 a ** - - - - - - - - - ** ** Test iauC2t06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2t06a, vvd ** ** This revision: 2013 August 7 */ { double tta, ttb, uta, utb, xp, yp, rc2t[3][3]; tta = 2400000.5; uta = 2400000.5; ttb = 53736.0; utb = 53736.0; xp = 2.55060238e-7; yp = 1.860359247e-6; iauC2t06a(tta, ttb, uta, utb, xp, yp, rc2t); vvd(rc2t[0][0], -0.1810332128305897282, 1e-12, "iauC2t06a", "11", status); vvd(rc2t[0][1], 0.9834769806938592296, 1e-12, "iauC2t06a", "12", status); vvd(rc2t[0][2], 0.6555550962998436505e-4, 1e-12, "iauC2t06a", "13", status); vvd(rc2t[1][0], -0.9834768134136214897, 1e-12, "iauC2t06a", "21", status); vvd(rc2t[1][1], -0.1810332203649130832, 1e-12, "iauC2t06a", "22", status); vvd(rc2t[1][2], 0.5749800844905594110e-3, 1e-12, "iauC2t06a", "23", status); vvd(rc2t[2][0], 0.5773474024748545878e-3, 1e-12, "iauC2t06a", "31", status); vvd(rc2t[2][1], 0.3961816829632690581e-4, 1e-12, "iauC2t06a", "32", status); vvd(rc2t[2][2], 0.9999998325501747785, 1e-12, "iauC2t06a", "33", status); } static void t_c2tcio(int *status) /* ** - - - - - - - - - ** t _ c 2 t c i o ** - - - - - - - - - ** ** Test iauC2tcio function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2tcio, vvd ** ** This revision: 2013 August 7 */ { double rc2i[3][3], era, rpom[3][3], rc2t[3][3]; rc2i[0][0] = 0.9999998323037164738; rc2i[0][1] = 0.5581526271714303683e-9; rc2i[0][2] = -0.5791308477073443903e-3; rc2i[1][0] = -0.2384266227524722273e-7; rc2i[1][1] = 0.9999999991917404296; rc2i[1][2] = -0.4020594955030704125e-4; rc2i[2][0] = 0.5791308472168153320e-3; rc2i[2][1] = 0.4020595661593994396e-4; rc2i[2][2] = 0.9999998314954572365; era = 1.75283325530307; rpom[0][0] = 0.9999999999999674705; rpom[0][1] = -0.1367174580728847031e-10; rpom[0][2] = 0.2550602379999972723e-6; rpom[1][0] = 0.1414624947957029721e-10; rpom[1][1] = 0.9999999999982694954; rpom[1][2] = -0.1860359246998866338e-5; rpom[2][0] = -0.2550602379741215275e-6; rpom[2][1] = 0.1860359247002413923e-5; rpom[2][2] = 0.9999999999982369658; iauC2tcio(rc2i, era, rpom, rc2t); vvd(rc2t[0][0], -0.1810332128307110439, 1e-12, "iauC2tcio", "11", status); vvd(rc2t[0][1], 0.9834769806938470149, 1e-12, "iauC2tcio", "12", status); vvd(rc2t[0][2], 0.6555535638685466874e-4, 1e-12, "iauC2tcio", "13", status); vvd(rc2t[1][0], -0.9834768134135996657, 1e-12, "iauC2tcio", "21", status); vvd(rc2t[1][1], -0.1810332203649448367, 1e-12, "iauC2tcio", "22", status); vvd(rc2t[1][2], 0.5749801116141106528e-3, 1e-12, "iauC2tcio", "23", status); vvd(rc2t[2][0], 0.5773474014081407076e-3, 1e-12, "iauC2tcio", "31", status); vvd(rc2t[2][1], 0.3961832391772658944e-4, 1e-12, "iauC2tcio", "32", status); vvd(rc2t[2][2], 0.9999998325501691969, 1e-12, "iauC2tcio", "33", status); } static void t_c2teqx(int *status) /* ** - - - - - - - - - ** t _ c 2 t e q x ** - - - - - - - - - ** ** Test iauC2teqx function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2teqx, vvd ** ** This revision: 2013 August 7 */ { double rbpn[3][3], gst, rpom[3][3], rc2t[3][3]; rbpn[0][0] = 0.9999989440476103608; rbpn[0][1] = -0.1332881761240011518e-2; rbpn[0][2] = -0.5790767434730085097e-3; rbpn[1][0] = 0.1332858254308954453e-2; rbpn[1][1] = 0.9999991109044505944; rbpn[1][2] = -0.4097782710401555759e-4; rbpn[2][0] = 0.5791308472168153320e-3; rbpn[2][1] = 0.4020595661593994396e-4; rbpn[2][2] = 0.9999998314954572365; gst = 1.754166138040730516; rpom[0][0] = 0.9999999999999674705; rpom[0][1] = -0.1367174580728847031e-10; rpom[0][2] = 0.2550602379999972723e-6; rpom[1][0] = 0.1414624947957029721e-10; rpom[1][1] = 0.9999999999982694954; rpom[1][2] = -0.1860359246998866338e-5; rpom[2][0] = -0.2550602379741215275e-6; rpom[2][1] = 0.1860359247002413923e-5; rpom[2][2] = 0.9999999999982369658; iauC2teqx(rbpn, gst, rpom, rc2t); vvd(rc2t[0][0], -0.1810332128528685730, 1e-12, "iauC2teqx", "11", status); vvd(rc2t[0][1], 0.9834769806897685071, 1e-12, "iauC2teqx", "12", status); vvd(rc2t[0][2], 0.6555535639982634449e-4, 1e-12, "iauC2teqx", "13", status); vvd(rc2t[1][0], -0.9834768134095211257, 1e-12, "iauC2teqx", "21", status); vvd(rc2t[1][1], -0.1810332203871023800, 1e-12, "iauC2teqx", "22", status); vvd(rc2t[1][2], 0.5749801116126438962e-3, 1e-12, "iauC2teqx", "23", status); vvd(rc2t[2][0], 0.5773474014081539467e-3, 1e-12, "iauC2teqx", "31", status); vvd(rc2t[2][1], 0.3961832391768640871e-4, 1e-12, "iauC2teqx", "32", status); vvd(rc2t[2][2], 0.9999998325501691969, 1e-12, "iauC2teqx", "33", status); } static void t_c2tpe(int *status) /* ** - - - - - - - - ** t _ c 2 t p e ** - - - - - - - - ** ** Test iauC2tpe function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2tpe, vvd ** ** This revision: 2013 August 7 */ { double tta, ttb, uta, utb, dpsi, deps, xp, yp, rc2t[3][3]; tta = 2400000.5; uta = 2400000.5; ttb = 53736.0; utb = 53736.0; deps = 0.4090789763356509900; dpsi = -0.9630909107115582393e-5; xp = 2.55060238e-7; yp = 1.860359247e-6; iauC2tpe(tta, ttb, uta, utb, dpsi, deps, xp, yp, rc2t); vvd(rc2t[0][0], -0.1813677995763029394, 1e-12, "iauC2tpe", "11", status); vvd(rc2t[0][1], 0.9023482206891683275, 1e-12, "iauC2tpe", "12", status); vvd(rc2t[0][2], -0.3909902938641085751, 1e-12, "iauC2tpe", "13", status); vvd(rc2t[1][0], -0.9834147641476804807, 1e-12, "iauC2tpe", "21", status); vvd(rc2t[1][1], -0.1659883635434995121, 1e-12, "iauC2tpe", "22", status); vvd(rc2t[1][2], 0.7309763898042819705e-1, 1e-12, "iauC2tpe", "23", status); vvd(rc2t[2][0], 0.1059685430673215247e-2, 1e-12, "iauC2tpe", "31", status); vvd(rc2t[2][1], 0.3977631855605078674, 1e-12, "iauC2tpe", "32", status); vvd(rc2t[2][2], 0.9174875068792735362, 1e-12, "iauC2tpe", "33", status); } static void t_c2txy(int *status) /* ** - - - - - - - - ** t _ c 2 t x y ** - - - - - - - - ** ** Test iauC2txy function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauC2txy, vvd ** ** This revision: 2013 August 7 */ { double tta, ttb, uta, utb, x, y, xp, yp, rc2t[3][3]; tta = 2400000.5; uta = 2400000.5; ttb = 53736.0; utb = 53736.0; x = 0.5791308486706011000e-3; y = 0.4020579816732961219e-4; xp = 2.55060238e-7; yp = 1.860359247e-6; iauC2txy(tta, ttb, uta, utb, x, y, xp, yp, rc2t); vvd(rc2t[0][0], -0.1810332128306279253, 1e-12, "iauC2txy", "11", status); vvd(rc2t[0][1], 0.9834769806938520084, 1e-12, "iauC2txy", "12", status); vvd(rc2t[0][2], 0.6555551248057665829e-4, 1e-12, "iauC2txy", "13", status); vvd(rc2t[1][0], -0.9834768134136142314, 1e-12, "iauC2txy", "21", status); vvd(rc2t[1][1], -0.1810332203649529312, 1e-12, "iauC2txy", "22", status); vvd(rc2t[1][2], 0.5749800843594139912e-3, 1e-12, "iauC2txy", "23", status); vvd(rc2t[2][0], 0.5773474028619264494e-3, 1e-12, "iauC2txy", "31", status); vvd(rc2t[2][1], 0.3961816546911624260e-4, 1e-12, "iauC2txy", "32", status); vvd(rc2t[2][2], 0.9999998325501746670, 1e-12, "iauC2txy", "33", status); } static void t_cal2jd(int *status) /* ** - - - - - - - - - ** t _ c a l 2 j d ** - - - - - - - - - ** ** Test iauCal2jd function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauCal2jd, vvd, viv ** ** This revision: 2013 August 7 */ { int j; double djm0, djm; j = iauCal2jd(2003, 06, 01, &djm0, &djm); vvd(djm0, 2400000.5, 0.0, "iauCal2jd", "djm0", status); vvd(djm, 52791.0, 0.0, "iauCal2jd", "djm", status); viv(j, 0, "iauCal2jd", "j", status); } static void t_cp(int *status) /* ** - - - - - ** t _ c p ** - - - - - ** ** Test iauCp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauCp, vvd ** ** This revision: 2013 August 7 */ { double p[3], c[3]; p[0] = 0.3; p[1] = 1.2; p[2] = -2.5; iauCp(p, c); vvd(c[0], 0.3, 0.0, "iauCp", "1", status); vvd(c[1], 1.2, 0.0, "iauCp", "2", status); vvd(c[2], -2.5, 0.0, "iauCp", "3", status); } static void t_cpv(int *status) /* ** - - - - - - ** t _ c p v ** - - - - - - ** ** Test iauCpv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauCpv, vvd ** ** This revision: 2013 August 7 */ { double pv[2][3], c[2][3]; pv[0][0] = 0.3; pv[0][1] = 1.2; pv[0][2] = -2.5; pv[1][0] = -0.5; pv[1][1] = 3.1; pv[1][2] = 0.9; iauCpv(pv, c); vvd(c[0][0], 0.3, 0.0, "iauCpv", "p1", status); vvd(c[0][1], 1.2, 0.0, "iauCpv", "p2", status); vvd(c[0][2], -2.5, 0.0, "iauCpv", "p3", status); vvd(c[1][0], -0.5, 0.0, "iauCpv", "v1", status); vvd(c[1][1], 3.1, 0.0, "iauCpv", "v2", status); vvd(c[1][2], 0.9, 0.0, "iauCpv", "v3", status); } static void t_cr(int *status) /* ** - - - - - ** t _ c r ** - - - - - ** ** Test iauCr function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauCr, vvd ** ** This revision: 2013 August 7 */ { double r[3][3], c[3][3]; r[0][0] = 2.0; r[0][1] = 3.0; r[0][2] = 2.0; r[1][0] = 3.0; r[1][1] = 2.0; r[1][2] = 3.0; r[2][0] = 3.0; r[2][1] = 4.0; r[2][2] = 5.0; iauCr(r, c); vvd(c[0][0], 2.0, 0.0, "iauCr", "11", status); vvd(c[0][1], 3.0, 0.0, "iauCr", "12", status); vvd(c[0][2], 2.0, 0.0, "iauCr", "13", status); vvd(c[1][0], 3.0, 0.0, "iauCr", "21", status); vvd(c[1][1], 2.0, 0.0, "iauCr", "22", status); vvd(c[1][2], 3.0, 0.0, "iauCr", "23", status); vvd(c[2][0], 3.0, 0.0, "iauCr", "31", status); vvd(c[2][1], 4.0, 0.0, "iauCr", "32", status); vvd(c[2][2], 5.0, 0.0, "iauCr", "33", status); } static void t_d2dtf(int *status ) /* ** - - - - - - - - ** t _ d 2 d t f ** - - - - - - - - ** ** Test iauD2dtf function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauD2dtf, viv ** ** This revision: 2013 August 7 */ { int j, iy, im, id, ihmsf[4]; j = iauD2dtf("UTC", 5, 2400000.5, 49533.99999, &iy, &im, &id, ihmsf); viv(iy, 1994, "iauD2dtf", "y", status); viv(im, 6, "iauD2dtf", "mo", status); viv(id, 30, "iauD2dtf", "d", status); viv(ihmsf[0], 23, "iauD2dtf", "h", status); viv(ihmsf[1], 59, "iauD2dtf", "m", status); viv(ihmsf[2], 60, "iauD2dtf", "s", status); viv(ihmsf[3], 13599, "iauD2dtf", "f", status); viv(j, 0, "iauD2dtf", "j", status); } static void t_d2tf(int *status) /* ** - - - - - - - ** t _ d 2 t f ** - - - - - - - ** ** Test iauD2tf function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauD2tf, viv, vvd ** ** This revision: 2013 August 7 */ { int ihmsf[4]; char s; iauD2tf(4, -0.987654321, &s, ihmsf); viv((int)s, '-', "iauD2tf", "s", status); viv(ihmsf[0], 23, "iauD2tf", "0", status); viv(ihmsf[1], 42, "iauD2tf", "1", status); viv(ihmsf[2], 13, "iauD2tf", "2", status); viv(ihmsf[3], 3333, "iauD2tf", "3", status); } static void t_dat(int *status) /* ** - - - - - - ** t _ d a t ** - - - - - - ** ** Test iauDat function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauDat, vvd, viv ** ** This revision: 2016 July 11 */ { int j; double deltat; j = iauDat(2003, 6, 1, 0.0, &deltat); vvd(deltat, 32.0, 0.0, "iauDat", "d1", status); viv(j, 0, "iauDat", "j1", status); j = iauDat(2008, 1, 17, 0.0, &deltat); vvd(deltat, 33.0, 0.0, "iauDat", "d2", status); viv(j, 0, "iauDat", "j2", status); j = iauDat(2017, 9, 1, 0.0, &deltat); vvd(deltat, 37.0, 0.0, "iauDat", "d3", status); viv(j, 0, "iauDat", "j3", status); } static void t_dtdb(int *status) /* ** - - - - - - - ** t _ d t d b ** - - - - - - - ** ** Test iauDtdb function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauDtdb, vvd ** ** This revision: 2013 August 7 */ { double dtdb; dtdb = iauDtdb(2448939.5, 0.123, 0.76543, 5.0123, 5525.242, 3190.0); vvd(dtdb, -0.1280368005936998991e-2, 1e-15, "iauDtdb", "", status); } static void t_dtf2d(int *status) /* ** - - - - - - - - ** t _ d t f 2 d ** - - - - - - - - ** ** Test iauDtf2d function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauDtf2d, vvd, viv ** ** This revision: 2013 August 7 */ { double u1, u2; int j; j = iauDtf2d("UTC", 1994, 6, 30, 23, 59, 60.13599, &u1, &u2); vvd(u1+u2, 2449534.49999, 1e-6, "iauDtf2d", "u", status); viv(j, 0, "iauDtf2d", "j", status); } static void t_eceq06(int *status) /* ** - - - - - ** t _ e c e q 0 6 ** - - - - - ** ** Test iauEceq06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEceq06, vvd ** ** This revision: 2016 March 12 */ { double date1, date2, dl, db, dr, dd; date1 = 2456165.5; date2 = 0.401182685; dl = 5.1; db = -0.9; iauEceq06(date1, date2, dl, db, &dr, &dd); vvd(dr, 5.533459733613627767, 1e-14, "iauEceq06", "dr", status); vvd(dd, -1.246542932554480576, 1e-14, "iauEceq06", "dd", status); } static void t_ecm06(int *status) /* ** - - - - - - - - ** t _ e c m 0 6 ** - - - - - - - - ** ** Test iauEcm06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEcm06, vvd ** ** This revision: 2016 March 12 */ { double date1, date2, rm[3][3]; date1 = 2456165.5; date2 = 0.401182685; iauEcm06(date1, date2, rm); vvd(rm[0][0], 0.9999952427708701137, 1e-14, "iauEcm06", "rm11", status); vvd(rm[0][1], -0.2829062057663042347e-2, 1e-14, "iauEcm06", "rm12", status); vvd(rm[0][2], -0.1229163741100017629e-2, 1e-14, "iauEcm06", "rm13", status); vvd(rm[1][0], 0.3084546876908653562e-2, 1e-14, "iauEcm06", "rm21", status); vvd(rm[1][1], 0.9174891871550392514, 1e-14, "iauEcm06", "rm22", status); vvd(rm[1][2], 0.3977487611849338124, 1e-14, "iauEcm06", "rm23", status); vvd(rm[2][0], 0.2488512951527405928e-5, 1e-14, "iauEcm06", "rm31", status); vvd(rm[2][1], -0.3977506604161195467, 1e-14, "iauEcm06", "rm32", status); vvd(rm[2][2], 0.9174935488232863071, 1e-14, "iauEcm06", "rm33", status); } static void t_ee00(int *status) /* ** - - - - - - - ** t _ e e 0 0 ** - - - - - - - ** ** Test iauEe00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEe00, vvd ** ** This revision: 2013 August 7 */ { double epsa, dpsi, ee; epsa = 0.4090789763356509900; dpsi = -0.9630909107115582393e-5; ee = iauEe00(2400000.5, 53736.0, epsa, dpsi); vvd(ee, -0.8834193235367965479e-5, 1e-18, "iauEe00", "", status); } static void t_ee00a(int *status) /* ** - - - - - - - - ** t _ e e 0 0 a ** - - - - - - - - ** ** Test iauEe00a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEe00a, vvd ** ** This revision: 2013 August 7 */ { double ee; ee = iauEe00a(2400000.5, 53736.0); vvd(ee, -0.8834192459222588227e-5, 1e-18, "iauEe00a", "", status); } static void t_ee00b(int *status) /* ** - - - - - - - - ** t _ e e 0 0 b ** - - - - - - - - ** ** Test iauEe00b function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEe00b, vvd ** ** This revision: 2013 August 7 */ { double ee; ee = iauEe00b(2400000.5, 53736.0); vvd(ee, -0.8835700060003032831e-5, 1e-18, "iauEe00b", "", status); } static void t_ee06a(int *status) /* ** - - - - - - - - ** t _ e e 0 6 a ** - - - - - - - - ** ** Test iauEe06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEe06a, vvd ** ** This revision: 2013 August 7 */ { double ee; ee = iauEe06a(2400000.5, 53736.0); vvd(ee, -0.8834195072043790156e-5, 1e-15, "iauEe06a", "", status); } static void t_eect00(int *status) /* ** - - - - - - - - - ** t _ e e c t 0 0 ** - - - - - - - - - ** ** Test iauEect00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEect00, vvd ** ** This revision: 2013 August 7 */ { double eect; eect = iauEect00(2400000.5, 53736.0); vvd(eect, 0.2046085004885125264e-8, 1e-20, "iauEect00", "", status); } static void t_eform(int *status) /* ** - - - - - - - - ** t _ e f o r m ** - - - - - - - - ** ** Test iauEform function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEform, viv, vvd ** ** This revision: 2016 March 12 */ { int j; double a, f; j = iauEform(0, &a, &f); viv(j, -1, "iauEform", "j0", status); j = iauEform(WGS84, &a, &f); viv(j, 0, "iauEform", "j1", status); vvd(a, 6378137.0, 1e-10, "iauEform", "a1", status); vvd(f, 0.3352810664747480720e-2, 1e-18, "iauEform", "f1", status); j = iauEform(GRS80, &a, &f); viv(j, 0, "iauEform", "j2", status); vvd(a, 6378137.0, 1e-10, "iauEform", "a2", status); vvd(f, 0.3352810681182318935e-2, 1e-18, "iauEform", "f2", status); j = iauEform(WGS72, &a, &f); viv(j, 0, "iauEform", "j2", status); vvd(a, 6378135.0, 1e-10, "iauEform", "a3", status); vvd(f, 0.3352779454167504862e-2, 1e-18, "iauEform", "f3", status); j = iauEform(4, &a, &f); viv(j, -1, "iauEform", "j3", status); } static void t_eo06a(int *status) /* ** - - - - - - - - ** t _ e o 0 6 a ** - - - - - - - - ** ** Test iauEo06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEo06a, vvd ** ** This revision: 2013 August 7 */ { double eo; eo = iauEo06a(2400000.5, 53736.0); vvd(eo, -0.1332882371941833644e-2, 1e-15, "iauEo06a", "", status); } static void t_eors(int *status) /* ** - - - - - - - ** t _ e o r s ** - - - - - - - ** ** Test iauEors function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEors, vvd ** ** This revision: 2013 August 7 */ { double rnpb[3][3], s, eo; rnpb[0][0] = 0.9999989440476103608; rnpb[0][1] = -0.1332881761240011518e-2; rnpb[0][2] = -0.5790767434730085097e-3; rnpb[1][0] = 0.1332858254308954453e-2; rnpb[1][1] = 0.9999991109044505944; rnpb[1][2] = -0.4097782710401555759e-4; rnpb[2][0] = 0.5791308472168153320e-3; rnpb[2][1] = 0.4020595661593994396e-4; rnpb[2][2] = 0.9999998314954572365; s = -0.1220040848472271978e-7; eo = iauEors(rnpb, s); vvd(eo, -0.1332882715130744606e-2, 1e-14, "iauEors", "", status); } static void t_epb(int *status) /* ** - - - - - - ** t _ e p b ** - - - - - - ** ** Test iauEpb function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEpb, vvd ** ** This revision: 2013 August 7 */ { double epb; epb = iauEpb(2415019.8135, 30103.18648); vvd(epb, 1982.418424159278580, 1e-12, "iauEpb", "", status); } static void t_epb2jd(int *status) /* ** - - - - - - - - - ** t _ e p b 2 j d ** - - - - - - - - - ** ** Test iauEpb2jd function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEpb2jd, vvd ** ** This revision: 2013 August 7 */ { double epb, djm0, djm; epb = 1957.3; iauEpb2jd(epb, &djm0, &djm); vvd(djm0, 2400000.5, 1e-9, "iauEpb2jd", "djm0", status); vvd(djm, 35948.1915101513, 1e-9, "iauEpb2jd", "mjd", status); } static void t_epj(int *status) /* ** - - - - - - ** t _ e p j ** - - - - - - ** ** Test iauEpj function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEpj, vvd ** ** This revision: 2013 August 7 */ { double epj; epj = iauEpj(2451545, -7392.5); vvd(epj, 1979.760438056125941, 1e-12, "iauEpj", "", status); } static void t_epj2jd(int *status) /* ** - - - - - - - - - ** t _ e p j 2 j d ** - - - - - - - - - ** ** Test iauEpj2jd function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEpj2jd, vvd ** ** This revision: 2013 August 7 */ { double epj, djm0, djm; epj = 1996.8; iauEpj2jd(epj, &djm0, &djm); vvd(djm0, 2400000.5, 1e-9, "iauEpj2jd", "djm0", status); vvd(djm, 50375.7, 1e-9, "iauEpj2jd", "mjd", status); } static void t_epv00(int *status) /* ** - - - - - - - - ** t _ e p v 0 0 ** - - - - - - - - ** ** Test iauEpv00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEpv00, vvd, viv ** ** This revision: 2013 August 7 */ { double pvh[2][3], pvb[2][3]; int j; j = iauEpv00(2400000.5, 53411.52501161, pvh, pvb); vvd(pvh[0][0], -0.7757238809297706813, 1e-14, "iauEpv00", "ph(x)", status); vvd(pvh[0][1], 0.5598052241363340596, 1e-14, "iauEpv00", "ph(y)", status); vvd(pvh[0][2], 0.2426998466481686993, 1e-14, "iauEpv00", "ph(z)", status); vvd(pvh[1][0], -0.1091891824147313846e-1, 1e-15, "iauEpv00", "vh(x)", status); vvd(pvh[1][1], -0.1247187268440845008e-1, 1e-15, "iauEpv00", "vh(y)", status); vvd(pvh[1][2], -0.5407569418065039061e-2, 1e-15, "iauEpv00", "vh(z)", status); vvd(pvb[0][0], -0.7714104440491111971, 1e-14, "iauEpv00", "pb(x)", status); vvd(pvb[0][1], 0.5598412061824171323, 1e-14, "iauEpv00", "pb(y)", status); vvd(pvb[0][2], 0.2425996277722452400, 1e-14, "iauEpv00", "pb(z)", status); vvd(pvb[1][0], -0.1091874268116823295e-1, 1e-15, "iauEpv00", "vb(x)", status); vvd(pvb[1][1], -0.1246525461732861538e-1, 1e-15, "iauEpv00", "vb(y)", status); vvd(pvb[1][2], -0.5404773180966231279e-2, 1e-15, "iauEpv00", "vb(z)", status); viv(j, 0, "iauEpv00", "j", status); } static void t_eqec06(int *status) /* ** - - - - - - - - - ** t _ e q e c 0 6 ** - - - - - - - - - ** ** Test iauEqec06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEqec06, vvd ** ** This revision: 2016 March 12 */ { double date1, date2, dr, dd, dl, db; date1 = 1234.5; date2 = 2440000.5; dr = 1.234; dd = 0.987; iauEqec06(date1, date2, dr, dd, &dl, &db); vvd(dl, 1.342509918994654619, 1e-14, "iauEqec06", "dl", status); vvd(db, 0.5926215259704608132, 1e-14, "iauEqec06", "db", status); } static void t_eqeq94(int *status) /* ** - - - - - - - - - ** t _ e q e q 9 4 ** - - - - - - - - - ** ** Test iauEqeq94 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEqeq94, vvd ** ** This revision: 2013 August 7 */ { double eqeq; eqeq = iauEqeq94(2400000.5, 41234.0); vvd(eqeq, 0.5357758254609256894e-4, 1e-17, "iauEqeq94", "", status); } static void t_era00(int *status) /* ** - - - - - - - - ** t _ e r a 0 0 ** - - - - - - - - ** ** Test iauEra00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauEra00, vvd ** ** This revision: 2013 August 7 */ { double era00; era00 = iauEra00(2400000.5, 54388.0); vvd(era00, 0.4022837240028158102, 1e-12, "iauEra00", "", status); } static void t_fad03(int *status) /* ** - - - - - - - - ** t _ f a d 0 3 ** - - - - - - - - ** ** Test iauFad03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFad03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFad03(0.80), 1.946709205396925672, 1e-12, "iauFad03", "", status); } static void t_fae03(int *status) /* ** - - - - - - - - ** t _ f a e 0 3 ** - - - - - - - - ** ** Test iauFae03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFae03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFae03(0.80), 1.744713738913081846, 1e-12, "iauFae03", "", status); } static void t_faf03(int *status) /* ** - - - - - - - - ** t _ f a f 0 3 ** - - - - - - - - ** ** Test iauFaf03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFaf03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFaf03(0.80), 0.2597711366745499518, 1e-12, "iauFaf03", "", status); } static void t_faju03(int *status) /* ** - - - - - - - - - ** t _ f a j u 0 3 ** - - - - - - - - - ** ** Test iauFaju03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFaju03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFaju03(0.80), 5.275711665202481138, 1e-12, "iauFaju03", "", status); } static void t_fal03(int *status) /* ** - - - - - - - - ** t _ f a l 0 3 ** - - - - - - - - ** ** Test iauFal03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFal03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFal03(0.80), 5.132369751108684150, 1e-12, "iauFal03", "", status); } static void t_falp03(int *status) /* ** - - - - - - - - - ** t _ f a l p 0 3 ** - - - - - - - - - ** ** Test iauFalp03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFalp03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFalp03(0.80), 6.226797973505507345, 1e-12, "iauFalp03", "", status); } static void t_fama03(int *status) /* ** - - - - - - - - - ** t _ f a m a 0 3 ** - - - - - - - - - ** ** Test iauFama03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFama03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFama03(0.80), 3.275506840277781492, 1e-12, "iauFama03", "", status); } static void t_fame03(int *status) /* ** - - - - - - - - - ** t _ f a m e 0 3 ** - - - - - - - - - ** ** Test iauFame03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFame03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFame03(0.80), 5.417338184297289661, 1e-12, "iauFame03", "", status); } static void t_fane03(int *status) /* ** - - - - - - - - - ** t _ f a n e 0 3 ** - - - - - - - - - ** ** Test iauFane03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFane03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFane03(0.80), 2.079343830860413523, 1e-12, "iauFane03", "", status); } static void t_faom03(int *status) /* ** - - - - - - - - - ** t _ f a o m 0 3 ** - - - - - - - - - ** ** Test iauFaom03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFaom03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFaom03(0.80), -5.973618440951302183, 1e-12, "iauFaom03", "", status); } static void t_fapa03(int *status) /* ** - - - - - - - - - ** t _ f a p a 0 3 ** - - - - - - - - - ** ** Test iauFapa03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFapa03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFapa03(0.80), 0.1950884762240000000e-1, 1e-12, "iauFapa03", "", status); } static void t_fasa03(int *status) /* ** - - - - - - - - - ** t _ f a s a 0 3 ** - - - - - - - - - ** ** Test iauFasa03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFasa03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFasa03(0.80), 5.371574539440827046, 1e-12, "iauFasa03", "", status); } static void t_faur03(int *status) /* ** - - - - - - - - - ** t _ f a u r 0 3 ** - - - - - - - - - ** ** Test iauFaur03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFaur03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFaur03(0.80), 5.180636450180413523, 1e-12, "iauFaur03", "", status); } static void t_fave03(int *status) /* ** - - - - - - - - - ** t _ f a v e 0 3 ** - - - - - - - - - ** ** Test iauFave03 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFave03, vvd ** ** This revision: 2013 August 7 */ { vvd(iauFave03(0.80), 3.424900460533758000, 1e-12, "iauFave03", "", status); } static void t_fk52h(int *status) /* ** - - - - - - - - ** t _ f k 5 2 h ** - - - - - - - - ** ** Test iauFk52h function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFk52h, vvd ** ** This revision: 2016 December 22 */ { double r5, d5, dr5, dd5, px5, rv5, rh, dh, drh, ddh, pxh, rvh; r5 = 1.76779433; d5 = -0.2917517103; dr5 = -1.91851572e-7; dd5 = -5.8468475e-6; px5 = 0.379210; rv5 = -7.6; iauFk52h(r5, d5, dr5, dd5, px5, rv5, &rh, &dh, &drh, &ddh, &pxh, &rvh); vvd(rh, 1.767794226299947632, 1e-14, "iauFk52h", "ra", status); vvd(dh, -0.2917516070530391757, 1e-14, "iauFk52h", "dec", status); vvd(drh, -0.19618741256057224e-6,1e-19, "iauFk52h", "dr5", status); vvd(ddh, -0.58459905176693911e-5, 1e-19, "iauFk52h", "dd5", status); vvd(pxh, 0.37921, 1e-14, "iauFk52h", "px", status); vvd(rvh, -7.6000000940000254, 1e-10, "iauFk52h", "rv", status); } static void t_fk5hip(int *status) /* ** - - - - - - - - - ** t _ f k 5 h i p ** - - - - - - - - - ** ** Test iauFk5hip function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFk5hip, vvd ** ** This revision: 2013 August 7 */ { double r5h[3][3], s5h[3]; iauFk5hip(r5h, s5h); vvd(r5h[0][0], 0.9999999999999928638, 1e-14, "iauFk5hip", "11", status); vvd(r5h[0][1], 0.1110223351022919694e-6, 1e-17, "iauFk5hip", "12", status); vvd(r5h[0][2], 0.4411803962536558154e-7, 1e-17, "iauFk5hip", "13", status); vvd(r5h[1][0], -0.1110223308458746430e-6, 1e-17, "iauFk5hip", "21", status); vvd(r5h[1][1], 0.9999999999999891830, 1e-14, "iauFk5hip", "22", status); vvd(r5h[1][2], -0.9647792498984142358e-7, 1e-17, "iauFk5hip", "23", status); vvd(r5h[2][0], -0.4411805033656962252e-7, 1e-17, "iauFk5hip", "31", status); vvd(r5h[2][1], 0.9647792009175314354e-7, 1e-17, "iauFk5hip", "32", status); vvd(r5h[2][2], 0.9999999999999943728, 1e-14, "iauFk5hip", "33", status); vvd(s5h[0], -0.1454441043328607981e-8, 1e-17, "iauFk5hip", "s1", status); vvd(s5h[1], 0.2908882086657215962e-8, 1e-17, "iauFk5hip", "s2", status); vvd(s5h[2], 0.3393695767766751955e-8, 1e-17, "iauFk5hip", "s3", status); } static void t_fk5hz(int *status) /* ** - - - - - - - - ** t _ f k 5 h z ** - - - - - - - - ** ** Test iauFk5hz function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFk5hz, vvd ** ** This revision: 2013 August 7 */ { double r5, d5, rh, dh; r5 = 1.76779433; d5 = -0.2917517103; iauFk5hz(r5, d5, 2400000.5, 54479.0, &rh, &dh); vvd(rh, 1.767794191464423978, 1e-12, "iauFk5hz", "ra", status); vvd(dh, -0.2917516001679884419, 1e-12, "iauFk5hz", "dec", status); } static void t_fw2m(int *status) /* ** - - - - - - - ** t _ f w 2 m ** - - - - - - - ** ** Test iauFw2m function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFw2m, vvd ** ** This revision: 2013 August 7 */ { double gamb, phib, psi, eps, r[3][3]; gamb = -0.2243387670997992368e-5; phib = 0.4091014602391312982; psi = -0.9501954178013015092e-3; eps = 0.4091014316587367472; iauFw2m(gamb, phib, psi, eps, r); vvd(r[0][0], 0.9999995505176007047, 1e-12, "iauFw2m", "11", status); vvd(r[0][1], 0.8695404617348192957e-3, 1e-12, "iauFw2m", "12", status); vvd(r[0][2], 0.3779735201865582571e-3, 1e-12, "iauFw2m", "13", status); vvd(r[1][0], -0.8695404723772016038e-3, 1e-12, "iauFw2m", "21", status); vvd(r[1][1], 0.9999996219496027161, 1e-12, "iauFw2m", "22", status); vvd(r[1][2], -0.1361752496887100026e-6, 1e-12, "iauFw2m", "23", status); vvd(r[2][0], -0.3779734957034082790e-3, 1e-12, "iauFw2m", "31", status); vvd(r[2][1], -0.1924880848087615651e-6, 1e-12, "iauFw2m", "32", status); vvd(r[2][2], 0.9999999285679971958, 1e-12, "iauFw2m", "33", status); } static void t_fw2xy(int *status) /* ** - - - - - - - - ** t _ f w 2 x y ** - - - - - - - - ** ** Test iauFw2xy function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauFw2xy, vvd ** ** This revision: 2013 August 7 */ { double gamb, phib, psi, eps, x, y; gamb = -0.2243387670997992368e-5; phib = 0.4091014602391312982; psi = -0.9501954178013015092e-3; eps = 0.4091014316587367472; iauFw2xy(gamb, phib, psi, eps, &x, &y); vvd(x, -0.3779734957034082790e-3, 1e-14, "iauFw2xy", "x", status); vvd(y, -0.1924880848087615651e-6, 1e-14, "iauFw2xy", "y", status); } static void t_g2icrs(int *status) /* ** - - - - - - - - - ** t _ g 2 i c r s ** - - - - - - - - - ** ** Test iauG2icrs function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauG2icrs, vvd ** ** This revision: 2015 January 30 */ { double dl, db, dr, dd; dl = 5.5850536063818546461558105; db = -0.7853981633974483096156608; iauG2icrs (dl, db, &dr, &dd); vvd(dr, 5.9338074302227188048671, 1e-14, "iauG2icrs", "R", status); vvd(dd, -1.1784870613579944551541, 1e-14, "iauG2icrs", "D", status); } static void t_gc2gd(int *status) /* ** - - - - - - - - ** t _ g c 2 g d ** - - - - - - - - ** ** Test iauGc2gd function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGc2gd, viv, vvd ** ** This revision: 2016 March 12 */ { int j; double xyz[] = {2e6, 3e6, 5.244e6}; double e, p, h; j = iauGc2gd(0, xyz, &e, &p, &h); viv(j, -1, "iauGc2gd", "j0", status); j = iauGc2gd(WGS84, xyz, &e, &p, &h); viv(j, 0, "iauGc2gd", "j1", status); vvd(e, 0.9827937232473290680, 1e-14, "iauGc2gd", "e1", status); vvd(p, 0.97160184819075459, 1e-14, "iauGc2gd", "p1", status); vvd(h, 331.4172461426059892, 1e-8, "iauGc2gd", "h1", status); j = iauGc2gd(GRS80, xyz, &e, &p, &h); viv(j, 0, "iauGc2gd", "j2", status); vvd(e, 0.9827937232473290680, 1e-14, "iauGc2gd", "e2", status); vvd(p, 0.97160184820607853, 1e-14, "iauGc2gd", "p2", status); vvd(h, 331.41731754844348, 1e-8, "iauGc2gd", "h2", status); j = iauGc2gd(WGS72, xyz, &e, &p, &h); viv(j, 0, "iauGc2gd", "j3", status); vvd(e, 0.9827937232473290680, 1e-14, "iauGc2gd", "e3", status); vvd(p, 0.9716018181101511937, 1e-14, "iauGc2gd", "p3", status); vvd(h, 333.2770726130318123, 1e-8, "iauGc2gd", "h3", status); j = iauGc2gd(4, xyz, &e, &p, &h); viv(j, -1, "iauGc2gd", "j4", status); } static void t_gc2gde(int *status) /* ** - - - - - - - - - ** t _ g c 2 g d e ** - - - - - - - - - ** ** Test iauGc2gde function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGc2gde, viv, vvd ** ** This revision: 2016 March 12 */ { int j; double a = 6378136.0, f = 0.0033528; double xyz[] = {2e6, 3e6, 5.244e6}; double e, p, h; j = iauGc2gde(a, f, xyz, &e, &p, &h); viv(j, 0, "iauGc2gde", "j", status); vvd(e, 0.9827937232473290680, 1e-14, "iauGc2gde", "e", status); vvd(p, 0.9716018377570411532, 1e-14, "iauGc2gde", "p", status); vvd(h, 332.36862495764397, 1e-8, "iauGc2gde", "h", status); } static void t_gd2gc(int *status) /* ** - - - - - - - - ** t _ g d 2 g c ** - - - - - - - - ** ** Test iauGd2gc function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGd2gc, viv, vvd ** ** This revision: 2016 March 12 */ { int j; double e = 3.1, p = -0.5, h = 2500.0; double xyz[3]; j = iauGd2gc(0, e, p, h, xyz); viv(j, -1, "iauGd2gc", "j0", status); j = iauGd2gc(WGS84, e, p, h, xyz); viv(j, 0, "iauGd2gc", "j1", status); vvd(xyz[0], -5599000.5577049947, 1e-7, "iauGd2gc", "1/1", status); vvd(xyz[1], 233011.67223479203, 1e-7, "iauGd2gc", "2/1", status); vvd(xyz[2], -3040909.4706983363, 1e-7, "iauGd2gc", "3/1", status); j = iauGd2gc(GRS80, e, p, h, xyz); viv(j, 0, "iauGd2gc", "j2", status); vvd(xyz[0], -5599000.5577260984, 1e-7, "iauGd2gc", "1/2", status); vvd(xyz[1], 233011.6722356702949, 1e-7, "iauGd2gc", "2/2", status); vvd(xyz[2], -3040909.4706095476, 1e-7, "iauGd2gc", "3/2", status); j = iauGd2gc(WGS72, e, p, h, xyz); viv(j, 0, "iauGd2gc", "j3", status); vvd(xyz[0], -5598998.7626301490, 1e-7, "iauGd2gc", "1/3", status); vvd(xyz[1], 233011.5975297822211, 1e-7, "iauGd2gc", "2/3", status); vvd(xyz[2], -3040908.6861467111, 1e-7, "iauGd2gc", "3/3", status); j = iauGd2gc(4, e, p, h, xyz); viv(j, -1, "iauGd2gc", "j4", status); } static void t_gd2gce(int *status) /* ** - - - - - - - - - ** t _ g d 2 g c e ** - - - - - - - - - ** ** Test iauGd2gce function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGd2gce, viv, vvd ** ** This revision: 2016 March 12 */ { int j; double a = 6378136.0, f = 0.0033528; double e = 3.1, p = -0.5, h = 2500.0; double xyz[3]; j = iauGd2gce(a, f, e, p, h, xyz); viv(j, 0, "iauGd2gce", "j", status); vvd(xyz[0], -5598999.6665116328, 1e-7, "iauGd2gce", "1", status); vvd(xyz[1], 233011.6351463057189, 1e-7, "iauGd2gce", "2", status); vvd(xyz[2], -3040909.0517314132, 1e-7, "iauGd2gce", "3", status); } static void t_gmst00(int *status) /* ** - - - - - - - - - ** t _ g m s t 0 0 ** - - - - - - - - - ** ** Test iauGmst00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGmst00, vvd ** ** This revision: 2013 August 7 */ { double theta; theta = iauGmst00(2400000.5, 53736.0, 2400000.5, 53736.0); vvd(theta, 1.754174972210740592, 1e-12, "iauGmst00", "", status); } static void t_gmst06(int *status) /* ** - - - - - - - - - ** t _ g m s t 0 6 ** - - - - - - - - - ** ** Test iauGmst06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGmst06, vvd ** ** This revision: 2013 August 7 */ { double theta; theta = iauGmst06(2400000.5, 53736.0, 2400000.5, 53736.0); vvd(theta, 1.754174971870091203, 1e-12, "iauGmst06", "", status); } static void t_gmst82(int *status) /* ** - - - - - - - - - ** t _ g m s t 8 2 ** - - - - - - - - - ** ** Test iauGmst82 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGmst82, vvd ** ** This revision: 2013 August 7 */ { double theta; theta = iauGmst82(2400000.5, 53736.0); vvd(theta, 1.754174981860675096, 1e-12, "iauGmst82", "", status); } static void t_gst00a(int *status) /* ** - - - - - - - - - ** t _ g s t 0 0 a ** - - - - - - - - - ** ** Test iauGst00a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGst00a, vvd ** ** This revision: 2013 August 7 */ { double theta; theta = iauGst00a(2400000.5, 53736.0, 2400000.5, 53736.0); vvd(theta, 1.754166138018281369, 1e-12, "iauGst00a", "", status); } static void t_gst00b(int *status) /* ** - - - - - - - - - ** t _ g s t 0 0 b ** - - - - - - - - - ** ** Test iauGst00b function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGst00b, vvd ** ** This revision: 2013 August 7 */ { double theta; theta = iauGst00b(2400000.5, 53736.0); vvd(theta, 1.754166136510680589, 1e-12, "iauGst00b", "", status); } static void t_gst06(int *status) /* ** - - - - - - - - ** t _ g s t 0 6 ** - - - - - - - - ** ** Test iauGst06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGst06, vvd ** ** This revision: 2013 August 7 */ { double rnpb[3][3], theta; rnpb[0][0] = 0.9999989440476103608; rnpb[0][1] = -0.1332881761240011518e-2; rnpb[0][2] = -0.5790767434730085097e-3; rnpb[1][0] = 0.1332858254308954453e-2; rnpb[1][1] = 0.9999991109044505944; rnpb[1][2] = -0.4097782710401555759e-4; rnpb[2][0] = 0.5791308472168153320e-3; rnpb[2][1] = 0.4020595661593994396e-4; rnpb[2][2] = 0.9999998314954572365; theta = iauGst06(2400000.5, 53736.0, 2400000.5, 53736.0, rnpb); vvd(theta, 1.754166138018167568, 1e-12, "iauGst06", "", status); } static void t_gst06a(int *status) /* ** - - - - - - - - - ** t _ g s t 0 6 a ** - - - - - - - - - ** ** Test iauGst06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGst06a, vvd ** ** This revision: 2013 August 7 */ { double theta; theta = iauGst06a(2400000.5, 53736.0, 2400000.5, 53736.0); vvd(theta, 1.754166137675019159, 1e-12, "iauGst06a", "", status); } static void t_gst94(int *status) /* ** - - - - - - - - ** t _ g s t 9 4 ** - - - - - - - - ** ** Test iauGst94 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauGst94, vvd ** ** This revision: 2013 August 7 */ { double theta; theta = iauGst94(2400000.5, 53736.0); vvd(theta, 1.754166136020645203, 1e-12, "iauGst94", "", status); } static void t_icrs2g(int *status) /* ** - - - - - - - - - ** t _ i c r s 2 g ** - - - - - - - - - ** ** Test iauIcrs2g function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauIcrs2g, vvd ** ** This revision: 2015 January 30 */ { double dr, dd, dl, db; dr = 5.9338074302227188048671087; dd = -1.1784870613579944551540570; iauIcrs2g (dr, dd, &dl, &db); vvd(dl, 5.5850536063818546461558, 1e-14, "iauIcrs2g", "L", status); vvd(db, -0.7853981633974483096157, 1e-14, "iauIcrs2g", "B", status); } static void t_h2fk5(int *status) /* ** - - - - - - - - ** t _ h 2 f k 5 ** - - - - - - - - ** ** Test iauH2fk5 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauH2fk5, vvd ** ** This revision: 2013 August 7 */ { double rh, dh, drh, ddh, pxh, rvh, r5, d5, dr5, dd5, px5, rv5; rh = 1.767794352; dh = -0.2917512594; drh = -2.76413026e-6; ddh = -5.92994449e-6; pxh = 0.379210; rvh = -7.6; iauH2fk5(rh, dh, drh, ddh, pxh, rvh, &r5, &d5, &dr5, &dd5, &px5, &rv5); vvd(r5, 1.767794455700065506, 1e-13, "iauH2fk5", "ra", status); vvd(d5, -0.2917513626469638890, 1e-13, "iauH2fk5", "dec", status); vvd(dr5, -0.27597945024511204e-5, 1e-18, "iauH2fk5", "dr5", status); vvd(dd5, -0.59308014093262838e-5, 1e-18, "iauH2fk5", "dd5", status); vvd(px5, 0.37921, 1e-13, "iauH2fk5", "px", status); vvd(rv5, -7.6000001309071126, 1e-10, "iauH2fk5", "rv", status); } static void t_hfk5z(int *status) /* ** - - - - - - - - ** t _ h f k 5 z ** - - - - - - - - ** ** Test iauHfk5z function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauHfk5z, vvd ** ** This revision: 2013 August 7 */ { double rh, dh, r5, d5, dr5, dd5; rh = 1.767794352; dh = -0.2917512594; iauHfk5z(rh, dh, 2400000.5, 54479.0, &r5, &d5, &dr5, &dd5); vvd(r5, 1.767794490535581026, 1e-13, "iauHfk5z", "ra", status); vvd(d5, -0.2917513695320114258, 1e-14, "iauHfk5z", "dec", status); vvd(dr5, 0.4335890983539243029e-8, 1e-22, "iauHfk5z", "dr5", status); vvd(dd5, -0.8569648841237745902e-9, 1e-23, "iauHfk5z", "dd5", status); } static void t_ir(int *status) /* ** - - - - - ** t _ i r ** - - - - - ** ** Test iauIr function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauIr, vvd ** ** This revision: 2013 August 7 */ { double r[3][3]; r[0][0] = 2.0; r[0][1] = 3.0; r[0][2] = 2.0; r[1][0] = 3.0; r[1][1] = 2.0; r[1][2] = 3.0; r[2][0] = 3.0; r[2][1] = 4.0; r[2][2] = 5.0; iauIr(r); vvd(r[0][0], 1.0, 0.0, "iauIr", "11", status); vvd(r[0][1], 0.0, 0.0, "iauIr", "12", status); vvd(r[0][2], 0.0, 0.0, "iauIr", "13", status); vvd(r[1][0], 0.0, 0.0, "iauIr", "21", status); vvd(r[1][1], 1.0, 0.0, "iauIr", "22", status); vvd(r[1][2], 0.0, 0.0, "iauIr", "23", status); vvd(r[2][0], 0.0, 0.0, "iauIr", "31", status); vvd(r[2][1], 0.0, 0.0, "iauIr", "32", status); vvd(r[2][2], 1.0, 0.0, "iauIr", "33", status); } static void t_jd2cal(int *status) /* ** - - - - - - - - - ** t _ j d 2 c a l ** - - - - - - - - - ** ** Test iauJd2cal function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauJd2cal, viv, vvd ** ** This revision: 2013 August 7 */ { double dj1, dj2, fd; int iy, im, id, j; dj1 = 2400000.5; dj2 = 50123.9999; j = iauJd2cal(dj1, dj2, &iy, &im, &id, &fd); viv(iy, 1996, "iauJd2cal", "y", status); viv(im, 2, "iauJd2cal", "m", status); viv(id, 10, "iauJd2cal", "d", status); vvd(fd, 0.9999, 1e-7, "iauJd2cal", "fd", status); viv(j, 0, "iauJd2cal", "j", status); } static void t_jdcalf(int *status) /* ** - - - - - - - - - ** t _ j d c a l f ** - - - - - - - - - ** ** Test iauJdcalf function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauJdcalf, viv ** ** This revision: 2013 August 7 */ { double dj1, dj2; int iydmf[4], j; dj1 = 2400000.5; dj2 = 50123.9999; j = iauJdcalf(4, dj1, dj2, iydmf); viv(iydmf[0], 1996, "iauJdcalf", "y", status); viv(iydmf[1], 2, "iauJdcalf", "m", status); viv(iydmf[2], 10, "iauJdcalf", "d", status); viv(iydmf[3], 9999, "iauJdcalf", "f", status); viv(j, 0, "iauJdcalf", "j", status); } static void t_ld(int *status) /* ** - - - - - ** t _ l d ** - - - - - ** ** Test iauLd function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauLd, vvd * ** This revision: 2013 October 2 */ { double bm, p[3], q[3], e[3], em, dlim, p1[3]; bm = 0.00028574; p[0] = -0.763276255; p[1] = -0.608633767; p[2] = -0.216735543; q[0] = -0.763276255; q[1] = -0.608633767; q[2] = -0.216735543; e[0] = 0.76700421; e[1] = 0.605629598; e[2] = 0.211937094; em = 8.91276983; dlim = 3e-10; iauLd(bm, p, q, e, em, dlim, p1); vvd(p1[0], -0.7632762548968159627, 1e-12, "iauLd", "1", status); vvd(p1[1], -0.6086337670823762701, 1e-12, "iauLd", "2", status); vvd(p1[2], -0.2167355431320546947, 1e-12, "iauLd", "3", status); } static void t_ldn(int *status) /* ** - - - - - - ** t _ l d n ** - - - - - - ** ** Test iauLdn function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauLdn, vvd ** ** This revision: 2013 October 2 */ { int n; iauLDBODY b[3]; double ob[3], sc[3], sn[3]; n = 3; b[0].bm = 0.00028574; b[0].dl = 3e-10; b[0].pv[0][0] = -7.81014427; b[0].pv[0][1] = -5.60956681; b[0].pv[0][2] = -1.98079819; b[0].pv[1][0] = 0.0030723249; b[0].pv[1][1] = -0.00406995477; b[0].pv[1][2] = -0.00181335842; b[1].bm = 0.00095435; b[1].dl = 3e-9; b[1].pv[0][0] = 0.738098796; b[1].pv[0][1] = 4.63658692; b[1].pv[0][2] = 1.9693136; b[1].pv[1][0] = -0.00755816922; b[1].pv[1][1] = 0.00126913722; b[1].pv[1][2] = 0.000727999001; b[2].bm = 1.0; b[2].dl = 6e-6; b[2].pv[0][0] = -0.000712174377; b[2].pv[0][1] = -0.00230478303; b[2].pv[0][2] = -0.00105865966; b[2].pv[1][0] = 6.29235213e-6; b[2].pv[1][1] = -3.30888387e-7; b[2].pv[1][2] = -2.96486623e-7; ob[0] = -0.974170437; ob[1] = -0.2115201; ob[2] = -0.0917583114; sc[0] = -0.763276255; sc[1] = -0.608633767; sc[2] = -0.216735543; iauLdn(n, b, ob, sc, sn); vvd(sn[0], -0.7632762579693333866, 1e-12, "iauLdn", "1", status); vvd(sn[1], -0.6086337636093002660, 1e-12, "iauLdn", "2", status); vvd(sn[2], -0.2167355420646328159, 1e-12, "iauLdn", "3", status); } static void t_ldsun(int *status) /* ** - - - - - - - - ** t _ l d s u n ** - - - - - - - - ** ** Test iauLdsun function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauLdsun, vvd ** ** This revision: 2013 October 2 */ { double p[3], e[3], em, p1[3]; p[0] = -0.763276255; p[1] = -0.608633767; p[2] = -0.216735543; e[0] = -0.973644023; e[1] = -0.20925523; e[2] = -0.0907169552; em = 0.999809214; iauLdsun(p, e, em, p1); vvd(p1[0], -0.7632762580731413169, 1e-12, "iauLdsun", "1", status); vvd(p1[1], -0.6086337635262647900, 1e-12, "iauLdsun", "2", status); vvd(p1[2], -0.2167355419322321302, 1e-12, "iauLdsun", "3", status); } static void t_lteceq(int *status) /* ** - - - - - - - - - ** t _ l t e c e q ** - - - - - - - - - ** ** Test iauLteceq function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauLteceq, vvd ** ** This revision: 2016 March 12 */ { double epj, dl, db, dr, dd; epj = 2500.0; dl = 1.5; db = 0.6; iauLteceq(epj, dl, db, &dr, &dd); vvd(dr, 1.275156021861921167, 1e-14, "iauLteceq", "dr", status); vvd(dd, 0.9966573543519204791, 1e-14, "iauLteceq", "dd", status); } static void t_ltecm(int *status) /* ** - - - - - - - - ** t _ l t e c m ** - - - - - - - - ** ** Test iauLtecm function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauLtecm, vvd ** ** This revision: 2016 March 12 */ { double epj, rm[3][3]; epj = -3000.0; iauLtecm(epj, rm); vvd(rm[0][0], 0.3564105644859788825, 1e-14, "iauLtecm", "rm11", status); vvd(rm[0][1], 0.8530575738617682284, 1e-14, "iauLtecm", "rm12", status); vvd(rm[0][2], 0.3811355207795060435, 1e-14, "iauLtecm", "rm13", status); vvd(rm[1][0], -0.9343283469640709942, 1e-14, "iauLtecm", "rm21", status); vvd(rm[1][1], 0.3247830597681745976, 1e-14, "iauLtecm", "rm22", status); vvd(rm[1][2], 0.1467872751535940865, 1e-14, "iauLtecm", "rm23", status); vvd(rm[2][0], 0.1431636191201167793e-2, 1e-14, "iauLtecm", "rm31", status); vvd(rm[2][1], -0.4084222566960599342, 1e-14, "iauLtecm", "rm32", status); vvd(rm[2][2], 0.9127919865189030899, 1e-14, "iauLtecm", "rm33", status); } static void t_lteqec(int *status) /* ** - - - - - - - - - ** t _ l t e q e c ** - - - - - - - - - ** ** Test iauLteqec function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauLteqec, vvd ** ** This revision: 2016 March 12 */ { double epj, dr, dd, dl, db; epj = -1500.0; dr = 1.234; dd = 0.987; iauLteqec(epj, dr, dd, &dl, &db); vvd(dl, 0.5039483649047114859, 1e-14, "iauLteqec", "dl", status); vvd(db, 0.5848534459726224882, 1e-14, "iauLteqec", "db", status); } static void t_ltp(int *status) /* ** - - - - - - ** t _ l t p ** - - - - - - ** ** Test iauLtp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauLtp, vvd ** ** This revision: 2016 March 12 */ { double epj, rp[3][3]; epj = 1666.666; iauLtp(epj, rp); vvd(rp[0][0], 0.9967044141159213819, 1e-14, "iauLtp", "rp11", status); vvd(rp[0][1], 0.7437801893193210840e-1, 1e-14, "iauLtp", "rp12", status); vvd(rp[0][2], 0.3237624409345603401e-1, 1e-14, "iauLtp", "rp13", status); vvd(rp[1][0], -0.7437802731819618167e-1, 1e-14, "iauLtp", "rp21", status); vvd(rp[1][1], 0.9972293894454533070, 1e-14, "iauLtp", "rp22", status); vvd(rp[1][2], -0.1205768842723593346e-2, 1e-14, "iauLtp", "rp23", status); vvd(rp[2][0], -0.3237622482766575399e-1, 1e-14, "iauLtp", "rp31", status); vvd(rp[2][1], -0.1206286039697609008e-2, 1e-14, "iauLtp", "rp32", status); vvd(rp[2][2], 0.9994750246704010914, 1e-14, "iauLtp", "rp33", status); } static void t_ltpb(int *status) /* ** - - - - - - - ** t _ l t p b ** - - - - - - - ** ** Test iauLtpb function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauLtpb, vvd ** ** This revision: 2016 March 12 */ { double epj, rpb[3][3]; epj = 1666.666; iauLtpb(epj, rpb); vvd(rpb[0][0], 0.9967044167723271851, 1e-14, "iauLtpb", "rpb11", status); vvd(rpb[0][1], 0.7437794731203340345e-1, 1e-14, "iauLtpb", "rpb12", status); vvd(rpb[0][2], 0.3237632684841625547e-1, 1e-14, "iauLtpb", "rpb13", status); vvd(rpb[1][0], -0.7437795663437177152e-1, 1e-14, "iauLtpb", "rpb21", status); vvd(rpb[1][1], 0.9972293947500013666, 1e-14, "iauLtpb", "rpb22", status); vvd(rpb[1][2], -0.1205741865911243235e-2, 1e-14, "iauLtpb", "rpb23", status); vvd(rpb[2][0], -0.3237630543224664992e-1, 1e-14, "iauLtpb", "rpb31", status); vvd(rpb[2][1], -0.1206316791076485295e-2, 1e-14, "iauLtpb", "rpb32", status); vvd(rpb[2][2], 0.9994750220222438819, 1e-14, "iauLtpb", "rpb33", status); } static void t_ltpecl(int *status) /* ** - - - - - - - - - ** t _ l t p e c l ** - - - - - - - - - ** ** Test iauLtpecl function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauLtpecl, vvd ** ** This revision: 2016 March 12 */ { double epj, vec[3]; epj = -1500.0; iauLtpecl(epj, vec); vvd(vec[0], 0.4768625676477096525e-3, 1e-14, "iauLtpecl", "vec1", status); vvd(vec[1], -0.4052259533091875112, 1e-14, "iauLtpecl", "vec2", status); vvd(vec[2], 0.9142164401096448012, 1e-14, "iauLtpecl", "vec3", status); } static void t_ltpequ(int *status) /* ** - - - - - - - - - ** t _ l t p e q u ** - - - - - - - - - ** ** Test iauLtpequ function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauLtpequ, vvd ** ** This revision: 2016 March 12 */ { double epj, veq[3]; epj = -2500.0; iauLtpequ(epj, veq); vvd(veq[0], -0.3586652560237326659, 1e-14, "iauLtpequ", "veq1", status); vvd(veq[1], -0.1996978910771128475, 1e-14, "iauLtpequ", "veq2", status); vvd(veq[2], 0.9118552442250819624, 1e-14, "iauLtpequ", "veq3", status); } static void t_num00a(int *status) /* ** - - - - - - - - - ** t _ n u m 0 0 a ** - - - - - - - - - ** ** Test iauNum00a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauNum00a, vvd ** ** This revision: 2013 August 7 */ { double rmatn[3][3]; iauNum00a(2400000.5, 53736.0, rmatn); vvd(rmatn[0][0], 0.9999999999536227949, 1e-12, "iauNum00a", "11", status); vvd(rmatn[0][1], 0.8836238544090873336e-5, 1e-12, "iauNum00a", "12", status); vvd(rmatn[0][2], 0.3830835237722400669e-5, 1e-12, "iauNum00a", "13", status); vvd(rmatn[1][0], -0.8836082880798569274e-5, 1e-12, "iauNum00a", "21", status); vvd(rmatn[1][1], 0.9999999991354655028, 1e-12, "iauNum00a", "22", status); vvd(rmatn[1][2], -0.4063240865362499850e-4, 1e-12, "iauNum00a", "23", status); vvd(rmatn[2][0], -0.3831194272065995866e-5, 1e-12, "iauNum00a", "31", status); vvd(rmatn[2][1], 0.4063237480216291775e-4, 1e-12, "iauNum00a", "32", status); vvd(rmatn[2][2], 0.9999999991671660338, 1e-12, "iauNum00a", "33", status); } static void t_num00b(int *status) /* ** - - - - - - - - - ** t _ n u m 0 0 b ** - - - - - - - - - ** ** Test iauNum00b function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauNum00b, vvd ** ** This revision: 2013 August 7 */ { double rmatn[3][3]; iauNum00b(2400000.5, 53736, rmatn); vvd(rmatn[0][0], 0.9999999999536069682, 1e-12, "iauNum00b", "11", status); vvd(rmatn[0][1], 0.8837746144871248011e-5, 1e-12, "iauNum00b", "12", status); vvd(rmatn[0][2], 0.3831488838252202945e-5, 1e-12, "iauNum00b", "13", status); vvd(rmatn[1][0], -0.8837590456632304720e-5, 1e-12, "iauNum00b", "21", status); vvd(rmatn[1][1], 0.9999999991354692733, 1e-12, "iauNum00b", "22", status); vvd(rmatn[1][2], -0.4063198798559591654e-4, 1e-12, "iauNum00b", "23", status); vvd(rmatn[2][0], -0.3831847930134941271e-5, 1e-12, "iauNum00b", "31", status); vvd(rmatn[2][1], 0.4063195412258168380e-4, 1e-12, "iauNum00b", "32", status); vvd(rmatn[2][2], 0.9999999991671806225, 1e-12, "iauNum00b", "33", status); } static void t_num06a(int *status) /* ** - - - - - - - - - ** t _ n u m 0 6 a ** - - - - - - - - - ** ** Test iauNum06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauNum06a, vvd ** ** This revision: 2013 August 7 */ { double rmatn[3][3]; iauNum06a(2400000.5, 53736, rmatn); vvd(rmatn[0][0], 0.9999999999536227668, 1e-12, "iauNum06a", "11", status); vvd(rmatn[0][1], 0.8836241998111535233e-5, 1e-12, "iauNum06a", "12", status); vvd(rmatn[0][2], 0.3830834608415287707e-5, 1e-12, "iauNum06a", "13", status); vvd(rmatn[1][0], -0.8836086334870740138e-5, 1e-12, "iauNum06a", "21", status); vvd(rmatn[1][1], 0.9999999991354657474, 1e-12, "iauNum06a", "22", status); vvd(rmatn[1][2], -0.4063240188248455065e-4, 1e-12, "iauNum06a", "23", status); vvd(rmatn[2][0], -0.3831193642839398128e-5, 1e-12, "iauNum06a", "31", status); vvd(rmatn[2][1], 0.4063236803101479770e-4, 1e-12, "iauNum06a", "32", status); vvd(rmatn[2][2], 0.9999999991671663114, 1e-12, "iauNum06a", "33", status); } static void t_numat(int *status) /* ** - - - - - - - - ** t _ n u m a t ** - - - - - - - - ** ** Test iauNumat function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauNumat, vvd ** ** This revision: 2013 August 7 */ { double epsa, dpsi, deps, rmatn[3][3]; epsa = 0.4090789763356509900; dpsi = -0.9630909107115582393e-5; deps = 0.4063239174001678826e-4; iauNumat(epsa, dpsi, deps, rmatn); vvd(rmatn[0][0], 0.9999999999536227949, 1e-12, "iauNumat", "11", status); vvd(rmatn[0][1], 0.8836239320236250577e-5, 1e-12, "iauNumat", "12", status); vvd(rmatn[0][2], 0.3830833447458251908e-5, 1e-12, "iauNumat", "13", status); vvd(rmatn[1][0], -0.8836083657016688588e-5, 1e-12, "iauNumat", "21", status); vvd(rmatn[1][1], 0.9999999991354654959, 1e-12, "iauNumat", "22", status); vvd(rmatn[1][2], -0.4063240865361857698e-4, 1e-12, "iauNumat", "23", status); vvd(rmatn[2][0], -0.3831192481833385226e-5, 1e-12, "iauNumat", "31", status); vvd(rmatn[2][1], 0.4063237480216934159e-4, 1e-12, "iauNumat", "32", status); vvd(rmatn[2][2], 0.9999999991671660407, 1e-12, "iauNumat", "33", status); } static void t_nut00a(int *status) /* ** - - - - - - - - - ** t _ n u t 0 0 a ** - - - - - - - - - ** ** Test iauNut00a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauNut00a, vvd ** ** This revision: 2013 August 7 */ { double dpsi, deps; iauNut00a(2400000.5, 53736.0, &dpsi, &deps); vvd(dpsi, -0.9630909107115518431e-5, 1e-13, "iauNut00a", "dpsi", status); vvd(deps, 0.4063239174001678710e-4, 1e-13, "iauNut00a", "deps", status); } static void t_nut00b(int *status) /* ** - - - - - - - - - ** t _ n u t 0 0 b ** - - - - - - - - - ** ** Test iauNut00b function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauNut00b, vvd ** ** This revision: 2013 August 7 */ { double dpsi, deps; iauNut00b(2400000.5, 53736.0, &dpsi, &deps); vvd(dpsi, -0.9632552291148362783e-5, 1e-13, "iauNut00b", "dpsi", status); vvd(deps, 0.4063197106621159367e-4, 1e-13, "iauNut00b", "deps", status); } static void t_nut06a(int *status) /* ** - - - - - - - - - ** t _ n u t 0 6 a ** - - - - - - - - - ** ** Test iauNut06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauNut06a, vvd ** ** This revision: 2013 August 7 */ { double dpsi, deps; iauNut06a(2400000.5, 53736.0, &dpsi, &deps); vvd(dpsi, -0.9630912025820308797e-5, 1e-13, "iauNut06a", "dpsi", status); vvd(deps, 0.4063238496887249798e-4, 1e-13, "iauNut06a", "deps", status); } static void t_nut80(int *status) /* ** - - - - - - - - ** t _ n u t 8 0 ** - - - - - - - - ** ** Test iauNut80 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauNut80, vvd ** ** This revision: 2013 August 7 */ { double dpsi, deps; iauNut80(2400000.5, 53736.0, &dpsi, &deps); vvd(dpsi, -0.9643658353226563966e-5, 1e-13, "iauNut80", "dpsi", status); vvd(deps, 0.4060051006879713322e-4, 1e-13, "iauNut80", "deps", status); } static void t_nutm80(int *status) /* ** - - - - - - - - - ** t _ n u t m 8 0 ** - - - - - - - - - ** ** Test iauNutm80 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauNutm80, vvd ** ** This revision: 2013 August 7 */ { double rmatn[3][3]; iauNutm80(2400000.5, 53736.0, rmatn); vvd(rmatn[0][0], 0.9999999999534999268, 1e-12, "iauNutm80", "11", status); vvd(rmatn[0][1], 0.8847935789636432161e-5, 1e-12, "iauNutm80", "12", status); vvd(rmatn[0][2], 0.3835906502164019142e-5, 1e-12, "iauNutm80", "13", status); vvd(rmatn[1][0], -0.8847780042583435924e-5, 1e-12, "iauNutm80", "21", status); vvd(rmatn[1][1], 0.9999999991366569963, 1e-12, "iauNutm80", "22", status); vvd(rmatn[1][2], -0.4060052702727130809e-4, 1e-12, "iauNutm80", "23", status); vvd(rmatn[2][0], -0.3836265729708478796e-5, 1e-12, "iauNutm80", "31", status); vvd(rmatn[2][1], 0.4060049308612638555e-4, 1e-12, "iauNutm80", "32", status); vvd(rmatn[2][2], 0.9999999991684415129, 1e-12, "iauNutm80", "33", status); } static void t_obl06(int *status) /* ** - - - - - - - - ** t _ o b l 0 6 ** - - - - - - - - ** ** Test iauObl06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauObl06, vvd ** ** This revision: 2013 August 7 */ { vvd(iauObl06(2400000.5, 54388.0), 0.4090749229387258204, 1e-14, "iauObl06", "", status); } static void t_obl80(int *status) /* ** - - - - - - - - ** t _ o b l 8 0 ** - - - - - - - - ** ** Test iauObl80 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauObl80, vvd ** ** This revision: 2013 August 7 */ { double eps0; eps0 = iauObl80(2400000.5, 54388.0); vvd(eps0, 0.4090751347643816218, 1e-14, "iauObl80", "", status); } static void t_p06e(int *status) /* ** - - - - - - - ** t _ p 0 6 e ** - - - - - - - ** ** Test iauP06e function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauP06e, vvd ** ** This revision: 2013 August 7 */ { double eps0, psia, oma, bpa, bqa, pia, bpia, epsa, chia, za, zetaa, thetaa, pa, gam, phi, psi; iauP06e(2400000.5, 52541.0, &eps0, &psia, &oma, &bpa, &bqa, &pia, &bpia, &epsa, &chia, &za, &zetaa, &thetaa, &pa, &gam, &phi, &psi); vvd(eps0, 0.4090926006005828715, 1e-14, "iauP06e", "eps0", status); vvd(psia, 0.6664369630191613431e-3, 1e-14, "iauP06e", "psia", status); vvd(oma , 0.4090925973783255982, 1e-14, "iauP06e", "oma", status); vvd(bpa, 0.5561149371265209445e-6, 1e-14, "iauP06e", "bpa", status); vvd(bqa, -0.6191517193290621270e-5, 1e-14, "iauP06e", "bqa", status); vvd(pia, 0.6216441751884382923e-5, 1e-14, "iauP06e", "pia", status); vvd(bpia, 3.052014180023779882, 1e-14, "iauP06e", "bpia", status); vvd(epsa, 0.4090864054922431688, 1e-14, "iauP06e", "epsa", status); vvd(chia, 0.1387703379530915364e-5, 1e-14, "iauP06e", "chia", status); vvd(za, 0.2921789846651790546e-3, 1e-14, "iauP06e", "za", status); vvd(zetaa, 0.3178773290332009310e-3, 1e-14, "iauP06e", "zetaa", status); vvd(thetaa, 0.2650932701657497181e-3, 1e-14, "iauP06e", "thetaa", status); vvd(pa, 0.6651637681381016344e-3, 1e-14, "iauP06e", "pa", status); vvd(gam, 0.1398077115963754987e-5, 1e-14, "iauP06e", "gam", status); vvd(phi, 0.4090864090837462602, 1e-14, "iauP06e", "phi", status); vvd(psi, 0.6664464807480920325e-3, 1e-14, "iauP06e", "psi", status); } static void t_p2pv(int *status) /* ** - - - - - - - ** t _ p 2 p v ** - - - - - - - ** ** Test iauP2pv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauP2pv, vvd ** ** This revision: 2013 August 7 */ { double p[3], pv[2][3]; p[0] = 0.25; p[1] = 1.2; p[2] = 3.0; pv[0][0] = 0.3; pv[0][1] = 1.2; pv[0][2] = -2.5; pv[1][0] = -0.5; pv[1][1] = 3.1; pv[1][2] = 0.9; iauP2pv(p, pv); vvd(pv[0][0], 0.25, 0.0, "iauP2pv", "p1", status); vvd(pv[0][1], 1.2, 0.0, "iauP2pv", "p2", status); vvd(pv[0][2], 3.0, 0.0, "iauP2pv", "p3", status); vvd(pv[1][0], 0.0, 0.0, "iauP2pv", "v1", status); vvd(pv[1][1], 0.0, 0.0, "iauP2pv", "v2", status); vvd(pv[1][2], 0.0, 0.0, "iauP2pv", "v3", status); } static void t_p2s(int *status) /* ** - - - - - - ** t _ p 2 s ** - - - - - - ** ** Test iauP2s function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauP2s, vvd ** ** This revision: 2013 August 7 */ { double p[3], theta, phi, r; p[0] = 100.0; p[1] = -50.0; p[2] = 25.0; iauP2s(p, &theta, &phi, &r); vvd(theta, -0.4636476090008061162, 1e-12, "iauP2s", "theta", status); vvd(phi, 0.2199879773954594463, 1e-12, "iauP2s", "phi", status); vvd(r, 114.5643923738960002, 1e-9, "iauP2s", "r", status); } static void t_pap(int *status) /* ** - - - - - - ** t _ p a p ** - - - - - - ** ** Test iauPap function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPap, vvd ** ** This revision: 2013 August 7 */ { double a[3], b[3], theta; a[0] = 1.0; a[1] = 0.1; a[2] = 0.2; b[0] = -3.0; b[1] = 1e-3; b[2] = 0.2; theta = iauPap(a, b); vvd(theta, 0.3671514267841113674, 1e-12, "iauPap", "", status); } static void t_pas(int *status) /* ** - - - - - - ** t _ p a s ** - - - - - - ** ** Test iauPas function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPas, vvd ** ** This revision: 2013 August 7 */ { double al, ap, bl, bp, theta; al = 1.0; ap = 0.1; bl = 0.2; bp = -1.0; theta = iauPas(al, ap, bl, bp); vvd(theta, -2.724544922932270424, 1e-12, "iauPas", "", status); } static void t_pb06(int *status) /* ** - - - - - - - ** t _ p b 0 6 ** - - - - - - - ** ** Test iauPb06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPb06, vvd ** ** This revision: 2013 August 7 */ { double bzeta, bz, btheta; iauPb06(2400000.5, 50123.9999, &bzeta, &bz, &btheta); vvd(bzeta, -0.5092634016326478238e-3, 1e-12, "iauPb06", "bzeta", status); vvd(bz, -0.3602772060566044413e-3, 1e-12, "iauPb06", "bz", status); vvd(btheta, -0.3779735537167811177e-3, 1e-12, "iauPb06", "btheta", status); } static void t_pdp(int *status) /* ** - - - - - - ** t _ p d p ** - - - - - - ** ** Test iauPdp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPdp, vvd ** ** This revision: 2013 August 7 */ { double a[3], b[3], adb; a[0] = 2.0; a[1] = 2.0; a[2] = 3.0; b[0] = 1.0; b[1] = 3.0; b[2] = 4.0; adb = iauPdp(a, b); vvd(adb, 20, 1e-12, "iauPdp", "", status); } static void t_pfw06(int *status) /* ** - - - - - - - - ** t _ p f w 0 6 ** - - - - - - - - ** ** Test iauPfw06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPfw06, vvd ** ** This revision: 2013 August 7 */ { double gamb, phib, psib, epsa; iauPfw06(2400000.5, 50123.9999, &gamb, &phib, &psib, &epsa); vvd(gamb, -0.2243387670997995690e-5, 1e-16, "iauPfw06", "gamb", status); vvd(phib, 0.4091014602391312808, 1e-12, "iauPfw06", "phib", status); vvd(psib, -0.9501954178013031895e-3, 1e-14, "iauPfw06", "psib", status); vvd(epsa, 0.4091014316587367491, 1e-12, "iauPfw06", "epsa", status); } static void t_plan94(int *status) /* ** - - - - - - - - - ** t _ p l a n 9 4 ** - - - - - - - - - ** ** Test iauPlan94 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPlan94, vvd, viv ** ** This revision: 2013 October 2 */ { double pv[2][3]; int j; j = iauPlan94(2400000.5, 1e6, 0, pv); vvd(pv[0][0], 0.0, 0.0, "iauPlan94", "x 1", status); vvd(pv[0][1], 0.0, 0.0, "iauPlan94", "y 1", status); vvd(pv[0][2], 0.0, 0.0, "iauPlan94", "z 1", status); vvd(pv[1][0], 0.0, 0.0, "iauPlan94", "xd 1", status); vvd(pv[1][1], 0.0, 0.0, "iauPlan94", "yd 1", status); vvd(pv[1][2], 0.0, 0.0, "iauPlan94", "zd 1", status); viv(j, -1, "iauPlan94", "j 1", status); j = iauPlan94(2400000.5, 1e6, 10, pv); viv(j, -1, "iauPlan94", "j 2", status); j = iauPlan94(2400000.5, -320000, 3, pv); vvd(pv[0][0], 0.9308038666832975759, 1e-11, "iauPlan94", "x 3", status); vvd(pv[0][1], 0.3258319040261346000, 1e-11, "iauPlan94", "y 3", status); vvd(pv[0][2], 0.1422794544481140560, 1e-11, "iauPlan94", "z 3", status); vvd(pv[1][0], -0.6429458958255170006e-2, 1e-11, "iauPlan94", "xd 3", status); vvd(pv[1][1], 0.1468570657704237764e-1, 1e-11, "iauPlan94", "yd 3", status); vvd(pv[1][2], 0.6406996426270981189e-2, 1e-11, "iauPlan94", "zd 3", status); viv(j, 1, "iauPlan94", "j 3", status); j = iauPlan94(2400000.5, 43999.9, 1, pv); vvd(pv[0][0], 0.2945293959257430832, 1e-11, "iauPlan94", "x 4", status); vvd(pv[0][1], -0.2452204176601049596, 1e-11, "iauPlan94", "y 4", status); vvd(pv[0][2], -0.1615427700571978153, 1e-11, "iauPlan94", "z 4", status); vvd(pv[1][0], 0.1413867871404614441e-1, 1e-11, "iauPlan94", "xd 4", status); vvd(pv[1][1], 0.1946548301104706582e-1, 1e-11, "iauPlan94", "yd 4", status); vvd(pv[1][2], 0.8929809783898904786e-2, 1e-11, "iauPlan94", "zd 4", status); viv(j, 0, "iauPlan94", "j 4", status); } static void t_pmat00(int *status) /* ** - - - - - - - - - ** t _ p m a t 0 0 ** - - - - - - - - - ** ** Test iauPmat00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPmat00, vvd ** ** This revision: 2013 August 7 */ { double rbp[3][3]; iauPmat00(2400000.5, 50123.9999, rbp); vvd(rbp[0][0], 0.9999995505175087260, 1e-12, "iauPmat00", "11", status); vvd(rbp[0][1], 0.8695405883617884705e-3, 1e-14, "iauPmat00", "12", status); vvd(rbp[0][2], 0.3779734722239007105e-3, 1e-14, "iauPmat00", "13", status); vvd(rbp[1][0], -0.8695405990410863719e-3, 1e-14, "iauPmat00", "21", status); vvd(rbp[1][1], 0.9999996219494925900, 1e-12, "iauPmat00", "22", status); vvd(rbp[1][2], -0.1360775820404982209e-6, 1e-14, "iauPmat00", "23", status); vvd(rbp[2][0], -0.3779734476558184991e-3, 1e-14, "iauPmat00", "31", status); vvd(rbp[2][1], -0.1925857585832024058e-6, 1e-14, "iauPmat00", "32", status); vvd(rbp[2][2], 0.9999999285680153377, 1e-12, "iauPmat00", "33", status); } static void t_pmat06(int *status) /* ** - - - - - - - - - ** t _ p m a t 0 6 ** - - - - - - - - - ** ** Test iauPmat06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPmat06, vvd ** ** This revision: 2013 August 7 */ { double rbp[3][3]; iauPmat06(2400000.5, 50123.9999, rbp); vvd(rbp[0][0], 0.9999995505176007047, 1e-12, "iauPmat06", "11", status); vvd(rbp[0][1], 0.8695404617348208406e-3, 1e-14, "iauPmat06", "12", status); vvd(rbp[0][2], 0.3779735201865589104e-3, 1e-14, "iauPmat06", "13", status); vvd(rbp[1][0], -0.8695404723772031414e-3, 1e-14, "iauPmat06", "21", status); vvd(rbp[1][1], 0.9999996219496027161, 1e-12, "iauPmat06", "22", status); vvd(rbp[1][2], -0.1361752497080270143e-6, 1e-14, "iauPmat06", "23", status); vvd(rbp[2][0], -0.3779734957034089490e-3, 1e-14, "iauPmat06", "31", status); vvd(rbp[2][1], -0.1924880847894457113e-6, 1e-14, "iauPmat06", "32", status); vvd(rbp[2][2], 0.9999999285679971958, 1e-12, "iauPmat06", "33", status); } static void t_pmat76(int *status) /* ** - - - - - - - - - ** t _ p m a t 7 6 ** - - - - - - - - - ** ** Test iauPmat76 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPmat76, vvd ** ** This revision: 2013 August 7 */ { double rmatp[3][3]; iauPmat76(2400000.5, 50123.9999, rmatp); vvd(rmatp[0][0], 0.9999995504328350733, 1e-12, "iauPmat76", "11", status); vvd(rmatp[0][1], 0.8696632209480960785e-3, 1e-14, "iauPmat76", "12", status); vvd(rmatp[0][2], 0.3779153474959888345e-3, 1e-14, "iauPmat76", "13", status); vvd(rmatp[1][0], -0.8696632209485112192e-3, 1e-14, "iauPmat76", "21", status); vvd(rmatp[1][1], 0.9999996218428560614, 1e-12, "iauPmat76", "22", status); vvd(rmatp[1][2], -0.1643284776111886407e-6, 1e-14, "iauPmat76", "23", status); vvd(rmatp[2][0], -0.3779153474950335077e-3, 1e-14, "iauPmat76", "31", status); vvd(rmatp[2][1], -0.1643306746147366896e-6, 1e-14, "iauPmat76", "32", status); vvd(rmatp[2][2], 0.9999999285899790119, 1e-12, "iauPmat76", "33", status); } static void t_pm(int *status) /* ** - - - - - ** t _ p m ** - - - - - ** ** Test iauPm function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPm, vvd ** ** This revision: 2013 August 7 */ { double p[3], r; p[0] = 0.3; p[1] = 1.2; p[2] = -2.5; r = iauPm(p); vvd(r, 2.789265136196270604, 1e-12, "iauPm", "", status); } static void t_pmp(int *status) /* ** - - - - - - ** t _ p m p ** - - - - - - ** ** Test iauPmp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPmp, vvd ** ** This revision: 2013 August 7 */ { double a[3], b[3], amb[3]; a[0] = 2.0; a[1] = 2.0; a[2] = 3.0; b[0] = 1.0; b[1] = 3.0; b[2] = 4.0; iauPmp(a, b, amb); vvd(amb[0], 1.0, 1e-12, "iauPmp", "0", status); vvd(amb[1], -1.0, 1e-12, "iauPmp", "1", status); vvd(amb[2], -1.0, 1e-12, "iauPmp", "2", status); } static void t_pmpx(int *status) /* ** - - - - - - - ** t _ p m p x ** - - - - - - - ** ** Test iauPmpx function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPmpx, vvd ** ** This revision: 2013 October 2 */ { double rc, dc, pr, pd, px, rv, pmt, pob[3], pco[3]; rc = 1.234; dc = 0.789; pr = 1e-5; pd = -2e-5; px = 1e-2; rv = 10.0; pmt = 8.75; pob[0] = 0.9; pob[1] = 0.4; pob[2] = 0.1; iauPmpx(rc, dc, pr, pd, px, rv, pmt, pob, pco); vvd(pco[0], 0.2328137623960308440, 1e-12, "iauPmpx", "1", status); vvd(pco[1], 0.6651097085397855317, 1e-12, "iauPmpx", "2", status); vvd(pco[2], 0.7095257765896359847, 1e-12, "iauPmpx", "3", status); } static void t_pmsafe(int *status) /* ** - - - - - - - - - ** t _ p m s a f e ** - - - - - - - - - ** ** Test iauPmsafe function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPmsafe, vvd, viv ** ** This revision: 2013 October 2 */ { int j; double ra1, dec1, pmr1, pmd1, px1, rv1, ep1a, ep1b, ep2a, ep2b, ra2, dec2, pmr2, pmd2, px2, rv2; ra1 = 1.234; dec1 = 0.789; pmr1 = 1e-5; pmd1 = -2e-5; px1 = 1e-2; rv1 = 10.0; ep1a = 2400000.5; ep1b = 48348.5625; ep2a = 2400000.5; ep2b = 51544.5; j = iauPmsafe(ra1, dec1, pmr1, pmd1, px1, rv1, ep1a, ep1b, ep2a, ep2b, &ra2, &dec2, &pmr2, &pmd2, &px2, &rv2); vvd(ra2, 1.234087484501017061, 1e-12, "iauPmsafe", "ra2", status); vvd(dec2, 0.7888249982450468574, 1e-12, "iauPmsafe", "dec2", status); vvd(pmr2, 0.9996457663586073988e-5, 1e-12, "iauPmsafe", "pmr2", status); vvd(pmd2, -0.2000040085106737816e-4, 1e-16, "iauPmsafe", "pmd2", status); vvd(px2, 0.9999997295356765185e-2, 1e-12, "iauPmsafe", "px2", status); vvd(rv2, 10.38468380113917014, 1e-10, "iauPmsafe", "rv2", status); viv ( j, 0, "iauPmsafe", "j", status); } static void t_pn(int *status) /* ** - - - - - ** t _ p n ** - - - - - ** ** Test iauPn function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPn, vvd ** ** This revision: 2013 August 7 */ { double p[3], r, u[3]; p[0] = 0.3; p[1] = 1.2; p[2] = -2.5; iauPn(p, &r, u); vvd(r, 2.789265136196270604, 1e-12, "iauPn", "r", status); vvd(u[0], 0.1075552109073112058, 1e-12, "iauPn", "u1", status); vvd(u[1], 0.4302208436292448232, 1e-12, "iauPn", "u2", status); vvd(u[2], -0.8962934242275933816, 1e-12, "iauPn", "u3", status); } static void t_pn00(int *status) /* ** - - - - - - - ** t _ p n 0 0 ** - - - - - - - ** ** Test iauPn00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPn00, vvd ** ** This revision: 2013 August 7 */ { double dpsi, deps, epsa, rb[3][3], rp[3][3], rbp[3][3], rn[3][3], rbpn[3][3]; dpsi = -0.9632552291149335877e-5; deps = 0.4063197106621141414e-4; iauPn00(2400000.5, 53736.0, dpsi, deps, &epsa, rb, rp, rbp, rn, rbpn); vvd(epsa, 0.4090791789404229916, 1e-12, "iauPn00", "epsa", status); vvd(rb[0][0], 0.9999999999999942498, 1e-12, "iauPn00", "rb11", status); vvd(rb[0][1], -0.7078279744199196626e-7, 1e-18, "iauPn00", "rb12", status); vvd(rb[0][2], 0.8056217146976134152e-7, 1e-18, "iauPn00", "rb13", status); vvd(rb[1][0], 0.7078279477857337206e-7, 1e-18, "iauPn00", "rb21", status); vvd(rb[1][1], 0.9999999999999969484, 1e-12, "iauPn00", "rb22", status); vvd(rb[1][2], 0.3306041454222136517e-7, 1e-18, "iauPn00", "rb23", status); vvd(rb[2][0], -0.8056217380986972157e-7, 1e-18, "iauPn00", "rb31", status); vvd(rb[2][1], -0.3306040883980552500e-7, 1e-18, "iauPn00", "rb32", status); vvd(rb[2][2], 0.9999999999999962084, 1e-12, "iauPn00", "rb33", status); vvd(rp[0][0], 0.9999989300532289018, 1e-12, "iauPn00", "rp11", status); vvd(rp[0][1], -0.1341647226791824349e-2, 1e-14, "iauPn00", "rp12", status); vvd(rp[0][2], -0.5829880927190296547e-3, 1e-14, "iauPn00", "rp13", status); vvd(rp[1][0], 0.1341647231069759008e-2, 1e-14, "iauPn00", "rp21", status); vvd(rp[1][1], 0.9999990999908750433, 1e-12, "iauPn00", "rp22", status); vvd(rp[1][2], -0.3837444441583715468e-6, 1e-14, "iauPn00", "rp23", status); vvd(rp[2][0], 0.5829880828740957684e-3, 1e-14, "iauPn00", "rp31", status); vvd(rp[2][1], -0.3984203267708834759e-6, 1e-14, "iauPn00", "rp32", status); vvd(rp[2][2], 0.9999998300623538046, 1e-12, "iauPn00", "rp33", status); vvd(rbp[0][0], 0.9999989300052243993, 1e-12, "iauPn00", "rbp11", status); vvd(rbp[0][1], -0.1341717990239703727e-2, 1e-14, "iauPn00", "rbp12", status); vvd(rbp[0][2], -0.5829075749891684053e-3, 1e-14, "iauPn00", "rbp13", status); vvd(rbp[1][0], 0.1341718013831739992e-2, 1e-14, "iauPn00", "rbp21", status); vvd(rbp[1][1], 0.9999990998959191343, 1e-12, "iauPn00", "rbp22", status); vvd(rbp[1][2], -0.3505759733565421170e-6, 1e-14, "iauPn00", "rbp23", status); vvd(rbp[2][0], 0.5829075206857717883e-3, 1e-14, "iauPn00", "rbp31", status); vvd(rbp[2][1], -0.4315219955198608970e-6, 1e-14, "iauPn00", "rbp32", status); vvd(rbp[2][2], 0.9999998301093036269, 1e-12, "iauPn00", "rbp33", status); vvd(rn[0][0], 0.9999999999536069682, 1e-12, "iauPn00", "rn11", status); vvd(rn[0][1], 0.8837746144872140812e-5, 1e-16, "iauPn00", "rn12", status); vvd(rn[0][2], 0.3831488838252590008e-5, 1e-16, "iauPn00", "rn13", status); vvd(rn[1][0], -0.8837590456633197506e-5, 1e-16, "iauPn00", "rn21", status); vvd(rn[1][1], 0.9999999991354692733, 1e-12, "iauPn00", "rn22", status); vvd(rn[1][2], -0.4063198798559573702e-4, 1e-16, "iauPn00", "rn23", status); vvd(rn[2][0], -0.3831847930135328368e-5, 1e-16, "iauPn00", "rn31", status); vvd(rn[2][1], 0.4063195412258150427e-4, 1e-16, "iauPn00", "rn32", status); vvd(rn[2][2], 0.9999999991671806225, 1e-12, "iauPn00", "rn33", status); vvd(rbpn[0][0], 0.9999989440499982806, 1e-12, "iauPn00", "rbpn11", status); vvd(rbpn[0][1], -0.1332880253640848301e-2, 1e-14, "iauPn00", "rbpn12", status); vvd(rbpn[0][2], -0.5790760898731087295e-3, 1e-14, "iauPn00", "rbpn13", status); vvd(rbpn[1][0], 0.1332856746979948745e-2, 1e-14, "iauPn00", "rbpn21", status); vvd(rbpn[1][1], 0.9999991109064768883, 1e-12, "iauPn00", "rbpn22", status); vvd(rbpn[1][2], -0.4097740555723063806e-4, 1e-14, "iauPn00", "rbpn23", status); vvd(rbpn[2][0], 0.5791301929950205000e-3, 1e-14, "iauPn00", "rbpn31", status); vvd(rbpn[2][1], 0.4020553681373702931e-4, 1e-14, "iauPn00", "rbpn32", status); vvd(rbpn[2][2], 0.9999998314958529887, 1e-12, "iauPn00", "rbpn33", status); } static void t_pn00a(int *status) /* ** - - - - - - - - ** t _ p n 0 0 a ** - - - - - - - - ** ** Test iauPn00a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPn00a, vvd ** ** This revision: 2013 August 7 */ { double dpsi, deps, epsa, rb[3][3], rp[3][3], rbp[3][3], rn[3][3], rbpn[3][3]; iauPn00a(2400000.5, 53736.0, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn); vvd(dpsi, -0.9630909107115518431e-5, 1e-12, "iauPn00a", "dpsi", status); vvd(deps, 0.4063239174001678710e-4, 1e-12, "iauPn00a", "deps", status); vvd(epsa, 0.4090791789404229916, 1e-12, "iauPn00a", "epsa", status); vvd(rb[0][0], 0.9999999999999942498, 1e-12, "iauPn00a", "rb11", status); vvd(rb[0][1], -0.7078279744199196626e-7, 1e-16, "iauPn00a", "rb12", status); vvd(rb[0][2], 0.8056217146976134152e-7, 1e-16, "iauPn00a", "rb13", status); vvd(rb[1][0], 0.7078279477857337206e-7, 1e-16, "iauPn00a", "rb21", status); vvd(rb[1][1], 0.9999999999999969484, 1e-12, "iauPn00a", "rb22", status); vvd(rb[1][2], 0.3306041454222136517e-7, 1e-16, "iauPn00a", "rb23", status); vvd(rb[2][0], -0.8056217380986972157e-7, 1e-16, "iauPn00a", "rb31", status); vvd(rb[2][1], -0.3306040883980552500e-7, 1e-16, "iauPn00a", "rb32", status); vvd(rb[2][2], 0.9999999999999962084, 1e-12, "iauPn00a", "rb33", status); vvd(rp[0][0], 0.9999989300532289018, 1e-12, "iauPn00a", "rp11", status); vvd(rp[0][1], -0.1341647226791824349e-2, 1e-14, "iauPn00a", "rp12", status); vvd(rp[0][2], -0.5829880927190296547e-3, 1e-14, "iauPn00a", "rp13", status); vvd(rp[1][0], 0.1341647231069759008e-2, 1e-14, "iauPn00a", "rp21", status); vvd(rp[1][1], 0.9999990999908750433, 1e-12, "iauPn00a", "rp22", status); vvd(rp[1][2], -0.3837444441583715468e-6, 1e-14, "iauPn00a", "rp23", status); vvd(rp[2][0], 0.5829880828740957684e-3, 1e-14, "iauPn00a", "rp31", status); vvd(rp[2][1], -0.3984203267708834759e-6, 1e-14, "iauPn00a", "rp32", status); vvd(rp[2][2], 0.9999998300623538046, 1e-12, "iauPn00a", "rp33", status); vvd(rbp[0][0], 0.9999989300052243993, 1e-12, "iauPn00a", "rbp11", status); vvd(rbp[0][1], -0.1341717990239703727e-2, 1e-14, "iauPn00a", "rbp12", status); vvd(rbp[0][2], -0.5829075749891684053e-3, 1e-14, "iauPn00a", "rbp13", status); vvd(rbp[1][0], 0.1341718013831739992e-2, 1e-14, "iauPn00a", "rbp21", status); vvd(rbp[1][1], 0.9999990998959191343, 1e-12, "iauPn00a", "rbp22", status); vvd(rbp[1][2], -0.3505759733565421170e-6, 1e-14, "iauPn00a", "rbp23", status); vvd(rbp[2][0], 0.5829075206857717883e-3, 1e-14, "iauPn00a", "rbp31", status); vvd(rbp[2][1], -0.4315219955198608970e-6, 1e-14, "iauPn00a", "rbp32", status); vvd(rbp[2][2], 0.9999998301093036269, 1e-12, "iauPn00a", "rbp33", status); vvd(rn[0][0], 0.9999999999536227949, 1e-12, "iauPn00a", "rn11", status); vvd(rn[0][1], 0.8836238544090873336e-5, 1e-14, "iauPn00a", "rn12", status); vvd(rn[0][2], 0.3830835237722400669e-5, 1e-14, "iauPn00a", "rn13", status); vvd(rn[1][0], -0.8836082880798569274e-5, 1e-14, "iauPn00a", "rn21", status); vvd(rn[1][1], 0.9999999991354655028, 1e-12, "iauPn00a", "rn22", status); vvd(rn[1][2], -0.4063240865362499850e-4, 1e-14, "iauPn00a", "rn23", status); vvd(rn[2][0], -0.3831194272065995866e-5, 1e-14, "iauPn00a", "rn31", status); vvd(rn[2][1], 0.4063237480216291775e-4, 1e-14, "iauPn00a", "rn32", status); vvd(rn[2][2], 0.9999999991671660338, 1e-12, "iauPn00a", "rn33", status); vvd(rbpn[0][0], 0.9999989440476103435, 1e-12, "iauPn00a", "rbpn11", status); vvd(rbpn[0][1], -0.1332881761240011763e-2, 1e-14, "iauPn00a", "rbpn12", status); vvd(rbpn[0][2], -0.5790767434730085751e-3, 1e-14, "iauPn00a", "rbpn13", status); vvd(rbpn[1][0], 0.1332858254308954658e-2, 1e-14, "iauPn00a", "rbpn21", status); vvd(rbpn[1][1], 0.9999991109044505577, 1e-12, "iauPn00a", "rbpn22", status); vvd(rbpn[1][2], -0.4097782710396580452e-4, 1e-14, "iauPn00a", "rbpn23", status); vvd(rbpn[2][0], 0.5791308472168152904e-3, 1e-14, "iauPn00a", "rbpn31", status); vvd(rbpn[2][1], 0.4020595661591500259e-4, 1e-14, "iauPn00a", "rbpn32", status); vvd(rbpn[2][2], 0.9999998314954572304, 1e-12, "iauPn00a", "rbpn33", status); } static void t_pn00b(int *status) /* ** - - - - - - - - ** t _ p n 0 0 b ** - - - - - - - - ** ** Test iauPn00b function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPn00b, vvd ** ** This revision: 2013 August 7 */ { double dpsi, deps, epsa, rb[3][3], rp[3][3], rbp[3][3], rn[3][3], rbpn[3][3]; iauPn00b(2400000.5, 53736.0, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn); vvd(dpsi, -0.9632552291148362783e-5, 1e-12, "iauPn00b", "dpsi", status); vvd(deps, 0.4063197106621159367e-4, 1e-12, "iauPn00b", "deps", status); vvd(epsa, 0.4090791789404229916, 1e-12, "iauPn00b", "epsa", status); vvd(rb[0][0], 0.9999999999999942498, 1e-12, "iauPn00b", "rb11", status); vvd(rb[0][1], -0.7078279744199196626e-7, 1e-16, "iauPn00b", "rb12", status); vvd(rb[0][2], 0.8056217146976134152e-7, 1e-16, "iauPn00b", "rb13", status); vvd(rb[1][0], 0.7078279477857337206e-7, 1e-16, "iauPn00b", "rb21", status); vvd(rb[1][1], 0.9999999999999969484, 1e-12, "iauPn00b", "rb22", status); vvd(rb[1][2], 0.3306041454222136517e-7, 1e-16, "iauPn00b", "rb23", status); vvd(rb[2][0], -0.8056217380986972157e-7, 1e-16, "iauPn00b", "rb31", status); vvd(rb[2][1], -0.3306040883980552500e-7, 1e-16, "iauPn00b", "rb32", status); vvd(rb[2][2], 0.9999999999999962084, 1e-12, "iauPn00b", "rb33", status); vvd(rp[0][0], 0.9999989300532289018, 1e-12, "iauPn00b", "rp11", status); vvd(rp[0][1], -0.1341647226791824349e-2, 1e-14, "iauPn00b", "rp12", status); vvd(rp[0][2], -0.5829880927190296547e-3, 1e-14, "iauPn00b", "rp13", status); vvd(rp[1][0], 0.1341647231069759008e-2, 1e-14, "iauPn00b", "rp21", status); vvd(rp[1][1], 0.9999990999908750433, 1e-12, "iauPn00b", "rp22", status); vvd(rp[1][2], -0.3837444441583715468e-6, 1e-14, "iauPn00b", "rp23", status); vvd(rp[2][0], 0.5829880828740957684e-3, 1e-14, "iauPn00b", "rp31", status); vvd(rp[2][1], -0.3984203267708834759e-6, 1e-14, "iauPn00b", "rp32", status); vvd(rp[2][2], 0.9999998300623538046, 1e-12, "iauPn00b", "rp33", status); vvd(rbp[0][0], 0.9999989300052243993, 1e-12, "iauPn00b", "rbp11", status); vvd(rbp[0][1], -0.1341717990239703727e-2, 1e-14, "iauPn00b", "rbp12", status); vvd(rbp[0][2], -0.5829075749891684053e-3, 1e-14, "iauPn00b", "rbp13", status); vvd(rbp[1][0], 0.1341718013831739992e-2, 1e-14, "iauPn00b", "rbp21", status); vvd(rbp[1][1], 0.9999990998959191343, 1e-12, "iauPn00b", "rbp22", status); vvd(rbp[1][2], -0.3505759733565421170e-6, 1e-14, "iauPn00b", "rbp23", status); vvd(rbp[2][0], 0.5829075206857717883e-3, 1e-14, "iauPn00b", "rbp31", status); vvd(rbp[2][1], -0.4315219955198608970e-6, 1e-14, "iauPn00b", "rbp32", status); vvd(rbp[2][2], 0.9999998301093036269, 1e-12, "iauPn00b", "rbp33", status); vvd(rn[0][0], 0.9999999999536069682, 1e-12, "iauPn00b", "rn11", status); vvd(rn[0][1], 0.8837746144871248011e-5, 1e-14, "iauPn00b", "rn12", status); vvd(rn[0][2], 0.3831488838252202945e-5, 1e-14, "iauPn00b", "rn13", status); vvd(rn[1][0], -0.8837590456632304720e-5, 1e-14, "iauPn00b", "rn21", status); vvd(rn[1][1], 0.9999999991354692733, 1e-12, "iauPn00b", "rn22", status); vvd(rn[1][2], -0.4063198798559591654e-4, 1e-14, "iauPn00b", "rn23", status); vvd(rn[2][0], -0.3831847930134941271e-5, 1e-14, "iauPn00b", "rn31", status); vvd(rn[2][1], 0.4063195412258168380e-4, 1e-14, "iauPn00b", "rn32", status); vvd(rn[2][2], 0.9999999991671806225, 1e-12, "iauPn00b", "rn33", status); vvd(rbpn[0][0], 0.9999989440499982806, 1e-12, "iauPn00b", "rbpn11", status); vvd(rbpn[0][1], -0.1332880253640849194e-2, 1e-14, "iauPn00b", "rbpn12", status); vvd(rbpn[0][2], -0.5790760898731091166e-3, 1e-14, "iauPn00b", "rbpn13", status); vvd(rbpn[1][0], 0.1332856746979949638e-2, 1e-14, "iauPn00b", "rbpn21", status); vvd(rbpn[1][1], 0.9999991109064768883, 1e-12, "iauPn00b", "rbpn22", status); vvd(rbpn[1][2], -0.4097740555723081811e-4, 1e-14, "iauPn00b", "rbpn23", status); vvd(rbpn[2][0], 0.5791301929950208873e-3, 1e-14, "iauPn00b", "rbpn31", status); vvd(rbpn[2][1], 0.4020553681373720832e-4, 1e-14, "iauPn00b", "rbpn32", status); vvd(rbpn[2][2], 0.9999998314958529887, 1e-12, "iauPn00b", "rbpn33", status); } static void t_pn06a(int *status) /* ** - - - - - - - - ** t _ p n 0 6 a ** - - - - - - - - ** ** Test iauPn06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPn06a, vvd ** ** This revision: 2013 August 7 */ { double dpsi, deps, epsa; double rb[3][3], rp[3][3], rbp[3][3], rn[3][3], rbpn[3][3]; iauPn06a(2400000.5, 53736.0, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn); vvd(dpsi, -0.9630912025820308797e-5, 1e-12, "iauPn06a", "dpsi", status); vvd(deps, 0.4063238496887249798e-4, 1e-12, "iauPn06a", "deps", status); vvd(epsa, 0.4090789763356509926, 1e-12, "iauPn06a", "epsa", status); vvd(rb[0][0], 0.9999999999999942497, 1e-12, "iauPn06a", "rb11", status); vvd(rb[0][1], -0.7078368960971557145e-7, 1e-14, "iauPn06a", "rb12", status); vvd(rb[0][2], 0.8056213977613185606e-7, 1e-14, "iauPn06a", "rb13", status); vvd(rb[1][0], 0.7078368694637674333e-7, 1e-14, "iauPn06a", "rb21", status); vvd(rb[1][1], 0.9999999999999969484, 1e-12, "iauPn06a", "rb22", status); vvd(rb[1][2], 0.3305943742989134124e-7, 1e-14, "iauPn06a", "rb23", status); vvd(rb[2][0], -0.8056214211620056792e-7, 1e-14, "iauPn06a", "rb31", status); vvd(rb[2][1], -0.3305943172740586950e-7, 1e-14, "iauPn06a", "rb32", status); vvd(rb[2][2], 0.9999999999999962084, 1e-12, "iauPn06a", "rb33", status); vvd(rp[0][0], 0.9999989300536854831, 1e-12, "iauPn06a", "rp11", status); vvd(rp[0][1], -0.1341646886204443795e-2, 1e-14, "iauPn06a", "rp12", status); vvd(rp[0][2], -0.5829880933488627759e-3, 1e-14, "iauPn06a", "rp13", status); vvd(rp[1][0], 0.1341646890569782183e-2, 1e-14, "iauPn06a", "rp21", status); vvd(rp[1][1], 0.9999990999913319321, 1e-12, "iauPn06a", "rp22", status); vvd(rp[1][2], -0.3835944216374477457e-6, 1e-14, "iauPn06a", "rp23", status); vvd(rp[2][0], 0.5829880833027867368e-3, 1e-14, "iauPn06a", "rp31", status); vvd(rp[2][1], -0.3985701514686976112e-6, 1e-14, "iauPn06a", "rp32", status); vvd(rp[2][2], 0.9999998300623534950, 1e-12, "iauPn06a", "rp33", status); vvd(rbp[0][0], 0.9999989300056797893, 1e-12, "iauPn06a", "rbp11", status); vvd(rbp[0][1], -0.1341717650545059598e-2, 1e-14, "iauPn06a", "rbp12", status); vvd(rbp[0][2], -0.5829075756493728856e-3, 1e-14, "iauPn06a", "rbp13", status); vvd(rbp[1][0], 0.1341717674223918101e-2, 1e-14, "iauPn06a", "rbp21", status); vvd(rbp[1][1], 0.9999990998963748448, 1e-12, "iauPn06a", "rbp22", status); vvd(rbp[1][2], -0.3504269280170069029e-6, 1e-14, "iauPn06a", "rbp23", status); vvd(rbp[2][0], 0.5829075211461454599e-3, 1e-14, "iauPn06a", "rbp31", status); vvd(rbp[2][1], -0.4316708436255949093e-6, 1e-14, "iauPn06a", "rbp32", status); vvd(rbp[2][2], 0.9999998301093032943, 1e-12, "iauPn06a", "rbp33", status); vvd(rn[0][0], 0.9999999999536227668, 1e-12, "iauPn06a", "rn11", status); vvd(rn[0][1], 0.8836241998111535233e-5, 1e-14, "iauPn06a", "rn12", status); vvd(rn[0][2], 0.3830834608415287707e-5, 1e-14, "iauPn06a", "rn13", status); vvd(rn[1][0], -0.8836086334870740138e-5, 1e-14, "iauPn06a", "rn21", status); vvd(rn[1][1], 0.9999999991354657474, 1e-12, "iauPn06a", "rn22", status); vvd(rn[1][2], -0.4063240188248455065e-4, 1e-14, "iauPn06a", "rn23", status); vvd(rn[2][0], -0.3831193642839398128e-5, 1e-14, "iauPn06a", "rn31", status); vvd(rn[2][1], 0.4063236803101479770e-4, 1e-14, "iauPn06a", "rn32", status); vvd(rn[2][2], 0.9999999991671663114, 1e-12, "iauPn06a", "rn33", status); vvd(rbpn[0][0], 0.9999989440480669738, 1e-12, "iauPn06a", "rbpn11", status); vvd(rbpn[0][1], -0.1332881418091915973e-2, 1e-14, "iauPn06a", "rbpn12", status); vvd(rbpn[0][2], -0.5790767447612042565e-3, 1e-14, "iauPn06a", "rbpn13", status); vvd(rbpn[1][0], 0.1332857911250989133e-2, 1e-14, "iauPn06a", "rbpn21", status); vvd(rbpn[1][1], 0.9999991109049141908, 1e-12, "iauPn06a", "rbpn22", status); vvd(rbpn[1][2], -0.4097767128546784878e-4, 1e-14, "iauPn06a", "rbpn23", status); vvd(rbpn[2][0], 0.5791308482835292617e-3, 1e-14, "iauPn06a", "rbpn31", status); vvd(rbpn[2][1], 0.4020580099454020310e-4, 1e-14, "iauPn06a", "rbpn32", status); vvd(rbpn[2][2], 0.9999998314954628695, 1e-12, "iauPn06a", "rbpn33", status); } static void t_pn06(int *status) /* ** - - - - - - - ** t _ p n 0 6 ** - - - - - - - ** ** Test iauPn06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPn06, vvd ** ** This revision: 2013 August 7 */ { double dpsi, deps, epsa, rb[3][3], rp[3][3], rbp[3][3], rn[3][3], rbpn[3][3]; dpsi = -0.9632552291149335877e-5; deps = 0.4063197106621141414e-4; iauPn06(2400000.5, 53736.0, dpsi, deps, &epsa, rb, rp, rbp, rn, rbpn); vvd(epsa, 0.4090789763356509926, 1e-12, "iauPn06", "epsa", status); vvd(rb[0][0], 0.9999999999999942497, 1e-12, "iauPn06", "rb11", status); vvd(rb[0][1], -0.7078368960971557145e-7, 1e-14, "iauPn06", "rb12", status); vvd(rb[0][2], 0.8056213977613185606e-7, 1e-14, "iauPn06", "rb13", status); vvd(rb[1][0], 0.7078368694637674333e-7, 1e-14, "iauPn06", "rb21", status); vvd(rb[1][1], 0.9999999999999969484, 1e-12, "iauPn06", "rb22", status); vvd(rb[1][2], 0.3305943742989134124e-7, 1e-14, "iauPn06", "rb23", status); vvd(rb[2][0], -0.8056214211620056792e-7, 1e-14, "iauPn06", "rb31", status); vvd(rb[2][1], -0.3305943172740586950e-7, 1e-14, "iauPn06", "rb32", status); vvd(rb[2][2], 0.9999999999999962084, 1e-12, "iauPn06", "rb33", status); vvd(rp[0][0], 0.9999989300536854831, 1e-12, "iauPn06", "rp11", status); vvd(rp[0][1], -0.1341646886204443795e-2, 1e-14, "iauPn06", "rp12", status); vvd(rp[0][2], -0.5829880933488627759e-3, 1e-14, "iauPn06", "rp13", status); vvd(rp[1][0], 0.1341646890569782183e-2, 1e-14, "iauPn06", "rp21", status); vvd(rp[1][1], 0.9999990999913319321, 1e-12, "iauPn06", "rp22", status); vvd(rp[1][2], -0.3835944216374477457e-6, 1e-14, "iauPn06", "rp23", status); vvd(rp[2][0], 0.5829880833027867368e-3, 1e-14, "iauPn06", "rp31", status); vvd(rp[2][1], -0.3985701514686976112e-6, 1e-14, "iauPn06", "rp32", status); vvd(rp[2][2], 0.9999998300623534950, 1e-12, "iauPn06", "rp33", status); vvd(rbp[0][0], 0.9999989300056797893, 1e-12, "iauPn06", "rbp11", status); vvd(rbp[0][1], -0.1341717650545059598e-2, 1e-14, "iauPn06", "rbp12", status); vvd(rbp[0][2], -0.5829075756493728856e-3, 1e-14, "iauPn06", "rbp13", status); vvd(rbp[1][0], 0.1341717674223918101e-2, 1e-14, "iauPn06", "rbp21", status); vvd(rbp[1][1], 0.9999990998963748448, 1e-12, "iauPn06", "rbp22", status); vvd(rbp[1][2], -0.3504269280170069029e-6, 1e-14, "iauPn06", "rbp23", status); vvd(rbp[2][0], 0.5829075211461454599e-3, 1e-14, "iauPn06", "rbp31", status); vvd(rbp[2][1], -0.4316708436255949093e-6, 1e-14, "iauPn06", "rbp32", status); vvd(rbp[2][2], 0.9999998301093032943, 1e-12, "iauPn06", "rbp33", status); vvd(rn[0][0], 0.9999999999536069682, 1e-12, "iauPn06", "rn11", status); vvd(rn[0][1], 0.8837746921149881914e-5, 1e-14, "iauPn06", "rn12", status); vvd(rn[0][2], 0.3831487047682968703e-5, 1e-14, "iauPn06", "rn13", status); vvd(rn[1][0], -0.8837591232983692340e-5, 1e-14, "iauPn06", "rn21", status); vvd(rn[1][1], 0.9999999991354692664, 1e-12, "iauPn06", "rn22", status); vvd(rn[1][2], -0.4063198798558931215e-4, 1e-14, "iauPn06", "rn23", status); vvd(rn[2][0], -0.3831846139597250235e-5, 1e-14, "iauPn06", "rn31", status); vvd(rn[2][1], 0.4063195412258792914e-4, 1e-14, "iauPn06", "rn32", status); vvd(rn[2][2], 0.9999999991671806293, 1e-12, "iauPn06", "rn33", status); vvd(rbpn[0][0], 0.9999989440504506688, 1e-12, "iauPn06", "rbpn11", status); vvd(rbpn[0][1], -0.1332879913170492655e-2, 1e-14, "iauPn06", "rbpn12", status); vvd(rbpn[0][2], -0.5790760923225655753e-3, 1e-14, "iauPn06", "rbpn13", status); vvd(rbpn[1][0], 0.1332856406595754748e-2, 1e-14, "iauPn06", "rbpn21", status); vvd(rbpn[1][1], 0.9999991109069366795, 1e-12, "iauPn06", "rbpn22", status); vvd(rbpn[1][2], -0.4097725651142641812e-4, 1e-14, "iauPn06", "rbpn23", status); vvd(rbpn[2][0], 0.5791301952321296716e-3, 1e-14, "iauPn06", "rbpn31", status); vvd(rbpn[2][1], 0.4020538796195230577e-4, 1e-14, "iauPn06", "rbpn32", status); vvd(rbpn[2][2], 0.9999998314958576778, 1e-12, "iauPn06", "rbpn33", status); } static void t_pnm00a(int *status) /* ** - - - - - - - - - ** t _ p n m 0 0 a ** - - - - - - - - - ** ** Test iauPnm00a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPnm00a, vvd ** ** This revision: 2013 August 7 */ { double rbpn[3][3]; iauPnm00a(2400000.5, 50123.9999, rbpn); vvd(rbpn[0][0], 0.9999995832793134257, 1e-12, "iauPnm00a", "11", status); vvd(rbpn[0][1], 0.8372384254137809439e-3, 1e-14, "iauPnm00a", "12", status); vvd(rbpn[0][2], 0.3639684306407150645e-3, 1e-14, "iauPnm00a", "13", status); vvd(rbpn[1][0], -0.8372535226570394543e-3, 1e-14, "iauPnm00a", "21", status); vvd(rbpn[1][1], 0.9999996486491582471, 1e-12, "iauPnm00a", "22", status); vvd(rbpn[1][2], 0.4132915262664072381e-4, 1e-14, "iauPnm00a", "23", status); vvd(rbpn[2][0], -0.3639337004054317729e-3, 1e-14, "iauPnm00a", "31", status); vvd(rbpn[2][1], -0.4163386925461775873e-4, 1e-14, "iauPnm00a", "32", status); vvd(rbpn[2][2], 0.9999999329094390695, 1e-12, "iauPnm00a", "33", status); } static void t_pnm00b(int *status) /* ** - - - - - - - - - ** t _ p n m 0 0 b ** - - - - - - - - - ** ** Test iauPnm00b function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPnm00b, vvd ** ** This revision: 2013 August 7 */ { double rbpn[3][3]; iauPnm00b(2400000.5, 50123.9999, rbpn); vvd(rbpn[0][0], 0.9999995832776208280, 1e-12, "iauPnm00b", "11", status); vvd(rbpn[0][1], 0.8372401264429654837e-3, 1e-14, "iauPnm00b", "12", status); vvd(rbpn[0][2], 0.3639691681450271771e-3, 1e-14, "iauPnm00b", "13", status); vvd(rbpn[1][0], -0.8372552234147137424e-3, 1e-14, "iauPnm00b", "21", status); vvd(rbpn[1][1], 0.9999996486477686123, 1e-12, "iauPnm00b", "22", status); vvd(rbpn[1][2], 0.4132832190946052890e-4, 1e-14, "iauPnm00b", "23", status); vvd(rbpn[2][0], -0.3639344385341866407e-3, 1e-14, "iauPnm00b", "31", status); vvd(rbpn[2][1], -0.4163303977421522785e-4, 1e-14, "iauPnm00b", "32", status); vvd(rbpn[2][2], 0.9999999329092049734, 1e-12, "iauPnm00b", "33", status); } static void t_pnm06a(int *status) /* ** - - - - - - - - - ** t _ p n m 0 6 a ** - - - - - - - - - ** ** Test iauPnm06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPnm06a, vvd ** ** This revision: 2013 August 7 */ { double rbpn[3][3]; iauPnm06a(2400000.5, 50123.9999, rbpn); vvd(rbpn[0][0], 0.9999995832794205484, 1e-12, "iauPnm06a", "11", status); vvd(rbpn[0][1], 0.8372382772630962111e-3, 1e-14, "iauPnm06a", "12", status); vvd(rbpn[0][2], 0.3639684771140623099e-3, 1e-14, "iauPnm06a", "13", status); vvd(rbpn[1][0], -0.8372533744743683605e-3, 1e-14, "iauPnm06a", "21", status); vvd(rbpn[1][1], 0.9999996486492861646, 1e-12, "iauPnm06a", "22", status); vvd(rbpn[1][2], 0.4132905944611019498e-4, 1e-14, "iauPnm06a", "23", status); vvd(rbpn[2][0], -0.3639337469629464969e-3, 1e-14, "iauPnm06a", "31", status); vvd(rbpn[2][1], -0.4163377605910663999e-4, 1e-14, "iauPnm06a", "32", status); vvd(rbpn[2][2], 0.9999999329094260057, 1e-12, "iauPnm06a", "33", status); } static void t_pnm80(int *status) /* ** - - - - - - - - ** t _ p n m 8 0 ** - - - - - - - - ** ** Test iauPnm80 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPnm80, vvd ** ** This revision: 2013 August 7 */ { double rmatpn[3][3]; iauPnm80(2400000.5, 50123.9999, rmatpn); vvd(rmatpn[0][0], 0.9999995831934611169, 1e-12, "iauPnm80", "11", status); vvd(rmatpn[0][1], 0.8373654045728124011e-3, 1e-14, "iauPnm80", "12", status); vvd(rmatpn[0][2], 0.3639121916933106191e-3, 1e-14, "iauPnm80", "13", status); vvd(rmatpn[1][0], -0.8373804896118301316e-3, 1e-14, "iauPnm80", "21", status); vvd(rmatpn[1][1], 0.9999996485439674092, 1e-12, "iauPnm80", "22", status); vvd(rmatpn[1][2], 0.4130202510421549752e-4, 1e-14, "iauPnm80", "23", status); vvd(rmatpn[2][0], -0.3638774789072144473e-3, 1e-14, "iauPnm80", "31", status); vvd(rmatpn[2][1], -0.4160674085851722359e-4, 1e-14, "iauPnm80", "32", status); vvd(rmatpn[2][2], 0.9999999329310274805, 1e-12, "iauPnm80", "33", status); } static void t_pom00(int *status) /* ** - - - - - - - - ** t _ p o m 0 0 ** - - - - - - - - ** ** Test iauPom00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPom00, vvd ** ** This revision: 2013 August 7 */ { double xp, yp, sp, rpom[3][3]; xp = 2.55060238e-7; yp = 1.860359247e-6; sp = -0.1367174580728891460e-10; iauPom00(xp, yp, sp, rpom); vvd(rpom[0][0], 0.9999999999999674721, 1e-12, "iauPom00", "11", status); vvd(rpom[0][1], -0.1367174580728846989e-10, 1e-16, "iauPom00", "12", status); vvd(rpom[0][2], 0.2550602379999972345e-6, 1e-16, "iauPom00", "13", status); vvd(rpom[1][0], 0.1414624947957029801e-10, 1e-16, "iauPom00", "21", status); vvd(rpom[1][1], 0.9999999999982695317, 1e-12, "iauPom00", "22", status); vvd(rpom[1][2], -0.1860359246998866389e-5, 1e-16, "iauPom00", "23", status); vvd(rpom[2][0], -0.2550602379741215021e-6, 1e-16, "iauPom00", "31", status); vvd(rpom[2][1], 0.1860359247002414021e-5, 1e-16, "iauPom00", "32", status); vvd(rpom[2][2], 0.9999999999982370039, 1e-12, "iauPom00", "33", status); } static void t_ppp(int *status) /* ** - - - - - - ** t _ p p p ** - - - - - - ** ** Test iauPpp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPpp, vvd ** ** This revision: 2013 August 7 */ { double a[3], b[3], apb[3]; a[0] = 2.0; a[1] = 2.0; a[2] = 3.0; b[0] = 1.0; b[1] = 3.0; b[2] = 4.0; iauPpp(a, b, apb); vvd(apb[0], 3.0, 1e-12, "iauPpp", "0", status); vvd(apb[1], 5.0, 1e-12, "iauPpp", "1", status); vvd(apb[2], 7.0, 1e-12, "iauPpp", "2", status); } static void t_ppsp(int *status) /* ** - - - - - - - ** t _ p p s p ** - - - - - - - ** ** Test iauPpsp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPpsp, vvd ** ** This revision: 2013 August 7 */ { double a[3], s, b[3], apsb[3]; a[0] = 2.0; a[1] = 2.0; a[2] = 3.0; s = 5.0; b[0] = 1.0; b[1] = 3.0; b[2] = 4.0; iauPpsp(a, s, b, apsb); vvd(apsb[0], 7.0, 1e-12, "iauPpsp", "0", status); vvd(apsb[1], 17.0, 1e-12, "iauPpsp", "1", status); vvd(apsb[2], 23.0, 1e-12, "iauPpsp", "2", status); } static void t_pr00(int *status) /* ** - - - - - - - ** t _ p r 0 0 ** - - - - - - - ** ** Test iauPr00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPr00, vvd ** ** This revision: 2013 August 7 */ { double dpsipr, depspr; iauPr00(2400000.5, 53736, &dpsipr, &depspr); vvd(dpsipr, -0.8716465172668347629e-7, 1e-22, "iauPr00", "dpsipr", status); vvd(depspr, -0.7342018386722813087e-8, 1e-22, "iauPr00", "depspr", status); } static void t_prec76(int *status) /* ** - - - - - - - - - ** t _ p r e c 7 6 ** - - - - - - - - - ** ** Test iauPrec76 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPrec76, vvd ** ** This revision: 2013 August 7 */ { double ep01, ep02, ep11, ep12, zeta, z, theta; ep01 = 2400000.5; ep02 = 33282.0; ep11 = 2400000.5; ep12 = 51544.0; iauPrec76(ep01, ep02, ep11, ep12, &zeta, &z, &theta); vvd(zeta, 0.5588961642000161243e-2, 1e-12, "iauPrec76", "zeta", status); vvd(z, 0.5589922365870680624e-2, 1e-12, "iauPrec76", "z", status); vvd(theta, 0.4858945471687296760e-2, 1e-12, "iauPrec76", "theta", status); } static void t_pv2p(int *status) /* ** - - - - - - - ** t _ p v 2 p ** - - - - - - - ** ** Test iauPv2p function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPv2p, vvd ** ** This revision: 2013 August 7 */ { double pv[2][3], p[3]; pv[0][0] = 0.3; pv[0][1] = 1.2; pv[0][2] = -2.5; pv[1][0] = -0.5; pv[1][1] = 3.1; pv[1][2] = 0.9; iauPv2p(pv, p); vvd(p[0], 0.3, 0.0, "iauPv2p", "1", status); vvd(p[1], 1.2, 0.0, "iauPv2p", "2", status); vvd(p[2], -2.5, 0.0, "iauPv2p", "3", status); } static void t_pv2s(int *status) /* ** - - - - - - - ** t _ p v 2 s ** - - - - - - - ** ** Test iauPv2s function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPv2s, vvd ** ** This revision: 2013 August 7 */ { double pv[2][3], theta, phi, r, td, pd, rd; pv[0][0] = -0.4514964673880165; pv[0][1] = 0.03093394277342585; pv[0][2] = 0.05594668105108779; pv[1][0] = 1.292270850663260e-5; pv[1][1] = 2.652814182060692e-6; pv[1][2] = 2.568431853930293e-6; iauPv2s(pv, &theta, &phi, &r, &td, &pd, &rd); vvd(theta, 3.073185307179586515, 1e-12, "iauPv2s", "theta", status); vvd(phi, 0.1229999999999999992, 1e-12, "iauPv2s", "phi", status); vvd(r, 0.4559999999999999757, 1e-12, "iauPv2s", "r", status); vvd(td, -0.7800000000000000364e-5, 1e-16, "iauPv2s", "td", status); vvd(pd, 0.9010000000000001639e-5, 1e-16, "iauPv2s", "pd", status); vvd(rd, -0.1229999999999999832e-4, 1e-16, "iauPv2s", "rd", status); } static void t_pvdpv(int *status) /* ** - - - - - - - - ** t _ p v d p v ** - - - - - - - - ** ** Test iauPvdpv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPvdpv, vvd ** ** This revision: 2013 August 7 */ { double a[2][3], b[2][3], adb[2]; a[0][0] = 2.0; a[0][1] = 2.0; a[0][2] = 3.0; a[1][0] = 6.0; a[1][1] = 0.0; a[1][2] = 4.0; b[0][0] = 1.0; b[0][1] = 3.0; b[0][2] = 4.0; b[1][0] = 0.0; b[1][1] = 2.0; b[1][2] = 8.0; iauPvdpv(a, b, adb); vvd(adb[0], 20.0, 1e-12, "iauPvdpv", "1", status); vvd(adb[1], 50.0, 1e-12, "iauPvdpv", "2", status); } static void t_pvm(int *status) /* ** - - - - - - ** t _ p v m ** - - - - - - ** ** Test iauPvm function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPvm, vvd ** ** This revision: 2013 August 7 */ { double pv[2][3], r, s; pv[0][0] = 0.3; pv[0][1] = 1.2; pv[0][2] = -2.5; pv[1][0] = 0.45; pv[1][1] = -0.25; pv[1][2] = 1.1; iauPvm(pv, &r, &s); vvd(r, 2.789265136196270604, 1e-12, "iauPvm", "r", status); vvd(s, 1.214495780149111922, 1e-12, "iauPvm", "s", status); } static void t_pvmpv(int *status) /* ** - - - - - - - - ** t _ p v m p v ** - - - - - - - - ** ** Test iauPvmpv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPvmpv, vvd ** ** This revision: 2013 August 7 */ { double a[2][3], b[2][3], amb[2][3]; a[0][0] = 2.0; a[0][1] = 2.0; a[0][2] = 3.0; a[1][0] = 5.0; a[1][1] = 6.0; a[1][2] = 3.0; b[0][0] = 1.0; b[0][1] = 3.0; b[0][2] = 4.0; b[1][0] = 3.0; b[1][1] = 2.0; b[1][2] = 1.0; iauPvmpv(a, b, amb); vvd(amb[0][0], 1.0, 1e-12, "iauPvmpv", "11", status); vvd(amb[0][1], -1.0, 1e-12, "iauPvmpv", "21", status); vvd(amb[0][2], -1.0, 1e-12, "iauPvmpv", "31", status); vvd(amb[1][0], 2.0, 1e-12, "iauPvmpv", "12", status); vvd(amb[1][1], 4.0, 1e-12, "iauPvmpv", "22", status); vvd(amb[1][2], 2.0, 1e-12, "iauPvmpv", "32", status); } static void t_pvppv(int *status) /* ** - - - - - - - - ** t _ p v p p v ** - - - - - - - - ** ** Test iauPvppv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPvppv, vvd ** ** This revision: 2013 August 7 */ { double a[2][3], b[2][3], apb[2][3]; a[0][0] = 2.0; a[0][1] = 2.0; a[0][2] = 3.0; a[1][0] = 5.0; a[1][1] = 6.0; a[1][2] = 3.0; b[0][0] = 1.0; b[0][1] = 3.0; b[0][2] = 4.0; b[1][0] = 3.0; b[1][1] = 2.0; b[1][2] = 1.0; iauPvppv(a, b, apb); vvd(apb[0][0], 3.0, 1e-12, "iauPvppv", "p1", status); vvd(apb[0][1], 5.0, 1e-12, "iauPvppv", "p2", status); vvd(apb[0][2], 7.0, 1e-12, "iauPvppv", "p3", status); vvd(apb[1][0], 8.0, 1e-12, "iauPvppv", "v1", status); vvd(apb[1][1], 8.0, 1e-12, "iauPvppv", "v2", status); vvd(apb[1][2], 4.0, 1e-12, "iauPvppv", "v3", status); } static void t_pvstar(int *status) /* ** - - - - - - - - - ** t _ p v s t a r ** - - - - - - - - - ** ** Test iauPvstar function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPvstar, vvd, viv ** ** This revision: 2013 August 7 */ { double pv[2][3], ra, dec, pmr, pmd, px, rv; int j; pv[0][0] = 126668.5912743160601; pv[0][1] = 2136.792716839935195; pv[0][2] = -245251.2339876830091; pv[1][0] = -0.4051854035740712739e-2; pv[1][1] = -0.6253919754866173866e-2; pv[1][2] = 0.1189353719774107189e-1; j = iauPvstar(pv, &ra, &dec, &pmr, &pmd, &px, &rv); vvd(ra, 0.1686756e-1, 1e-12, "iauPvstar", "ra", status); vvd(dec, -1.093989828, 1e-12, "iauPvstar", "dec", status); vvd(pmr, -0.178323516e-4, 1e-16, "iauPvstar", "pmr", status); vvd(pmd, 0.2336024047e-5, 1e-16, "iauPvstar", "pmd", status); vvd(px, 0.74723, 1e-12, "iauPvstar", "px", status); vvd(rv, -21.6, 1e-11, "iauPvstar", "rv", status); viv(j, 0, "iauPvstar", "j", status); } static void t_pvtob(int *status) /* ** - - - - - - - - ** t _ p v t o b ** - - - - - - - - ** ** Test iauPvtob function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPvtob, vvd ** ** This revision: 2013 October 2 */ { double elong, phi, hm, xp, yp, sp, theta, pv[2][3]; elong = 2.0; phi = 0.5; hm = 3000.0; xp = 1e-6; yp = -0.5e-6; sp = 1e-8; theta = 5.0; iauPvtob(elong, phi, hm, xp, yp, sp, theta, pv); vvd(pv[0][0], 4225081.367071159207, 1e-5, "iauPvtob", "p(1)", status); vvd(pv[0][1], 3681943.215856198144, 1e-5, "iauPvtob", "p(2)", status); vvd(pv[0][2], 3041149.399241260785, 1e-5, "iauPvtob", "p(3)", status); vvd(pv[1][0], -268.4915389365998787, 1e-9, "iauPvtob", "v(1)", status); vvd(pv[1][1], 308.0977983288903123, 1e-9, "iauPvtob", "v(2)", status); vvd(pv[1][2], 0, 0, "iauPvtob", "v(3)", status); } static void t_pvu(int *status) /* ** - - - - - - ** t _ p v u ** - - - - - - ** ** Test iauPvu function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPvu, vvd ** ** This revision: 2013 August 7 */ { double pv[2][3], upv[2][3]; pv[0][0] = 126668.5912743160734; pv[0][1] = 2136.792716839935565; pv[0][2] = -245251.2339876830229; pv[1][0] = -0.4051854035740713039e-2; pv[1][1] = -0.6253919754866175788e-2; pv[1][2] = 0.1189353719774107615e-1; iauPvu(2920.0, pv, upv); vvd(upv[0][0], 126656.7598605317105, 1e-12, "iauPvu", "p1", status); vvd(upv[0][1], 2118.531271155726332, 1e-12, "iauPvu", "p2", status); vvd(upv[0][2], -245216.5048590656190, 1e-12, "iauPvu", "p3", status); vvd(upv[1][0], -0.4051854035740713039e-2, 1e-12, "iauPvu", "v1", status); vvd(upv[1][1], -0.6253919754866175788e-2, 1e-12, "iauPvu", "v2", status); vvd(upv[1][2], 0.1189353719774107615e-1, 1e-12, "iauPvu", "v3", status); } static void t_pvup(int *status) /* ** - - - - - - - ** t _ p v u p ** - - - - - - - ** ** Test iauPvup function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPvup, vvd ** ** This revision: 2013 August 7 */ { double pv[2][3], p[3]; pv[0][0] = 126668.5912743160734; pv[0][1] = 2136.792716839935565; pv[0][2] = -245251.2339876830229; pv[1][0] = -0.4051854035740713039e-2; pv[1][1] = -0.6253919754866175788e-2; pv[1][2] = 0.1189353719774107615e-1; iauPvup(2920.0, pv, p); vvd(p[0], 126656.7598605317105, 1e-12, "iauPvup", "1", status); vvd(p[1], 2118.531271155726332, 1e-12, "iauPvup", "2", status); vvd(p[2], -245216.5048590656190, 1e-12, "iauPvup", "3", status); } static void t_pvxpv(int *status) /* ** - - - - - - - - ** t _ p v x p v ** - - - - - - - - ** ** Test iauPvxpv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPvxpv, vvd ** ** This revision: 2013 August 7 */ { double a[2][3], b[2][3], axb[2][3]; a[0][0] = 2.0; a[0][1] = 2.0; a[0][2] = 3.0; a[1][0] = 6.0; a[1][1] = 0.0; a[1][2] = 4.0; b[0][0] = 1.0; b[0][1] = 3.0; b[0][2] = 4.0; b[1][0] = 0.0; b[1][1] = 2.0; b[1][2] = 8.0; iauPvxpv(a, b, axb); vvd(axb[0][0], -1.0, 1e-12, "iauPvxpv", "p1", status); vvd(axb[0][1], -5.0, 1e-12, "iauPvxpv", "p2", status); vvd(axb[0][2], 4.0, 1e-12, "iauPvxpv", "p3", status); vvd(axb[1][0], -2.0, 1e-12, "iauPvxpv", "v1", status); vvd(axb[1][1], -36.0, 1e-12, "iauPvxpv", "v2", status); vvd(axb[1][2], 22.0, 1e-12, "iauPvxpv", "v3", status); } static void t_pxp(int *status) /* ** - - - - - - ** t _ p x p ** - - - - - - ** ** Test iauPxp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauPxp, vvd ** ** This revision: 2013 August 7 */ { double a[3], b[3], axb[3]; a[0] = 2.0; a[1] = 2.0; a[2] = 3.0; b[0] = 1.0; b[1] = 3.0; b[2] = 4.0; iauPxp(a, b, axb); vvd(axb[0], -1.0, 1e-12, "iauPxp", "1", status); vvd(axb[1], -5.0, 1e-12, "iauPxp", "2", status); vvd(axb[2], 4.0, 1e-12, "iauPxp", "3", status); } static void t_refco(int *status) /* ** - - - - - - - - ** t _ r e f c o ** - - - - - - - - ** ** Test iauRefco function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauRefco, vvd ** ** This revision: 2013 October 2 */ { double phpa, tc, rh, wl, refa, refb; phpa = 800.0; tc = 10.0; rh = 0.9; wl = 0.4; iauRefco(phpa, tc, rh, wl, &refa, &refb); vvd(refa, 0.2264949956241415009e-3, 1e-15, "iauRefco", "refa", status); vvd(refb, -0.2598658261729343970e-6, 1e-18, "iauRefco", "refb", status); } static void t_rm2v(int *status) /* ** - - - - - - - ** t _ r m 2 v ** - - - - - - - ** ** Test iauRm2v function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauRm2v, vvd ** ** This revision: 2013 August 7 */ { double r[3][3], w[3]; r[0][0] = 0.00; r[0][1] = -0.80; r[0][2] = -0.60; r[1][0] = 0.80; r[1][1] = -0.36; r[1][2] = 0.48; r[2][0] = 0.60; r[2][1] = 0.48; r[2][2] = -0.64; iauRm2v(r, w); vvd(w[0], 0.0, 1e-12, "iauRm2v", "1", status); vvd(w[1], 1.413716694115406957, 1e-12, "iauRm2v", "2", status); vvd(w[2], -1.884955592153875943, 1e-12, "iauRm2v", "3", status); } static void t_rv2m(int *status) /* ** - - - - - - - ** t _ r v 2 m ** - - - - - - - ** ** Test iauRv2m function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauRv2m, vvd ** ** This revision: 2013 August 7 */ { double w[3], r[3][3]; w[0] = 0.0; w[1] = 1.41371669; w[2] = -1.88495559; iauRv2m(w, r); vvd(r[0][0], -0.7071067782221119905, 1e-14, "iauRv2m", "11", status); vvd(r[0][1], -0.5656854276809129651, 1e-14, "iauRv2m", "12", status); vvd(r[0][2], -0.4242640700104211225, 1e-14, "iauRv2m", "13", status); vvd(r[1][0], 0.5656854276809129651, 1e-14, "iauRv2m", "21", status); vvd(r[1][1], -0.0925483394532274246, 1e-14, "iauRv2m", "22", status); vvd(r[1][2], -0.8194112531408833269, 1e-14, "iauRv2m", "23", status); vvd(r[2][0], 0.4242640700104211225, 1e-14, "iauRv2m", "31", status); vvd(r[2][1], -0.8194112531408833269, 1e-14, "iauRv2m", "32", status); vvd(r[2][2], 0.3854415612311154341, 1e-14, "iauRv2m", "33", status); } static void t_rx(int *status) /* ** - - - - - ** t _ r x ** - - - - - ** ** Test iauRx function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauRx, vvd ** ** This revision: 2013 August 7 */ { double phi, r[3][3]; phi = 0.3456789; r[0][0] = 2.0; r[0][1] = 3.0; r[0][2] = 2.0; r[1][0] = 3.0; r[1][1] = 2.0; r[1][2] = 3.0; r[2][0] = 3.0; r[2][1] = 4.0; r[2][2] = 5.0; iauRx(phi, r); vvd(r[0][0], 2.0, 0.0, "iauRx", "11", status); vvd(r[0][1], 3.0, 0.0, "iauRx", "12", status); vvd(r[0][2], 2.0, 0.0, "iauRx", "13", status); vvd(r[1][0], 3.839043388235612460, 1e-12, "iauRx", "21", status); vvd(r[1][1], 3.237033249594111899, 1e-12, "iauRx", "22", status); vvd(r[1][2], 4.516714379005982719, 1e-12, "iauRx", "23", status); vvd(r[2][0], 1.806030415924501684, 1e-12, "iauRx", "31", status); vvd(r[2][1], 3.085711545336372503, 1e-12, "iauRx", "32", status); vvd(r[2][2], 3.687721683977873065, 1e-12, "iauRx", "33", status); } static void t_rxp(int *status) /* ** - - - - - - ** t _ r x p ** - - - - - - ** ** Test iauRxp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauRxp, vvd ** ** This revision: 2013 August 7 */ { double r[3][3], p[3], rp[3]; r[0][0] = 2.0; r[0][1] = 3.0; r[0][2] = 2.0; r[1][0] = 3.0; r[1][1] = 2.0; r[1][2] = 3.0; r[2][0] = 3.0; r[2][1] = 4.0; r[2][2] = 5.0; p[0] = 0.2; p[1] = 1.5; p[2] = 0.1; iauRxp(r, p, rp); vvd(rp[0], 5.1, 1e-12, "iauRxp", "1", status); vvd(rp[1], 3.9, 1e-12, "iauRxp", "2", status); vvd(rp[2], 7.1, 1e-12, "iauRxp", "3", status); } static void t_rxpv(int *status) /* ** - - - - - - - ** t _ r x p v ** - - - - - - - ** ** Test iauRxpv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauRxpv, vvd ** ** This revision: 2013 August 7 */ { double r[3][3], pv[2][3], rpv[2][3]; r[0][0] = 2.0; r[0][1] = 3.0; r[0][2] = 2.0; r[1][0] = 3.0; r[1][1] = 2.0; r[1][2] = 3.0; r[2][0] = 3.0; r[2][1] = 4.0; r[2][2] = 5.0; pv[0][0] = 0.2; pv[0][1] = 1.5; pv[0][2] = 0.1; pv[1][0] = 1.5; pv[1][1] = 0.2; pv[1][2] = 0.1; iauRxpv(r, pv, rpv); vvd(rpv[0][0], 5.1, 1e-12, "iauRxpv", "11", status); vvd(rpv[1][0], 3.8, 1e-12, "iauRxpv", "12", status); vvd(rpv[0][1], 3.9, 1e-12, "iauRxpv", "21", status); vvd(rpv[1][1], 5.2, 1e-12, "iauRxpv", "22", status); vvd(rpv[0][2], 7.1, 1e-12, "iauRxpv", "31", status); vvd(rpv[1][2], 5.8, 1e-12, "iauRxpv", "32", status); } static void t_rxr(int *status) /* ** - - - - - - ** t _ r x r ** - - - - - - ** ** Test iauRxr function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauRxr, vvd ** ** This revision: 2013 August 7 */ { double a[3][3], b[3][3], atb[3][3]; a[0][0] = 2.0; a[0][1] = 3.0; a[0][2] = 2.0; a[1][0] = 3.0; a[1][1] = 2.0; a[1][2] = 3.0; a[2][0] = 3.0; a[2][1] = 4.0; a[2][2] = 5.0; b[0][0] = 1.0; b[0][1] = 2.0; b[0][2] = 2.0; b[1][0] = 4.0; b[1][1] = 1.0; b[1][2] = 1.0; b[2][0] = 3.0; b[2][1] = 0.0; b[2][2] = 1.0; iauRxr(a, b, atb); vvd(atb[0][0], 20.0, 1e-12, "iauRxr", "11", status); vvd(atb[0][1], 7.0, 1e-12, "iauRxr", "12", status); vvd(atb[0][2], 9.0, 1e-12, "iauRxr", "13", status); vvd(atb[1][0], 20.0, 1e-12, "iauRxr", "21", status); vvd(atb[1][1], 8.0, 1e-12, "iauRxr", "22", status); vvd(atb[1][2], 11.0, 1e-12, "iauRxr", "23", status); vvd(atb[2][0], 34.0, 1e-12, "iauRxr", "31", status); vvd(atb[2][1], 10.0, 1e-12, "iauRxr", "32", status); vvd(atb[2][2], 15.0, 1e-12, "iauRxr", "33", status); } static void t_ry(int *status) /* ** - - - - - ** t _ r y ** - - - - - ** ** Test iauRy function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauRy, vvd ** ** This revision: 2013 August 7 */ { double theta, r[3][3]; theta = 0.3456789; r[0][0] = 2.0; r[0][1] = 3.0; r[0][2] = 2.0; r[1][0] = 3.0; r[1][1] = 2.0; r[1][2] = 3.0; r[2][0] = 3.0; r[2][1] = 4.0; r[2][2] = 5.0; iauRy(theta, r); vvd(r[0][0], 0.8651847818978159930, 1e-12, "iauRy", "11", status); vvd(r[0][1], 1.467194920539316554, 1e-12, "iauRy", "12", status); vvd(r[0][2], 0.1875137911274457342, 1e-12, "iauRy", "13", status); vvd(r[1][0], 3, 1e-12, "iauRy", "21", status); vvd(r[1][1], 2, 1e-12, "iauRy", "22", status); vvd(r[1][2], 3, 1e-12, "iauRy", "23", status); vvd(r[2][0], 3.500207892850427330, 1e-12, "iauRy", "31", status); vvd(r[2][1], 4.779889022262298150, 1e-12, "iauRy", "32", status); vvd(r[2][2], 5.381899160903798712, 1e-12, "iauRy", "33", status); } static void t_rz(int *status) /* ** - - - - - ** t _ r z ** - - - - - ** ** Test iauRz function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauRz, vvd ** ** This revision: 2013 August 7 */ { double psi, r[3][3]; psi = 0.3456789; r[0][0] = 2.0; r[0][1] = 3.0; r[0][2] = 2.0; r[1][0] = 3.0; r[1][1] = 2.0; r[1][2] = 3.0; r[2][0] = 3.0; r[2][1] = 4.0; r[2][2] = 5.0; iauRz(psi, r); vvd(r[0][0], 2.898197754208926769, 1e-12, "iauRz", "11", status); vvd(r[0][1], 3.500207892850427330, 1e-12, "iauRz", "12", status); vvd(r[0][2], 2.898197754208926769, 1e-12, "iauRz", "13", status); vvd(r[1][0], 2.144865911309686813, 1e-12, "iauRz", "21", status); vvd(r[1][1], 0.865184781897815993, 1e-12, "iauRz", "22", status); vvd(r[1][2], 2.144865911309686813, 1e-12, "iauRz", "23", status); vvd(r[2][0], 3.0, 1e-12, "iauRz", "31", status); vvd(r[2][1], 4.0, 1e-12, "iauRz", "32", status); vvd(r[2][2], 5.0, 1e-12, "iauRz", "33", status); } static void t_s00a(int *status) /* ** - - - - - - - ** t _ s 0 0 a ** - - - - - - - ** ** Test iauS00a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauS00a, vvd ** ** This revision: 2013 August 7 */ { double s; s = iauS00a(2400000.5, 52541.0); vvd(s, -0.1340684448919163584e-7, 1e-18, "iauS00a", "", status); } static void t_s00b(int *status) /* ** - - - - - - - ** t _ s 0 0 b ** - - - - - - - ** ** Test iauS00b function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauS00b, vvd ** ** This revision: 2013 August 7 */ { double s; s = iauS00b(2400000.5, 52541.0); vvd(s, -0.1340695782951026584e-7, 1e-18, "iauS00b", "", status); } static void t_s00(int *status) /* ** - - - - - - ** t _ s 0 0 ** - - - - - - ** ** Test iauS00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauS00, vvd ** ** This revision: 2013 August 7 */ { double x, y, s; x = 0.5791308486706011000e-3; y = 0.4020579816732961219e-4; s = iauS00(2400000.5, 53736.0, x, y); vvd(s, -0.1220036263270905693e-7, 1e-18, "iauS00", "", status); } static void t_s06a(int *status) /* ** - - - - - - - ** t _ s 0 6 a ** - - - - - - - ** ** Test iauS06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauS06a, vvd ** ** This revision: 2013 August 7 */ { double s; s = iauS06a(2400000.5, 52541.0); vvd(s, -0.1340680437291812383e-7, 1e-18, "iauS06a", "", status); } static void t_s06(int *status) /* ** - - - - - - ** t _ s 0 6 ** - - - - - - ** ** Test iauS06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauS06, vvd ** ** This revision: 2013 August 7 */ { double x, y, s; x = 0.5791308486706011000e-3; y = 0.4020579816732961219e-4; s = iauS06(2400000.5, 53736.0, x, y); vvd(s, -0.1220032213076463117e-7, 1e-18, "iauS06", "", status); } static void t_s2c(int *status) /* ** - - - - - - ** t _ s 2 c ** - - - - - - ** ** Test iauS2c function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauS2c, vvd ** ** This revision: 2013 August 7 */ { double c[3]; iauS2c(3.0123, -0.999, c); vvd(c[0], -0.5366267667260523906, 1e-12, "iauS2c", "1", status); vvd(c[1], 0.0697711109765145365, 1e-12, "iauS2c", "2", status); vvd(c[2], -0.8409302618566214041, 1e-12, "iauS2c", "3", status); } static void t_s2p(int *status) /* ** - - - - - - ** t _ s 2 p ** - - - - - - ** ** Test iauS2p function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauS2p, vvd ** ** This revision: 2013 August 7 */ { double p[3]; iauS2p(-3.21, 0.123, 0.456, p); vvd(p[0], -0.4514964673880165228, 1e-12, "iauS2p", "x", status); vvd(p[1], 0.0309339427734258688, 1e-12, "iauS2p", "y", status); vvd(p[2], 0.0559466810510877933, 1e-12, "iauS2p", "z", status); } static void t_s2pv(int *status) /* ** - - - - - - - ** t _ s 2 p v ** - - - - - - - ** ** Test iauS2pv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauS2pv, vvd ** ** This revision: 2013 August 7 */ { double pv[2][3]; iauS2pv(-3.21, 0.123, 0.456, -7.8e-6, 9.01e-6, -1.23e-5, pv); vvd(pv[0][0], -0.4514964673880165228, 1e-12, "iauS2pv", "x", status); vvd(pv[0][1], 0.0309339427734258688, 1e-12, "iauS2pv", "y", status); vvd(pv[0][2], 0.0559466810510877933, 1e-12, "iauS2pv", "z", status); vvd(pv[1][0], 0.1292270850663260170e-4, 1e-16, "iauS2pv", "vx", status); vvd(pv[1][1], 0.2652814182060691422e-5, 1e-16, "iauS2pv", "vy", status); vvd(pv[1][2], 0.2568431853930292259e-5, 1e-16, "iauS2pv", "vz", status); } static void t_s2xpv(int *status) /* ** - - - - - - - - ** t _ s 2 x p v ** - - - - - - - - ** ** Test iauS2xpv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauS2xpv, vvd ** ** This revision: 2013 August 7 */ { double s1, s2, pv[2][3], spv[2][3]; s1 = 2.0; s2 = 3.0; pv[0][0] = 0.3; pv[0][1] = 1.2; pv[0][2] = -2.5; pv[1][0] = 0.5; pv[1][1] = 2.3; pv[1][2] = -0.4; iauS2xpv(s1, s2, pv, spv); vvd(spv[0][0], 0.6, 1e-12, "iauS2xpv", "p1", status); vvd(spv[0][1], 2.4, 1e-12, "iauS2xpv", "p2", status); vvd(spv[0][2], -5.0, 1e-12, "iauS2xpv", "p3", status); vvd(spv[1][0], 1.5, 1e-12, "iauS2xpv", "v1", status); vvd(spv[1][1], 6.9, 1e-12, "iauS2xpv", "v2", status); vvd(spv[1][2], -1.2, 1e-12, "iauS2xpv", "v3", status); } static void t_sepp(int *status) /* ** - - - - - - - ** t _ s e p p ** - - - - - - - ** ** Test iauSepp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauSepp, vvd ** ** This revision: 2013 August 7 */ { double a[3], b[3], s; a[0] = 1.0; a[1] = 0.1; a[2] = 0.2; b[0] = -3.0; b[1] = 1e-3; b[2] = 0.2; s = iauSepp(a, b); vvd(s, 2.860391919024660768, 1e-12, "iauSepp", "", status); } static void t_seps(int *status) /* ** - - - - - - - ** t _ s e p s ** - - - - - - - ** ** Test iauSeps function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauSeps, vvd ** ** This revision: 2013 August 7 */ { double al, ap, bl, bp, s; al = 1.0; ap = 0.1; bl = 0.2; bp = -3.0; s = iauSeps(al, ap, bl, bp); vvd(s, 2.346722016996998842, 1e-14, "iauSeps", "", status); } static void t_sp00(int *status) /* ** - - - - - - - ** t _ s p 0 0 ** - - - - - - - ** ** Test iauSp00 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauSp00, vvd ** ** This revision: 2013 August 7 */ { vvd(iauSp00(2400000.5, 52541.0), -0.6216698469981019309e-11, 1e-12, "iauSp00", "", status); } static void t_starpm(int *status) /* ** - - - - - - - - - ** t _ s t a r p m ** - - - - - - - - - ** ** Test iauStarpm function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauStarpm, vvd, viv ** ** This revision: 2013 August 7 */ { double ra1, dec1, pmr1, pmd1, px1, rv1; double ra2, dec2, pmr2, pmd2, px2, rv2; int j; ra1 = 0.01686756; dec1 = -1.093989828; pmr1 = -1.78323516e-5; pmd1 = 2.336024047e-6; px1 = 0.74723; rv1 = -21.6; j = iauStarpm(ra1, dec1, pmr1, pmd1, px1, rv1, 2400000.5, 50083.0, 2400000.5, 53736.0, &ra2, &dec2, &pmr2, &pmd2, &px2, &rv2); vvd(ra2, 0.01668919069414242368, 1e-13, "iauStarpm", "ra", status); vvd(dec2, -1.093966454217127879, 1e-13, "iauStarpm", "dec", status); vvd(pmr2, -0.1783662682155932702e-4, 1e-17, "iauStarpm", "pmr", status); vvd(pmd2, 0.2338092915987603664e-5, 1e-17, "iauStarpm", "pmd", status); vvd(px2, 0.7473533835323493644, 1e-13, "iauStarpm", "px", status); vvd(rv2, -21.59905170476860786, 1e-11, "iauStarpm", "rv", status); viv(j, 0, "iauStarpm", "j", status); } static void t_starpv(int *status) /* ** - - - - - - - - - ** t _ s t a r p v ** - - - - - - - - - ** ** Test iauStarpv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauStarpv, vvd, viv ** ** This revision: 2013 August 7 */ { double ra, dec, pmr, pmd, px, rv, pv[2][3]; int j; ra = 0.01686756; dec = -1.093989828; pmr = -1.78323516e-5; pmd = 2.336024047e-6; px = 0.74723; rv = -21.6; j = iauStarpv(ra, dec, pmr, pmd, px, rv, pv); vvd(pv[0][0], 126668.5912743160601, 1e-10, "iauStarpv", "11", status); vvd(pv[0][1], 2136.792716839935195, 1e-12, "iauStarpv", "12", status); vvd(pv[0][2], -245251.2339876830091, 1e-10, "iauStarpv", "13", status); vvd(pv[1][0], -0.4051854035740712739e-2, 1e-13, "iauStarpv", "21", status); vvd(pv[1][1], -0.6253919754866173866e-2, 1e-15, "iauStarpv", "22", status); vvd(pv[1][2], 0.1189353719774107189e-1, 1e-13, "iauStarpv", "23", status); viv(j, 0, "iauStarpv", "j", status); } static void t_sxp(int *status) /* ** - - - - - - ** t _ s x p ** - - - - - - ** ** Test iauSxp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauSxp, vvd ** ** This revision: 2013 August 7 */ { double s, p[3], sp[3]; s = 2.0; p[0] = 0.3; p[1] = 1.2; p[2] = -2.5; iauSxp(s, p, sp); vvd(sp[0], 0.6, 0.0, "iauSxp", "1", status); vvd(sp[1], 2.4, 0.0, "iauSxp", "2", status); vvd(sp[2], -5.0, 0.0, "iauSxp", "3", status); } static void t_sxpv(int *status) /* ** - - - - - - - ** t _ s x p v ** - - - - - - - ** ** Test iauSxpv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauSxpv, vvd ** ** This revision: 2013 August 7 */ { double s, pv[2][3], spv[2][3]; s = 2.0; pv[0][0] = 0.3; pv[0][1] = 1.2; pv[0][2] = -2.5; pv[1][0] = 0.5; pv[1][1] = 3.2; pv[1][2] = -0.7; iauSxpv(s, pv, spv); vvd(spv[0][0], 0.6, 0.0, "iauSxpv", "p1", status); vvd(spv[0][1], 2.4, 0.0, "iauSxpv", "p2", status); vvd(spv[0][2], -5.0, 0.0, "iauSxpv", "p3", status); vvd(spv[1][0], 1.0, 0.0, "iauSxpv", "v1", status); vvd(spv[1][1], 6.4, 0.0, "iauSxpv", "v2", status); vvd(spv[1][2], -1.4, 0.0, "iauSxpv", "v3", status); } static void t_taitt(int *status) /* ** - - - - - - - - ** t _ t a i t t ** - - - - - - - - ** ** Test iauTaitt function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTaitt, vvd, viv ** ** This revision: 2013 August 7 */ { double t1, t2; int j; j = iauTaitt(2453750.5, 0.892482639, &t1, &t2); vvd(t1, 2453750.5, 1e-6, "iauTaitt", "t1", status); vvd(t2, 0.892855139, 1e-12, "iauTaitt", "t2", status); viv(j, 0, "iauTaitt", "j", status); } static void t_taiut1(int *status) /* ** - - - - - - - - - ** t _ t a i u t 1 ** - - - - - - - - - ** ** Test iauTaiut1 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTaiut1, vvd, viv ** ** This revision: 2013 August 7 */ { double u1, u2; int j; j = iauTaiut1(2453750.5, 0.892482639, -32.6659, &u1, &u2); vvd(u1, 2453750.5, 1e-6, "iauTaiut1", "u1", status); vvd(u2, 0.8921045614537037037, 1e-12, "iauTaiut1", "u2", status); viv(j, 0, "iauTaiut1", "j", status); } static void t_taiutc(int *status) /* ** - - - - - - - - - ** t _ t a i u t c ** - - - - - - - - - ** ** Test iauTaiutc function. ** ** Returned: ** status LOGICAL TRUE = success, FALSE = fail ** ** Called: iauTaiutc, vvd, viv ** ** This revision: 2013 October 3 */ { double u1, u2; int j; j = iauTaiutc(2453750.5, 0.892482639, &u1, &u2); vvd(u1, 2453750.5, 1e-6, "iauTaiutc", "u1", status); vvd(u2, 0.8921006945555555556, 1e-12, "iauTaiutc", "u2", status); viv(j, 0, "iauTaiutc", "j", status); } static void t_tcbtdb(int *status) /* ** - - - - - - - - - ** t _ t c b t d b ** - - - - - - - - - ** ** Test iauTcbtdb function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTcbtdb, vvd, viv ** ** This revision: 2013 August 7 */ { double b1, b2; int j; j = iauTcbtdb(2453750.5, 0.893019599, &b1, &b2); vvd(b1, 2453750.5, 1e-6, "iauTcbtdb", "b1", status); vvd(b2, 0.8928551362746343397, 1e-12, "iauTcbtdb", "b2", status); viv(j, 0, "iauTcbtdb", "j", status); } static void t_tcgtt(int *status) /* ** - - - - - - - - ** t _ t c g t t ** - - - - - - - - ** ** Test iauTcgtt function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTcgtt, vvd, viv ** ** This revision: 2013 August 7 */ { double t1, t2; int j; j = iauTcgtt(2453750.5, 0.892862531, &t1, &t2); vvd(t1, 2453750.5, 1e-6, "iauTcgtt", "t1", status); vvd(t2, 0.8928551387488816828, 1e-12, "iauTcgtt", "t2", status); viv(j, 0, "iauTcgtt", "j", status); } static void t_tdbtcb(int *status) /* ** - - - - - - - - - ** t _ t d b t c b ** - - - - - - - - - ** ** Test iauTdbtcb function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTdbtcb, vvd, viv ** ** This revision: 2013 August 7 */ { double b1, b2; int j; j = iauTdbtcb(2453750.5, 0.892855137, &b1, &b2); vvd( b1, 2453750.5, 1e-6, "iauTdbtcb", "b1", status); vvd( b2, 0.8930195997253656716, 1e-12, "iauTdbtcb", "b2", status); viv(j, 0, "iauTdbtcb", "j", status); } static void t_tdbtt(int *status) /* ** - - - - - - - - ** t _ t d b t t ** - - - - - - - - ** ** Test iauTdbtt function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTdbtt, vvd, viv ** ** This revision: 2013 August 7 */ { double t1, t2; int j; j = iauTdbtt(2453750.5, 0.892855137, -0.000201, &t1, &t2); vvd(t1, 2453750.5, 1e-6, "iauTdbtt", "t1", status); vvd(t2, 0.8928551393263888889, 1e-12, "iauTdbtt", "t2", status); viv(j, 0, "iauTdbtt", "j", status); } static void t_tf2a(int *status) /* ** - - - - - - - ** t _ t f 2 a ** - - - - - - - ** ** Test iauTf2a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTf2a, vvd, viv ** ** This revision: 2013 August 7 */ { double a; int j; j = iauTf2a('+', 4, 58, 20.2, &a); vvd(a, 1.301739278189537429, 1e-12, "iauTf2a", "a", status); viv(j, 0, "iauTf2a", "j", status); } static void t_tf2d(int *status) /* ** - - - - - - - ** t _ t f 2 d ** - - - - - - - ** ** Test iauTf2d function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTf2d, vvd, viv ** ** This revision: 2013 August 7 */ { double d; int j; j = iauTf2d(' ', 23, 55, 10.9, &d); vvd(d, 0.9966539351851851852, 1e-12, "iauTf2d", "d", status); viv(j, 0, "iauTf2d", "j", status); } static void t_tr(int *status) /* ** - - - - - ** t _ t r ** - - - - - ** ** Test iauTr function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTr, vvd ** ** This revision: 2013 August 7 */ { double r[3][3], rt[3][3]; r[0][0] = 2.0; r[0][1] = 3.0; r[0][2] = 2.0; r[1][0] = 3.0; r[1][1] = 2.0; r[1][2] = 3.0; r[2][0] = 3.0; r[2][1] = 4.0; r[2][2] = 5.0; iauTr(r, rt); vvd(rt[0][0], 2.0, 0.0, "iauTr", "11", status); vvd(rt[0][1], 3.0, 0.0, "iauTr", "12", status); vvd(rt[0][2], 3.0, 0.0, "iauTr", "13", status); vvd(rt[1][0], 3.0, 0.0, "iauTr", "21", status); vvd(rt[1][1], 2.0, 0.0, "iauTr", "22", status); vvd(rt[1][2], 4.0, 0.0, "iauTr", "23", status); vvd(rt[2][0], 2.0, 0.0, "iauTr", "31", status); vvd(rt[2][1], 3.0, 0.0, "iauTr", "32", status); vvd(rt[2][2], 5.0, 0.0, "iauTr", "33", status); } static void t_trxp(int *status) /* ** - - - - - - - ** t _ t r x p ** - - - - - - - ** ** Test iauTrxp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTrxp, vvd ** ** This revision: 2013 August 7 */ { double r[3][3], p[3], trp[3]; r[0][0] = 2.0; r[0][1] = 3.0; r[0][2] = 2.0; r[1][0] = 3.0; r[1][1] = 2.0; r[1][2] = 3.0; r[2][0] = 3.0; r[2][1] = 4.0; r[2][2] = 5.0; p[0] = 0.2; p[1] = 1.5; p[2] = 0.1; iauTrxp(r, p, trp); vvd(trp[0], 5.2, 1e-12, "iauTrxp", "1", status); vvd(trp[1], 4.0, 1e-12, "iauTrxp", "2", status); vvd(trp[2], 5.4, 1e-12, "iauTrxp", "3", status); } static void t_trxpv(int *status) /* ** - - - - - - - - ** t _ t r x p v ** - - - - - - - - ** ** Test iauTrxpv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTrxpv, vvd ** ** This revision: 2013 August 7 */ { double r[3][3], pv[2][3], trpv[2][3]; r[0][0] = 2.0; r[0][1] = 3.0; r[0][2] = 2.0; r[1][0] = 3.0; r[1][1] = 2.0; r[1][2] = 3.0; r[2][0] = 3.0; r[2][1] = 4.0; r[2][2] = 5.0; pv[0][0] = 0.2; pv[0][1] = 1.5; pv[0][2] = 0.1; pv[1][0] = 1.5; pv[1][1] = 0.2; pv[1][2] = 0.1; iauTrxpv(r, pv, trpv); vvd(trpv[0][0], 5.2, 1e-12, "iauTrxpv", "p1", status); vvd(trpv[0][1], 4.0, 1e-12, "iauTrxpv", "p1", status); vvd(trpv[0][2], 5.4, 1e-12, "iauTrxpv", "p1", status); vvd(trpv[1][0], 3.9, 1e-12, "iauTrxpv", "v1", status); vvd(trpv[1][1], 5.3, 1e-12, "iauTrxpv", "v2", status); vvd(trpv[1][2], 4.1, 1e-12, "iauTrxpv", "v3", status); } static void t_tttai(int *status) /* ** - - - - - - - - ** t _ t t t a i ** - - - - - - - - ** ** Test iauTttai function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTttai, vvd, viv ** ** This revision: 2013 August 7 */ { double a1, a2; int j; j = iauTttai(2453750.5, 0.892482639, &a1, &a2); vvd(a1, 2453750.5, 1e-6, "iauTttai", "a1", status); vvd(a2, 0.892110139, 1e-12, "iauTttai", "a2", status); viv(j, 0, "iauTttai", "j", status); } static void t_tttcg(int *status) /* ** - - - - - - - - ** t _ t t t c g ** - - - - - - - - ** ** Test iauTttcg function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTttcg, vvd, viv ** ** This revision: 2013 August 7 */ { double g1, g2; int j; j = iauTttcg(2453750.5, 0.892482639, &g1, &g2); vvd( g1, 2453750.5, 1e-6, "iauTttcg", "g1", status); vvd( g2, 0.8924900312508587113, 1e-12, "iauTttcg", "g2", status); viv(j, 0, "iauTttcg", "j", status); } static void t_tttdb(int *status) /* ** - - - - - - - - ** t _ t t t d b ** - - - - - - - - ** ** Test iauTttdb function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTttdb, vvd, viv ** ** This revision: 2013 August 7 */ { double b1, b2; int j; j = iauTttdb(2453750.5, 0.892855139, -0.000201, &b1, &b2); vvd(b1, 2453750.5, 1e-6, "iauTttdb", "b1", status); vvd(b2, 0.8928551366736111111, 1e-12, "iauTttdb", "b2", status); viv(j, 0, "iauTttdb", "j", status); } static void t_ttut1(int *status) /* ** - - - - - - - - ** t _ t t u t 1 ** - - - - - - - - ** ** Test iauTtut1 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauTtut1, vvd, viv ** ** This revision: 2013 August 7 */ { double u1, u2; int j; j = iauTtut1(2453750.5, 0.892855139, 64.8499, &u1, &u2); vvd(u1, 2453750.5, 1e-6, "iauTtut1", "u1", status); vvd(u2, 0.8921045614537037037, 1e-12, "iauTtut1", "u2", status); viv(j, 0, "iauTtut1", "j", status); } static void t_ut1tai(int *status) /* ** - - - - - - - - - ** t _ u t 1 t a i ** - - - - - - - - - ** ** Test iauUt1tai function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauUt1tai, vvd, viv ** ** This revision: 2013 August 7 */ { double a1, a2; int j; j = iauUt1tai(2453750.5, 0.892104561, -32.6659, &a1, &a2); vvd(a1, 2453750.5, 1e-6, "iauUt1tai", "a1", status); vvd(a2, 0.8924826385462962963, 1e-12, "iauUt1tai", "a2", status); viv(j, 0, "iauUt1tai", "j", status); } static void t_ut1tt(int *status) /* ** - - - - - - - - ** t _ u t 1 t t ** - - - - - - - - ** ** Test iauUt1tt function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauUt1tt, vvd, viv ** ** This revision: 2013 October 3 */ { double t1, t2; int j; j = iauUt1tt(2453750.5, 0.892104561, 64.8499, &t1, &t2); vvd(t1, 2453750.5, 1e-6, "iauUt1tt", "t1", status); vvd(t2, 0.8928551385462962963, 1e-12, "iauUt1tt", "t2", status); viv(j, 0, "iauUt1tt", "j", status); } static void t_ut1utc(int *status) /* ** - - - - - - - - - ** t _ u t 1 u t c ** - - - - - - - - - ** ** Test iauUt1utc function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauUt1utc, vvd, viv ** ** This revision: 2013 August 7 */ { double u1, u2; int j; j = iauUt1utc(2453750.5, 0.892104561, 0.3341, &u1, &u2); vvd(u1, 2453750.5, 1e-6, "iauUt1utc", "u1", status); vvd(u2, 0.8921006941018518519, 1e-12, "iauUt1utc", "u2", status); viv(j, 0, "iauUt1utc", "j", status); } static void t_utctai(int *status) /* ** - - - - - - - - - ** t _ u t c t a i ** - - - - - - - - - ** ** Test iauUtctai function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauUtctai, vvd, viv ** ** This revision: 2013 August 7 */ { double u1, u2; int j; j = iauUtctai(2453750.5, 0.892100694, &u1, &u2); vvd(u1, 2453750.5, 1e-6, "iauUtctai", "u1", status); vvd(u2, 0.8924826384444444444, 1e-12, "iauUtctai", "u2", status); viv(j, 0, "iauUtctai", "j", status); } static void t_utcut1(int *status) /* ** - - - - - - - - - ** t _ u t c u t 1 ** - - - - - - - - - ** ** Test iauUtcut1 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauUtcut1, vvd, viv ** ** This revision: 2013 August 7 */ { double u1, u2; int j; j = iauUtcut1(2453750.5, 0.892100694, 0.3341, &u1, &u2); vvd(u1, 2453750.5, 1e-6, "iauUtcut1", "u1", status); vvd(u2, 0.8921045608981481481, 1e-12, "iauUtcut1", "u2", status); viv(j, 0, "iauUtcut1", "j", status); } static void t_xy06(int *status) /* ** - - - - - - - ** t _ x y 0 6 ** - - - - - - - ** ** Test iauXy06 function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauXy06, vvd ** ** This revision: 2013 August 7 */ { double x, y; iauXy06(2400000.5, 53736.0, &x, &y); vvd(x, 0.5791308486706010975e-3, 1e-15, "iauXy06", "x", status); vvd(y, 0.4020579816732958141e-4, 1e-16, "iauXy06", "y", status); } static void t_xys00a(int *status) /* ** - - - - - - - - - ** t _ x y s 0 0 a ** - - - - - - - - - ** ** Test iauXys00a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauXys00a, vvd ** ** This revision: 2013 August 7 */ { double x, y, s; iauXys00a(2400000.5, 53736.0, &x, &y, &s); vvd(x, 0.5791308472168152904e-3, 1e-14, "iauXys00a", "x", status); vvd(y, 0.4020595661591500259e-4, 1e-15, "iauXys00a", "y", status); vvd(s, -0.1220040848471549623e-7, 1e-18, "iauXys00a", "s", status); } static void t_xys00b(int *status) /* ** - - - - - - - - - ** t _ x y s 0 0 b ** - - - - - - - - - ** ** Test iauXys00b function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauXys00b, vvd ** ** This revision: 2013 August 7 */ { double x, y, s; iauXys00b(2400000.5, 53736.0, &x, &y, &s); vvd(x, 0.5791301929950208873e-3, 1e-14, "iauXys00b", "x", status); vvd(y, 0.4020553681373720832e-4, 1e-15, "iauXys00b", "y", status); vvd(s, -0.1220027377285083189e-7, 1e-18, "iauXys00b", "s", status); } static void t_xys06a(int *status) /* ** - - - - - - - - - ** t _ x y s 0 6 a ** - - - - - - - - - ** ** Test iauXys06a function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauXys06a, vvd ** ** This revision: 2013 August 7 */ { double x, y, s; iauXys06a(2400000.5, 53736.0, &x, &y, &s); vvd(x, 0.5791308482835292617e-3, 1e-14, "iauXys06a", "x", status); vvd(y, 0.4020580099454020310e-4, 1e-15, "iauXys06a", "y", status); vvd(s, -0.1220032294164579896e-7, 1e-18, "iauXys06a", "s", status); } static void t_zp(int *status) /* ** - - - - - ** t _ z p ** - - - - - ** ** Test iauZp function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauZp, vvd ** ** This revision: 2013 August 7 */ { double p[3]; p[0] = 0.3; p[1] = 1.2; p[2] = -2.5; iauZp(p); vvd(p[0], 0.0, 0.0, "iauZp", "1", status); vvd(p[1], 0.0, 0.0, "iauZp", "2", status); vvd(p[2], 0.0, 0.0, "iauZp", "3", status); } static void t_zpv(int *status) /* ** - - - - - - ** t _ z p v ** - - - - - - ** ** Test iauZpv function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauZpv, vvd ** ** This revision: 2013 August 7 */ { double pv[2][3]; pv[0][0] = 0.3; pv[0][1] = 1.2; pv[0][2] = -2.5; pv[1][0] = -0.5; pv[1][1] = 3.1; pv[1][2] = 0.9; iauZpv(pv); vvd(pv[0][0], 0.0, 0.0, "iauZpv", "p1", status); vvd(pv[0][1], 0.0, 0.0, "iauZpv", "p2", status); vvd(pv[0][2], 0.0, 0.0, "iauZpv", "p3", status); vvd(pv[1][0], 0.0, 0.0, "iauZpv", "v1", status); vvd(pv[1][1], 0.0, 0.0, "iauZpv", "v2", status); vvd(pv[1][2], 0.0, 0.0, "iauZpv", "v3", status); } static void t_zr(int *status) /* ** - - - - - ** t _ z r ** - - - - - ** ** Test iauZr function. ** ** Returned: ** status int FALSE = success, TRUE = fail ** ** Called: iauZr, vvd ** ** This revision: 2013 August 7 */ { double r[3][3]; r[0][0] = 2.0; r[1][0] = 3.0; r[2][0] = 2.0; r[0][1] = 3.0; r[1][1] = 2.0; r[2][1] = 3.0; r[0][2] = 3.0; r[1][2] = 4.0; r[2][2] = 5.0; iauZr(r); vvd(r[0][0], 0.0, 0.0, "iauZr", "00", status); vvd(r[1][0], 0.0, 0.0, "iauZr", "01", status); vvd(r[2][0], 0.0, 0.0, "iauZr", "02", status); vvd(r[0][1], 0.0, 0.0, "iauZr", "10", status); vvd(r[1][1], 0.0, 0.0, "iauZr", "11", status); vvd(r[2][1], 0.0, 0.0, "iauZr", "12", status); vvd(r[0][2], 0.0, 0.0, "iauZr", "20", status); vvd(r[1][2], 0.0, 0.0, "iauZr", "21", status); vvd(r[2][2], 0.0, 0.0, "iauZr", "22", status); } int main(int argc, char *argv[]) /* ** - - - - - ** m a i n ** - - - - - ** ** This revision: 2016 March 12 */ { int status; /* If any command-line argument, switch to verbose reporting. */ if (argc > 1) { verbose = 1; argv[0][0] += 0; /* to avoid compiler warnings */ } /* Preset the &status to FALSE = success. */ status = 0; /* Test all of the SOFA functions. */ t_a2af(&status); t_a2tf(&status); t_ab(&status); t_af2a(&status); t_anp(&status); t_anpm(&status); t_apcg(&status); t_apcg13(&status); t_apci(&status); t_apci13(&status); t_apco(&status); t_apco13(&status); t_apcs(&status); t_apcs13(&status); t_aper(&status); t_aper13(&status); t_apio(&status); t_apio13(&status); t_atci13(&status); t_atciq(&status); t_atciqn(&status); t_atciqz(&status); t_atco13(&status); t_atic13(&status); t_aticq(&status); t_aticqn(&status); t_atio13(&status); t_atioq(&status); t_atoc13(&status); t_atoi13(&status); t_atoiq(&status); t_bi00(&status); t_bp00(&status); t_bp06(&status); t_bpn2xy(&status); t_c2i00a(&status); t_c2i00b(&status); t_c2i06a(&status); t_c2ibpn(&status); t_c2ixy(&status); t_c2ixys(&status); t_c2s(&status); t_c2t00a(&status); t_c2t00b(&status); t_c2t06a(&status); t_c2tcio(&status); t_c2teqx(&status); t_c2tpe(&status); t_c2txy(&status); t_cal2jd(&status); t_cp(&status); t_cpv(&status); t_cr(&status); t_d2dtf(&status); t_d2tf(&status); t_dat(&status); t_dtdb(&status); t_dtf2d(&status); t_eceq06(&status); t_ecm06(&status); t_ee00(&status); t_ee00a(&status); t_ee00b(&status); t_ee06a(&status); t_eect00(&status); t_eform(&status); t_eo06a(&status); t_eors(&status); t_epb(&status); t_epb2jd(&status); t_epj(&status); t_epj2jd(&status); t_epv00(&status); t_eqec06(&status); t_eqeq94(&status); t_era00(&status); t_fad03(&status); t_fae03(&status); t_faf03(&status); t_faju03(&status); t_fal03(&status); t_falp03(&status); t_fama03(&status); t_fame03(&status); t_fane03(&status); t_faom03(&status); t_fapa03(&status); t_fasa03(&status); t_faur03(&status); t_fave03(&status); t_fk52h(&status); t_fk5hip(&status); t_fk5hz(&status); t_fw2m(&status); t_fw2xy(&status); t_g2icrs(&status); t_gc2gd(&status); t_gc2gde(&status); t_gd2gc(&status); t_gd2gce(&status); t_gmst00(&status); t_gmst06(&status); t_gmst82(&status); t_gst00a(&status); t_gst00b(&status); t_gst06(&status); t_gst06a(&status); t_gst94(&status); t_h2fk5(&status); t_hfk5z(&status); t_icrs2g(&status); t_ir(&status); t_jd2cal(&status); t_jdcalf(&status); t_ld(&status); t_ldn(&status); t_ldsun(&status); t_lteceq(&status); t_ltecm(&status); t_lteqec(&status); t_ltp(&status); t_ltpb(&status); t_ltpecl(&status); t_ltpequ(&status); t_num00a(&status); t_num00b(&status); t_num06a(&status); t_numat(&status); t_nut00a(&status); t_nut00b(&status); t_nut06a(&status); t_nut80(&status); t_nutm80(&status); t_obl06(&status); t_obl80(&status); t_p06e(&status); t_p2pv(&status); t_p2s(&status); t_pap(&status); t_pas(&status); t_pb06(&status); t_pdp(&status); t_pfw06(&status); t_plan94(&status); t_pmat00(&status); t_pmat06(&status); t_pmat76(&status); t_pm(&status); t_pmp(&status); t_pmpx(&status); t_pmsafe(&status); t_pn(&status); t_pn00(&status); t_pn00a(&status); t_pn00b(&status); t_pn06a(&status); t_pn06(&status); t_pnm00a(&status); t_pnm00b(&status); t_pnm06a(&status); t_pnm80(&status); t_pom00(&status); t_ppp(&status); t_ppsp(&status); t_pr00(&status); t_prec76(&status); t_pv2p(&status); t_pv2s(&status); t_pvdpv(&status); t_pvm(&status); t_pvmpv(&status); t_pvppv(&status); t_pvstar(&status); t_pvtob(&status); t_pvu(&status); t_pvup(&status); t_pvxpv(&status); t_pxp(&status); t_refco(&status); t_rm2v(&status); t_rv2m(&status); t_rx(&status); t_rxp(&status); t_rxpv(&status); t_rxr(&status); t_ry(&status); t_rz(&status); t_s00a(&status); t_s00b(&status); t_s00(&status); t_s06a(&status); t_s06(&status); t_s2c(&status); t_s2p(&status); t_s2pv(&status); t_s2xpv(&status); t_sepp(&status); t_seps(&status); t_sp00(&status); t_starpm(&status); t_starpv(&status); t_sxp(&status); t_sxpv(&status); t_taitt(&status); t_taiut1(&status); t_taiutc(&status); t_tcbtdb(&status); t_tcgtt(&status); t_tdbtcb(&status); t_tdbtt(&status); t_tf2a(&status); t_tf2d(&status); t_tr(&status); t_trxp(&status); t_trxpv(&status); t_tttai(&status); t_tttcg(&status); t_tttdb(&status); t_ttut1(&status); t_ut1tai(&status); t_ut1tt(&status) ; t_ut1utc(&status); t_utctai(&status); t_utcut1(&status); t_xy06(&status); t_xys00a(&status); t_xys00b(&status); t_xys06a(&status); t_zp(&status); t_zpv(&status); t_zr(&status); /* Report, set up an appropriate exit status, and finish. */ if (status) { printf("t_sofa_c validation failed!\n"); } else { printf("t_sofa_c validation successful\n"); } return status; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/tttai.c0000644000113000011300000001330513027221063014454 0ustar bellsbells#include "sofa.h" int iauTttai(double tt1, double tt2, double *tai1, double *tai2) /* ** - - - - - - - - - ** i a u T t t a i ** - - - - - - - - - ** ** Time scale transformation: Terrestrial Time, TT, to International ** Atomic Time, TAI. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned: ** tai1,tai2 double TAI as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Note: ** ** tt1+tt2 is Julian Date, apportioned in any convenient way between ** the two arguments, for example where tt1 is the Julian Day Number ** and tt2 is the fraction of a day. The returned tai1,tai2 follow ** suit. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* TT minus TAI (days). */ static const double dtat = TTMTAI/DAYSEC; /* Result, safeguarding precision. */ if ( tt1 > tt2 ) { *tai1 = tt1; *tai2 = tt2 - dtat; } else { *tai1 = tt1 - dtat; *tai2 = tt2; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/tttcg.c0000644000113000011300000001341513027221063014456 0ustar bellsbells#include "sofa.h" int iauTttcg(double tt1, double tt2, double *tcg1, double *tcg2) /* ** - - - - - - - - - ** i a u T t t c g ** - - - - - - - - - ** ** Time scale transformation: Terrestrial Time, TT, to Geocentric ** Coordinate Time, TCG. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned: ** tcg1,tcg2 double TCG as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Note: ** ** tt1+tt2 is Julian Date, apportioned in any convenient way between ** the two arguments, for example where tt1 is the Julian Day Number ** and tt2 is the fraction of a day. The returned tcg1,tcg2 follow ** suit. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** IAU 2000 Resolution B1.9 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* 1977 Jan 1 00:00:32.184 TT, as MJD */ static const double t77t = DJM77 + TTMTAI/DAYSEC; /* TT to TCG rate */ static const double elgg = ELG/(1.0-ELG); /* Result, safeguarding precision. */ if ( tt1 > tt2 ) { *tcg1 = tt1; *tcg2 = tt2 + ( ( tt1 - DJM0 ) + ( tt2 - t77t ) ) * elgg; } else { *tcg1 = tt1 + ( ( tt2 - DJM0 ) + ( tt1 - t77t ) ) * elgg; *tcg2 = tt2; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/tttdb.c0000644000113000011300000001427513027221063014457 0ustar bellsbells#include "sofa.h" int iauTttdb(double tt1, double tt2, double dtr, double *tdb1, double *tdb2) /* ** - - - - - - - - - ** i a u T t t d b ** - - - - - - - - - ** ** Time scale transformation: Terrestrial Time, TT, to Barycentric ** Dynamical Time, TDB. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tt1,tt2 double TT as a 2-part Julian Date ** dtr double TDB-TT in seconds ** ** Returned: ** tdb1,tdb2 double TDB as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tt1+tt2 is Julian Date, apportioned in any convenient way between ** the two arguments, for example where tt1 is the Julian Day Number ** and tt2 is the fraction of a day. The returned tdb1,tdb2 follow ** suit. ** ** 2) The argument dtr represents the quasi-periodic component of the ** GR transformation between TT and TCB. It is dependent upon the ** adopted solar-system ephemeris, and can be obtained by numerical ** integration, by interrogating a precomputed time ephemeris or by ** evaluating a model such as that implemented in the SOFA function ** iauDtdb. The quantity is dominated by an annual term of 1.7 ms ** amplitude. ** ** 3) TDB is essentially the same as Teph, the time argument for the JPL ** solar system ephemerides. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** IAU 2006 Resolution 3 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dtrd; /* Result, safeguarding precision. */ dtrd = dtr / DAYSEC; if ( tt1 > tt2 ) { *tdb1 = tt1; *tdb2 = tt2 + dtrd; } else { *tdb1 = tt1 + dtrd; *tdb2 = tt2; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ttut1.c0000644000113000011300000001322613027221063014412 0ustar bellsbells#include "sofa.h" int iauTtut1(double tt1, double tt2, double dt, double *ut11, double *ut12) /* ** - - - - - - - - - ** i a u T t u t 1 ** - - - - - - - - - ** ** Time scale transformation: Terrestrial Time, TT, to Universal Time, ** UT1. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tt1,tt2 double TT as a 2-part Julian Date ** dt double TT-UT1 in seconds ** ** Returned: ** ut11,ut12 double UT1 as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tt1+tt2 is Julian Date, apportioned in any convenient way between ** the two arguments, for example where tt1 is the Julian Day Number ** and tt2 is the fraction of a day. The returned ut11,ut12 follow ** suit. ** ** 2) The argument dt is classical Delta T. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dtd; /* Result, safeguarding precision. */ dtd = dt / DAYSEC; if ( tt1 > tt2 ) { *ut11 = tt1; *ut12 = tt2 - dtd; } else { *ut11 = tt1 - dtd; *ut12 = tt2; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ut1tai.c0000644000113000011300000001337613027221063014546 0ustar bellsbells#include "sofa.h" int iauUt1tai(double ut11, double ut12, double dta, double *tai1, double *tai2) /* ** - - - - - - - - - - ** i a u U t 1 t a i ** - - - - - - - - - - ** ** Time scale transformation: Universal Time, UT1, to International ** Atomic Time, TAI. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** ut11,ut12 double UT1 as a 2-part Julian Date ** dta double UT1-TAI in seconds ** ** Returned: ** tai1,tai2 double TAI as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) ut11+ut12 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where ut11 is the Julian ** Day Number and ut12 is the fraction of a day. The returned ** tai1,tai2 follow suit. ** ** 2) The argument dta, i.e. UT1-TAI, is an observed quantity, and is ** available from IERS tabulations. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dtad; /* Result, safeguarding precision. */ dtad = dta / DAYSEC; if ( ut11 > ut12 ) { *tai1 = ut11; *tai2 = ut12 - dtad; } else { *tai1 = ut11 - dtad; *tai2 = ut12; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ut1tt.c0000644000113000011300000001323213027221063014407 0ustar bellsbells#include "sofa.h" int iauUt1tt(double ut11, double ut12, double dt, double *tt1, double *tt2) /* ** - - - - - - - - - ** i a u U t 1 t t ** - - - - - - - - - ** ** Time scale transformation: Universal Time, UT1, to Terrestrial ** Time, TT. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** ut11,ut12 double UT1 as a 2-part Julian Date ** dt double TT-UT1 in seconds ** ** Returned: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) ut11+ut12 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where ut11 is the Julian ** Day Number and ut12 is the fraction of a day. The returned ** tt1,tt2 follow suit. ** ** 2) The argument dt is classical Delta T. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double dtd; /* Result, safeguarding precision. */ dtd = dt / DAYSEC; if ( ut11 > ut12 ) { *tt1 = ut11; *tt2 = ut12 + dtd; } else { *tt1 = ut11 + dtd; *tt2 = ut12; } /* Status (always OK). */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/ut1utc.c0000644000113000011300000002110213027221063014546 0ustar bellsbells#include "sofa.h" int iauUt1utc(double ut11, double ut12, double dut1, double *utc1, double *utc2) /* ** - - - - - - - - - - ** i a u U t 1 u t c ** - - - - - - - - - - ** ** Time scale transformation: Universal Time, UT1, to Coordinated ** Universal Time, UTC. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** ut11,ut12 double UT1 as a 2-part Julian Date (Note 1) ** dut1 double Delta UT1: UT1-UTC in seconds (Note 2) ** ** Returned: ** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 3,4) ** ** Returned (function value): ** int status: +1 = dubious year (Note 5) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) ut11+ut12 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where ut11 is the Julian ** Day Number and ut12 is the fraction of a day. The returned utc1 ** and utc2 form an analogous pair, except that a special convention ** is used, to deal with the problem of leap seconds - see Note 3. ** ** 2) Delta UT1 can be obtained from tabulations provided by the ** International Earth Rotation and Reference Systems Service. The ** value changes abruptly by 1s at a leap second; however, close to ** a leap second the algorithm used here is tolerant of the "wrong" ** choice of value being made. ** ** 3) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The convention in the present ** function is that the returned quasi JD day UTC1+UTC2 represents ** UTC days whether the length is 86399, 86400 or 86401 SI seconds. ** ** 4) The function iauD2dtf can be used to transform the UTC quasi-JD ** into calendar date and clock time, including UTC leap second ** handling. ** ** 5) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** Called: ** iauJd2cal JD to Gregorian calendar ** iauDat delta(AT) = TAI-UTC ** iauCal2jd Gregorian calendar to JD ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int big1; int i, iy, im, id, js; double duts, u1, u2, d1, dats1, d2, fd, dats2, ddats, us1, us2, du; /* UT1-UTC in seconds. */ duts = dut1; /* Put the two parts of the UT1 into big-first order. */ big1 = ( ut11 >= ut12 ); if ( big1 ) { u1 = ut11; u2 = ut12; } else { u1 = ut12; u2 = ut11; } /* See if the UT1 can possibly be in a leap-second day. */ d1 = u1; dats1 = 0; for ( i = -1; i <= 3; i++ ) { d2 = u2 + (double) i; if ( iauJd2cal(d1, d2, &iy, &im, &id, &fd) ) return -1; js = iauDat(iy, im, id, 0.0, &dats2); if ( js < 0 ) return -1; if ( i == - 1 ) dats1 = dats2; ddats = dats2 - dats1; if ( fabs(ddats) >= 0.5 ) { /* Yes, leap second nearby: ensure UT1-UTC is "before" value. */ if ( ddats * duts >= 0 ) duts -= ddats; /* UT1 for the start of the UTC day that ends in a leap. */ if ( iauCal2jd(iy, im, id, &d1, &d2) ) return -1; us1 = d1; us2 = d2 - 1.0 + duts/DAYSEC; /* Is the UT1 after this point? */ du = u1 - us1; du += u2 - us2; if ( du > 0 ) { /* Yes: fraction of the current UTC day that has elapsed. */ fd = du * DAYSEC / ( DAYSEC + ddats ); /* Ramp UT1-UTC to bring about SOFA's JD(UTC) convention. */ duts += ddats * ( fd <= 1.0 ? fd : 1.0 ); } /* Done. */ break; } dats1 = dats2; } /* Subtract the (possibly adjusted) UT1-UTC from UT1 to give UTC. */ u2 -= duts / DAYSEC; /* Result, safeguarding precision. */ if ( big1 ) { *utc1 = u1; *utc2 = u2; } else { *utc1 = u2; *utc2 = u1; } /* Status. */ return js; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/utctai.c0000644000113000011300000002011713027221063014617 0ustar bellsbells#include "sofa.h" int iauUtctai(double utc1, double utc2, double *tai1, double *tai2) /* ** - - - - - - - - - - ** i a u U t c t a i ** - - - - - - - - - - ** ** Time scale transformation: Coordinated Universal Time, UTC, to ** International Atomic Time, TAI. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-4) ** ** Returned: ** tai1,tai2 double TAI as a 2-part Julian Date (Note 5) ** ** Returned (function value): ** int status: +1 = dubious year (Note 3) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** 2) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The convention in the present ** function is that the JD day represents UTC days whether the ** length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era ** there were smaller jumps (in either direction) each time the ** linear UTC(TAI) expression was changed, and these "mini-leaps" ** are also included in the SOFA convention. ** ** 3) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 4) The function iauDtf2d converts from calendar date and time of day ** into 2-part Julian Date, and in the case of UTC implements the ** leap-second-ambiguity convention described above. ** ** 5) The returned TAI1,TAI2 are such that their sum is the TAI Julian ** Date. ** ** Called: ** iauJd2cal JD to Gregorian calendar ** iauDat delta(AT) = TAI-UTC ** iauCal2jd Gregorian calendar to JD ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** This revision: 2013 July 26 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. ** */ { int big1; int iy, im, id, j, iyt, imt, idt; double u1, u2, fd, dat0, dat12, w, dat24, dlod, dleap, z1, z2, a2; /* Put the two parts of the UTC into big-first order. */ big1 = ( utc1 >= utc2 ); if ( big1 ) { u1 = utc1; u2 = utc2; } else { u1 = utc2; u2 = utc1; } /* Get TAI-UTC at 0h today. */ j = iauJd2cal(u1, u2, &iy, &im, &id, &fd); if ( j ) return j; j = iauDat(iy, im, id, 0.0, &dat0); if ( j < 0 ) return j; /* Get TAI-UTC at 12h today (to detect drift). */ j = iauDat(iy, im, id, 0.5, &dat12); if ( j < 0 ) return j; /* Get TAI-UTC at 0h tomorrow (to detect jumps). */ j = iauJd2cal(u1+1.5, u2-fd, &iyt, &imt, &idt, &w); if ( j ) return j; j = iauDat(iyt, imt, idt, 0.0, &dat24); if ( j < 0 ) return j; /* Separate TAI-UTC change into per-day (DLOD) and any jump (DLEAP). */ dlod = 2.0 * (dat12 - dat0); dleap = dat24 - (dat0 + dlod); /* Remove any scaling applied to spread leap into preceding day. */ fd *= (DAYSEC+dleap)/DAYSEC; /* Scale from (pre-1972) UTC seconds to SI seconds. */ fd *= (DAYSEC+dlod)/DAYSEC; /* Today's calendar date to 2-part JD. */ if ( iauCal2jd(iy, im, id, &z1, &z2) ) return -1; /* Assemble the TAI result, preserving the UTC split and order. */ a2 = z1 - u1; a2 += z2; a2 += fd + dat0/DAYSEC; if ( big1 ) { *tai1 = u1; *tai2 = a2; } else { *tai1 = a2; *tai2 = u1; } /* Status. */ return j; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/utcut1.c0000644000113000011300000001644213027221063014561 0ustar bellsbells#include "sofa.h" int iauUtcut1(double utc1, double utc2, double dut1, double *ut11, double *ut12) /* ** - - - - - - - - - - ** i a u U t c u t 1 ** - - - - - - - - - - ** ** Time scale transformation: Coordinated Universal Time, UTC, to ** Universal Time, UT1. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-4) ** dut1 double Delta UT1 = UT1-UTC in seconds (Note 5) ** ** Returned: ** ut11,ut12 double UT1 as a 2-part Julian Date (Note 6) ** ** Returned (function value): ** int status: +1 = dubious year (Note 3) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** 2) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The convention in the present ** function is that the JD day represents UTC days whether the ** length is 86399, 86400 or 86401 SI seconds. ** ** 3) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 4) The function iauDtf2d converts from calendar date and time of ** day into 2-part Julian Date, and in the case of UTC implements ** the leap-second-ambiguity convention described above. ** ** 5) Delta UT1 can be obtained from tabulations provided by the ** International Earth Rotation and Reference Systems Service. ** It is the caller's responsibility to supply a dut1 argument ** containing the UT1-UTC value that matches the given UTC. ** ** 6) The returned ut11,ut12 are such that their sum is the UT1 Julian ** Date. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** Called: ** iauJd2cal JD to Gregorian calendar ** iauDat delta(AT) = TAI-UTC ** iauUtctai UTC to TAI ** iauTaiut1 TAI to UT1 ** ** This revision: 2013 August 12 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { int iy, im, id, js, jw; double w, dat, dta, tai1, tai2; /* Look up TAI-UTC. */ if ( iauJd2cal(utc1, utc2, &iy, &im, &id, &w) ) return -1; js = iauDat ( iy, im, id, 0.0, &dat); if ( js < 0 ) return -1; /* Form UT1-TAI. */ dta = dut1 - dat; /* UTC to TAI to UT1. */ jw = iauUtctai(utc1, utc2, &tai1, &tai2); if ( jw < 0 ) { return -1; } else if ( jw > 0 ) { js = jw; } if ( iauTaiut1(tai1, tai2, dta, ut11, ut12) ) return -1; /* Status. */ return js; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/xy06.c0000644000113000011300000040505413027221063014143 0ustar bellsbells#include "sofa.h" void iauXy06(double date1, double date2, double *x, double *y) /* ** - - - - - - - - ** i a u X y 0 6 ** - - - - - - - - ** ** X,Y coordinates of celestial intermediate pole from series based ** on IAU 2006 precession and IAU 2000A nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** x,y double CIP X,Y coordinates (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The X,Y coordinates are those of the unit vector towards the ** celestial intermediate pole. They represent the combined effects ** of frame bias, precession and nutation. ** ** 3) The fundamental arguments used are as adopted in IERS Conventions ** (2003) and are from Simon et al. (1994) and Souchay et al. ** (1999). ** ** 4) This is an alternative to the angles-based method, via the SOFA ** function iauFw2xy and as used in iauXys06a for example. The two ** methods agree at the 1 microarcsecond level (at present), a ** negligible amount compared with the intrinsic accuracy of the ** models. However, it would be unwise to mix the two methods ** (angles-based and series-based) in a single application. ** ** Called: ** iauFal03 mean anomaly of the Moon ** iauFalp03 mean anomaly of the Sun ** iauFaf03 mean argument of the latitude of the Moon ** iauFad03 mean elongation of the Moon from the Sun ** iauFaom03 mean longitude of the Moon's ascending node ** iauFame03 mean longitude of Mercury ** iauFave03 mean longitude of Venus ** iauFae03 mean longitude of Earth ** iauFama03 mean longitude of Mars ** iauFaju03 mean longitude of Jupiter ** iauFasa03 mean longitude of Saturn ** iauFaur03 mean longitude of Uranus ** iauFane03 mean longitude of Neptune ** iauFapa03 general accumulated precession in longitude ** ** References: ** ** Capitaine, N., Wallace, P.T. & Chapront, J., 2003, ** Astron.Astrophys., 412, 567 ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G. & Laskar, J., Astron.Astrophys., 1994, 282, 663 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M., 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** This revision: 2013 August 21 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { /* Maximum power of T in the polynomials for X and Y */ enum { MAXPT = 5 }; /* Polynomial coefficients (arcsec, X then Y). */ static const double xyp[2][MAXPT+1] = { { -0.016617, 2004.191898, -0.4297829, -0.19861834, 0.000007578, 0.0000059285 }, { -0.006951, -0.025896, -22.4072747, 0.00190059, 0.001112526, 0.0000001358 } }; /* Fundamental-argument multipliers: luni-solar terms */ static const int mfals[][5] = { /* 1-10 */ { 0, 0, 0, 0, 1 }, { 0, 0, 2, -2, 2 }, { 0, 0, 2, 0, 2 }, { 0, 0, 0, 0, 2 }, { 0, 1, 0, 0, 0 }, { 0, 1, 2, -2, 2 }, { 1, 0, 0, 0, 0 }, { 0, 0, 2, 0, 1 }, { 1, 0, 2, 0, 2 }, { 0, 1, -2, 2, -2 }, /* 11-20 */ { 0, 0, 2, -2, 1 }, { 1, 0, -2, 0, -2 }, { 1, 0, 0, -2, 0 }, { 1, 0, 0, 0, 1 }, { 1, 0, 0, 0, -1 }, { 1, 0, -2, -2, -2 }, { 1, 0, 2, 0, 1 }, { 2, 0, -2, 0, -1 }, { 0, 0, 0, 2, 0 }, { 0, 0, 2, 2, 2 }, /* 21-30 */ { 2, 0, 0, -2, 0 }, { 0, 2, -2, 2, -2 }, { 2, 0, 2, 0, 2 }, { 1, 0, 2, -2, 2 }, { 1, 0, -2, 0, -1 }, { 2, 0, 0, 0, 0 }, { 0, 0, 2, 0, 0 }, { 0, 1, 0, 0, 1 }, { 1, 0, 0, -2, -1 }, { 0, 2, 2, -2, 2 }, /* 31-40 */ { 0, 0, 2, -2, 0 }, { 1, 0, 0, -2, 1 }, { 0, 1, 0, 0, -1 }, { 0, 2, 0, 0, 0 }, { 1, 0, -2, -2, -1 }, { 1, 0, 2, 2, 2 }, { 0, 1, 2, 0, 2 }, { 2, 0, -2, 0, 0 }, { 0, 0, 2, 2, 1 }, { 0, 1, -2, 0, -2 }, /* 41-50 */ { 0, 0, 0, 2, 1 }, { 1, 0, 2, -2, 1 }, { 2, 0, 0, -2, -1 }, { 2, 0, 2, -2, 2 }, { 2, 0, 2, 0, 1 }, { 0, 0, 0, 2, -1 }, { 0, 1, -2, 2, -1 }, { 1, 1, 0, -2, 0 }, { 2, 0, 0, -2, 1 }, { 1, 0, 0, 2, 0 }, /* 51-60 */ { 0, 1, 2, -2, 1 }, { 1, -1, 0, 0, 0 }, { 0, 1, -1, 1, -1 }, { 2, 0, -2, 0, -2 }, { 0, 1, 0, -2, 0 }, { 1, 0, 0, -1, 0 }, { 3, 0, 2, 0, 2 }, { 0, 0, 0, 1, 0 }, { 1, -1, 2, 0, 2 }, { 1, 1, -2, -2, -2 }, /* 61-70 */ { 1, 0, -2, 0, 0 }, { 2, 0, 0, 0, -1 }, { 0, 1, -2, -2, -2 }, { 1, 1, 2, 0, 2 }, { 2, 0, 0, 0, 1 }, { 1, 1, 0, 0, 0 }, { 1, 0, -2, 2, -1 }, { 1, 0, 2, 0, 0 }, { 1, -1, 0, -1, 0 }, { 1, 0, 0, 0, 2 }, /* 71-80 */ { 1, 0, -1, 0, -1 }, { 0, 0, 2, 1, 2 }, { 1, 0, -2, -4, -2 }, { 1, -1, 0, -1, -1 }, { 1, 0, 2, 2, 1 }, { 0, 2, -2, 2, -1 }, { 1, 0, 0, 0, -2 }, { 2, 0, -2, -2, -2 }, { 1, 1, 2, -2, 2 }, { 2, 0, -2, -4, -2 }, /* 81-90 */ { 1, 0, -4, 0, -2 }, { 2, 0, 2, -2, 1 }, { 1, 0, 0, -1, -1 }, { 2, 0, 2, 2, 2 }, { 3, 0, 0, 0, 0 }, { 1, 0, 0, 2, 1 }, { 0, 0, 2, -2, -1 }, { 3, 0, 2, -2, 2 }, { 0, 0, 4, -2, 2 }, { 1, 0, 0, -4, 0 }, /* 91-100 */ { 0, 1, 2, 0, 1 }, { 2, 0, 0, -4, 0 }, { 1, 1, 0, -2, -1 }, { 2, 0, -2, 0, 1 }, { 0, 0, 2, 0, -1 }, { 0, 1, -2, 0, -1 }, { 0, 1, 0, 0, 2 }, { 0, 0, 2, -1, 2 }, { 0, 0, 2, 4, 2 }, { 2, 1, 0, -2, 0 }, /* 101-110 */ { 1, 1, 0, -2, 1 }, { 1, -1, 0, -2, 0 }, { 1, -1, 0, -1, -2 }, { 1, -1, 0, 0, 1 }, { 0, 1, -2, 2, 0 }, { 0, 1, 0, 0, -2 }, { 1, -1, 2, 2, 2 }, { 1, 0, 0, 2, -1 }, { 1, -1, -2, -2, -2 }, { 3, 0, 2, 0, 1 }, /* 111-120 */ { 0, 1, 2, 2, 2 }, { 1, 0, 2, -2, 0 }, { 1, 1, -2, -2, -1 }, { 1, 0, 2, -4, 1 }, { 0, 1, -2, -2, -1 }, { 2, -1, 2, 0, 2 }, { 0, 0, 0, 2, 2 }, { 1, -1, 2, 0, 1 }, { 1, -1, -2, 0, -2 }, { 0, 1, 0, 2, 0 }, /* 121-130 */ { 0, 1, 2, -2, 0 }, { 0, 0, 0, 1, 1 }, { 1, 0, -2, -2, 0 }, { 0, 3, 2, -2, 2 }, { 2, 1, 2, 0, 2 }, { 1, 1, 0, 0, 1 }, { 2, 0, 0, 2, 0 }, { 1, 1, 2, 0, 1 }, { 1, 0, 0, -2, -2 }, { 1, 0, -2, 2, 0 }, /* 131-140 */ { 1, 0, -1, 0, -2 }, { 0, 1, 0, -2, 1 }, { 0, 1, 0, 1, 0 }, { 0, 0, 0, 1, -1 }, { 1, 0, -2, 2, -2 }, { 1, -1, 0, 0, -1 }, { 0, 0, 0, 4, 0 }, { 1, -1, 0, 2, 0 }, { 1, 0, 2, 1, 2 }, { 1, 0, 2, -1, 2 }, /* 141-150 */ { 0, 0, 2, 1, 1 }, { 1, 0, 0, -2, 2 }, { 1, 0, -2, 0, 1 }, { 1, 0, -2, -4, -1 }, { 0, 0, 2, 2, 0 }, { 1, 1, 2, -2, 1 }, { 1, 0, -2, 1, -1 }, { 0, 0, 1, 0, 1 }, { 2, 0, -2, -2, -1 }, { 4, 0, 2, 0, 2 }, /* 151-160 */ { 2, -1, 0, 0, 0 }, { 2, 1, 2, -2, 2 }, { 0, 1, 2, 1, 2 }, { 1, 0, 4, -2, 2 }, { 1, 1, 0, 0, -1 }, { 2, 0, 2, 0, 0 }, { 2, 0, -2, -4, -1 }, { 1, 0, -1, 0, 0 }, { 1, 0, 0, 1, 0 }, { 0, 1, 0, 2, 1 }, /* 161-170 */ { 1, 0, -4, 0, -1 }, { 1, 0, 0, -4, -1 }, { 2, 0, 2, 2, 1 }, { 2, 1, 0, 0, 0 }, { 0, 0, 2, -3, 2 }, { 1, 2, 0, -2, 0 }, { 0, 3, 0, 0, 0 }, { 0, 0, 4, 0, 2 }, { 0, 0, 2, -4, 1 }, { 2, 0, 0, -2, -2 }, /* 171-180 */ { 1, 1, -2, -4, -2 }, { 0, 1, 0, -2, -1 }, { 0, 0, 0, 4, 1 }, { 3, 0, 2, -2, 1 }, { 1, 0, 2, 4, 2 }, { 1, 1, -2, 0, -2 }, { 0, 0, 4, -2, 1 }, { 2, -2, 0, -2, 0 }, { 2, 1, 0, -2, -1 }, { 0, 2, 0, -2, 0 }, /* 181-190 */ { 1, 0, 0, -1, 1 }, { 1, 1, 2, 2, 2 }, { 3, 0, 0, 0, -1 }, { 2, 0, 0, -4, -1 }, { 3, 0, 2, 2, 2 }, { 0, 0, 2, 4, 1 }, { 0, 2, -2, -2, -2 }, { 1, -1, 0, -2, -1 }, { 0, 0, 2, -1, 1 }, { 2, 0, 0, 2, 1 }, /* 191-200 */ { 1, -1, -2, 2, -1 }, { 0, 0, 0, 2, -2 }, { 2, 0, 0, -4, 1 }, { 1, 0, 0, -4, 1 }, { 2, 0, 2, -4, 1 }, { 4, 0, 2, -2, 2 }, { 2, 1, -2, 0, -1 }, { 2, 1, -2, -4, -2 }, { 3, 0, 0, -4, 0 }, { 1, -1, 2, 2, 1 }, /* 201-210 */ { 1, -1, -2, 0, -1 }, { 0, 2, 0, 0, 1 }, { 1, 2, -2, -2, -2 }, { 1, 1, 0, -4, 0 }, { 2, 0, 0, -2, 2 }, { 0, 2, 2, -2, 1 }, { 1, 0, 2, 0, -1 }, { 2, 1, 0, -2, 1 }, { 2, -1, -2, 0, -1 }, { 1, -1, -2, -2, -1 }, /* 211-220 */ { 0, 1, -2, 1, -2 }, { 1, 0, -4, 2, -2 }, { 0, 1, 2, 2, 1 }, { 3, 0, 0, 0, 1 }, { 2, -1, 2, 2, 2 }, { 0, 1, -2, -4, -2 }, { 1, 0, -2, -3, -2 }, { 2, 0, 0, 0, 2 }, { 1, -1, 0, -2, -2 }, { 2, 0, -2, 2, -1 }, /* 221-230 */ { 0, 2, -2, 0, -2 }, { 3, 0, -2, 0, -1 }, { 2, -1, 2, 0, 1 }, { 1, 0, -2, -1, -2 }, { 0, 0, 2, 0, 3 }, { 2, 0, -4, 0, -2 }, { 2, 1, 0, -4, 0 }, { 1, 1, -2, 1, -1 }, { 0, 2, 2, 0, 2 }, { 1, -1, 2, -2, 2 }, /* 231-240 */ { 1, -1, 0, -2, 1 }, { 2, 1, 2, 0, 1 }, { 1, 0, 2, -4, 2 }, { 1, 1, -2, 0, -1 }, { 1, 1, 0, 2, 0 }, { 1, 0, 0, -3, 0 }, { 2, 0, 2, -1, 2 }, { 0, 2, 0, 0, -1 }, { 2, -1, 0, -2, 0 }, { 4, 0, 0, 0, 0 }, /* 241-250 */ { 2, 1, -2, -2, -2 }, { 0, 2, -2, 2, 0 }, { 1, 0, 2, 1, 1 }, { 1, 0, -1, 0, -3 }, { 3, -1, 2, 0, 2 }, { 2, 0, 2, -2, 0 }, { 1, -2, 0, 0, 0 }, { 2, 0, 0, 0, -2 }, { 1, 0, 0, 4, 0 }, { 0, 1, 0, 1, 1 }, /* 251-260 */ { 1, 0, 2, 2, 0 }, { 0, 1, 0, 2, -1 }, { 0, 1, 0, 1, -1 }, { 0, 0, 2, -2, 3 }, { 3, 1, 2, 0, 2 }, { 1, 1, 2, 1, 2 }, { 1, 1, -2, 2, -1 }, { 2, -1, 2, -2, 2 }, { 1, -2, 2, 0, 2 }, { 1, 0, 2, -4, 0 }, /* 261-270 */ { 0, 0, 1, 0, 0 }, { 1, 0, 2, -3, 1 }, { 1, -2, 0, -2, 0 }, { 2, 0, 0, 2, -1 }, { 1, 1, 2, -4, 1 }, { 4, 0, 2, 0, 1 }, { 0, 1, 2, 1, 1 }, { 1, 2, 2, -2, 2 }, { 2, 0, 2, 1, 2 }, { 2, 1, 2, -2, 1 }, /* 271-280 */ { 1, 0, 2, -1, 1 }, { 1, 0, 4, -2, 1 }, { 1, -1, 2, -2, 1 }, { 0, 1, 0, -4, 0 }, { 3, 0, -2, -2, -2 }, { 0, 0, 4, -4, 2 }, { 2, 0, -4, -2, -2 }, { 2, -2, 0, -2, -1 }, { 1, 0, 2, -2, -1 }, { 2, 0, -2, -6, -2 }, /* 281-290 */ { 1, 0, -2, 1, -2 }, { 1, 0, -2, 2, 1 }, { 1, -1, 0, 2, -1 }, { 1, 0, -2, 1, 0 }, { 2, -1, 0, -2, 1 }, { 1, -1, 0, 2, 1 }, { 2, 0, -2, -2, 0 }, { 1, 0, 2, -3, 2 }, { 0, 0, 0, 4, -1 }, { 2, -1, 0, 0, 1 }, /* 291-300 */ { 2, 0, 4, -2, 2 }, { 0, 0, 2, 3, 2 }, { 0, 1, 4, -2, 2 }, { 0, 1, -2, 2, 1 }, { 1, 1, 0, 2, 1 }, { 1, 0, 0, 4, 1 }, { 0, 0, 4, 0, 1 }, { 2, 0, 0, -3, 0 }, { 1, 0, 0, -1, -2 }, { 1, -2, -2, -2, -2 }, /* 301-310 */ { 3, 0, 0, 2, 0 }, { 2, 0, 2, -4, 2 }, { 1, 1, -2, -4, -1 }, { 1, 0, -2, -6, -2 }, { 2, -1, 0, 0, -1 }, { 2, -1, 0, 2, 0 }, { 0, 1, 2, -2, -1 }, { 1, 1, 0, 1, 0 }, { 1, 2, 0, -2, -1 }, { 1, 0, 0, 1, -1 }, /* 311-320 */ { 0, 0, 1, 0, 2 }, { 3, 1, 2, -2, 2 }, { 1, 0, -4, -2, -2 }, { 1, 0, 2, 4, 1 }, { 1, -2, 2, 2, 2 }, { 1, -1, -2, -4, -2 }, { 0, 0, 2, -4, 2 }, { 0, 0, 2, -3, 1 }, { 2, 1, -2, 0, 0 }, { 3, 0, -2, -2, -1 }, /* 321-330 */ { 2, 0, 2, 4, 2 }, { 0, 0, 0, 0, 3 }, { 2, -1, -2, -2, -2 }, { 2, 0, 0, -1, 0 }, { 3, 0, 2, -4, 2 }, { 2, 1, 2, 2, 2 }, { 0, 0, 3, 0, 3 }, { 1, 1, 2, 2, 1 }, { 2, 1, 0, 0, -1 }, { 1, 2, 0, -2, 1 }, /* 331-340 */ { 3, 0, 2, 2, 1 }, { 1, -1, -2, 2, -2 }, { 1, 1, 0, -1, 0 }, { 1, 2, 0, 0, 0 }, { 1, 0, 4, 0, 2 }, { 1, -1, 2, 4, 2 }, { 2, 1, 0, 0, 1 }, { 1, 0, 0, 2, 2 }, { 1, -1, -2, 2, 0 }, { 0, 2, -2, -2, -1 }, /* 341-350 */ { 2, 0, -2, 0, 2 }, { 5, 0, 2, 0, 2 }, { 3, 0, -2, -6, -2 }, { 1, -1, 2, -1, 2 }, { 3, 0, 0, -4, -1 }, { 1, 0, 0, 1, 1 }, { 1, 0, -4, 2, -1 }, { 0, 1, 2, -4, 1 }, { 1, 2, 2, 0, 2 }, { 0, 1, 0, -2, -2 }, /* 351-360 */ { 0, 0, 2, -1, 0 }, { 1, 0, 1, 0, 1 }, { 0, 2, 0, -2, 1 }, { 3, 0, 2, 0, 0 }, { 1, 1, -2, 1, 0 }, { 2, 1, -2, -4, -1 }, { 3, -1, 0, 0, 0 }, { 2, -1, -2, 0, 0 }, { 4, 0, 2, -2, 1 }, { 2, 0, -2, 2, 0 }, /* 361-370 */ { 1, 1, 2, -2, 0 }, { 1, 0, -2, 4, -1 }, { 1, 0, -2, -2, 1 }, { 2, 0, 2, -4, 0 }, { 1, 1, 0, -2, -2 }, { 1, 1, -2, -2, 0 }, { 1, 0, 1, -2, 1 }, { 2, -1, -2, -4, -2 }, { 3, 0, -2, 0, -2 }, { 0, 1, -2, -2, 0 }, /* 371-380 */ { 3, 0, 0, -2, -1 }, { 1, 0, -2, -3, -1 }, { 0, 1, 0, -4, -1 }, { 1, -2, 2, -2, 1 }, { 0, 1, -2, 1, -1 }, { 1, -1, 0, 0, 2 }, { 2, 0, 0, 1, 0 }, { 1, -2, 0, 2, 0 }, { 1, 2, -2, -2, -1 }, { 0, 0, 4, -4, 1 }, /* 381-390 */ { 0, 1, 2, 4, 2 }, { 0, 1, -4, 2, -2 }, { 3, 0, -2, 0, 0 }, { 2, -1, 2, 2, 1 }, { 0, 1, -2, -4, -1 }, { 4, 0, 2, 2, 2 }, { 2, 0, -2, -3, -2 }, { 2, 0, 0, -6, 0 }, { 1, 0, 2, 0, 3 }, { 3, 1, 0, 0, 0 }, /* 391-400 */ { 3, 0, 0, -4, 1 }, { 1, -1, 2, 0, 0 }, { 1, -1, 0, -4, 0 }, { 2, 0, -2, 2, -2 }, { 1, 1, 0, -2, 2 }, { 4, 0, 0, -2, 0 }, { 2, 2, 0, -2, 0 }, { 0, 1, 2, 0, 0 }, { 1, 1, 0, -4, 1 }, { 1, 0, 0, -4, -2 }, /* 401-410 */ { 0, 0, 0, 1, 2 }, { 3, 0, 0, 2, 1 }, { 1, 1, 0, -4, -1 }, { 0, 0, 2, 2, -1 }, { 1, 1, 2, 0, 0 }, { 1, -1, 2, -4, 1 }, { 1, 1, 0, 0, 2 }, { 0, 0, 2, 6, 2 }, { 4, 0, -2, -2, -1 }, { 2, 1, 0, -4, -1 }, /* 411-420 */ { 0, 0, 0, 3, 1 }, { 1, -1, -2, 0, 0 }, { 0, 0, 2, 1, 0 }, { 1, 0, 0, 2, -2 }, { 3, -1, 2, 2, 2 }, { 3, -1, 2, -2, 2 }, { 1, 0, 0, -1, 2 }, { 1, -2, 2, -2, 2 }, { 0, 1, 0, 2, 2 }, { 0, 1, -2, -1, -2 }, /* 421-430 */ { 1, 1, -2, 0, 0 }, { 0, 2, 2, -2, 0 }, { 3, -1, -2, -1, -2 }, { 1, 0, 0, -6, 0 }, { 1, 0, -2, -4, 0 }, { 2, 1, 0, -4, 1 }, { 2, 0, 2, 0, -1 }, { 2, 0, -4, 0, -1 }, { 0, 0, 3, 0, 2 }, { 2, 1, -2, -2, -1 }, /* 431-440 */ { 1, -2, 0, 0, 1 }, { 2, -1, 0, -4, 0 }, { 0, 0, 0, 3, 0 }, { 5, 0, 2, -2, 2 }, { 1, 2, -2, -4, -2 }, { 1, 0, 4, -4, 2 }, { 0, 0, 4, -1, 2 }, { 3, 1, 0, -4, 0 }, { 3, 0, 0, -6, 0 }, { 2, 0, 0, 2, 2 }, /* 441-450 */ { 2, -2, 2, 0, 2 }, { 1, 0, 0, -3, 1 }, { 1, -2, -2, 0, -2 }, { 1, -1, -2, -3, -2 }, { 0, 0, 2, -2, -2 }, { 2, 0, -2, -4, 0 }, { 1, 0, -4, 0, 0 }, { 0, 1, 0, -1, 0 }, { 4, 0, 0, 0, -1 }, { 3, 0, 2, -1, 2 }, /* 451-460 */ { 3, -1, 2, 0, 1 }, { 2, 0, 2, -1, 1 }, { 1, 2, 2, -2, 1 }, { 1, 1, 0, 2, -1 }, { 0, 2, 2, 0, 1 }, { 3, 1, 2, 0, 1 }, { 1, 1, 2, 1, 1 }, { 1, 1, 0, -1, 1 }, { 1, -2, 0, -2, -1 }, { 4, 0, 0, -4, 0 }, /* 461-470 */ { 2, 1, 0, 2, 0 }, { 1, -1, 0, 4, 0 }, { 0, 1, 0, -2, 2 }, { 0, 0, 2, 0, -2 }, { 1, 0, -1, 0, 1 }, { 3, 0, 2, -2, 0 }, { 2, 0, 2, 2, 0 }, { 1, 2, 0, -4, 0 }, { 1, -1, 0, -3, 0 }, { 0, 1, 0, 4, 0 }, /* 471 - 480 */ { 0, 1, -2, 0, 0 }, { 2, 2, 2, -2, 2 }, { 0, 0, 0, 1, -2 }, { 0, 2, -2, 0, -1 }, { 4, 0, 2, -4, 2 }, { 2, 0, -4, 2, -2 }, { 2, -1, -2, 0, -2 }, { 1, 1, 4, -2, 2 }, { 1, 1, 2, -4, 2 }, { 1, 0, 2, 3, 2 }, /* 481-490 */ { 1, 0, 0, 4, -1 }, { 0, 0, 0, 4, 2 }, { 2, 0, 0, 4, 0 }, { 1, 1, -2, 2, 0 }, { 2, 1, 2, 1, 2 }, { 2, 1, 2, -4, 1 }, { 2, 0, 2, 1, 1 }, { 2, 0, -4, -2, -1 }, { 2, 0, -2, -6, -1 }, { 2, -1, 2, -1, 2 }, /* 491-500 */ { 1, -2, 2, 0, 1 }, { 1, -2, 0, -2, 1 }, { 1, -1, 0, -4, -1 }, { 0, 2, 2, 2, 2 }, { 0, 2, -2, -4, -2 }, { 0, 1, 2, 3, 2 }, { 0, 1, 0, -4, 1 }, { 3, 0, 0, -2, 1 }, { 2, 1, -2, 0, 1 }, { 2, 0, 4, -2, 1 }, /* 501-510 */ { 2, 0, 0, -3, -1 }, { 2, -2, 0, -2, 1 }, { 2, -1, 2, -2, 1 }, { 1, 0, 0, -6, -1 }, { 1, -2, 0, 0, -1 }, { 1, -2, -2, -2, -1 }, { 0, 1, 4, -2, 1 }, { 0, 0, 2, 3, 1 }, { 2, -1, 0, -1, 0 }, { 1, 3, 0, -2, 0 }, /* 511-520 */ { 0, 3, 0, -2, 0 }, { 2, -2, 2, -2, 2 }, { 0, 0, 4, -2, 0 }, { 4, -1, 2, 0, 2 }, { 2, 2, -2, -4, -2 }, { 4, 1, 2, 0, 2 }, { 4, -1, -2, -2, -2 }, { 2, 1, 0, -2, -2 }, { 2, 1, -2, -6, -2 }, { 2, 0, 0, -1, 1 }, /* 521-530 */ { 2, -1, -2, 2, -1 }, { 1, 1, -2, 2, -2 }, { 1, 1, -2, -3, -2 }, { 1, 0, 3, 0, 3 }, { 1, 0, -2, 1, 1 }, { 1, 0, -2, 0, 2 }, { 1, -1, 2, 1, 2 }, { 1, -1, 0, 0, -2 }, { 1, -1, -4, 2, -2 }, { 0, 3, -2, -2, -2 }, /* 531-540 */ { 0, 1, 0, 4, 1 }, { 0, 0, 4, 2, 2 }, { 3, 0, -2, -2, 0 }, { 2, -2, 0, 0, 0 }, { 1, 1, 2, -4, 0 }, { 1, 1, 0, -3, 0 }, { 1, 0, 2, -3, 0 }, { 1, -1, 2, -2, 0 }, { 0, 2, 0, 2, 0 }, { 0, 0, 2, 4, 0 }, /* 541-550 */ { 1, 0, 1, 0, 0 }, { 3, 1, 2, -2, 1 }, { 3, 0, 4, -2, 2 }, { 3, 0, 2, 1, 2 }, { 3, 0, 0, 2, -1 }, { 3, 0, 0, 0, 2 }, { 3, 0, -2, 2, -1 }, { 2, 0, 4, -4, 2 }, { 2, 0, 2, -3, 2 }, { 2, 0, 0, 4, 1 }, /* 551-560 */ { 2, 0, 0, -3, 1 }, { 2, 0, -4, 2, -1 }, { 2, 0, -2, -2, 1 }, { 2, -2, 2, 2, 2 }, { 2, -2, 0, -2, -2 }, { 2, -1, 0, 2, 1 }, { 2, -1, 0, 2, -1 }, { 1, 1, 2, 4, 2 }, { 1, 1, 0, 1, 1 }, { 1, 1, 0, 1, -1 }, /* 561-570 */ { 1, 1, -2, -6, -2 }, { 1, 0, 0, -3, -1 }, { 1, 0, -4, -2, -1 }, { 1, 0, -2, -6, -1 }, { 1, -2, 2, 2, 1 }, { 1, -2, -2, 2, -1 }, { 1, -1, -2, -4, -1 }, { 0, 2, 0, 0, 2 }, { 0, 1, 2, -4, 2 }, { 0, 1, -2, 4, -1 }, /* 571-580 */ { 5, 0, 0, 0, 0 }, { 3, 0, 0, -3, 0 }, { 2, 2, 0, -4, 0 }, { 1, -1, 2, 2, 0 }, { 0, 1, 0, 3, 0 }, { 4, 0, -2, 0, -1 }, { 3, 0, -2, -6, -1 }, { 3, 0, -2, -1, -1 }, { 2, 1, 2, 2, 1 }, { 2, 1, 0, 2, 1 }, /* 581-590 */ { 2, 0, 2, 4, 1 }, { 2, 0, 2, -6, 1 }, { 2, 0, 2, -2, -1 }, { 2, 0, 0, -6, -1 }, { 2, -1, -2, -2, -1 }, { 1, 2, 2, 0, 1 }, { 1, 2, 0, 0, 1 }, { 1, 0, 4, 0, 1 }, { 1, 0, 2, -6, 1 }, { 1, 0, 2, -4, -1 }, /* 591-600 */ { 1, 0, -1, -2, -1 }, { 1, -1, 2, 4, 1 }, { 1, -1, 2, -3, 1 }, { 1, -1, 0, 4, 1 }, { 1, -1, -2, 1, -1 }, { 0, 1, 2, -2, 3 }, { 3, 0, 0, -2, 0 }, { 1, 0, 1, -2, 0 }, { 0, 2, 0, -4, 0 }, { 0, 0, 2, -4, 0 }, /* 601-610 */ { 0, 0, 1, -1, 0 }, { 0, 0, 0, 6, 0 }, { 0, 2, 0, 0, -2 }, { 0, 1, -2, 2, -3 }, { 4, 0, 0, 2, 0 }, { 3, 0, 0, -1, 0 }, { 3, -1, 0, 2, 0 }, { 2, 1, 0, 1, 0 }, { 2, 1, 0, -6, 0 }, { 2, -1, 2, 0, 0 }, /* 611-620 */ { 1, 0, 2, -1, 0 }, { 1, -1, 0, 1, 0 }, { 1, -1, -2, -2, 0 }, { 0, 1, 2, 2, 0 }, { 0, 0, 2, -3, 0 }, { 2, 2, 0, -2, -1 }, { 2, -1, -2, 0, 1 }, { 1, 2, 2, -4, 1 }, { 0, 1, 4, -4, 2 }, { 0, 0, 0, 3, 2 }, /* 621-630 */ { 5, 0, 2, 0, 1 }, { 4, 1, 2, -2, 2 }, { 4, 0, -2, -2, 0 }, { 3, 1, 2, 2, 2 }, { 3, 1, 0, -2, 0 }, { 3, 1, -2, -6, -2 }, { 3, 0, 0, 0, -2 }, { 3, 0, -2, -4, -2 }, { 3, -1, 0, -3, 0 }, { 3, -1, 0, -2, 0 }, /* 631-640 */ { 2, 1, 2, 0, 0 }, { 2, 1, 2, -4, 2 }, { 2, 1, 2, -2, 0 }, { 2, 1, 0, -3, 0 }, { 2, 1, -2, 0, -2 }, { 2, 0, 0, -4, 2 }, { 2, 0, 0, -4, -2 }, { 2, 0, -2, -5, -2 }, { 2, -1, 2, 4, 2 }, { 2, -1, 0, -2, 2 }, /* 641-650 */ { 1, 3, -2, -2, -2 }, { 1, 1, 0, 0, -2 }, { 1, 1, 0, -6, 0 }, { 1, 1, -2, 1, -2 }, { 1, 1, -2, -1, -2 }, { 1, 0, 2, 1, 0 }, { 1, 0, 0, 3, 0 }, { 1, 0, 0, -4, 2 }, { 1, 0, -2, 4, -2 }, { 1, -2, 0, -1, 0 }, /* 651-NFLS */ { 0, 1, -4, 2, -1 }, { 1, 0, -2, 0, -3 }, { 0, 0, 4, -4, 4 } }; /* Number of frequencies: luni-solar */ static const int NFLS = (int) (sizeof mfals / sizeof (int) / 5); /* Fundamental-argument multipliers: planetary terms */ static const int mfapl[][14] = { /* 1-10 */ { 0, 0, 1, -1, 1, 0, 0, -1, 0, -2, 5, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -2 }, { 0, 0, 1, -1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0 }, /* 11-20 */ { 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, -1 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 2, -5, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 2, -8, 3, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 6, -8, 3, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0 }, /* 21-30 */ { 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2 }, { 0, 0, 1, -1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1 }, { 2, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, /* 31-40 */ { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 1 }, { 2, 0, 0, -2, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0 }, /* 41-50 */ { 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, -2 }, { 0, 0, 1, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2 }, { 1, 0, 0, 0, 0, 0,-18, 16, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2 }, /* 51-60 */ { 0, 0, 1, -1, 1, 0, -5, 7, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, 0, 0, 0,-10, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 0, 0, -5, 6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2 }, { 1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1 }, { 1, 0, -2, 0, -2, 0, 0, 4, -8, 3, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, /* 61-70 */ { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, -2 }, { 0, 0, 1, -1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 8,-11, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0 }, /* 71-80 */ { 0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 2 }, { 0, 0, 1, -1, 1, 0, 0, -5, 8, -3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 0 }, /* 81-90 */ { 2, 0, 0, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, -1 }, { 2, 0, 0, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 8,-13, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 5, 0, 0, 0 }, { 1, 0, 0, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2 }, { 1, 0, 0, 0, -1, 0,-18, 16, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, -5, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 }, /* 91-100 */ { 1, 0, 0, -2, 0, 0, 19,-21, 3, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, -8, 13, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2 }, { 1, 0, 0, 0, 1, 0,-18, 16, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 6,-16, 4, 5, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0, -2 }, /* 101-110 */ { 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 }, { 2, 0, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, -1, 0, 0, -2, 0, 3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2 }, /* 111-120 */ { 0, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2 }, { 0, 0, 2, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0 }, { 2, 0, 0, -2, 0, 0, -6, 8, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0 }, /* 121-130 */ { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 8,-10, 0, 0, 0, 0, 0, -2 }, { 0, 0, 1, -1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, -2 }, { 1, 0, 0, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0 }, /* 131-140 */ { 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 4, 0, -3, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 1, 0, 2, -3, 0, 0, 0, 0, 0, 0 }, /* 141-150 */ { 1, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 9,-11, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, -4, 5, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, 2 }, /* 151-160 */ { 1, 0, 0, -1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, -4, 10, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, -2 }, { 0, 0, 2, -2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 0 }, /* 161-170 */ { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 2 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0 }, { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, -9, 13, 0, 0, 0, 0, 0 }, { 2, 0, 2, 0, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0 }, /* 171-180 */ { 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, -2 }, { 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0 }, { 1, 0, 0, -1, -1, 0, -3, 4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1 }, { 1, 0, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0 }, { 1, 0, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, -2, 4, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0 }, /* 181-190 */ { 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1 }, { 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, -8, 3, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 7, -8, 3, 0, 0, 0, 2 }, { 0, 0, 0, 0, 1, 0, -3, 5, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, -5, 7, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 1 }, /* 191-200 */ { 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 7,-10, 0, 0, 0, 0, 0, -2 }, { 1, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -5, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -1 }, { 0, 0, 1, -1, 1, 0, 0, -9, 15, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0 }, /* 201-210 */ { 0, 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 2 }, { 2, 0, 0, -2, 1, 0, -6, 8, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, -1 }, { 0, 0, 1, -1, 1, 0, 3, -6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 8,-14, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, /* 211-220 */ { 0, 0, 0, 0, 1, 0, 0, 8,-15, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2 }, { 2, 0, -1, -1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0 }, /* 221-230 */ { 2, 0, 0, -2, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, -9, 4, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, -2 }, /* 231-240 */ { 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1 }, { 0, 0, 0, 0, 0, 0, 7,-11, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 3, -5, 4, 0, 0, 0, 0, 2 }, { 0, 0, 1, -1, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0 }, { 2, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, -2 }, { 0, 0, 1, -1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, -1 }, /* 241-250 */ { 0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 1, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 2, -4, 0, -3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 2 }, { 0, 0, 2, -2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0 }, /* 251-260 */ { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0 }, { 1, 0, -2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 5, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 1 }, /* 261-270 */ { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -5, 0, 0, 2 }, { 2, 0, 0, -2, -1, 0, 0, -2, 0, 0, 5, 0, 0, 0 }, { 2, 0, 0, -2, -1, 0, -6, 8, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, -5, 0, 0, 2 }, { 0, 0, 0, 0, 1, 0, 3, -7, 4, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 }, /* 271-280 */ { 0, 0, 1, -1, 0, 0, 0, -1, 0, -2, 5, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 6,-15, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2 }, { 1, 0, 0, -1, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, -3, 7, -4, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, 2 }, /* 281-290 */ { 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 1 }, { 0, 0, 2, -2, 2, 0, -5, 6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 6,-11, 0, 0, 0, 0, -2 }, /* 291-300 */ { 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, -2 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 9,-12, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 1 }, { 0, 0, 1, -1, 0, 0, -8, 12, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, -1 }, /* 301-310 */ { 0, 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, -2 }, { 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, -1 }, { 0, 0, 1, -1, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, -5, 0, 0, 0, 0, -2 }, { 2, 0, 0, -2, 0, 0, 0, -2, 0, 3, -1, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 2 }, /* 311-320 */ { 0, 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, -1 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 3, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, 2, -4, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1 }, { 0, 0, 1, -1, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2 }, { 0, 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0 }, /* 321-330 */ { 0, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 5, 0, -3, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0 }, { 2, 0, -1, -1, -1, 0, 0, -1, 0, 3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 5,-10, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 1 }, { 0, 0, 2, -2, 1, -1, 0, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0 }, /* 331-340 */ { 0, 0, 0, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, -2, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 }, { 0, 0, 2, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, -8, 11, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 2, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 2, -6, 0, 0, 0, 0, 0, -2 }, /* 341-350 */ { 0, 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 7,-13, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2 }, { 0, 0, 2, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 8,-10, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 1 }, /* 351-360 */ { 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0 }, { 2, 0, 0, -2, -1, 0, 0, -5, 6, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, -2 }, { 2, 0, -1, -1, -1, 0, 0, 3, -7, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0 }, { 0, 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0 }, /* 361-370 */ { 2, 0, 0, -2, 0, 0, 0, -2, 0, 4, -3, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 6,-11, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, 1, 0, 0, -6, 8, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 6, -5, 0, 0, 0, 0, 2 }, { 1, 0, -2, -2, -2, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1 }, /* 371-380 */ { 0, 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0, 1, -6, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2 }, { 0, 0, 0, 0, 0, 0, 3, -5, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 7,-13, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2 }, /* 381-390 */ { 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, -8, 15, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, -2, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, { 2, 0, -1, -1, -1, 0, 0, -1, 0, 2, 0, 0, 0, 0 }, { 1, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 1, 0, -1, 1, -1, 0,-18, 17, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, 0, 2, 0, 0, 1, 0, -1, 0, 0, 0, 0 }, { 0, 0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0 }, { 0, 0, 2, -2, -1, 0, -5, 6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0 }, /* 391-400 */ { 0, 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 8,-16, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2 }, { 0, 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0 }, { 2, 0, -1, -1, -2, 0, 0, -1, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, 0, -1 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, -2, 4, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2 }, { 2, 0, 0, -2, -1, 0, 0, -2, 0, 4, -5, 0, 0, 0 }, /* 401-410 */ { 2, 0, 0, -2, -1, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, { 2, 0, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0 }, { 1, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, -1, -1, 0, 0, -2, 2, 0, 0, 0, 0, 0 }, { 1, 0, -1, -1, -1, 0, 20,-20, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 5, -8, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0 }, /* 411-420 */ { 0, 0, 0, 0, 0, 0, 9,-11, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1 }, { 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, -2, 0, 0, 0 }, { 0, 0, 1, -1, 2, 0, 0, -1, 0, -2, 5, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0 }, /* 421-430 */ { 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 2, -6, 0, 0, 0, 0, -2 }, { 1, 0, 0, -2, 0, 0, 20,-21, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 8,-12, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 2, 0, 0, -1, 0, -1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 8,-12, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 9,-17, 0, 0, 0, 0, 0 }, /* 431-440 */ { 0, 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 2, -7, 0, 0, 0, 0, -2 }, { 1, 0, 0, -1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0 }, { 1, 0, -2, 0, -2, 0,-10, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, -2 }, { 1, 0, -2, -2, -2, 0, 0, -2, 0, 3, 0, 0, 0, 0 }, { 1, 0, -1, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, /* 441-450 */ { 0, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0 }, { 0, 0, 1, -1, 2, 0, -5, 7, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 5,-10, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, -5, 0, 0, 0, -2 }, /* 451-460 */ { 0, 0, 0, 0, 0, 0, 0, 1, 0, -5, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 5, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 1 }, { 1, 0, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0 }, { 2, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, -2 }, /* 461-470 */ { 1, 0, 0, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, -5, 5, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 1, -3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -4, 6, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0 }, { 0, 0, 1, -1, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0 }, /* 471-480 */ { 0, 0, 0, 0, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 7,-10, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 3, -8, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 2 }, /* 481-490 */ { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1 }, { 2, 0, 0, -2, -1, 0, 0, -6, 8, 0, 0, 0, 0, 0 }, { 2, 0, -1, -1, 1, 0, 0, 3, -7, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, -7, 9, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, -1 }, /* 491-500 */ { 0, 0, 1, -1, 2, 0, -8, 12, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 1, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, 1, 0, 0, -5, 6, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, -1, 0, 0, -2, 0, 3, -1, 0, 0, 0 }, { 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 1, 0, 0, -2, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, /* 501-510 */ { 1, 0, 0, -1, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0 }, { 1, 0, -1, 0, -1, 0, -3, 5, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, -4, 4, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, -8, 11, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 0, 0, 0, -9, 13, 0, 0, 0, 0, 0 }, { 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, 1, -4, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, 0, -1, 0, 1, -3, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, 7,-13, 0, 0, 0, 0, 0 }, /* 511-520 */ { 0, 0, 0, 0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 7,-11, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 1 }, /* 521-530 */ { 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 9,-17, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0 }, { 2, 0, 0, -2, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0 }, /* 531-540 */ { 2, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0 }, { 1, 0, 0, 0, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0 }, { 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, -2, 0, 0, 17,-16, 0, -2, 0, 0, 0, 0 }, { 1, 0, 0, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 3, 0, -4, 0, 0, 0, 0 }, /* 541-550 */ { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2 }, { 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2 }, { 2, 0, 0, -2, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0 }, { 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 }, { 1, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, -2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, -2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0 }, { 1, 0, 0, -2, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0 }, /* 551-560 */ { 1, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, -4, 5, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 }, /* 561-570 */ { 0, 0, 0, 0, 0, 0, 8, -9, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0 }, { 2, 0, -2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0 }, { 1, 0, 0, 0, 1, 0,-10, 3, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, 0, -1, 0,-10, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0 }, /* 571-580 */ { 0, 0, 2, 0, 2, 0, -2, 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0 }, { 2, 0, 2, -2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0 }, { 2, 0, 1, -3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0 }, { 2, 0, 0, -2, 0, 0, 0, -2, 0, 5, -5, 0, 0, 0 }, { 2, 0, 0, -2, 0, 0, 0, -2, 0, 1, 5, 0, 0, 0 }, { 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0 }, /* 581-590 */ { 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0 }, { 2, 0, 0, -2, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0 }, { 2, 0, -2, 0, -2, 0, 0, 5, -9, 0, 0, 0, 0, 0 }, { 2, 0, -1, -1, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0 }, { 1, 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0 }, { 1, 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0 }, { 1, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0 }, { 1, 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0 }, { 1, 0, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0 }, { 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0 }, /* 591-600 */ { 1, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 }, { 1, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0 }, { 1, 0, -2, -2, -2, 0, 0, 1, 0, -1, 0, 0, 0, 0 }, { 1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 1, 0, -1, -1, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0 }, { 0, 0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0 }, { 0, 0, 2, -2, 1, 0, 0,-10, 15, 0, 0, 0, 0, 0 }, { 0, 0, 2, -2, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0 }, /* 601-610 */ { 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, -1, 0, 0, 0 }, { 0, 0, 1, -1, 2, 0, -3, 4, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, -4, 6, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, -1, -1, 0, -5, 7, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0 }, /* 611-620 */ { 0, 0, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 9,-13, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 8,-14, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 8,-11, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -2 }, /* 621-630 */ { 0, 0, 0, 0, 0, 0, 5, -6, -4, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 7,-12, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, -2 }, /* 631-640 */ { 0, 0, 0, 0, 0, 0, 0, 6, -8, 1, 5, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 5, 0, -4, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, -1 }, { 0, 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 5,-16, 4, 5, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 5,-13, 0, 0, 0, 0, -2 }, /* 641-650 */ { 0, 0, 0, 0, 0, 0, 0, 3, 0, -5, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 3, -9, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 3, -7, 0, 0, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 2, -8, 1, 5, 0, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -5, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 5, 0, 0, 0 }, /* 651-NFPL */ { 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -6, 3, 0, -2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 }, { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 } }; /* Number of frequencies: planetary */ static const int NFPL = (int) (sizeof mfapl / sizeof (int) / 14); /* Pointers into amplitudes array, one pointer per frequency */ static const int nc[] = { /* 1-100 */ 1, 21, 37, 51, 65, 79, 91, 103, 115, 127, 139, 151, 163, 172, 184, 196, 207, 219, 231, 240, 252, 261, 273, 285, 297, 309, 318, 327, 339, 351, 363, 372, 384, 396, 405, 415, 423, 435, 444, 452, 460, 467, 474, 482, 490, 498, 506, 513, 521, 528, 536, 543, 551, 559, 566, 574, 582, 590, 597, 605, 613, 620, 628, 636, 644, 651, 658, 666, 674, 680, 687, 695, 702, 710, 717, 725, 732, 739, 746, 753, 760, 767, 774, 782, 790, 798, 805, 812, 819, 826, 833, 840, 846, 853, 860, 867, 874, 881, 888, 895, /* 101-200 */ 901, 908, 914, 921, 928, 934, 941, 948, 955, 962, 969, 976, 982, 989, 996, 1003, 1010, 1017, 1024, 1031, 1037, 1043, 1050, 1057, 1064, 1071, 1078, 1084, 1091, 1098, 1104, 1112, 1118, 1124, 1131, 1138, 1145, 1151, 1157, 1164, 1171, 1178, 1185, 1192, 1199, 1205, 1212, 1218, 1226, 1232, 1239, 1245, 1252, 1259, 1266, 1272, 1278, 1284, 1292, 1298, 1304, 1310, 1316, 1323, 1329, 1335, 1341, 1347, 1353, 1359, 1365, 1371, 1377, 1383, 1389, 1396, 1402, 1408, 1414, 1420, 1426, 1434, 1440, 1446, 1452, 1459, 1465, 1471, 1477, 1482, 1488, 1493, 1499, 1504, 1509, 1514, 1520, 1527, 1532, 1538, /* 201-300 */ 1543, 1548, 1553, 1558, 1564, 1569, 1574, 1579, 1584, 1589, 1594, 1596, 1598, 1600, 1602, 1605, 1608, 1610, 1612, 1617, 1619, 1623, 1625, 1627, 1629, 1632, 1634, 1640, 1642, 1644, 1646, 1648, 1650, 1652, 1654, 1658, 1660, 1662, 1664, 1668, 1670, 1672, 1673, 1675, 1679, 1681, 1683, 1684, 1686, 1688, 1690, 1693, 1695, 1697, 1701, 1703, 1705, 1707, 1709, 1711, 1712, 1715, 1717, 1721, 1723, 1725, 1727, 1729, 1731, 1733, 1735, 1737, 1739, 1741, 1743, 1745, 1747, 1749, 1751, 1753, 1755, 1757, 1759, 1761, 1762, 1764, 1766, 1768, 1769, 1771, 1773, 1775, 1777, 1779, 1781, 1783, 1785, 1787, 1788, 1790, /* 301-400 */ 1792, 1794, 1796, 1798, 1800, 1802, 1804, 1806, 1807, 1809, 1811, 1815, 1817, 1819, 1821, 1823, 1825, 1827, 1829, 1831, 1833, 1835, 1837, 1839, 1840, 1842, 1844, 1848, 1850, 1852, 1854, 1856, 1858, 1859, 1860, 1862, 1864, 1866, 1868, 1869, 1871, 1873, 1875, 1877, 1879, 1881, 1883, 1885, 1887, 1889, 1891, 1892, 1896, 1898, 1900, 1901, 1903, 1905, 1907, 1909, 1910, 1911, 1913, 1915, 1919, 1921, 1923, 1927, 1929, 1931, 1933, 1935, 1937, 1939, 1943, 1945, 1947, 1948, 1949, 1951, 1953, 1955, 1957, 1958, 1960, 1962, 1964, 1966, 1968, 1970, 1971, 1973, 1974, 1975, 1977, 1979, 1980, 1981, 1982, 1984, /* 401-500 */ 1986, 1988, 1990, 1992, 1994, 1995, 1997, 1999, 2001, 2003, 2005, 2007, 2008, 2009, 2011, 2013, 2015, 2017, 2019, 2021, 2023, 2024, 2025, 2027, 2029, 2031, 2033, 2035, 2037, 2041, 2043, 2045, 2046, 2047, 2049, 2051, 2053, 2055, 2056, 2057, 2059, 2061, 2063, 2065, 2067, 2069, 2070, 2071, 2072, 2074, 2076, 2078, 2080, 2082, 2084, 2086, 2088, 2090, 2092, 2094, 2095, 2096, 2097, 2099, 2101, 2105, 2106, 2107, 2108, 2109, 2110, 2111, 2113, 2115, 2119, 2121, 2123, 2125, 2127, 2129, 2131, 2133, 2135, 2136, 2137, 2139, 2141, 2143, 2145, 2147, 2149, 2151, 2153, 2155, 2157, 2159, 2161, 2163, 2165, 2167, /* 501-600 */ 2169, 2171, 2173, 2175, 2177, 2179, 2181, 2183, 2185, 2186, 2187, 2188, 2192, 2193, 2195, 2197, 2199, 2201, 2203, 2205, 2207, 2209, 2211, 2213, 2217, 2219, 2221, 2223, 2225, 2227, 2229, 2231, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 2240, 2241, 2244, 2246, 2248, 2250, 2252, 2254, 2256, 2258, 2260, 2262, 2264, 2266, 2268, 2270, 2272, 2274, 2276, 2278, 2280, 2282, 2284, 2286, 2288, 2290, 2292, 2294, 2296, 2298, 2300, 2302, 2303, 2304, 2305, 2306, 2307, 2309, 2311, 2313, 2315, 2317, 2319, 2321, 2323, 2325, 2327, 2329, 2331, 2333, 2335, 2337, 2341, 2343, 2345, 2347, 2349, 2351, 2352, 2355, 2356, /* 601-700 */ 2357, 2358, 2359, 2361, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 2370, 2371, 2372, 2373, 2374, 2376, 2378, 2380, 2382, 2384, 2385, 2386, 2387, 2388, 2389, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 2397, 2398, 2399, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 2410, 2411, 2412, 2413, 2414, 2415, 2417, 2418, 2430, 2438, 2445, 2453, 2460, 2468, 2474, 2480, 2488, 2496, 2504, 2512, 2520, 2527, 2535, 2543, 2550, 2558, 2566, 2574, 2580, 2588, 2596, 2604, 2612, 2619, 2627, 2634, 2642, 2648, 2656, 2664, 2671, 2679, 2685, 2693, 2701, 2709, 2717, 2725, 2733, 2739, 2747, 2753, 2761, 2769, /* 701-800 */ 2777, 2785, 2793, 2801, 2809, 2817, 2825, 2833, 2841, 2848, 2856, 2864, 2872, 2878, 2884, 2892, 2898, 2906, 2914, 2922, 2930, 2938, 2944, 2952, 2958, 2966, 2974, 2982, 2988, 2996, 3001, 3009, 3017, 3025, 3032, 3039, 3045, 3052, 3059, 3067, 3069, 3076, 3083, 3090, 3098, 3105, 3109, 3111, 3113, 3120, 3124, 3128, 3132, 3136, 3140, 3144, 3146, 3150, 3158, 3161, 3165, 3166, 3168, 3172, 3176, 3180, 3182, 3185, 3189, 3193, 3194, 3197, 3200, 3204, 3208, 3212, 3216, 3219, 3221, 3222, 3226, 3230, 3234, 3238, 3242, 3243, 3247, 3251, 3254, 3258, 3262, 3266, 3270, 3274, 3275, 3279, 3283, 3287, 3289, 3293, /* 801-900 */ 3296, 3300, 3303, 3307, 3311, 3315, 3319, 3321, 3324, 3327, 3330, 3334, 3338, 3340, 3342, 3346, 3350, 3354, 3358, 3361, 3365, 3369, 3373, 3377, 3381, 3385, 3389, 3393, 3394, 3398, 3402, 3406, 3410, 3413, 3417, 3421, 3425, 3429, 3433, 3435, 3439, 3443, 3446, 3450, 3453, 3457, 3458, 3461, 3464, 3468, 3472, 3476, 3478, 3481, 3485, 3489, 3493, 3497, 3501, 3505, 3507, 3511, 3514, 3517, 3521, 3524, 3525, 3527, 3529, 3533, 3536, 3540, 3541, 3545, 3548, 3551, 3555, 3559, 3563, 3567, 3569, 3570, 3574, 3576, 3578, 3582, 3586, 3590, 3593, 3596, 3600, 3604, 3608, 3612, 3616, 3620, 3623, 3626, 3630, 3632, /* 901-1000 */ 3636, 3640, 3643, 3646, 3648, 3652, 3656, 3660, 3664, 3667, 3669, 3671, 3675, 3679, 3683, 3687, 3689, 3693, 3694, 3695, 3699, 3703, 3705, 3707, 3710, 3713, 3717, 3721, 3725, 3729, 3733, 3736, 3740, 3744, 3748, 3752, 3754, 3757, 3759, 3763, 3767, 3770, 3773, 3777, 3779, 3783, 3786, 3790, 3794, 3798, 3801, 3805, 3809, 3813, 3817, 3821, 3825, 3827, 3831, 3835, 3836, 3837, 3840, 3844, 3848, 3852, 3856, 3859, 3863, 3867, 3869, 3871, 3875, 3879, 3883, 3887, 3890, 3894, 3898, 3901, 3905, 3909, 3913, 3917, 3921, 3922, 3923, 3924, 3926, 3930, 3932, 3936, 3938, 3940, 3944, 3948, 3952, 3956, 3959, 3963, /* 1001-1100 */ 3965, 3969, 3973, 3977, 3979, 3981, 3982, 3986, 3989, 3993, 3997, 4001, 4004, 4006, 4009, 4012, 4016, 4020, 4024, 4026, 4028, 4032, 4036, 4040, 4044, 4046, 4050, 4054, 4058, 4060, 4062, 4063, 4064, 4068, 4071, 4075, 4077, 4081, 4083, 4087, 4089, 4091, 4095, 4099, 4101, 4103, 4105, 4107, 4111, 4115, 4119, 4123, 4127, 4129, 4131, 4135, 4139, 4141, 4143, 4145, 4149, 4153, 4157, 4161, 4165, 4169, 4173, 4177, 4180, 4183, 4187, 4191, 4195, 4198, 4201, 4205, 4209, 4212, 4213, 4216, 4217, 4221, 4223, 4226, 4230, 4234, 4236, 4240, 4244, 4248, 4252, 4256, 4258, 4262, 4264, 4266, 4268, 4270, 4272, 4276, /* 1101-1200 */ 4279, 4283, 4285, 4287, 4289, 4293, 4295, 4299, 4300, 4301, 4305, 4309, 4313, 4317, 4319, 4323, 4325, 4329, 4331, 4333, 4335, 4337, 4341, 4345, 4349, 4351, 4353, 4357, 4361, 4365, 4367, 4369, 4373, 4377, 4381, 4383, 4387, 4389, 4391, 4395, 4399, 4403, 4407, 4411, 4413, 4414, 4415, 4418, 4419, 4421, 4423, 4427, 4429, 4431, 4433, 4435, 4437, 4439, 4443, 4446, 4450, 4452, 4456, 4458, 4460, 4462, 4466, 4469, 4473, 4477, 4481, 4483, 4487, 4489, 4491, 4493, 4497, 4499, 4501, 4504, 4506, 4510, 4513, 4514, 4515, 4518, 4521, 4522, 4525, 4526, 4527, 4530, 4533, 4534, 4537, 4541, 4542, 4543, 4544, 4545, /* 1201-1300 */ 4546, 4547, 4550, 4553, 4554, 4555, 4558, 4561, 4564, 4567, 4568, 4571, 4574, 4575, 4578, 4581, 4582, 4585, 4586, 4588, 4590, 4592, 4596, 4598, 4602, 4604, 4608, 4612, 4613, 4616, 4619, 4622, 4623, 4624, 4625, 4626, 4629, 4632, 4633, 4636, 4639, 4640, 4641, 4642, 4643, 4644, 4645, 4648, 4649, 4650, 4651, 4652, 4653, 4656, 4657, 4660, 4661, 4664, 4667, 4670, 4671, 4674, 4675, 4676, 4677, 4678, 4681, 4682, 4683, 4684, 4687, 4688, 4689, 4692, 4693, 4696, 4697, 4700, 4701, 4702, 4703, 4704, 4707, 4708, 4711, 4712, 4715, 4716, 4717, 4718, 4719, 4720, 4721, 4722, 4723, 4726, 4729, 4730, 4733, 4736, /* 1301-(NFLS+NFPL) */ 4737, 4740, 4741, 4742, 4745, 4746, 4749, 4752, 4753 }; /* Amplitude coefficients (microarcsec); indexed using the nc array. */ static const double a[] = { /* 1-105 */ -6844318.44, 9205236.26,1328.67,1538.18, 205833.11, 153041.79, -3309.73, 853.32,2037.98, -2301.27, 81.46, 120.56, -20.39, -15.22, 1.73, -1.61, -0.10, 0.11, -0.02, -0.02, -523908.04, 573033.42,-544.75,-458.66, 12814.01, 11714.49, 198.97,-290.91, 155.74,-143.27, -2.75, -1.03, -1.27, -1.16, 0.00, -0.01, -90552.22, 97846.69, 111.23, 137.41,2187.91,2024.68, 41.44, -51.26, 26.92, -24.46, -0.46, -0.28, -0.22, -0.20, 82168.76, -89618.24, -27.64, -29.05, -2004.36, -1837.32, -36.07, 48.00, -24.43, 22.41, 0.47, 0.24, 0.20, 0.18, 58707.02,7387.02, 470.05,-192.40, 164.33, -1312.21, -179.73, -28.93, -17.36, -1.83, -0.50, 3.57, 0.00, 0.13, -20557.78, 22438.42, -20.84, -17.40, 501.82, 459.68, 59.20, -67.30, 6.08, -5.61, -1.36, -1.19, 28288.28, -674.99, -34.69, 35.80, -15.07,-632.54, -11.19, 0.78, -8.41, 0.17, 0.01, 0.07, -15406.85, 20069.50, 15.12, /* 106-219 */ 31.80, 448.76, 344.50, -5.77, 1.41, 4.59, -5.02, 0.17, 0.24, -11991.74, 12902.66, 32.46, 36.70, 288.49, 268.14, 5.70, -7.06, 3.57, -3.23, -0.06, -0.04, -8584.95, -9592.72, 4.42, -13.20,-214.50, 192.06, 23.87, 29.83, 2.54, 2.40, 0.60, -0.48,5095.50, -6918.22, 7.19, 3.92,-154.91,-113.94, 2.86, -1.04, -1.52, 1.73, -0.07, -0.10, -4910.93, -5331.13, 0.76, 0.40,-119.21, 109.81, 2.16, 3.20, 1.46, 1.33, 0.04, -0.02, -6245.02,-123.48, -6.68, -8.20, -2.76, 139.64, 2.71, 0.15, 1.86,2511.85, -3323.89, 1.07, -0.90, -74.33, -56.17, 1.16, -0.01, -0.75, 0.83, -0.02, -0.04,2307.58,3143.98, -7.52, 7.50, 70.31, -51.60, 1.46, 0.16, -0.69, -0.79, 0.02, -0.05,2372.58,2554.51, 5.93, -6.60, 57.12, -53.05, -0.96, -1.24, -0.71, -0.64, -0.01, -2053.16,2636.13, 5.13, 7.80, 58.94, 45.91, -0.42, -0.12, 0.61, -0.66, 0.02, 0.03, -1825.49, /* 220-339 */ -2423.59, 1.23, -2.00, -54.19, 40.82, -1.07, -1.02, 0.54, 0.61, -0.04, 0.04,2521.07,-122.28, -5.97, 2.90, -2.73, -56.37, -0.82, 0.13, -0.75, -1534.09,1645.01, 6.29, 6.80, 36.78, 34.30, 0.92, -1.25, 0.46, -0.41, -0.02, -0.01,1898.27, 47.70, -0.72, 2.50, 1.07, -42.45, -0.94, 0.02, -0.56, -1292.02, -1387.00, 0.00, 0.00, -31.01, 28.89, 0.68, 0.00, 0.38, 0.35, -0.01, -0.01, -1234.96,1323.81, 5.21, 5.90, 29.60, 27.61, 0.74, -1.22, 0.37, -0.33, -0.02, -0.01,1137.48, -1233.89, -0.04, -0.30, -27.59, -25.43, -0.61, 1.00, -0.34, 0.31, 0.01, 0.01,-813.13, -1075.60, 0.40, 0.30, -24.05, 18.18, -0.40, -0.01, 0.24, 0.27, -0.01, 0.01,1163.22, -60.90, -2.94, 1.30, -1.36, -26.01, -0.58, 0.07, -0.35,1029.70, -55.55, -2.63, 1.10, -1.25, -23.02, -0.52, 0.06, -0.31,-556.26, 852.85, 3.16, -4.48, 19.06, 12.44, -0.81, -0.27, 0.17, -0.21, 0.00, 0.02,-603.52, /* 340-467 */ -800.34, 0.44, 0.10, -17.90, 13.49, -0.08, -0.01, 0.18, 0.20, -0.01, 0.01,-628.24, 684.99, -0.64, -0.50, 15.32, 14.05, 3.18, -4.19, 0.19, -0.17, -0.09, -0.07,-866.48, -16.26, 0.52, -1.30, -0.36, 19.37, 0.43, -0.01, 0.26, -512.37, 695.54, -1.47, -1.40, 15.55, 11.46, -0.16, 0.03, 0.15, -0.17, 0.01, 0.01, 506.65, 643.75, 2.54, -2.62, 14.40, -11.33, -0.77, -0.06, -0.15, -0.16, 0.00, 0.01, 664.57, 16.81, -0.40, 1.00, 0.38, -14.86, -3.71, -0.09, -0.20, 405.91, 522.11, 0.99, -1.50, 11.67, -9.08, -0.25, -0.02, -0.12, -0.13,-305.78, 326.60, 1.75, 1.90, 7.30, 6.84, 0.20, -0.04, 300.99,-325.03, -0.44, -0.50, -7.27, -6.73, -1.01, 0.01, 0.00, 0.08, 0.00, 0.02, 438.51, 10.47, -0.56, -0.20, 0.24, -9.81, -0.24, 0.01, -0.13, -264.02, 335.24, 0.99, 1.40, 7.49, 5.90, -0.27, -0.02, 284.09, 307.03, 0.32, -0.40, 6.87, -6.35, -0.99, -0.01, -250.54, 327.11, 0.08, 0.40, 7.31, 5.60, -0.30, 230.72, /* 468-595 */ -304.46, 0.08, -0.10, -6.81, -5.16, 0.27, 229.78, 304.17, -0.60, 0.50, 6.80, -5.14, 0.33, 0.01, 256.30,-276.81, -0.28, -0.40, -6.19, -5.73, -0.14, 0.01,-212.82, 269.45, 0.84, 1.20, 6.02, 4.76, 0.14, -0.02, 196.64, 272.05, -0.84, 0.90, 6.08, -4.40, 0.35, 0.02, 188.95, 272.22, -0.12, 0.30, 6.09, -4.22, 0.34,-292.37, -5.10, -0.32, -0.40, -0.11, 6.54, 0.14, 0.01, 161.79,-220.67, 0.24, 0.10, -4.93, -3.62, -0.08, 261.54, -19.94, -0.95, 0.20, -0.45, -5.85, -0.13, 0.02, 142.16,-190.79, 0.20, 0.10, -4.27, -3.18, -0.07, 187.95, -4.11, -0.24, 0.30, -0.09, -4.20, -0.09, 0.01, 0.00, 0.00, -79.08, 167.90, 0.04, 0.00, 3.75, 1.77, 121.98, 131.04, -0.08, 0.10, 2.93, -2.73, -0.06,-172.95, -8.11, -0.40, -0.20, -0.18, 3.87, 0.09, 0.01,-160.15, -55.30, -14.04, 13.90, -1.23, 3.58, 0.40, 0.31,-115.40, 123.20, 0.60, 0.70, 2.75, 2.58, 0.08, -0.01,-168.26, -2.00, 0.20, -0.20, -0.04, 3.76, /* 596-723 */ 0.08,-114.49, 123.20, 0.32, 0.40, 2.75, 2.56, 0.07, -0.01, 112.14, 120.70, 0.28, -0.30, 2.70, -2.51, -0.07, -0.01, 161.34, 4.03, 0.20, 0.20, 0.09, -3.61, -0.08, 91.31, 126.64, -0.40, 0.40, 2.83, -2.04, -0.04, 0.01, 105.29, 112.90, 0.44, -0.50, 2.52, -2.35, -0.07, -0.01, 98.69,-106.20, -0.28, -0.30, -2.37, -2.21, -0.06, 0.01, 86.74,-112.94, -0.08, -0.20, -2.53, -1.94, -0.05,-134.81, 3.51, 0.20, -0.20, 0.08, 3.01, 0.07, 79.03, 107.31, -0.24, 0.20, 2.40, -1.77, -0.04, 0.01, 132.81, -10.77, -0.52, 0.10, -0.24, -2.97, -0.07, 0.01,-130.31, -0.90, 0.04, 0.00, 0.00, 2.91, -78.56, 85.32, 0.00, 0.00, 1.91, 1.76, 0.04, 0.00, 0.00, -41.53, 89.10, 0.02, 0.00, 1.99, 0.93, 66.03, -71.00, -0.20, -0.20, -1.59, -1.48, -0.04, 60.50, 64.70, 0.36, -0.40, 1.45, -1.35, -0.04, -0.01, -52.27, -70.01, 0.00, 0.00, -1.57, 1.17, 0.03, -52.95, 66.29, 0.32, 0.40, 1.48, 1.18, 0.04, /* 724-851 */ -0.01, 51.02, 67.25, 0.00, 0.00, 1.50, -1.14, -0.03, -55.66, -60.92, 0.16, -0.20, -1.36, 1.24, 0.03, -54.81, -59.20, -0.08, 0.20, -1.32, 1.23, 0.03, 51.32, -55.60, 0.00, 0.00, -1.24, -1.15, -0.03, 48.29, 51.80, 0.20, -0.20, 1.16, -1.08, -0.03, -45.59, -49.00, -0.12, 0.10, -1.10, 1.02, 0.03, 40.54, -52.69, -0.04, -0.10, -1.18, -0.91, -0.02, -40.58, -49.51, -1.00, 1.00, -1.11, 0.91, 0.04, 0.02, -43.76, 46.50, 0.36, 0.40, 1.04, 0.98, 0.03, -0.01, 62.65, -5.00, -0.24, 0.00, -0.11, -1.40, -0.03, 0.01, -38.57, 49.59, 0.08, 0.10, 1.11, 0.86, 0.02, -33.22, -44.04, 0.08, -0.10, -0.98, 0.74, 0.02, 37.15, -39.90, -0.12, -0.10, -0.89, -0.83, -0.02, 36.68, -39.50, -0.04, -0.10, -0.88, -0.82, -0.02, -53.22, -3.91, -0.20, 0.00, -0.09, 1.19, 0.03, 32.43, -42.19, -0.04, -0.10, -0.94, -0.73, -0.02, -51.00, -2.30, -0.12, -0.10, 0.00, 1.14, -29.53, -39.11, 0.04, 0.00, -0.87, 0.66, /* 852-979 */ 0.02, 28.50, -38.92, -0.08, -0.10, -0.87, -0.64, -0.02, 26.54, 36.95, -0.12, 0.10, 0.83, -0.59, -0.01, 26.54, 34.59, 0.04, -0.10, 0.77, -0.59, -0.02, 28.35, -32.55, -0.16, 0.20, -0.73, -0.63, -0.01, -28.00, 30.40, 0.00, 0.00, 0.68, 0.63, 0.01, -27.61, 29.40, 0.20, 0.20, 0.66, 0.62, 0.02, 40.33, 0.40, -0.04, 0.10, 0.00, -0.90, -23.28, 31.61, -0.08, -0.10, 0.71, 0.52, 0.01, 37.75, 0.80, 0.04, 0.10, 0.00, -0.84, 23.66, 25.80, 0.00, 0.00, 0.58, -0.53, -0.01, 21.01, -27.91, 0.00, 0.00, -0.62, -0.47, -0.01, -34.81, 2.89, 0.04, 0.00, 0.00, 0.78, -23.49, -25.31, 0.00, 0.00, -0.57, 0.53, 0.01, -23.47, 25.20, 0.16, 0.20, 0.56, 0.52, 0.02, 19.58, 27.50, -0.12, 0.10, 0.62, -0.44, -0.01, -22.67, -24.40, -0.08, 0.10, -0.55, 0.51, 0.01, -19.97, 25.00, 0.12, 0.20, 0.56, 0.45, 0.01, 21.28, -22.80, -0.08, -0.10, -0.51, -0.48, -0.01, -30.47, 0.91, 0.04, 0.00, /* 980-1107 */ 0.00, 0.68, 18.58, 24.00, 0.04, -0.10, 0.54, -0.42, -0.01, -18.02, 24.40, -0.04, -0.10, 0.55, 0.40, 0.01, 17.74, 22.50, 0.08, -0.10, 0.50, -0.40, -0.01, -19.41, 20.70, 0.08, 0.10, 0.46, 0.43, 0.01, -18.64, 20.11, 0.00, 0.00, 0.45, 0.42, 0.01, -16.75, 21.60, 0.04, 0.10, 0.48, 0.37, 0.01, -18.42, -20.00, 0.00, 0.00, -0.45, 0.41, 0.01, -26.77, 1.41, 0.08, 0.00, 0.00, 0.60, -26.17, -0.19, 0.00, 0.00, 0.00, 0.59, -15.52, 20.51, 0.00, 0.00, 0.46, 0.35, 0.01, -25.42, -1.91, -0.08, 0.00, -0.04, 0.57, 0.45, -17.42, 18.10, 0.00, 0.00, 0.40, 0.39, 0.01, 16.39, -17.60, -0.08, -0.10, -0.39, -0.37, -0.01, -14.37, 18.91, 0.00, 0.00, 0.42, 0.32, 0.01, 23.39, -2.40, -0.12, 0.00, 0.00, -0.52, 14.32, -18.50, -0.04, -0.10, -0.41, -0.32, -0.01, 15.69, 17.08, 0.00, 0.00, 0.38, -0.35, -0.01, -22.99, 0.50, 0.04, 0.00, 0.00, 0.51, 0.00, 0.00, 14.47, -17.60, /* 1108-1235 */ -0.01, 0.00, -0.39, -0.32, -13.33, 18.40, -0.04, -0.10, 0.41, 0.30, 22.47, -0.60, -0.04, 0.00, 0.00, -0.50, -12.78, -17.41, 0.04, 0.00, -0.39, 0.29, 0.01, -14.10, -15.31, 0.04, 0.00, -0.34, 0.32, 0.01, 11.98, 16.21, -0.04, 0.00, 0.36, -0.27, -0.01, 19.65, -1.90, -0.08, 0.00, 0.00, -0.44, 19.61, -1.50, -0.08, 0.00, 0.00, -0.44, 13.41, -14.30, -0.04, -0.10, -0.32, -0.30, -0.01, -13.29, 14.40, 0.00, 0.00, 0.32, 0.30, 0.01, 11.14, -14.40, -0.04, 0.00, -0.32, -0.25, -0.01, 12.24, -13.38, 0.04, 0.00, -0.30, -0.27, -0.01, 10.07, -13.81, 0.04, 0.00, -0.31, -0.23, -0.01, 10.46, 13.10, 0.08, -0.10, 0.29, -0.23, -0.01, 16.55, -1.71, -0.08, 0.00, 0.00, -0.37, 9.75, -12.80, 0.00, 0.00, -0.29, -0.22, -0.01, 9.11, 12.80, 0.00, 0.00, 0.29, -0.20, 0.00, 0.00, -6.44, -13.80, 0.00, 0.00, -0.31, 0.14, -9.19, -12.00, 0.00, 0.00, -0.27, 0.21, -10.30, 10.90, 0.08, 0.10, /* 1236-1363 */ 0.24, 0.23, 0.01, 14.92, -0.80, -0.04, 0.00, 0.00, -0.33, 10.02, -10.80, 0.00, 0.00, -0.24, -0.22, -0.01, -9.75, 10.40, 0.04, 0.00, 0.23, 0.22, 0.01, 9.67, -10.40, -0.04, 0.00, -0.23, -0.22, -0.01, -8.28, -11.20, 0.04, 0.00, -0.25, 0.19, 13.32, -1.41, -0.08, 0.00, 0.00, -0.30, 8.27, 10.50, 0.04, 0.00, 0.23, -0.19, 0.00, 0.00, 13.13, 0.00, 0.00, 0.00, 0.00, -0.29, -12.93, 0.70, 0.04, 0.00, 0.00, 0.29, 7.91, -10.20, 0.00, 0.00, -0.23, -0.18, -7.84, -10.00, -0.04, 0.00, -0.22, 0.18, 7.44, 9.60, 0.00, 0.00, 0.21, -0.17, -7.64, 9.40, 0.08, 0.10, 0.21, 0.17, 0.01, -11.38, 0.60, 0.04, 0.00, 0.00, 0.25, -7.48, 8.30, 0.00, 0.00, 0.19, 0.17, -10.98, -0.20, 0.00, 0.00, 0.00, 0.25, 10.98, 0.20, 0.00, 0.00, 0.00, -0.25, 7.40, -7.90, -0.04, 0.00, -0.18, -0.17, -6.09, 8.40, -0.04, 0.00, 0.19, 0.14, -6.94, -7.49, 0.00, 0.00, -0.17, /* 1364-1491 */ 0.16, 6.92, 7.50, 0.04, 0.00, 0.17, -0.15, 6.20, 8.09, 0.00, 0.00, 0.18, -0.14, -6.12, 7.80, 0.04, 0.00, 0.17, 0.14, 5.85, -7.50, 0.00, 0.00, -0.17, -0.13, -6.48, 6.90, 0.08, 0.10, 0.15, 0.14, 0.01, 6.32, 6.90, 0.00, 0.00, 0.15, -0.14, 5.61, -7.20, 0.00, 0.00, -0.16, -0.13, 9.07, 0.00, 0.00, 0.00, 0.00, -0.20, 5.25, 6.90, 0.00, 0.00, 0.15, -0.12, -8.47, -0.40, 0.00, 0.00, 0.00, 0.19, 6.32, -5.39, -1.11, 1.10, -0.12, -0.14, 0.02, 0.02, 5.73, -6.10, -0.04, 0.00, -0.14, -0.13, 4.70, 6.60, -0.04, 0.00, 0.15, -0.11, -4.90, -6.40, 0.00, 0.00, -0.14, 0.11, -5.33, 5.60, 0.04, 0.10, 0.13, 0.12, 0.01, -4.81, 6.00, 0.04, 0.00, 0.13, 0.11, 5.13, 5.50, 0.04, 0.00, 0.12, -0.11, 4.50, 5.90, 0.00, 0.00, 0.13, -0.10, -4.22, 6.10, 0.00, 0.00, 0.14, -4.53, 5.70, 0.00, 0.00, 0.13, 0.10, 4.18, 5.70, 0.00, 0.00, /* 1492-1619 */ 0.13, -4.75, -5.19, 0.00, 0.00, -0.12, 0.11, -4.06, 5.60, 0.00, 0.00, 0.13, -3.98, 5.60, -0.04, 0.00, 0.13, 4.02, -5.40, 0.00, 0.00, -0.12, 4.49, -4.90, -0.04, 0.00, -0.11, -0.10, -3.62, -5.40, -0.16, 0.20, -0.12, 0.00, 0.01, 4.38, 4.80, 0.00, 0.00, 0.11, -6.40, -0.10, 0.00, 0.00, 0.00, 0.14, -3.98, 5.00, 0.04, 0.00, 0.11, -3.82, -5.00, 0.00, 0.00, -0.11, -3.71, 5.07, 0.00, 0.00, 0.11, 4.14, 4.40, 0.00, 0.00, 0.10, -6.01, -0.50, -0.04, 0.00, 0.00, 0.13, -4.04, 4.39, 0.00, 0.00, 0.10, 3.45, -4.72, 0.00, 0.00, -0.11, 3.31, 4.71, 0.00, 0.00, 0.11, 3.26, -4.50, 0.00, 0.00, -0.10, -3.26, -4.50, 0.00, 0.00, -0.10, -3.34, -4.40, 0.00, 0.00, -0.10, -3.74, -4.00, 3.70, 4.00, 3.34, -4.30, 3.30, -4.30, -3.66, 3.90, 0.04, 3.66, 3.90, 0.04, -3.62, -3.90, -3.61, 3.90, -0.20, 5.30, 0.00, 0.00, 0.12, 3.06, 4.30, 3.30, /* 1620-1747 */ 4.00, 0.40, 0.20, 3.10, 4.10, -3.06, 3.90, -3.30, -3.60, -3.30, 3.36, 0.01, 3.14, 3.40, -4.57, -0.20, 0.00, 0.00, 0.00, 0.10, -2.70, -3.60, 2.94, -3.20, -2.90, 3.20, 2.47, -3.40, 2.55, -3.30, 2.80, -3.08, 2.51, 3.30, -4.10, 0.30, -0.12, -0.10, 4.10, 0.20, -2.74, 3.00, 2.46, 3.23, -3.66, 1.20, -0.20, 0.20, 3.74, -0.40, -2.51, -2.80, -3.74, 2.27, -2.90, 0.00, 0.00, -2.50, 2.70, -2.51, 2.60, -3.50, 0.20, 3.38, -2.22, -2.50, 3.26, -0.40, 1.95, -2.60, 3.22, -0.40, -0.04, -1.79, -2.60, 1.91, 2.50, 0.74, 3.05, -0.04, 0.08, 2.11, -2.30, -2.11, 2.20, -1.87, -2.40, 2.03, -2.20, -2.03, 2.20, 2.98, 0.00, 0.00, 2.98, -1.71, 2.40, 2.94, -0.10, -0.12, 0.10, 1.67, 2.40, -1.79, 2.30, -1.79, 2.20, -1.67, 2.20, 1.79, -2.00, 1.87, -1.90, 1.63, -2.10, -1.59, 2.10, 1.55, -2.10, -1.55, 2.10, -2.59, -0.20, -1.75, -1.90, -1.75, 1.90, -1.83, /* 1748-1875 */ -1.80, 1.51, 2.00, -1.51, -2.00, 1.71, 1.80, 1.31, 2.10, -1.43, 2.00, 1.43, 2.00, -2.43, -1.51, 1.90, -1.47, 1.90, 2.39, 0.20, -2.39, 1.39, 1.90, 1.39, -1.80, 1.47, -1.60, 1.47, -1.60, 1.43, -1.50, -1.31, 1.60, 1.27, -1.60, -1.27, 1.60, 1.27, -1.60, 2.03, 1.35, 1.50, -1.39, -1.40, 1.95, -0.20, -1.27, 1.49, 1.19, 1.50, 1.27, 1.40, 1.15, 1.50, 1.87, -0.10, -1.12, -1.50, 1.87, -1.11, -1.50, -1.11, -1.50, 0.00, 0.00, 1.19, 1.40, 1.27, -1.30, -1.27, -1.30, -1.15, 1.40, -1.23, 1.30, -1.23, -1.30, 1.22, -1.29, 1.07, -1.40, 1.75, -0.20, -1.03, -1.40, -1.07, 1.20, -1.03, 1.15, 1.07, 1.10, 1.51, -1.03, 1.10, 1.03, -1.10, 0.00, 0.00, -1.03, -1.10, 0.91, -1.20, -0.88, -1.20, -0.88, 1.20, -0.95, 1.10, -0.95, -1.10, 1.43, -1.39, 0.95, -1.00, -0.95, 1.00, -0.80, 1.10, 0.91, -1.00, -1.35, 0.88, 1.00, -0.83, 1.00, -0.91, 0.90, 0.91, /* 1876-2003 */ 0.90, 0.88, -0.90, -0.76, -1.00, -0.76, 1.00, 0.76, 1.00, -0.72, 1.00, 0.84, -0.90, 0.84, 0.90, 1.23, 0.00, 0.00, -0.52, -1.10, -0.68, 1.00, 1.19, -0.20, 1.19, 0.76, 0.90, 1.15, -0.10, 1.15, -0.10, 0.72, -0.90, -1.15, -1.15, 0.68, 0.90, -0.68, 0.90, -1.11, 0.00, 0.00, 0.20, 0.79, 0.80, -1.11, -0.10, 0.00, 0.00, -0.48, -1.00, -0.76, -0.80, -0.72, -0.80, -1.07, -0.10, 0.64, 0.80, -0.64, -0.80, 0.64, 0.80, 0.40, 0.60, 0.52, -0.50, -0.60, -0.80, -0.71, 0.70, -0.99, 0.99, 0.56, 0.80, -0.56, 0.80, 0.68, -0.70, 0.68, 0.70, -0.95, -0.64, 0.70, 0.64, 0.70, -0.60, 0.70, -0.60, -0.70, -0.91, -0.10, -0.51, 0.76, -0.91, -0.56, 0.70, 0.88, 0.88, -0.63, -0.60, 0.55, -0.60, -0.80, 0.80, -0.80, -0.52, 0.60, 0.52, 0.60, 0.52, -0.60, -0.48, 0.60, 0.48, 0.60, 0.48, 0.60, -0.76, 0.44, -0.60, 0.52, -0.50, -0.52, 0.50, 0.40, 0.60, -0.40, /* 2004-2131 */ -0.60, 0.40, -0.60, 0.72, -0.72, -0.51, -0.50, -0.48, 0.50, 0.48, -0.50, -0.48, 0.50, -0.48, 0.50, 0.48, -0.50, -0.48, -0.50, -0.68, -0.68, 0.44, 0.50, -0.64, -0.10, -0.64, -0.10, -0.40, 0.50, 0.40, 0.50, 0.40, 0.50, 0.00, 0.00, -0.40, -0.50, -0.36, -0.50, 0.36, -0.50, 0.60, -0.60, 0.40, -0.40, 0.40, 0.40, -0.40, 0.40, -0.40, 0.40, -0.56, -0.56, 0.36, -0.40, -0.36, 0.40, 0.36, -0.40, -0.36, -0.40, 0.36, 0.40, 0.36, 0.40, -0.52, 0.52, 0.52, 0.32, 0.40, -0.32, 0.40, -0.32, 0.40, -0.32, 0.40, 0.32, -0.40, -0.32, -0.40, 0.32, -0.40, 0.28, -0.40, -0.28, 0.40, 0.28, -0.40, 0.28, 0.40, 0.48, -0.48, 0.48, 0.36, -0.30, -0.36, -0.30, 0.00, 0.00, 0.20, 0.40, -0.44, 0.44, -0.44, -0.44, -0.44, -0.44, 0.32, -0.30, 0.32, 0.30, 0.24, 0.30, -0.12, -0.10, -0.28, 0.30, 0.28, 0.30, 0.28, 0.30, 0.28, -0.30, 0.28, -0.30, 0.28, -0.30, 0.28, /* 2132-2259 */ 0.30, -0.28, 0.30, 0.40, 0.40, -0.24, 0.30, 0.24, -0.30, 0.24, -0.30, -0.24, -0.30, 0.24, 0.30, 0.24, -0.30, -0.24, 0.30, 0.24, -0.30, -0.24, -0.30, 0.24, -0.30, 0.24, 0.30, -0.24, 0.30, -0.24, 0.30, 0.20, -0.30, 0.20, -0.30, 0.20, -0.30, 0.20, 0.30, 0.20, -0.30, 0.20, -0.30, 0.20, 0.30, 0.20, 0.30, -0.20, -0.30, 0.20, -0.30, 0.20, -0.30, -0.36, -0.36, -0.36, -0.04, 0.30, 0.12, -0.10, -0.32, -0.24, 0.20, 0.24, 0.20, 0.20, -0.20, -0.20, -0.20, -0.20, -0.20, 0.20, 0.20, 0.20, -0.20, 0.20, 0.20, 0.20, 0.20, -0.20, -0.20, 0.00, 0.00, -0.20, -0.20, -0.20, 0.20, -0.20, 0.20, 0.20, -0.20, -0.20, -0.20, 0.20, 0.20, 0.20, 0.20, 0.20, -0.20, 0.20, -0.20, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, -0.28, 0.28, 0.12, 0.00, 0.24, 0.16, -0.20, 0.16, -0.20, 0.16, -0.20, 0.16, 0.20, -0.16, 0.20, 0.16, 0.20, -0.16, 0.20, -0.16, 0.20, /* 2260-2387 */ -0.16, 0.20, 0.16, -0.20, 0.16, 0.20, 0.16, -0.20, -0.16, 0.20, -0.16, -0.20, -0.16, 0.20, 0.16, 0.20, 0.16, -0.20, 0.16, -0.20, 0.16, 0.20, 0.16, 0.20, 0.16, 0.20, -0.16, -0.20, 0.16, 0.20, -0.16, 0.20, 0.16, 0.20, -0.16, -0.20, 0.16, -0.20, 0.16, -0.20, -0.16, -0.20, 0.24, -0.24, -0.24, 0.24, 0.24, 0.12, 0.20, 0.12, 0.20, -0.12, -0.20, 0.12, -0.20, 0.12, -0.20, -0.12, 0.20, -0.12, 0.20, -0.12, -0.20, 0.12, 0.20, 0.12, 0.20, 0.12, -0.20, -0.12, 0.20, 0.12, -0.20, -0.12, 0.20, 0.12, 0.20, 0.00, 0.00, -0.12, 0.20, -0.12, 0.20, 0.12, -0.20, -0.12, 0.20, 0.12, 0.20, 0.00, -0.21, -0.20, 0.00, 0.00, 0.20, -0.20, -0.20, -0.20, 0.20, -0.16, -0.10, 0.00, 0.17, 0.16, 0.16, 0.16, 0.16, -0.16, 0.16, 0.16, -0.16, 0.16, -0.16, 0.16, 0.12, 0.10, 0.12, -0.10, -0.12, 0.10, -0.12, 0.10, 0.12, -0.10, -0.12, 0.12, -0.12, 0.12, /* 2388-2515 */ -0.12, 0.12, -0.12, -0.12, -0.12, -0.12, -0.12, -0.12, -0.12, 0.12, 0.12, 0.12, 0.12, -0.12, -0.12, 0.12, 0.12, 0.12, -0.12, 0.12, -0.12, -0.12, -0.12, 0.12, -0.12, -0.12, 0.12, 0.00, 0.11, 0.11,-122.67, 164.70, 203.78, 273.50, 3.58, 2.74, 6.18, -4.56, 0.00, -0.04, 0.00, -0.07, 57.44, -77.10, 95.82, 128.60, -1.77, -1.28, 2.85, -2.14, 82.14, 89.50, 0.00, 0.00, 2.00, -1.84, -0.04, 47.73, -64.10, 23.79, 31.90, -1.45, -1.07, 0.69, -0.53, -46.38, 50.50, 0.00, 0.00, 1.13, 1.04, 0.02, -18.38, 0.00, 63.80, 0.00, 0.00, 0.41, 0.00, -1.43, 59.07, 0.00, 0.00, 0.00, 0.00, -1.32, 57.28, 0.00, 0.00, 0.00, 0.00, -1.28, -48.65, 0.00, -1.15, 0.00, 0.00, 1.09, 0.00, 0.03, -18.30, 24.60, -17.30, -23.20, 0.56, 0.41, -0.51, 0.39, -16.91, 26.90, 8.43, 13.30, 0.60, 0.38, 0.31, -0.19, 1.23, -1.70, -19.13, -25.70, -0.03, -0.03, -0.58, 0.43, -0.72, 0.90, -17.34, -23.30, /* 2516-2643 */ 0.03, 0.02, -0.52, 0.39, -19.49, -21.30, 0.00, 0.00, -0.48, 0.44, 0.01, 20.57, -20.10, 0.64, 0.70, -0.45, -0.46, 0.00, -0.01, 4.89, 5.90, -16.55, 19.90, 0.14, -0.11, 0.44, 0.37, 18.22, 19.80, 0.00, 0.00, 0.44, -0.41, -0.01, 4.89, -5.30, -16.51, -18.00, -0.11, -0.11, -0.41, 0.37, -17.86, 0.00, 17.10, 0.00, 0.00, 0.40, 0.00, -0.38, 0.32, 0.00, 24.42, 0.00, 0.00, -0.01, 0.00, -0.55, -23.79, 0.00, 0.00, 0.00, 0.00, 0.53, 14.72, -16.00, -0.32, 0.00, -0.36, -0.33, -0.01, 0.01, 3.34, -4.50, 11.86, 15.90, -0.11, -0.07, 0.35, -0.27, -3.26, 4.40, 11.62, 15.60, 0.09, 0.07, 0.35, -0.26, -19.53, 0.00, 5.09, 0.00, 0.00, 0.44, 0.00, -0.11, -13.48, 14.70, 0.00, 0.00, 0.33, 0.30, 0.01, 10.86, -14.60, 3.18, 4.30, -0.33, -0.24, 0.09, -0.07, -11.30, -15.10, 0.00, 0.00, -0.34, 0.25, 0.01, 2.03, -2.70, 10.82, 14.50, -0.07, -0.05, 0.32, -0.24, 17.46, 0.00, /* 2644-2771 */ 0.00, 0.00, 0.00, -0.39, 16.43, 0.00, 0.52, 0.00, 0.00, -0.37, 0.00, -0.01, 9.35, 0.00, 13.29, 0.00, 0.00, -0.21, 0.00, -0.30, -10.42, 11.40, 0.00, 0.00, 0.25, 0.23, 0.01, 0.44, 0.50, -10.38, 11.30, 0.02, -0.01, 0.25, 0.23, -14.64, 0.00, 0.00, 0.00, 0.00, 0.33, 0.56, 0.80, -8.67, 11.70, 0.02, -0.01, 0.26, 0.19, 13.88, 0.00, -2.47, 0.00, 0.00, -0.31, 0.00, 0.06, -1.99, 2.70, 7.72, 10.30, 0.06, 0.04, 0.23, -0.17, -0.20, 0.00, 13.05, 0.00, 0.00, 0.00, 0.00, -0.29, 6.92, -9.30, 3.34, 4.50, -0.21, -0.15, 0.10, -0.07, -6.60, 0.00, 10.70, 0.00, 0.00, 0.15, 0.00, -0.24, -8.04, -8.70, 0.00, 0.00, -0.19, 0.18, -10.58, 0.00, -3.10, 0.00, 0.00, 0.24, 0.00, 0.07, -7.32, 8.00, -0.12, -0.10, 0.18, 0.16, 1.63, 1.70, 6.96, -7.60, 0.03, -0.04, -0.17, -0.16, -3.62, 0.00, 9.86, 0.00, 0.00, 0.08, 0.00, -0.22, 0.20, -0.20, -6.88, /* 2772-2899 */ -7.50, 0.00, 0.00, -0.17, 0.15, -8.99, 0.00, 4.02, 0.00, 0.00, 0.20, 0.00, -0.09, -1.07, 1.40, -5.69, -7.70, 0.03, 0.02, -0.17, 0.13, 6.48, -7.20, -0.48, -0.50, -0.16, -0.14, -0.01, 0.01, 5.57, -7.50, 1.07, 1.40, -0.17, -0.12, 0.03, -0.02, 8.71, 0.00, 3.54, 0.00, 0.00, -0.19, 0.00, -0.08, 0.40, 0.00, 9.27, 0.00, 0.00, -0.01, 0.00, -0.21, -6.13, 6.70, -1.19, -1.30, 0.15, 0.14, -0.03, 0.03, 5.21, -5.70, -2.51, -2.60, -0.13, -0.12, -0.06, 0.06, 5.69, -6.20, -0.12, -0.10, -0.14, -0.13, -0.01, 2.03, -2.70, 4.53, 6.10, -0.06, -0.05, 0.14, -0.10, 5.01, 5.50, -2.51, 2.70, 0.12, -0.11, 0.06, 0.06, -1.91, 2.60, -4.38, -5.90, 0.06, 0.04, -0.13, 0.10, 4.65, -6.30, 0.00, 0.00, -0.14, -0.10, -5.29, 5.70, 0.00, 0.00, 0.13, 0.12, -2.23, -4.00, -4.65, 4.20, -0.09, 0.05, 0.10, 0.10, -4.53, 6.10, 0.00, 0.00, 0.14, 0.10, 2.47, 2.70, /* 2900-3027 */ -4.46, 4.90, 0.06, -0.06, 0.11, 0.10, -5.05, 5.50, 0.84, 0.90, 0.12, 0.11, 0.02, -0.02, 4.97, -5.40, -1.71, 0.00, -0.12, -0.11, 0.00, 0.04, -0.99, -1.30, 4.22, -5.70, -0.03, 0.02, -0.13, -0.09, 0.99, 1.40, 4.22, -5.60, 0.03, -0.02, -0.13, -0.09, -4.69, -5.20, 0.00, 0.00, -0.12, 0.10, -3.42, 0.00, 6.09, 0.00, 0.00, 0.08, 0.00, -0.14, -4.65, -5.10, 0.00, 0.00, -0.11, 0.10, 0.00, 0.00, -4.53, -5.00, 0.00, 0.00, -0.11, 0.10, -2.43, -2.70, -3.82, 4.20, -0.06, 0.05, 0.10, 0.09, 0.00, 0.00, -4.53, 4.90, 0.00, 0.00, 0.11, 0.10, -4.49, -4.90, 0.00, 0.00, -0.11, 0.10, 2.67, -2.90, -3.62, -3.90, -0.06, -0.06, -0.09, 0.08, 3.94, -5.30, 0.00, 0.00, -0.12, -3.38, 3.70, -2.78, -3.10, 0.08, 0.08, -0.07, 0.06, 3.18, -3.50, -2.82, -3.10, -0.08, -0.07, -0.07, 0.06, -5.77, 0.00, 1.87, 0.00, 0.00, 0.13, 0.00, -0.04, 3.54, -4.80, -0.64, /* 3028-3155 */ -0.90, -0.11, 0.00, -0.02, -3.50, -4.70, 0.68, -0.90, -0.11, 0.00, -0.02, 5.49, 0.00, 0.00, 0.00, 0.00, -0.12, 1.83, -2.50, 2.63, 3.50, -0.06, 0.00, 0.08, 3.02, -4.10, 0.68, 0.90, -0.09, 0.00, 0.02, 0.00, 0.00, 5.21, 0.00, 0.00, 0.00, 0.00, -0.12, -3.54, 3.80, 2.70, 3.60, -1.35, 1.80, 0.08, 0.00, 0.04, -2.90, 3.90, 0.68, 0.90, 0.09, 0.00, 0.02, 0.80, -1.10, -2.78, -3.70, -0.02, 0.00, -0.08, 4.10, 0.00, -2.39, 0.00, 0.00, -0.09, 0.00, 0.05, -1.59, 2.10, 2.27, 3.00, 0.05, 0.00, 0.07, -2.63, 3.50, -0.48, -0.60, -2.94, -3.20, -2.94, 3.20, 2.27, -3.00, -1.11, -1.50, -0.07, 0.00, -0.03, -0.56, -0.80, -2.35, 3.10, 0.00, -0.60, -3.42, 1.90, -0.12, -0.10, 2.63, -2.90, 2.51, 2.80, -0.64, 0.70, -0.48, -0.60, 2.19, -2.90, 0.24, -0.30, 2.15, 2.90, 2.15, -2.90, 0.52, 0.70, 2.07, -2.80, -3.10, 0.00, 1.79, 0.00, 0.00, 0.07, /* 3156-3283 */ 0.00, -0.04, 0.88, 0.00, -3.46, 2.11, 2.80, -0.36, 0.50, 3.54, -0.20, -3.50, -1.39, 1.50, -1.91, -2.10, -1.47, 2.00, 1.39, 1.90, 2.07, -2.30, 0.91, 1.00, 1.99, -2.70, 3.30, 0.00, 0.60, -0.44, -0.70, -1.95, 2.60, 2.15, -2.40, -0.60, -0.70, 3.30, 0.84, 0.00, -3.10, -3.10, 0.00, -0.72, -0.32, 0.40, -1.87, -2.50, 1.87, -2.50, 0.32, 0.40, -0.24, 0.30, -1.87, -2.50, -0.24, -0.30, 1.87, -2.50, -2.70, 0.00, 1.55, 2.03, 2.20, -2.98, -1.99, -2.20, 0.12, -0.10, -0.40, 0.50, 1.59, 2.10, 0.00, 0.00, -1.79, 2.00, -1.03, 1.40, -1.15, -1.60, 0.32, 0.50, 1.39, -1.90, 2.35, -1.27, 1.70, 0.60, 0.80, -0.32, -0.40, 1.35, -1.80, 0.44, 0.00, 2.23, -0.84, 0.90, -1.27, -1.40, -1.47, 1.60, -0.28, -0.30, -0.28, 0.40, -1.27, -1.70, 0.28, -0.40, -1.43, -1.50, 0.00, 0.00, -1.27, -1.70, 2.11, -0.32, -0.40, -1.23, 1.60, 1.19, -1.30, -0.72, -0.80, 0.72, /* 3284-3411 */ -0.80, -1.15, -1.30, -1.35, -1.50, -1.19, -1.60, -0.12, 0.20, 1.79, 0.00, -0.88, -0.28, 0.40, 1.11, 1.50, -1.83, 0.00, 0.56, -0.12, 0.10, -1.27, -1.40, 0.00, 0.00, 1.15, 1.50, -0.12, 0.20, 1.11, 1.50, 0.36, -0.50, -1.07, -1.40, -1.11, 1.50, 1.67, 0.00, 0.80, -1.11, 0.00, 1.43, 1.23, -1.30, -0.24, -1.19, -1.30, -0.24, 0.20, -0.44, -0.90, -0.95, 1.10, 1.07, -1.40, 1.15, -1.30, 1.03, -1.10, -0.56, -0.60, -0.68, 0.90, -0.76, -1.00, -0.24, -0.30, 0.95, -1.30, 0.56, 0.70, 0.84, -1.10, -0.56, 0.00, -1.55, 0.91, -1.30, 0.28, 0.30, 0.16, -0.20, 0.95, 1.30, 0.40, -0.50, -0.88, -1.20, 0.95, -1.10, -0.48, -0.50, 0.00, 0.00, -1.07, 1.20, 0.44, -0.50, 0.95, 1.10, 0.00, 0.00, 0.92, -1.30, 0.95, 1.00, -0.52, 0.60, 1.59, 0.24, -0.40, 0.91, 1.20, 0.84, -1.10, -0.44, -0.60, 0.84, 1.10, -0.44, 0.60, -0.44, 0.60, -0.84, -1.10, -0.80, 0.00, /* 3412-3539 */ 1.35, 0.76, 0.20, -0.91, -1.00, 0.20, -0.30, -0.91, -1.20, -0.95, 1.00, -0.48, -0.50, 0.88, 1.00, 0.48, -0.50, -0.95, -1.10, 0.20, -0.20, -0.99, 1.10, -0.84, 1.10, -0.24, -0.30, 0.20, -0.30, 0.84, 1.10, -1.39, 0.00, -0.28, -0.16, 0.20, 0.84, 1.10, 0.00, 0.00, 1.39, 0.00, 0.00, -0.95, 1.00, 1.35, -0.99, 0.00, 0.88, -0.52, 0.00, -1.19, 0.20, 0.20, 0.76, -1.00, 0.00, 0.00, 0.76, 1.00, 0.00, 0.00, 0.76, 1.00, -0.76, 1.00, 0.00, 0.00, 1.23, 0.76, 0.80, -0.32, 0.40, -0.72, 0.80, -0.40, -0.40, 0.00, 0.00, -0.80, -0.90, -0.68, 0.90, -0.16, -0.20, -0.16, -0.20, 0.68, -0.90, -0.36, 0.50, -0.56, -0.80, 0.72, -0.90, 0.44, -0.60, -0.48, -0.70, -0.16, 0.00, -1.11, 0.32, 0.00, -1.07, 0.60, -0.80, -0.28, -0.40, -0.64, 0.00, 0.91, 1.11, 0.64, -0.90, 0.76, -0.80, 0.00, 0.00, -0.76, -0.80, 1.03, 0.00, -0.36, -0.64, -0.70, 0.36, -0.40, /* 3540-3667 */ 1.07, 0.36, -0.50, -0.52, -0.70, 0.60, 0.00, 0.88, 0.95, 0.00, 0.48, 0.16, -0.20, 0.60, 0.80, 0.16, -0.20, -0.60, -0.80, 0.00, -1.00, 0.12, 0.20, 0.16, -0.20, 0.68, 0.70, 0.59, -0.80, -0.99, -0.56, -0.60, 0.36, -0.40, -0.68, -0.70, -0.68, -0.70, -0.36, -0.50, -0.44, 0.60, 0.64, 0.70, -0.12, 0.10, -0.52, 0.60, 0.36, 0.40, 0.00, 0.00, 0.95, -0.84, 0.00, 0.44, 0.56, 0.60, 0.32, -0.30, 0.00, 0.00, 0.60, 0.70, 0.00, 0.00, 0.60, 0.70, -0.12, -0.20, 0.52, -0.70, 0.00, 0.00, 0.56, 0.70, -0.12, 0.10, -0.52, -0.70, 0.00, 0.00, 0.88, -0.76, 0.00, -0.44, 0.00, 0.00, -0.52, -0.70, 0.52, -0.70, 0.36, -0.40, -0.44, -0.50, 0.00, 0.00, 0.60, 0.60, 0.84, 0.00, 0.12, -0.24, 0.00, 0.80, -0.56, 0.60, -0.32, -0.30, 0.48, -0.50, 0.28, -0.30, -0.48, -0.50, 0.12, 0.20, 0.48, -0.60, 0.48, 0.60, -0.12, 0.20, 0.24, 0.00, 0.76, -0.52, /* 3668-3795 */ -0.60, -0.52, 0.60, 0.48, -0.50, -0.24, -0.30, 0.12, -0.10, 0.48, 0.60, 0.52, -0.20, 0.36, 0.40, -0.44, 0.50, -0.24, -0.30, -0.48, -0.60, -0.44, -0.60, -0.12, 0.10, 0.76, 0.76, 0.20, -0.20, 0.48, 0.50, 0.40, -0.50, -0.24, -0.30, 0.44, -0.60, 0.44, -0.60, 0.36, 0.00, -0.64, 0.72, 0.00, -0.12, 0.00, -0.10, -0.40, -0.60, -0.20, -0.20, -0.44, 0.50, -0.44, 0.50, 0.20, 0.20, -0.44, -0.50, 0.20, -0.20, -0.20, 0.20, -0.44, -0.50, 0.64, 0.00, 0.32, -0.36, 0.50, -0.20, -0.30, 0.12, -0.10, 0.48, 0.50, -0.12, 0.30, -0.36, -0.50, 0.00, 0.00, 0.48, 0.50, -0.48, 0.50, 0.68, 0.00, -0.12, 0.56, -0.40, 0.44, -0.50, -0.12, -0.10, 0.24, 0.30, -0.40, 0.40, 0.64, 0.00, -0.24, 0.64, 0.00, -0.20, 0.00, 0.00, 0.44, -0.50, 0.44, 0.50, -0.12, 0.20, -0.36, -0.50, 0.12, 0.00, 0.64, -0.40, 0.50, 0.00, 0.10, 0.00, 0.00, -0.40, 0.50, 0.00, 0.00, /* 3796-3923 */ -0.40, -0.50, 0.56, 0.00, 0.28, 0.00, 0.10, 0.36, 0.50, 0.00, -0.10, 0.36, -0.50, 0.36, 0.50, 0.00, -0.10, 0.24, -0.20, -0.36, -0.40, 0.16, 0.20, 0.40, -0.40, 0.00, 0.00, -0.36, -0.50, -0.36, -0.50, -0.32, -0.50, -0.12, 0.10, 0.20, 0.20, -0.36, 0.40, -0.60, 0.60, 0.28, 0.00, 0.52, 0.12, -0.10, 0.40, 0.40, 0.00, -0.50, 0.20, -0.20, -0.32, 0.40, 0.16, 0.20, -0.16, 0.20, 0.32, 0.40, 0.56, 0.00, -0.12, 0.32, -0.40, -0.16, -0.20, 0.00, 0.00, 0.40, 0.40, -0.40, -0.40, -0.40, 0.40, -0.36, 0.40, 0.12, 0.10, 0.00, 0.10, 0.36, 0.40, 0.00, -0.10, 0.36, 0.40, -0.36, 0.40, 0.00, 0.10, 0.32, 0.00, 0.44, 0.12, 0.20, 0.28, -0.40, 0.00, 0.00, 0.36, 0.40, 0.32, -0.40, -0.16, 0.12, 0.10, 0.32, -0.40, 0.20, 0.30, -0.24, 0.30, 0.00, 0.10, 0.32, 0.40, 0.00, -0.10, -0.32, -0.40, -0.32, 0.40, 0.00, 0.10, -0.52, -0.52, 0.52, /* 3924-4051 */ 0.32, -0.40, 0.00, 0.00, 0.32, 0.40, 0.32, -0.40, 0.00, 0.00, -0.32, -0.40, -0.32, 0.40, 0.32, 0.40, 0.00, 0.00, 0.32, 0.40, 0.00, 0.00, -0.32, -0.40, 0.00, 0.00, 0.32, 0.40, 0.16, 0.20, 0.32, -0.30, -0.16, 0.00, -0.48, -0.20, 0.20, -0.28, -0.30, 0.28, -0.40, 0.00, 0.00, 0.28, -0.40, 0.00, 0.00, 0.28, -0.40, 0.00, 0.00, -0.28, -0.40, 0.28, 0.40, -0.28, -0.40, -0.48, -0.20, 0.20, 0.24, 0.30, 0.44, 0.00, 0.16, 0.24, 0.30, 0.16, -0.20, 0.24, 0.30, -0.12, 0.20, 0.20, 0.30, -0.16, 0.20, 0.00, 0.00, 0.44, -0.32, 0.30, 0.24, 0.00, -0.36, 0.36, 0.00, 0.24, 0.12, -0.20, 0.20, 0.30, -0.12, 0.00, -0.28, 0.30, -0.24, 0.30, 0.12, 0.10, -0.28, -0.30, -0.28, 0.30, 0.00, 0.00, -0.28, -0.30, 0.00, 0.00, -0.28, -0.30, 0.00, 0.00, 0.28, 0.30, 0.00, 0.00, -0.28, -0.30, -0.28, 0.30, 0.00, 0.00, -0.28, -0.30, 0.00, 0.00, /* 4052-4179 */ 0.28, 0.30, 0.00, 0.00, -0.28, 0.30, 0.28, -0.30, -0.28, 0.30, 0.40, 0.40, -0.24, 0.30, 0.00, -0.10, 0.16, 0.00, 0.36, -0.20, 0.30, -0.12, -0.10, -0.24, -0.30, 0.00, 0.00, -0.24, 0.30, -0.24, 0.30, 0.00, 0.00, -0.24, 0.30, -0.24, 0.30, 0.24, -0.30, 0.00, 0.00, 0.24, -0.30, 0.00, 0.00, 0.24, 0.30, 0.24, -0.30, 0.24, 0.30, -0.24, 0.30, -0.24, 0.30, -0.20, 0.20, -0.16, -0.20, 0.00, 0.00, -0.32, 0.20, 0.00, 0.10, 0.20, -0.30, 0.20, -0.20, 0.12, 0.20, -0.16, 0.20, 0.16, 0.20, 0.20, 0.30, 0.20, 0.30, 0.00, 0.00, -0.20, 0.30, 0.00, 0.00, 0.20, 0.30, -0.20, -0.30, -0.20, -0.30, 0.20, -0.30, 0.00, 0.00, 0.20, 0.30, 0.00, 0.00, 0.20, 0.30, 0.00, 0.00, 0.20, 0.30, 0.00, 0.00, 0.20, 0.30, 0.00, 0.00, 0.20, -0.30, 0.00, 0.00, -0.20, -0.30, 0.00, 0.00, -0.20, 0.30, 0.00, 0.00, -0.20, 0.30, 0.00, 0.00, 0.36, /* 4180-4307 */ 0.00, 0.00, 0.36, 0.12, 0.10, -0.24, 0.20, 0.12, -0.20, -0.16, -0.20, -0.13, 0.10, 0.22, 0.21, 0.20, 0.00, -0.28, 0.32, 0.00, -0.12, -0.20, -0.20, 0.12, -0.10, 0.12, 0.10, -0.20, 0.20, 0.00, 0.00, -0.32, 0.32, 0.00, 0.00, 0.32, 0.32, 0.00, 0.00, -0.24, -0.20, 0.24, 0.20, 0.20, 0.00, -0.24, 0.00, 0.00, -0.24, -0.20, 0.00, 0.00, 0.24, 0.20, -0.24, -0.20, 0.00, 0.00, -0.24, 0.20, 0.16, -0.20, 0.12, 0.10, 0.20, 0.20, 0.00, -0.10, -0.12, 0.10, -0.16, -0.20, -0.12, -0.10, -0.16, 0.20, 0.20, 0.20, 0.00, 0.00, -0.20, 0.20, -0.20, 0.20, -0.20, 0.20, -0.20, 0.20, 0.20, -0.20, -0.20, -0.20, 0.00, 0.00, -0.20, 0.20, 0.20, 0.00, -0.20, 0.00, 0.00, -0.20, 0.20, -0.20, 0.20, -0.20, -0.20, -0.20, -0.20, 0.00, 0.00, 0.20, 0.20, 0.20, 0.20, 0.12, -0.20, -0.12, -0.10, 0.28, -0.28, 0.16, -0.20, 0.00, -0.10, 0.00, 0.10, -0.16, /* 4308-4435 */ 0.20, 0.00, -0.10, -0.16, -0.20, 0.00, -0.10, 0.16, -0.20, 0.16, -0.20, 0.00, 0.00, 0.16, 0.20, -0.16, 0.20, 0.00, 0.00, 0.16, 0.20, 0.16, -0.20, 0.16, -0.20, -0.16, 0.20, 0.16, -0.20, 0.00, 0.00, 0.16, 0.20, 0.00, 0.00, 0.16, 0.20, 0.00, 0.00, -0.16, -0.20, 0.16, -0.20, -0.16, -0.20, 0.00, 0.00, -0.16, -0.20, 0.00, 0.00, -0.16, 0.20, 0.00, 0.00, 0.16, -0.20, 0.16, 0.20, 0.16, 0.20, 0.00, 0.00, -0.16, -0.20, 0.00, 0.00, -0.16, -0.20, 0.00, 0.00, 0.16, 0.20, 0.16, 0.20, 0.00, 0.00, 0.16, 0.20, 0.16, -0.20, 0.16, 0.20, 0.00, 0.00, -0.16, 0.20, 0.00, 0.10, 0.12, -0.20, 0.12, -0.20, 0.00, -0.10, 0.00, -0.10, 0.12, 0.20, 0.00, -0.10, -0.12, 0.20, -0.15, 0.20, -0.24, 0.24, 0.00, 0.00, 0.24, 0.24, 0.12, -0.20, -0.12, -0.20, 0.00, 0.00, 0.12, 0.20, 0.12, -0.20, 0.12, 0.20, 0.12, 0.20, 0.12, 0.20, 0.12, /* 4436-4563 */ -0.20, -0.12, 0.20, 0.00, 0.00, 0.12, 0.20, 0.12, 0.00, -0.20, 0.00, 0.00, -0.12, -0.20, 0.12, -0.20, 0.00, 0.00, 0.12, 0.20, -0.12, 0.20, -0.12, 0.20, 0.12, -0.20, 0.00, 0.00, 0.12, 0.20, 0.20, 0.00, 0.12, 0.00, 0.00, -0.12, 0.20, 0.00, 0.00, -0.12, -0.20, 0.00, 0.00, -0.12, -0.20, -0.12, -0.20, 0.00, 0.00, 0.12, -0.20, 0.12, -0.20, 0.12, 0.20, -0.12, -0.20, 0.00, 0.00, 0.12, -0.20, 0.12, -0.20, 0.12, 0.20, 0.12, 0.00, 0.20, -0.12, -0.20, 0.00, 0.00, 0.12, 0.20, -0.16, 0.00, 0.16, -0.20, 0.20, 0.00, 0.00, -0.20, 0.00, 0.00, -0.20, 0.20, 0.00, 0.00, 0.20, 0.20, -0.20, 0.00, 0.00, -0.20, 0.12, 0.00, -0.16, 0.20, 0.00, 0.00, 0.20, 0.12, -0.10, 0.00, 0.10, 0.16, -0.16, -0.16, -0.16, -0.16, -0.16, 0.00, 0.00, -0.16, 0.00, 0.00, -0.16, -0.16, -0.16, 0.00, 0.00, -0.16, 0.00, 0.00, 0.16, 0.00, 0.00, 0.16, /* 4564-4691 */ 0.00, 0.00, 0.16, 0.16, 0.00, 0.00, -0.16, 0.00, 0.00, -0.16, -0.16, 0.00, 0.00, 0.16, 0.00, 0.00, -0.16, -0.16, 0.00, 0.00, -0.16, -0.16, 0.12, 0.10, 0.12, -0.10, 0.12, 0.10, 0.00, 0.00, 0.12, 0.10, -0.12, 0.10, 0.00, 0.00, 0.12, 0.10, 0.12, -0.10, 0.00, 0.00, -0.12, -0.10, 0.00, 0.00, 0.12, 0.10, 0.12, 0.00, 0.00, 0.12, 0.00, 0.00, -0.12, 0.00, 0.00, 0.12, 0.12, 0.12, 0.12, 0.12, 0.00, 0.00, 0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00, 0.12, 0.00, 0.00, 0.12, -0.12, -0.12, 0.12, 0.12, -0.12, -0.12, 0.00, 0.00, 0.12, -0.12, 0.12, 0.12, -0.12, -0.12, 0.00, 0.00, -0.12, -0.12, 0.00, 0.00, -0.12, 0.12, 0.00, 0.00, 0.12, 0.00, 0.00, 0.12, 0.00, 0.00, 0.12, -0.12, 0.00, 0.00, -0.12, 0.12, -0.12, -0.12, 0.12, 0.00, 0.00, 0.12, 0.12, 0.12, -0.12, 0.00, 0.00, -0.12, -0.12, -0.12, 0.00, 0.00, -0.12, /* 4692-NA */ -0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00, -0.12, -0.12, -0.12, -0.12, 0.12, 0.00, 0.00, 0.12, -0.12, 0.00, 0.00, -0.12, -0.12, 0.00, 0.00, 0.12, -0.12, -0.12, -0.12, -0.12, 0.12, 0.12, -0.12, -0.12, 0.00, 0.00, -0.12, 0.00, 0.00, -0.12, 0.12, 0.00, 0.00, 0.12, 0.00, 0.00, -0.12, -0.12, 0.00, 0.00, -0.12, -0.12, 0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00, 0.12, 0.00, 0.00, 0.12, 0.12, 0.08, 0.00, 0.04 }; /* Number of amplitude coefficients */ static const int NA = (int) (sizeof a / sizeof (double)); /* Amplitude usage: X or Y, sin or cos, power of T. */ static const int jaxy[] = {0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1}; static const int jasc[] = {0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0}; static const int japt[] = {0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4}; /* Miscellaneous */ double t, w, pt[MAXPT+1], fa[14], xypr[2], xypl[2], xyls[2], arg, sc[2]; int jpt, i, j, jxy, ialast, ifreq, m, ia, jsc; /*--------------------------------------------------------------------*/ /* Interval between fundamental date J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Powers of T. */ w = 1.0; for (jpt = 0; jpt <= MAXPT; jpt++) { pt[jpt] = w; w *= t; } /* Initialize totals in X and Y: polynomial, luni-solar, planetary. */ for (jxy = 0; jxy < 2; jxy++) { xypr[jxy] = 0.0; xyls[jxy] = 0.0; xypl[jxy] = 0.0; } /* --------------------------------- */ /* Fundamental arguments (IERS 2003) */ /* --------------------------------- */ /* Mean anomaly of the Moon. */ fa[0] = iauFal03(t); /* Mean anomaly of the Sun. */ fa[1] = iauFalp03(t); /* Mean argument of the latitude of the Moon. */ fa[2] = iauFaf03(t); /* Mean elongation of the Moon from the Sun. */ fa[3] = iauFad03(t); /* Mean longitude of the ascending node of the Moon. */ fa[4] = iauFaom03(t); /* Planetary longitudes, Mercury through Neptune. */ fa[5] = iauFame03(t); fa[6] = iauFave03(t); fa[7] = iauFae03(t); fa[8] = iauFama03(t); fa[9] = iauFaju03(t); fa[10] = iauFasa03(t); fa[11] = iauFaur03(t); fa[12] = iauFane03(t); /* General accumulated precession in longitude. */ fa[13] = iauFapa03(t); /* -------------------------------------- */ /* Polynomial part of precession-nutation */ /* -------------------------------------- */ for (jxy = 0; jxy < 2; jxy++) { for (j = MAXPT; j >= 0; j--) { xypr[jxy] += xyp[jxy][j] * pt[j]; } } /* ---------------------------------- */ /* Nutation periodic terms, planetary */ /* ---------------------------------- */ /* Work backwards through the coefficients per frequency list. */ ialast = NA; for (ifreq = NFPL-1; ifreq >= 0; ifreq--) { /* Obtain the argument functions. */ arg = 0.0; for (i = 0; i < 14; i++) { m = mfapl[ifreq][i]; if (m != 0) arg += (double)m * fa[i]; } sc[0] = sin(arg); sc[1] = cos(arg); /* Work backwards through the amplitudes at this frequency. */ ia = nc[ifreq+NFLS]; for (i = ialast; i >= ia; i--) { /* Coefficient number (0 = 1st). */ j = i-ia; /* X or Y. */ jxy = jaxy[j]; /* Sin or cos. */ jsc = jasc[j]; /* Power of T. */ jpt = japt[j]; /* Accumulate the component. */ xypl[jxy] += a[i-1] * sc[jsc] * pt[jpt]; } ialast = ia-1; } /* ----------------------------------- */ /* Nutation periodic terms, luni-solar */ /* ----------------------------------- */ /* Continue working backwards through the number of coefficients list. */ for (ifreq = NFLS-1; ifreq >= 0; ifreq--) { /* Obtain the argument functions. */ arg = 0.0; for (i = 0; i < 5; i++) { m = mfals[ifreq][i]; if (m != 0) arg += (double)m * fa[i]; } sc[0] = sin(arg); sc[1] = cos(arg); /* Work backwards through the amplitudes at this frequency. */ ia = nc[ifreq]; for (i = ialast; i >= ia; i--) { /* Coefficient number (0 = 1st). */ j = i-ia; /* X or Y. */ jxy = jaxy[j]; /* Sin or cos. */ jsc = jasc[j]; /* Power of T. */ jpt = japt[j]; /* Accumulate the component. */ xyls[jxy] += a[i-1] * sc[jsc] * pt[jpt]; } ialast = ia-1; } /* ------------------------------------ */ /* Results: CIP unit vector components */ /* ------------------------------------ */ *x = DAS2R * (xypr[0] + (xyls[0] + xypl[0]) / 1e6); *y = DAS2R * (xypr[1] + (xyls[1] + xypl[1]) / 1e6); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/xys00a.c0000644000113000011300000001556013027221063014460 0ustar bellsbells#include "sofa.h" void iauXys00a(double date1, double date2, double *x, double *y, double *s) /* ** - - - - - - - - - - ** i a u X y s 0 0 a ** - - - - - - - - - - ** ** For a given TT date, compute the X,Y coordinates of the Celestial ** Intermediate Pole and the CIO locator s, using the IAU 2000A ** precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** x,y double Celestial Intermediate Pole (Note 2) ** s double the CIO locator s (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y ** components of the unit vector in the Geocentric Celestial ** Reference System. ** ** 3) The CIO locator s (in radians) positions the Celestial ** Intermediate Origin on the equator of the CIP. ** ** 4) A faster, but slightly less accurate result (about 1 mas for ** X,Y), can be obtained by using instead the iauXys00b function. ** ** Called: ** iauPnm00a classical NPB matrix, IAU 2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS00 the CIO locator s, given X,Y, IAU 2000A ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rbpn[3][3]; /* Form the bias-precession-nutation matrix, IAU 2000A. */ iauPnm00a(date1, date2, rbpn); /* Extract X,Y. */ iauBpn2xy(rbpn, x, y); /* Obtain s. */ *s = iauS00(date1, date2, *x, *y); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/xys00b.c0000644000113000011300000001554213027221063014461 0ustar bellsbells#include "sofa.h" void iauXys00b(double date1, double date2, double *x, double *y, double *s) /* ** - - - - - - - - - - ** i a u X y s 0 0 b ** - - - - - - - - - - ** ** For a given TT date, compute the X,Y coordinates of the Celestial ** Intermediate Pole and the CIO locator s, using the IAU 2000B ** precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** x,y double Celestial Intermediate Pole (Note 2) ** s double the CIO locator s (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y ** components of the unit vector in the Geocentric Celestial ** Reference System. ** ** 3) The CIO locator s (in radians) positions the Celestial ** Intermediate Origin on the equator of the CIP. ** ** 4) The present function is faster, but slightly less accurate (about ** 1 mas in X,Y), than the iauXys00a function. ** ** Called: ** iauPnm00b classical NPB matrix, IAU 2000B ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS00 the CIO locator s, given X,Y, IAU 2000A ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rbpn[3][3]; /* Form the bias-precession-nutation matrix, IAU 2000A. */ iauPnm00b(date1, date2, rbpn); /* Extract X,Y. */ iauBpn2xy(rbpn, x, y); /* Obtain s. */ *s = iauS00(date1, date2, *x, *y); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/xys06a.c0000644000113000011300000001562013027221063014463 0ustar bellsbells#include "sofa.h" void iauXys06a(double date1, double date2, double *x, double *y, double *s) /* ** - - - - - - - - - - ** i a u X y s 0 6 a ** - - - - - - - - - - ** ** For a given TT date, compute the X,Y coordinates of the Celestial ** Intermediate Pole and the CIO locator s, using the IAU 2006 ** precession and IAU 2000A nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** x,y double Celestial Intermediate Pole (Note 2) ** s double the CIO locator s (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y components ** of the unit vector in the Geocentric Celestial Reference System. ** ** 3) The CIO locator s (in radians) positions the Celestial ** Intermediate Origin on the equator of the CIP. ** ** 4) Series-based solutions for generating X and Y are also available: ** see Capitaine & Wallace (2006) and iauXy06. ** ** Called: ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rbpn[3][3]; /* Form the bias-precession-nutation matrix, IAU 2006/2000A. */ iauPnm06a(date1, date2, rbpn); /* Extract X,Y. */ iauBpn2xy(rbpn, x, y); /* Obtain s. */ *s = iauS06(date1, date2, *x, *y); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/zp.c0000644000113000011300000001132413027221063013757 0ustar bellsbells#include "sofa.h" void iauZp(double p[3]) /* ** - - - - - - ** i a u Z p ** - - - - - - ** ** Zero a p-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Returned: ** p double[3] p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { p[0] = 0.0; p[1] = 0.0; p[2] = 0.0; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/zpv.c0000644000113000011300000001141213027221063014143 0ustar bellsbells#include "sofa.h" void iauZpv(double pv[2][3]) /* ** - - - - - - - ** i a u Z p v ** - - - - - - - ** ** Zero a pv-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Returned: ** pv double[2][3] pv-vector ** ** Called: ** iauZp zero p-vector ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { iauZp(pv[0]); iauZp(pv[1]); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/zr.c0000644000113000011300000001154713027221063013770 0ustar bellsbells#include "sofa.h" void iauZr(double r[3][3]) /* ** - - - - - - ** i a u Z r ** - - - - - - ** ** Initialize an r-matrix to the null matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Returned: ** r double[3][3] r-matrix ** ** This revision: 2013 June 18 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { r[0][0] = 0.0; r[0][1] = 0.0; r[0][2] = 0.0; r[1][0] = 0.0; r[1][1] = 0.0; r[1][2] = 0.0; r[2][0] = 0.0; r[2][1] = 0.0; r[2][2] = 0.0; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ } sofa/20160503_c/c/src/sofa.h0000644000113000011300000006125313027221063014271 0ustar bellsbells#ifndef SOFAHDEF #define SOFAHDEF /* ** - - - - - - - ** s o f a . h ** - - - - - - - ** ** Prototype function declarations for SOFA library. ** ** This file is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** This revision: 2016 March 10 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ #include "sofam.h" #include "math.h" #ifdef __cplusplus extern "C" { #endif /* Astronomy/Calendars */ int iauCal2jd(int iy, int im, int id, double *djm0, double *djm); double iauEpb(double dj1, double dj2); void iauEpb2jd(double epb, double *djm0, double *djm); double iauEpj(double dj1, double dj2); void iauEpj2jd(double epj, double *djm0, double *djm); int iauJd2cal(double dj1, double dj2, int *iy, int *im, int *id, double *fd); int iauJdcalf(int ndp, double dj1, double dj2, int iymdf[4]); /* Astronomy/Astrometry */ void iauAb(double pnat[3], double v[3], double s, double bm1, double ppr[3]); void iauApcg(double date1, double date2, double ebpv[2][3], double ehp[3], iauASTROM *astrom); void iauApcg13(double date1, double date2, iauASTROM *astrom); void iauApci(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, iauASTROM *astrom); void iauApci13(double date1, double date2, iauASTROM *astrom, double *eo); void iauApco(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, double theta, double elong, double phi, double hm, double xp, double yp, double sp, double refa, double refb, iauASTROM *astrom); int iauApco13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom, double *eo); void iauApcs(double date1, double date2, double pv[2][3], double ebpv[2][3], double ehp[3], iauASTROM *astrom); void iauApcs13(double date1, double date2, double pv[2][3], iauASTROM *astrom); void iauAper(double theta, iauASTROM *astrom); void iauAper13(double ut11, double ut12, iauASTROM *astrom); void iauApio(double sp, double theta, double elong, double phi, double hm, double xp, double yp, double refa, double refb, iauASTROM *astrom); int iauApio13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom); void iauAtci13(double rc, double dc, double pr, double pd, double px, double rv, double date1, double date2, double *ri, double *di, double *eo); void iauAtciq(double rc, double dc, double pr, double pd, double px, double rv, iauASTROM *astrom, double *ri, double *di); void iauAtciqn(double rc, double dc, double pr, double pd, double px, double rv, iauASTROM *astrom, int n, iauLDBODY b[], double *ri, double *di); void iauAtciqz(double rc, double dc, iauASTROM *astrom, double *ri, double *di); int iauAtco13(double rc, double dc, double pr, double pd, double px, double rv, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *aob, double *zob, double *hob, double *dob, double *rob, double *eo); void iauAtic13(double ri, double di, double date1, double date2, double *rc, double *dc, double *eo); void iauAticq(double ri, double di, iauASTROM *astrom, double *rc, double *dc); void iauAticqn(double ri, double di, iauASTROM *astrom, int n, iauLDBODY b[], double *rc, double *dc); int iauAtio13(double ri, double di, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *aob, double *zob, double *hob, double *dob, double *rob); void iauAtioq(double ri, double di, iauASTROM *astrom, double *aob, double *zob, double *hob, double *dob, double *rob); int iauAtoc13(const char *type, double ob1, double ob2, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *rc, double *dc); int iauAtoi13(const char *type, double ob1, double ob2, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *ri, double *di); void iauAtoiq(const char *type, double ob1, double ob2, iauASTROM *astrom, double *ri, double *di); void iauLd(double bm, double p[3], double q[3], double e[3], double em, double dlim, double p1[3]); void iauLdn(int n, iauLDBODY b[], double ob[3], double sc[3], double sn[3]); void iauLdsun(double p[3], double e[3], double em, double p1[3]); void iauPmpx(double rc, double dc, double pr, double pd, double px, double rv, double pmt, double pob[3], double pco[3]); int iauPmsafe(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2); void iauPvtob(double elong, double phi, double height, double xp, double yp, double sp, double theta, double pv[2][3]); void iauRefco(double phpa, double tc, double rh, double wl, double *refa, double *refb); /* Astronomy/Ephemerides */ int iauEpv00(double date1, double date2, double pvh[2][3], double pvb[2][3]); int iauPlan94(double date1, double date2, int np, double pv[2][3]); /* Astronomy/FundamentalArgs */ double iauFad03(double t); double iauFae03(double t); double iauFaf03(double t); double iauFaju03(double t); double iauFal03(double t); double iauFalp03(double t); double iauFama03(double t); double iauFame03(double t); double iauFane03(double t); double iauFaom03(double t); double iauFapa03(double t); double iauFasa03(double t); double iauFaur03(double t); double iauFave03(double t); /* Astronomy/PrecNutPolar */ void iauBi00(double *dpsibi, double *depsbi, double *dra); void iauBp00(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]); void iauBp06(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]); void iauBpn2xy(double rbpn[3][3], double *x, double *y); void iauC2i00a(double date1, double date2, double rc2i[3][3]); void iauC2i00b(double date1, double date2, double rc2i[3][3]); void iauC2i06a(double date1, double date2, double rc2i[3][3]); void iauC2ibpn(double date1, double date2, double rbpn[3][3], double rc2i[3][3]); void iauC2ixy(double date1, double date2, double x, double y, double rc2i[3][3]); void iauC2ixys(double x, double y, double s, double rc2i[3][3]); void iauC2t00a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]); void iauC2t00b(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]); void iauC2t06a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]); void iauC2tcio(double rc2i[3][3], double era, double rpom[3][3], double rc2t[3][3]); void iauC2teqx(double rbpn[3][3], double gst, double rpom[3][3], double rc2t[3][3]); void iauC2tpe(double tta, double ttb, double uta, double utb, double dpsi, double deps, double xp, double yp, double rc2t[3][3]); void iauC2txy(double tta, double ttb, double uta, double utb, double x, double y, double xp, double yp, double rc2t[3][3]); double iauEo06a(double date1, double date2); double iauEors(double rnpb[3][3], double s); void iauFw2m(double gamb, double phib, double psi, double eps, double r[3][3]); void iauFw2xy(double gamb, double phib, double psi, double eps, double *x, double *y); void iauLtp(double epj, double rp[3][3]); void iauLtpb(double epj, double rpb[3][3]); void iauLtpecl(double epj, double vec[3]); void iauLtpequ(double epj, double veq[3]); void iauNum00a(double date1, double date2, double rmatn[3][3]); void iauNum00b(double date1, double date2, double rmatn[3][3]); void iauNum06a(double date1, double date2, double rmatn[3][3]); void iauNumat(double epsa, double dpsi, double deps, double rmatn[3][3]); void iauNut00a(double date1, double date2, double *dpsi, double *deps); void iauNut00b(double date1, double date2, double *dpsi, double *deps); void iauNut06a(double date1, double date2, double *dpsi, double *deps); void iauNut80(double date1, double date2, double *dpsi, double *deps); void iauNutm80(double date1, double date2, double rmatn[3][3]); double iauObl06(double date1, double date2); double iauObl80(double date1, double date2); void iauP06e(double date1, double date2, double *eps0, double *psia, double *oma, double *bpa, double *bqa, double *pia, double *bpia, double *epsa, double *chia, double *za, double *zetaa, double *thetaa, double *pa, double *gam, double *phi, double *psi); void iauPb06(double date1, double date2, double *bzeta, double *bz, double *btheta); void iauPfw06(double date1, double date2, double *gamb, double *phib, double *psib, double *epsa); void iauPmat00(double date1, double date2, double rbp[3][3]); void iauPmat06(double date1, double date2, double rbp[3][3]); void iauPmat76(double date1, double date2, double rmatp[3][3]); void iauPn00(double date1, double date2, double dpsi, double deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]); void iauPn00a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]); void iauPn00b(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]); void iauPn06(double date1, double date2, double dpsi, double deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]); void iauPn06a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]); void iauPnm00a(double date1, double date2, double rbpn[3][3]); void iauPnm00b(double date1, double date2, double rbpn[3][3]); void iauPnm06a(double date1, double date2, double rnpb[3][3]); void iauPnm80(double date1, double date2, double rmatpn[3][3]); void iauPom00(double xp, double yp, double sp, double rpom[3][3]); void iauPr00(double date1, double date2, double *dpsipr, double *depspr); void iauPrec76(double date01, double date02, double date11, double date12, double *zeta, double *z, double *theta); double iauS00(double date1, double date2, double x, double y); double iauS00a(double date1, double date2); double iauS00b(double date1, double date2); double iauS06(double date1, double date2, double x, double y); double iauS06a(double date1, double date2); double iauSp00(double date1, double date2); void iauXy06(double date1, double date2, double *x, double *y); void iauXys00a(double date1, double date2, double *x, double *y, double *s); void iauXys00b(double date1, double date2, double *x, double *y, double *s); void iauXys06a(double date1, double date2, double *x, double *y, double *s); /* Astronomy/RotationAndTime */ double iauEe00(double date1, double date2, double epsa, double dpsi); double iauEe00a(double date1, double date2); double iauEe00b(double date1, double date2); double iauEe06a(double date1, double date2); double iauEect00(double date1, double date2); double iauEqeq94(double date1, double date2); double iauEra00(double dj1, double dj2); double iauGmst00(double uta, double utb, double tta, double ttb); double iauGmst06(double uta, double utb, double tta, double ttb); double iauGmst82(double dj1, double dj2); double iauGst00a(double uta, double utb, double tta, double ttb); double iauGst00b(double uta, double utb); double iauGst06(double uta, double utb, double tta, double ttb, double rnpb[3][3]); double iauGst06a(double uta, double utb, double tta, double ttb); double iauGst94(double uta, double utb); /* Astronomy/SpaceMotion */ int iauPvstar(double pv[2][3], double *ra, double *dec, double *pmr, double *pmd, double *px, double *rv); int iauStarpv(double ra, double dec, double pmr, double pmd, double px, double rv, double pv[2][3]); /* Astronomy/StarCatalogs */ void iauFk52h(double r5, double d5, double dr5, double dd5, double px5, double rv5, double *rh, double *dh, double *drh, double *ddh, double *pxh, double *rvh); void iauFk5hip(double r5h[3][3], double s5h[3]); void iauFk5hz(double r5, double d5, double date1, double date2, double *rh, double *dh); void iauH2fk5(double rh, double dh, double drh, double ddh, double pxh, double rvh, double *r5, double *d5, double *dr5, double *dd5, double *px5, double *rv5); void iauHfk5z(double rh, double dh, double date1, double date2, double *r5, double *d5, double *dr5, double *dd5); int iauStarpm(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2); /* Astronomy/EclipticCoordinates */ void iauEceq06(double date1, double date2, double dl, double db, double *dr, double *dd); void iauEcm06(double date1, double date2, double rm[3][3]); void iauEqec06(double date1, double date2, double dr, double dd, double *dl, double *db); void iauLteceq(double epj, double dl, double db, double *dr, double *dd); void iauLtecm(double epj, double rm[3][3]); void iauLteqec(double epj, double dr, double dd, double *dl, double *db); /* Astronomy/GalacticCoordinates */ void iauG2icrs(double dl, double db, double *dr, double *dd); void iauIcrs2g(double dr, double dd, double *dl, double *db); /* Astronomy/GeodeticGeocentric */ int iauEform(int n, double *a, double *f); int iauGc2gd(int n, double xyz[3], double *elong, double *phi, double *height); int iauGc2gde(double a, double f, double xyz[3], double *elong, double *phi, double *height); int iauGd2gc(int n, double elong, double phi, double height, double xyz[3]); int iauGd2gce(double a, double f, double elong, double phi, double height, double xyz[3]); /* Astronomy/Timescales */ int iauD2dtf(const char *scale, int ndp, double d1, double d2, int *iy, int *im, int *id, int ihmsf[4]); int iauDat(int iy, int im, int id, double fd, double *deltat); double iauDtdb(double date1, double date2, double ut, double elong, double u, double v); int iauDtf2d(const char *scale, int iy, int im, int id, int ihr, int imn, double sec, double *d1, double *d2); int iauTaitt(double tai1, double tai2, double *tt1, double *tt2); int iauTaiut1(double tai1, double tai2, double dta, double *ut11, double *ut12); int iauTaiutc(double tai1, double tai2, double *utc1, double *utc2); int iauTcbtdb(double tcb1, double tcb2, double *tdb1, double *tdb2); int iauTcgtt(double tcg1, double tcg2, double *tt1, double *tt2); int iauTdbtcb(double tdb1, double tdb2, double *tcb1, double *tcb2); int iauTdbtt(double tdb1, double tdb2, double dtr, double *tt1, double *tt2); int iauTttai(double tt1, double tt2, double *tai1, double *tai2); int iauTttcg(double tt1, double tt2, double *tcg1, double *tcg2); int iauTttdb(double tt1, double tt2, double dtr, double *tdb1, double *tdb2); int iauTtut1(double tt1, double tt2, double dt, double *ut11, double *ut12); int iauUt1tai(double ut11, double ut12, double dta, double *tai1, double *tai2); int iauUt1tt(double ut11, double ut12, double dt, double *tt1, double *tt2); int iauUt1utc(double ut11, double ut12, double dut1, double *utc1, double *utc2); int iauUtctai(double utc1, double utc2, double *tai1, double *tai2); int iauUtcut1(double utc1, double utc2, double dut1, double *ut11, double *ut12); /* VectorMatrix/AngleOps */ void iauA2af(int ndp, double angle, char *sign, int idmsf[4]); void iauA2tf(int ndp, double angle, char *sign, int ihmsf[4]); int iauAf2a(char s, int ideg, int iamin, double asec, double *rad); double iauAnp(double a); double iauAnpm(double a); void iauD2tf(int ndp, double days, char *sign, int ihmsf[4]); int iauTf2a(char s, int ihour, int imin, double sec, double *rad); int iauTf2d(char s, int ihour, int imin, double sec, double *days); /* VectorMatrix/BuildRotations */ void iauRx(double phi, double r[3][3]); void iauRy(double theta, double r[3][3]); void iauRz(double psi, double r[3][3]); /* VectorMatrix/CopyExtendExtract */ void iauCp(double p[3], double c[3]); void iauCpv(double pv[2][3], double c[2][3]); void iauCr(double r[3][3], double c[3][3]); void iauP2pv(double p[3], double pv[2][3]); void iauPv2p(double pv[2][3], double p[3]); /* VectorMatrix/Initialization */ void iauIr(double r[3][3]); void iauZp(double p[3]); void iauZpv(double pv[2][3]); void iauZr(double r[3][3]); /* VectorMatrix/MatrixOps */ void iauRxr(double a[3][3], double b[3][3], double atb[3][3]); void iauTr(double r[3][3], double rt[3][3]); /* VectorMatrix/MatrixVectorProducts */ void iauRxp(double r[3][3], double p[3], double rp[3]); void iauRxpv(double r[3][3], double pv[2][3], double rpv[2][3]); void iauTrxp(double r[3][3], double p[3], double trp[3]); void iauTrxpv(double r[3][3], double pv[2][3], double trpv[2][3]); /* VectorMatrix/RotationVectors */ void iauRm2v(double r[3][3], double w[3]); void iauRv2m(double w[3], double r[3][3]); /* VectorMatrix/SeparationAndAngle */ double iauPap(double a[3], double b[3]); double iauPas(double al, double ap, double bl, double bp); double iauSepp(double a[3], double b[3]); double iauSeps(double al, double ap, double bl, double bp); /* VectorMatrix/SphericalCartesian */ void iauC2s(double p[3], double *theta, double *phi); void iauP2s(double p[3], double *theta, double *phi, double *r); void iauPv2s(double pv[2][3], double *theta, double *phi, double *r, double *td, double *pd, double *rd); void iauS2c(double theta, double phi, double c[3]); void iauS2p(double theta, double phi, double r, double p[3]); void iauS2pv(double theta, double phi, double r, double td, double pd, double rd, double pv[2][3]); /* VectorMatrix/VectorOps */ double iauPdp(double a[3], double b[3]); double iauPm(double p[3]); void iauPmp(double a[3], double b[3], double amb[3]); void iauPn(double p[3], double *r, double u[3]); void iauPpp(double a[3], double b[3], double apb[3]); void iauPpsp(double a[3], double s, double b[3], double apsb[3]); void iauPvdpv(double a[2][3], double b[2][3], double adb[2]); void iauPvm(double pv[2][3], double *r, double *s); void iauPvmpv(double a[2][3], double b[2][3], double amb[2][3]); void iauPvppv(double a[2][3], double b[2][3], double apb[2][3]); void iauPvu(double dt, double pv[2][3], double upv[2][3]); void iauPvup(double dt, double pv[2][3], double p[3]); void iauPvxpv(double a[2][3], double b[2][3], double axb[2][3]); void iauPxp(double a[3], double b[3], double axb[3]); void iauS2xpv(double s1, double s2, double pv[2][3], double spv[2][3]); void iauSxp(double s, double p[3], double sp[3]); void iauSxpv(double s, double pv[2][3], double spv[2][3]); #ifdef __cplusplus } #endif #endif /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ sofa/20160503_c/c/src/sofam.h0000644000113000011300000002101013027221063014431 0ustar bellsbells#ifndef SOFAMHDEF #define SOFAMHDEF /* ** - - - - - - - - ** s o f a m . h ** - - - - - - - - ** ** Macros used by SOFA library. ** ** This file is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Please note that the constants defined below are to be used only in ** the context of the SOFA software, and have no other official IAU ** status. In addition, self consistency is not guaranteed. ** ** This revision: 2013 August 27 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ /* Star-independent astrometry parameters */ typedef struct { double pmt; /* PM time interval (SSB, Julian years) */ double eb[3]; /* SSB to observer (vector, au) */ double eh[3]; /* Sun to observer (unit vector) */ double em; /* distance from Sun to observer (au) */ double v[3]; /* barycentric observer velocity (vector, c) */ double bm1; /* sqrt(1-|v|^2): reciprocal of Lorenz factor */ double bpn[3][3]; /* bias-precession-nutation matrix */ double along; /* longitude + s' + dERA(DUT) (radians) */ double phi; /* geodetic latitude (radians) */ double xpl; /* polar motion xp wrt local meridian (radians) */ double ypl; /* polar motion yp wrt local meridian (radians) */ double sphi; /* sine of geodetic latitude */ double cphi; /* cosine of geodetic latitude */ double diurab; /* magnitude of diurnal aberration vector */ double eral; /* "local" Earth rotation angle (radians) */ double refa; /* refraction constant A (radians) */ double refb; /* refraction constant B (radians) */ } iauASTROM; /* (Vectors eb, eh, em and v are all with respect to BCRS axes.) */ /* Body parameters for light deflection */ typedef struct { double bm; /* mass of the body (solar masses) */ double dl; /* deflection limiter (radians^2/2) */ double pv[2][3]; /* barycentric PV of the body (au, au/day) */ } iauLDBODY; /* Pi */ #define DPI (3.141592653589793238462643) /* 2Pi */ #define D2PI (6.283185307179586476925287) /* Radians to degrees */ #define DR2D (57.29577951308232087679815) /* Degrees to radians */ #define DD2R (1.745329251994329576923691e-2) /* Radians to arcseconds */ #define DR2AS (206264.8062470963551564734) /* Arcseconds to radians */ #define DAS2R (4.848136811095359935899141e-6) /* Seconds of time to radians */ #define DS2R (7.272205216643039903848712e-5) /* Arcseconds in a full circle */ #define TURNAS (1296000.0) /* Milliarcseconds to radians */ #define DMAS2R (DAS2R / 1e3) /* Length of tropical year B1900 (days) */ #define DTY (365.242198781) /* Seconds per day. */ #define DAYSEC (86400.0) /* Days per Julian year */ #define DJY (365.25) /* Days per Julian century */ #define DJC (36525.0) /* Days per Julian millennium */ #define DJM (365250.0) /* Reference epoch (J2000.0), Julian Date */ #define DJ00 (2451545.0) /* Julian Date of Modified Julian Date zero */ #define DJM0 (2400000.5) /* Reference epoch (J2000.0), Modified Julian Date */ #define DJM00 (51544.5) /* 1977 Jan 1.0 as MJD */ #define DJM77 (43144.0) /* TT minus TAI (s) */ #define TTMTAI (32.184) /* Astronomical unit (m) */ #define DAU (149597870e3) /* Speed of light (m/s) */ #define CMPS 299792458.0 /* Light time for 1 au (s) */ #define AULT 499.004782 /* Speed of light (AU per day) */ #define DC (DAYSEC / AULT) /* L_G = 1 - d(TT)/d(TCG) */ #define ELG (6.969290134e-10) /* L_B = 1 - d(TDB)/d(TCB), and TDB (s) at TAI 1977/1/1.0 */ #define ELB (1.550519768e-8) #define TDB0 (-6.55e-5) /* Schwarzschild radius of the Sun (au) */ /* = 2 * 1.32712440041e20 / (2.99792458e8)^2 / 1.49597870700e11 */ #define SRS 1.97412574336e-8 /* dint(A) - truncate to nearest whole number towards zero (double) */ #define dint(A) ((A)<0.0?ceil(A):floor(A)) /* dnint(A) - round to nearest whole number (double) */ #define dnint(A) ((A)<0.0?ceil((A)-0.5):floor((A)+0.5)) /* dsign(A,B) - magnitude of A with sign of B (double) */ #define dsign(A,B) ((B)<0.0?-fabs(A):fabs(A)) /* max(A,B) - larger (most +ve) of two numbers (generic) */ #define gmax(A,B) (((A)>(B))?(A):(B)) /* min(A,B) - smaller (least +ve) of two numbers (generic) */ #define gmin(A,B) (((A)<(B))?(A):(B)) /* Reference ellipsoids */ #define WGS84 1 #define GRS80 2 #define WGS72 3 #endif /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ sofa/20160503_c/c/src/makefile0000644000113000011300000006357513027221063014701 0ustar bellsbells#----------------------------------------------------------------------- # # Description: make file for the ANSI-C version of SOFA. This # make file creates a Unix .a library. Designed for Linux/gcc but # can be adapted for other platforms or run in an appropriate way # by means of the macros CCOMPC (compiler command), CFLAGF (qualifiers # for compiling functions) and CFLAGX (qualifiers for compiling # executables). # # Usage: # # To build the library: # # make # # To install the library and include files: # # make install # # To delete all object files: # # make clean # # To build and run the test program using the installed library: # # make test # # Also: # make all same as make # make uninstall deinstall the library and header files # make check test the build # make installcheck same as make test # make distclean delete all generated binaries # make realclean same as distclean # # Last revision: 2016 March 9 # # Copyright International Astronomical Union. All rights reserved. # #----------------------------------------------------------------------- #----------------------------------------------------------------------- # # DEFINITIONS # #----------------------------------------------------------------------- #----YOU MAY HAVE TO MODIFY THE NEXT FEW DEFINITIONS----- # Specify the installation home directory. INSTALL_DIR = $(HOME) # Specify the installation directory for the library. SOFA_LIB_DIR = $(INSTALL_DIR)/lib/ # Specify the installation directory for the include files. SOFA_INC_DIR = $(INSTALL_DIR)/include/ # This software is compilable only by ANSI C compilers - give the name # of your preferred C compiler (CCOMPC) and compilation flags (CFLAGF # for functions, CFLAGX for executables) here. CCOMPC = gcc CFLAGF = -c -pedantic -Wall -W -O CFLAGX = -pedantic -Wall -W -O #----YOU SHOULDN'T HAVE TO MODIFY ANYTHING BELOW THIS LINE--------- SHELL = /bin/sh # The list of installation directories. INSTALL_DIRS = $(SOFA_LIB_DIR) $(SOFA_INC_DIR) # Name the SOFA/C library in its source and target locations. SOFA_LIB_NAME = libsofa_c.a SOFA_LIB = $(SOFA_LIB_DIR)$(SOFA_LIB_NAME) # Name the SOFA/C testbed in its source and target locations. SOFA_TEST_NAME = t_sofa_c.c SOFA_TEST = t_sofa_c # Name the SOFA/C includes in their source and target locations. SOFA_INC_NAMES = sofa.h sofam.h SOFA_INC = $(SOFA_INC_DIR)sofa.h $(SOFA_INC_DIR)sofam.h # The list of SOFA/C library object files. SOFA_OBS = iauA2af.o \ iauA2tf.o \ iauAb.o \ iauAf2a.o \ iauAnp.o \ iauAnpm.o \ iauApcg.o \ iauApcg13.o \ iauApci.o \ iauApci13.o \ iauApco.o \ iauApco13.o \ iauApcs.o \ iauApcs13.o \ iauAper.o \ iauAper13.o \ iauApio.o \ iauApio13.o \ iauAtci13.o \ iauAtciq.o \ iauAtciqn.o \ iauAtciqz.o \ iauAtco13.o \ iauAtic13.o \ iauAticq.o \ iauAticqn.o \ iauAtio13.o \ iauAtioq.o \ iauAtoc13.o \ iauAtoi13.o \ iauAtoiq.o \ iauBi00.o \ iauBp00.o \ iauBp06.o \ iauBpn2xy.o \ iauC2i00a.o \ iauC2i00b.o \ iauC2i06a.o \ iauC2ibpn.o \ iauC2ixy.o \ iauC2ixys.o \ iauC2s.o \ iauC2t00a.o \ iauC2t00b.o \ iauC2t06a.o \ iauC2tcio.o \ iauC2teqx.o \ iauC2tpe.o \ iauC2txy.o \ iauCal2jd.o \ iauCp.o \ iauCpv.o \ iauCr.o \ iauD2dtf.o \ iauD2tf.o \ iauDat.o \ iauDtdb.o \ iauDtf2d.o \ iauEceq06.o \ iauEcm06.o \ iauEqec06.o \ iauEe00.o \ iauEe00a.o \ iauEe00b.o \ iauEe06a.o \ iauEect00.o \ iauEform.o \ iauEo06a.o \ iauEors.o \ iauEpb.o \ iauEpb2jd.o \ iauEpj.o \ iauEpj2jd.o \ iauEpv00.o \ iauEqeq94.o \ iauEra00.o \ iauFad03.o \ iauFae03.o \ iauFaf03.o \ iauFaju03.o \ iauFal03.o \ iauFalp03.o \ iauFama03.o \ iauFame03.o \ iauFane03.o \ iauFaom03.o \ iauFapa03.o \ iauFasa03.o \ iauFaur03.o \ iauFave03.o \ iauFk52h.o \ iauFk5hip.o \ iauFk5hz.o \ iauFw2m.o \ iauFw2xy.o \ iauG2icrs.o \ iauGc2gd.o \ iauGc2gde.o \ iauGd2gc.o \ iauGd2gce.o \ iauGmst00.o \ iauGmst06.o \ iauGmst82.o \ iauGst00a.o \ iauGst00b.o \ iauGst06.o \ iauGst06a.o \ iauGst94.o \ iauH2fk5.o \ iauHfk5z.o \ iauIcrs2g.o \ iauIr.o \ iauJd2cal.o \ iauJdcalf.o \ iauLd.o \ iauLdn.o \ iauLdsun.o \ iauLteceq.o \ iauLtecm.o \ iauLteqec.o \ iauLtp.o \ iauLtpb.o \ iauLtpecl.o \ iauLtpequ.o \ iauNum00a.o \ iauNum00b.o \ iauNum06a.o \ iauNumat.o \ iauNut00a.o \ iauNut00b.o \ iauNut06a.o \ iauNut80.o \ iauNutm80.o \ iauObl06.o \ iauObl80.o \ iauP06e.o \ iauP2pv.o \ iauP2s.o \ iauPap.o \ iauPas.o \ iauPb06.o \ iauPdp.o \ iauPfw06.o \ iauPlan94.o \ iauPm.o \ iauPmat00.o \ iauPmat06.o \ iauPmat76.o \ iauPmp.o \ iauPmpx.o \ iauPmsafe.o \ iauPn.o \ iauPn00.o \ iauPn00a.o \ iauPn00b.o \ iauPn06.o \ iauPn06a.o \ iauPnm00a.o \ iauPnm00b.o \ iauPnm06a.o \ iauPnm80.o \ iauPom00.o \ iauPpp.o \ iauPpsp.o \ iauPr00.o \ iauPrec76.o \ iauPv2p.o \ iauPv2s.o \ iauPvdpv.o \ iauPvm.o \ iauPvmpv.o \ iauPvppv.o \ iauPvstar.o \ iauPvtob.o \ iauPvu.o \ iauPvup.o \ iauPvxpv.o \ iauPxp.o \ iauRefco.o \ iauRm2v.o \ iauRv2m.o \ iauRx.o \ iauRxp.o \ iauRxpv.o \ iauRxr.o \ iauRy.o \ iauRz.o \ iauS00.o \ iauS00a.o \ iauS00b.o \ iauS06.o \ iauS06a.o \ iauS2c.o \ iauS2p.o \ iauS2pv.o \ iauS2xpv.o \ iauSepp.o \ iauSeps.o \ iauSp00.o \ iauStarpm.o \ iauStarpv.o \ iauSxp.o \ iauSxpv.o \ iauTaitt.o \ iauTaiut1.o \ iauTaiutc.o \ iauTcbtdb.o \ iauTcgtt.o \ iauTdbtcb.o \ iauTdbtt.o \ iauTf2a.o \ iauTf2d.o \ iauTr.o \ iauTrxp.o \ iauTrxpv.o \ iauTttai.o \ iauTttcg.o \ iauTttdb.o \ iauTtut1.o \ iauUt1tai.o \ iauUt1tt.o \ iauUt1utc.o \ iauUtctai.o \ iauUtcut1.o \ iauXy06.o \ iauXys00a.o \ iauXys00b.o \ iauXys06a.o \ iauZp.o \ iauZpv.o \ iauZr.o #----------------------------------------------------------------------- # # TARGETS # #----------------------------------------------------------------------- # Build (but do not install) the library. all : $(SOFA_LIB_NAME) -@ echo "" -@ echo "*** Now type 'make test'" \ " to install the library and run tests ***" -@ echo "" # Install the library and header files. install $(SOFA_LIB) : $(INSTALL_DIRS) $(SOFA_LIB_NAME) $(SOFA_INC) cp $(SOFA_LIB_NAME) $(SOFA_LIB_DIR) # Deinstall the library and header files. uninstall: - $(RM) $(SOFA_LIB) $(SOFA_INC) # Test the build. check: $(SOFA_TEST_NAME) $(SOFA_INC_NAMES) $(SOFA_LIB_NAME) $(CCOMPC) $(CFLAGX) $(SOFA_TEST_NAME) $(SOFA_LIB_NAME) \ -lm -o $(SOFA_TEST) ./$(SOFA_TEST) # Test the installed library. installcheck test: $(SOFA_TEST_NAME) $(SOFA_INC) $(SOFA_LIB) $(CCOMPC) $(CFLAGX) $(SOFA_TEST_NAME) -I$(SOFA_INC_DIR) \ -L$(SOFA_LIB_DIR) -lsofa_c -lm -o $(SOFA_TEST) ./$(SOFA_TEST) # Delete object files. clean : - $(RM) $(SOFA_OBS) # Delete all generated binaries in the current directory. realclean distclean : clean - $(RM) $(SOFA_LIB_NAME) $(SOFA_TEST) # Create the installation directories if not already present. $(INSTALL_DIRS): mkdir -p $@ # Build the library. $(SOFA_LIB_NAME): $(SOFA_OBS) ar ru $(SOFA_LIB_NAME) $? # Install the header files. $(SOFA_INC) : $(INSTALL_DIRS) $(SOFA_INC_NAMES) cp $(SOFA_INC_NAMES) $(SOFA_INC_DIR) #----------------------------------------------------------------------- # The list of object file dependencies iauA2af.o : a2af.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ a2af.c iauA2tf.o : a2tf.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ a2tf.c iauAb.o : ab.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ab.c iauAf2a.o : af2a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ af2a.c iauAnp.o : anp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ anp.c iauAnpm.o : anpm.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ anpm.c iauApcg.o : apcg.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ apcg.c iauApcg13.o : apcg13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ apcg13.c iauApci.o : apci.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ apci.c iauApci13.o : apci13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ apci13.c iauApco.o : apco.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ apco.c iauApco13.o : apco13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ apco13.c iauApcs.o : apcs.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ apcs.c iauApcs13.o : apcs13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ apcs13.c iauAper.o : aper.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ aper.c iauAper13.o : aper13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ aper13.c iauApio.o : apio.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ apio.c iauApio13.o : apio13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ apio13.c iauAtci13.o : atci13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atci13.c iauAtciq.o : atciq.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atciq.c iauAtciqn.o : atciqn.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atciqn.c iauAtciqz.o : atciqz.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atciqz.c iauAtco13.o : atco13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atco13.c iauAtic13.o : atic13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atic13.c iauAticq.o : aticq.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ aticq.c iauAticqn.o : aticqn.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ aticqn.c iauAtio13.o : atio13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atio13.c iauAtioq.o : atioq.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atioq.c iauAtoc13.o : atoc13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atoc13.c iauAtoi13.o : atoi13.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atoi13.c iauAtoiq.o : atoiq.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ atoiq.c iauBi00.o : bi00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ bi00.c iauBp00.o : bp00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ bp00.c iauBp06.o : bp06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ bp06.c iauBpn2xy.o : bpn2xy.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ bpn2xy.c iauC2i00a.o : c2i00a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2i00a.c iauC2i00b.o : c2i00b.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2i00b.c iauC2i06a.o : c2i06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2i06a.c iauC2ibpn.o : c2ibpn.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2ibpn.c iauC2ixy.o : c2ixy.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2ixy.c iauC2ixys.o : c2ixys.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2ixys.c iauC2s.o : c2s.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2s.c iauC2t00a.o : c2t00a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2t00a.c iauC2t00b.o : c2t00b.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2t00b.c iauC2t06a.o : c2t06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2t06a.c iauC2tcio.o : c2tcio.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2tcio.c iauC2teqx.o : c2teqx.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2teqx.c iauC2tpe.o : c2tpe.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2tpe.c iauC2txy.o : c2txy.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ c2txy.c iauCal2jd.o : cal2jd.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ cal2jd.c iauCp.o : cp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ cp.c iauCpv.o : cpv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ cpv.c iauCr.o : cr.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ cr.c iauD2dtf.o : d2dtf.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ d2dtf.c iauD2tf.o : d2tf.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ d2tf.c iauDat.o : dat.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ dat.c iauDtdb.o : dtdb.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ dtdb.c iauDtf2d.o : dtf2d.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ dtf2d.c iauEceq06.o : eceq06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ eceq06.c iauEcm06.o : ecm06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ecm06.c iauEqec06.o : eqec06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ eqec06.c iauEe00.o : ee00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ee00.c iauEe00a.o : ee00a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ee00a.c iauEe00b.o : ee00b.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ee00b.c iauEe06a.o : ee06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ee06a.c iauEect00.o : eect00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ eect00.c iauEform.o : eform.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ eform.c iauEo06a.o : eo06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ eo06a.c iauEors.o : eors.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ eors.c iauEpb.o : epb.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ epb.c iauEpb2jd.o : epb2jd.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ epb2jd.c iauEpj.o : epj.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ epj.c iauEpj2jd.o : epj2jd.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ epj2jd.c iauEpv00.o : epv00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ epv00.c iauEqeq94.o : eqeq94.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ eqeq94.c iauEra00.o : era00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ era00.c iauFad03.o : fad03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fad03.c iauFae03.o : fae03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fae03.c iauFaf03.o : faf03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ faf03.c iauFaju03.o : faju03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ faju03.c iauFal03.o : fal03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fal03.c iauFalp03.o : falp03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ falp03.c iauFama03.o : fama03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fama03.c iauFame03.o : fame03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fame03.c iauFane03.o : fane03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fane03.c iauFaom03.o : faom03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ faom03.c iauFapa03.o : fapa03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fapa03.c iauFasa03.o : fasa03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fasa03.c iauFaur03.o : faur03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ faur03.c iauFave03.o : fave03.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fave03.c iauFk52h.o : fk52h.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fk52h.c iauFk5hip.o : fk5hip.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fk5hip.c iauFk5hz.o : fk5hz.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fk5hz.c iauFw2m.o : fw2m.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fw2m.c iauFw2xy.o : fw2xy.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ fw2xy.c iauG2icrs.o : g2icrs.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ g2icrs.c iauGc2gd.o : gc2gd.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gc2gd.c iauGc2gde.o : gc2gde.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gc2gde.c iauGd2gc.o : gd2gc.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gd2gc.c iauGd2gce.o : gd2gce.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gd2gce.c iauGmst00.o : gmst00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gmst00.c iauGmst06.o : gmst06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gmst06.c iauGmst82.o : gmst82.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gmst82.c iauGst00a.o : gst00a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gst00a.c iauGst00b.o : gst00b.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gst00b.c iauGst06.o : gst06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gst06.c iauGst06a.o : gst06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gst06a.c iauGst94.o : gst94.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ gst94.c iauH2fk5.o : h2fk5.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ h2fk5.c iauHfk5z.o : hfk5z.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ hfk5z.c iauIcrs2g.o : icrs2g.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ icrs2g.c iauIr.o : ir.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ir.c iauJd2cal.o : jd2cal.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ jd2cal.c iauJdcalf.o : jdcalf.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ jdcalf.c iauLd.o : ld.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ld.c iauLdn.o : ldn.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ldn.c iauLdsun.o : ldsun.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ldsun.c iauLteceq.o : lteceq.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ lteceq.c iauLtecm.o : ltecm.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ltecm.c iauLteqec.o : lteqec.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ lteqec.c iauLtp.o : ltp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ltp.c iauLtpb.o : ltpb.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ltpb.c iauLtpecl.o : ltpecl.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ltpecl.c iauLtpequ.o : ltpequ.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ltpequ.c iauNum00a.o : num00a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ num00a.c iauNum00b.o : num00b.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ num00b.c iauNum06a.o : num06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ num06a.c iauNumat.o : numat.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ numat.c iauNut00a.o : nut00a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ nut00a.c iauNut00b.o : nut00b.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ nut00b.c iauNut06a.o : nut06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ nut06a.c iauNut80.o : nut80.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ nut80.c iauNutm80.o : nutm80.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ nutm80.c iauObl06.o : obl06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ obl06.c iauObl80.o : obl80.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ obl80.c iauP06e.o : p06e.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ p06e.c iauP2pv.o : p2pv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ p2pv.c iauP2s.o : p2s.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ p2s.c iauPap.o : pap.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pap.c iauPas.o : pas.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pas.c iauPb06.o : pb06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pb06.c iauPdp.o : pdp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pdp.c iauPfw06.o : pfw06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pfw06.c iauPlan94.o : plan94.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ plan94.c iauPm.o : pm.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pm.c iauPmat00.o : pmat00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pmat00.c iauPmat06.o : pmat06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pmat06.c iauPmat76.o : pmat76.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pmat76.c iauPmp.o : pmp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pmp.c iauPmpx.o : pmpx.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pmpx.c iauPmsafe.o : pmsafe.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pmsafe.c iauPn.o : pn.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pn.c iauPn00.o : pn00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pn00.c iauPn00a.o : pn00a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pn00a.c iauPn00b.o : pn00b.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pn00b.c iauPn06.o : pn06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pn06.c iauPn06a.o : pn06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pn06a.c iauPnm00a.o : pnm00a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pnm00a.c iauPnm00b.o : pnm00b.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pnm00b.c iauPnm06a.o : pnm06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pnm06a.c iauPnm80.o : pnm80.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pnm80.c iauPom00.o : pom00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pom00.c iauPpp.o : ppp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ppp.c iauPpsp.o : ppsp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ppsp.c iauPr00.o : pr00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pr00.c iauPrec76.o : prec76.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ prec76.c iauPv2p.o : pv2p.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pv2p.c iauPv2s.o : pv2s.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pv2s.c iauPvdpv.o : pvdpv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pvdpv.c iauPvm.o : pvm.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pvm.c iauPvmpv.o : pvmpv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pvmpv.c iauPvppv.o : pvppv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pvppv.c iauPvstar.o : pvstar.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pvstar.c iauPvtob.o : pvtob.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pvtob.c iauPvu.o : pvu.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pvu.c iauPvup.o : pvup.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pvup.c iauPvxpv.o : pvxpv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pvxpv.c iauPxp.o : pxp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ pxp.c iauRefco.o : refco.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ refco.c iauRm2v.o : rm2v.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ rm2v.c iauRv2m.o : rv2m.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ rv2m.c iauRx.o : rx.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ rx.c iauRxp.o : rxp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ rxp.c iauRxpv.o : rxpv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ rxpv.c iauRxr.o : rxr.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ rxr.c iauRy.o : ry.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ry.c iauRz.o : rz.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ rz.c iauS00.o : s00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ s00.c iauS00a.o : s00a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ s00a.c iauS00b.o : s00b.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ s00b.c iauS06.o : s06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ s06.c iauS06a.o : s06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ s06a.c iauS2c.o : s2c.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ s2c.c iauS2p.o : s2p.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ s2p.c iauS2pv.o : s2pv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ s2pv.c iauS2xpv.o : s2xpv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ s2xpv.c iauSepp.o : sepp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ sepp.c iauSeps.o : seps.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ seps.c iauSp00.o : sp00.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ sp00.c iauStarpm.o : starpm.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ starpm.c iauStarpv.o : starpv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ starpv.c iauSxp.o : sxp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ sxp.c iauSxpv.o : sxpv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ sxpv.c iauTaitt.o : taitt.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ taitt.c iauTaiut1.o : taiut1.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ taiut1.c iauTaiutc.o : taiutc.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ taiutc.c iauTcbtdb.o : tcbtdb.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ tcbtdb.c iauTcgtt.o : tcgtt.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ tcgtt.c iauTdbtcb.o : tdbtcb.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ tdbtcb.c iauTdbtt.o : tdbtt.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ tdbtt.c iauTf2a.o : tf2a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ tf2a.c iauTf2d.o : tf2d.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ tf2d.c iauTr.o : tr.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ tr.c iauTrxp.o : trxp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ trxp.c iauTrxpv.o : trxpv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ trxpv.c iauTttai.o : tttai.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ tttai.c iauTttcg.o : tttcg.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ tttcg.c iauTttdb.o : tttdb.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ tttdb.c iauTtut1.o : ttut1.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ttut1.c iauUt1tai.o : ut1tai.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ut1tai.c iauUt1tt.o : ut1tt.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ut1tt.c iauUt1utc.o : ut1utc.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ ut1utc.c iauUtctai.o : utctai.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ utctai.c iauUtcut1.o : utcut1.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ utcut1.c iauXy06.o : xy06.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ xy06.c iauXys00a.o : xys00a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ xys00a.c iauXys00b.o : xys00b.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ xys00b.c iauXys06a.o : xys06a.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ xys06a.c iauZp.o : zp.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ zp.c iauZpv.o : zpv.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ zpv.c iauZr.o : zr.c sofa.h sofam.h $(CCOMPC) $(CFLAGF) -o $@ zr.c #----------------------------------------------------------------------- sofa/20160503_c/c/doc/0000775000113000011300000000000013027221066013144 5ustar bellsbellssofa/20160503_c/c/doc/board.pdf0000644000113000011300000000340213027221063014720 0ustar bellsbells%PDF-1.2 %쏢 5 0 obj <> stream xTR@}Wjd(ۆX-_А1L_ޟ*5)*)tsU.QTav'P>ڡ}ւ+Qk.4+jK>JFpWZ.E@4|p /F+޲lL%Kff˭Dl.ѯ<4ynVe␖KC[>0(Jo8H-%?ʄ/Ԃs9~gDZtAnƑ3\})Z˄;B%3v@cY`K߫{_p?=Ro# \>˙L!$I<5c$$C<8`1Q}_fUr>?|b ג5vLRܘux kS;j#} U^^:~P%E!a ]|!*, Ltykw7n0^/t~endstream endobj 6 0 obj 729 endobj 4 0 obj <> /Contents 5 0 R >> endobj 3 0 obj << /Type /Pages /Kids [ 4 0 R ] /Count 1 >> endobj 1 0 obj <> endobj 8 0 obj <> endobj 7 0 obj <> endobj 9 0 obj <> endobj 2 0 obj <>endobj xref 0 10 0000000000 65535 f 0000001033 00000 n 0000001258 00000 n 0000000974 00000 n 0000000833 00000 n 0000000015 00000 n 0000000814 00000 n 0000001110 00000 n 0000001081 00000 n 0000001187 00000 n trailer << /Size 10 /Root 1 0 R /Info 2 0 R /ID [<6A8F2812EBF2B362D073CEDF85029968><6A8F2812EBF2B362D073CEDF85029968>] >> startxref 1441 %%EOF sofa/20160503_c/c/doc/board.lis0000644000113000011300000000246713027221063014750 0ustar bellsbellsboard.lis 2015 December 6 IAU STANDARDS OF FUNDAMENTAL ASTRONOMY BOARD Current Membership John Bangert - United States Naval Observatory, retired Steven Bell - Her Majesty's Nautical Almanac Office Nicole Capitaine - Paris Observatory William Folkner - Jet Propulsion Laboratory Mickal Gastineau - Paris Observatory, IMCCE Catherine Hohenkerk - Her Majesty's Nautical Almanac Office (Chair) Li Jinling - Shanghai Astronomical Observatory Brian Luzum - United States Naval Observatory (IERS) Zinovy Malkin - Pulkovo Observatory, St Petersburg Jeffrey Percival - University of Wisconsin Wendy Puatua - United States Naval Observatory Scott Ransom - National Radio Astronomy Observatory Patrick Wallace - RAL Space, retired Past Members Wim Brouw University of Groningen Mark Calabretta Australia Telescope National Facility Anne-Marie Gontier Paris Observatory George Hobbs Australia Telescope National Facility George Kaplan United States Naval Observatory Dennis McCarthy United States Naval Observatory Skip Newhall Jet Propulsion Laboratory Jin Wen-Jing Shanghai Observatory The e-mail for the Board chair is Catherine.Hohenkerk@ukho.gov.uk sofa/20160503_c/c/doc/changes.lis0000644000113000011300000003337313027221063015271 0ustar bellsbells Updates for SOFA Release 12 : 2016 May -------------------------------------- Changes/updates fall into the following categories: 1. The addition of four routines to the Precession/Nutation/Polar Motion section, which deliver long-term (+/-200,000 years) precession using the model of Vondrak, Capitaine and Wallace (2011, 2012). 2. Introduction of a new section entitled Ecliptic Coordinates. This section consists of six routines dealing with the transformation between equatorial and ecliptic coordinates using either the IAU 2006 precession model or the long-term precession model of Vondrak et al. 3. Separate Earth Attitude Cookbooks for Fortran and C users, replacing the existing Fortran-only edition. 4. Some documentation corrections. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + FORTRAN Routines ---------------- New routines that implement a long-term precession model: iau_LTP Precession matrix, J2000.0 to date using the Vondrak et al. long-term model. iau_LTPB Precession+bias matrix, J2000.0 to date using the Vondrak et al. long-term model. iau_LTPECL Precession (Vondrak et al. long-term) of the ecliptic. A unit vector representing the direction of the ecliptic pole with respect to the J2000.0 mean equator and equinox. iau_LTPEQU Precession (Vondrak et al. long-term) of the equator. A unit vector representing the direction of the pole of the equator with respect to the J2000.0 mean equator and equinox. Routines comprising a new section on ecliptic coordinates: iau_ECEQ06 Ecliptic coords to equatorial: transformation of longitude and latitude (mean equinox and ecliptic of date) to mean J2000.0 right ascension and declination, using IAU 2006 precession. iau_ECM06 ICRS (equatorial) to ecliptic rotation matrix using IAU 2006 precession. iau_EQEC06 Equatorial to ecliptic coords: transformation of ICRS right ascension and declination to ecliptic longitude and latitude (mean equinox and ecliptic of date) using IAU 2006 precession. iau_LTECEQ Ecliptic coords to equatorial: transformation of ecliptic longitude and latitude (mean equinox and ecliptic of date) to mean J2000.0 right ascension and declination, using the Vondrak et al. long-term precession. iau_LTECM ICRS (equatorial) to ecliptic rotation matrix using the Vondrak et al. long-term precession. iau_LTEQEC Equatorial to ecliptic coords: transformation of ICRS right ascension and declination to ecliptic longitude and latitude (mean equinox and ecliptic of date) using the Vondrak et al. long-term precession. Updated: t_sofa_f.for Test program, incorporating the ten new routines. Revisions: iau_ATCO13 List of called routines corrected. iau_ATIO13 List of called routines corrected. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ANSI C Routines --------------- New functions that implement a long-term precession model: iauLtp Precession matrix, J2000.0 to date using the Vondrak et al. long-term model. A new routine. iauLtpb Precession+bias matrix, J2000.0 to date using the Vondrak et al. long-term model. A new routine. iauLtpecl Precession (Vondrak et al. long-term) of the ecliptic. A unit vector representing the direction of the ecliptic pole with respect to the J2000.0 mean equator and equinox. A new routine. iauLtpequ Precession (Vondrak et al. long-term) of the equator. A unit vector representing the direction of the pole of the equator with respect to the J2000.0 mean equator and equinox. A new routine. Functions comprising a new section on ecliptic coordinates: iauEceq06 Ecliptic coords to equatorial: transformation of longitude and latitude (mean equinox and ecliptic of date) to mean J2000.0 right ascension and declination, using IAU 2006 precession. iauEcm06 ICRS (equatorial) to ecliptic rotation matrix using IAU 2006 precession. iauEqec06 Equatorial to ecliptic coords: transformation of ICRS right ascension and declination to ecliptic longitude and latitude (mean equinox and ecliptic of date) using IAU 2006 precession. iauLteceq Ecliptic coords to equatorial: transformation of ecliptic longitude and latitude (mean equinox and ecliptic of date) to mean J2000.0 right ascension and declination, using the Vondrak et al. long-term precession. iauLtecm ICRS (equatorial) to ecliptic rotation matrix using the Vondrak et al. long-term precession. iauLteqec Equatorial to ecliptic coords: transformation of ICRS right ascension and declination to ecliptic longitude and latitude (mean equinox and ecliptic of date) using the Vondrak et al. long-term precession. Updated: sofa.h Addition of prototypes for the ten new functions listed above. t_sofa_c Updated test program incorporating the ten new routines, plus a handful of constants extended to more decimal places. Revisions: iauAtco13 List of called functions corrected. iauAtio13 List of called functions corrected. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Documentation: board.lis Inclusion of the new board members. title.lis Release number and date updated. intro.lis Updated to reflect the updates and additions of this 12th release. sofa_lib.lis New routines added. sofa_pn_f.pdf SOFA Earth Attitude Cookbook for those using Fortran. The former Fortran-only version was called sofa_pn.pdf. A few typographic corrections have been made. sofa_pn_c.pdf SOFA Earth Attitude Cookbook for those using ANSI C. Like the former Fortran-only version but with function names and argument lists appropriate for the C case. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + End of Updates 2016 April 8 CYH/SAB + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Updates for SOFA Release 12a : 2016 July - - - - - - - - - - - - - - - - - - - - - Summary of Changes ------------------ Changes/updates for this minor release (12a) fall into the following categories: 1. A leap second at the end of December 2016, requires updates to the iau_DAT (dat.for) and iauDat (Dat.c) routines. The test-bed programs t_sofa_f.for and t_sofa_c.c are also updated to test this change. 2. The routines iau_LDSUN and iauLdsun, that calculate the deflection of starlight by the Sun, have changed, though without affecting the results for normal use. As a defensive measure, an internal threshold value tapers off the returned value for cases close to the center of the solar disk so that it becomes zero rather than infinity at the center. By making the formerly fixed threshold value depend on observer location, it has been possible to make the onset of the defensive measure less abrupt, which has greatly improved round-trip closure even for impossible (i.e. occulted) cases. For a terrestrial observer, the new threshold corresponds to a distance of about 5 arcminutes (formerly 9 arcseconds) from the center of the disk. 3. Documentation updates and corrections. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + FORTRAN Routines ---------------- iau_DAT a leap second is now required in UTC for 2016 December 31. iau_LDSUN internal threshold value changed from 1D-9 to DLIM, where DLIM = 1D-6 / MAX(EM*EM,1D0) and EM is the distance in au from the Sun to the observer. t_sofa_f this test program has been modified to test the updated leap second routine. Documentation ------------- sofa_ast_f Astrometry cookbook has been modified to take account of the updated LDSUN routine. sofa_ts_f Version number of this cookbook corrected. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ANSI C: ------- iauDat a leap second is now required in UTC for 2016 December 31. iauLdsun internal threshold value changed from 1e-9 to dlim, where dlim = 1e-6 / (em*em > 1.0 ? em*em : 1.0) and em is the distance in au from the Sun to the observer. Cr In the list of "Returned:" arguments listed in the documentation the one argument was listed as "char[]" rather than just "c". t_sofa_c this test program has been modified to test the updated leap second routine. Documentation ------------- sofa_ast_c Astrometry cookbook has been modified to take account of the updated Ldsun routine. sofa_ts_c Version number of this cookbook corrected. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + End of Updates 2016 July 18 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Updates for SOFA Release 12b : 2016 Dec 21 - - - - - - - - - - - - - - - - - - - - - Summary of Changes ------------------ Changes/updates for this minor release (12b) fall into the following categories: 1. iauJd2cal and iauJdcalf, coding change to removing inconsistent results on certain processors and compilers. 2. iauStarpv coding change to deliver better precision. 3. iau_REFCO, coding change (Fortran only). This only affects cases when the input temperature is "outlandish", i.e. outside the range of -15 to +200 degrees Celsius. 4. Documentation - minor update. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + FORTRAN Routines ---------------- iau_STARPV An expression (sqrt(1-x)-1), where x is usually tiny, has been replaced with (-x/(sqrt(1-x)+1) to improve numerical precision. iau_REFCO The line that forms the temperature (TK) in degrees Kelvin uses the the input temperature (TC), rather than T, the TC restricted to the "safe" range of -15 degrees Celsius to +200 degrees Celsius. Documentation ------------- sofa_ts_f Julian epoch 2000 has changed to Julian epoch 2000.0. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ANSI C: ------- iauJd2cal Change in coding (see below); iauJdcalf Change in coding; The current C versions of the JD2CAL and JDCALF routines can, under certain special circumstances, produce incorrect results. The coding of the new versions has been changed to remove this possibility. The Fortran versions do not have the problem. The misbehavior has been detected only under the following circumstances: * on Intel and AMD processors; * when compiled with the GNU C compiler (gcc); * on any operating system that produces a 32-bit executable file; * with certain combinations of compiler flags, such as "-fno-caller-saves -m32"; and * Julian dates split (dj1+dj2) such that dj2 is in the range 0.1 to 0.5. Calling iauJd2cal or iauJdcalf in these circumstances sometimes returns a result one day too small. As an example, take 2014 September 24 at 19:12:00, which is Julian date 2456925.3 (exactly). If we elect to split the JD as follows: dj1 = 2456925.0, dj2 = 0.3, then the old iauJd2cal returns 2014 9 23 0.8, which is incorrect, while the new iauJd2cal returns the correct 2014 9 24 0.8. iauStarpv An expression (sqrt(1-x)-1), where x is usually tiny, has been replaced with (-x/(sqrt(1-x)+1) to improve numerical precision. Documentation ------------- sofa_ts_c Julian epoch 2000 has changed to Julian epoch 2000.0. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + End of Updates 2016 Dec 21 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Updates for SOFA Release 12c : 2016 Dec 23 - - - - - - - - - - - - - - - - - - - - - Summary of Changes ------------------ Changes/updates for this minor release (12c) fall into the category of changes to the test-bed routines only. Minor release 12c differs from 12b only in terms of the Fortran and ANSI C test-bed routines. 1. The test-bed programs t_sofa_f.for and t_sofa_c.c have been updated to reflect changes introduced in the minor release 12b described above. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + FORTRAN Routines ---------------- t_sofa_f this test program has been modified to reflect the changes introduced in minor release 12b described above. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ANSI C: ------- t_sofa_c this test program has been modified to reflect the changes introduced in minor release 12b described above. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + End of Updates 2016 Dec 23 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + sofa/20160503_c/c/doc/consts.lis0000644000113000011300000000247313027221063015167 0ustar bellsbellsconsts.lis 2008 September 30 SOFA Fortran constants ---------------------- These must be used exactly as presented below. * Pi DOUBLE PRECISION DPI PARAMETER ( DPI = 3.141592653589793238462643D0 ) * 2Pi DOUBLE PRECISION D2PI PARAMETER ( D2PI = 6.283185307179586476925287D0 ) * Radians to hours DOUBLE PRECISION DR2H PARAMETER ( DR2H = 3.819718634205488058453210D0 ) * Radians to seconds DOUBLE PRECISION DR2S PARAMETER ( DR2S = 13750.98708313975701043156D0 ) * Radians to degrees DOUBLE PRECISION DR2D PARAMETER ( DR2D = 57.29577951308232087679815D0 ) * Radians to arc seconds DOUBLE PRECISION DR2AS PARAMETER ( DR2AS = 206264.8062470963551564734D0 ) * Hours to radians DOUBLE PRECISION DH2R PARAMETER ( DH2R = 0.2617993877991494365385536D0 ) * Seconds to radians DOUBLE PRECISION DS2R PARAMETER ( DS2R = 7.272205216643039903848712D-5 ) * Degrees to radians DOUBLE PRECISION DD2R PARAMETER ( DD2R = 1.745329251994329576923691D-2 ) * Arc seconds to radians DOUBLE PRECISION DAS2R PARAMETER ( DAS2R = 4.848136811095359935899141D-6 ) SOFA C constants ---------------- The constants used by the C version of SOFA are defined in the header file sofam.h. sofa/20160503_c/c/doc/contents.lis0000644000113000011300000000077413027221063015515 0ustar bellsbellscontents.lis 2008 October 8 -------- CONTENTS -------- 1) Introduction 2) The SOFA Astronomy Library 3) The SOFA Vector/Matrix Library 4) The individual routines A1 The SOFA copyright notice A2 Constants A3 SOFA Board membership sofa/20160503_c/c/doc/copyr.lis0000644000113000011300000001050713027221063015007 0ustar bellsbellscopyr.lis 2015 January 5 COPYRIGHT NOTICE Text equivalent to the following appears at the end of every SOFA routine. (There are small formatting differences between the Fortran and C versions.) *+---------------------------------------------------------------------- * * Copyright (C) 2016 * Standards Of Fundamental Astronomy Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND * CONDITIONS WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Board ("SOFA"). * * 2. Permission is granted to anyone to use the SOFA software for any * purpose, including commercial applications, free of charge and * without payment of royalties, subject to the conditions and * restrictions listed below. * * 3. You (the user) may copy and distribute SOFA source code to others, * and use and adapt its code and algorithms in your own software, * on a world-wide, royalty-free basis. That portion of your * distribution that does not consist of intact and unchanged copies * of SOFA source code files is a "derived work" that must comply * with the following requirements: * * a) Your work shall be marked or carry a statement that it * (i) uses routines and computations derived by you from * software provided by SOFA under license to you; and * (ii) does not itself constitute software provided by and/or * endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon, contains and/or differs * from the original SOFA software. * * c) The names of all routines in your derived work shall not * include the prefix "iau" or "sofa" or trivial modifications * thereof such as changes of case. * * d) The origin of the SOFA components of your derived work must * not be misrepresented; you must not claim that you wrote the * original software, nor file a patent application for SOFA * software or algorithms embedded in the SOFA software. * * e) These requirements must be reproduced intact in any source * distribution and shall apply to anyone to whom you have * granted a further right to modify the source code of your * derived work. * * Note that, as originally distributed, the SOFA software is * intended to be a definitive implementation of the IAU standards, * and consequently third-party modifications are discouraged. All * variations, no matter how minor, must be explicitly marked as * such, as explained above. * * 4. You shall not cause the SOFA software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or * by inappropriate modification. * * 5. The SOFA software is provided "as is" and SOFA makes no warranty * as to its use or performance. SOFA does not and cannot warrant * the performance or results which the user may obtain by using the * SOFA software. SOFA makes no warranties, express or implied, as * to non-infringement of third party rights, merchantability, or * fitness for any particular purpose. In no event will SOFA be * liable to the user for any consequential, incidental, or special * damages, including any lost profits or lost savings, even if a * SOFA representative has been advised of such damages, or for any * claim by any third party. * * 6. The provision of any version of the SOFA software under the terms * and conditions specified herein does not imply that future * versions will also be made available under the same terms and * conditions. * * In any published work or commercial product which uses the SOFA * software directly, acknowledgement (see www.iausofa.org) is * appreciated. * * Correspondence concerning SOFA software should be addressed as * follows: * * By email: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- sofa/20160503_c/c/doc/intro.lis0000644000113000011300000002261313027221063015007 0ustar bellsbellsintro.lis 2016 March 14 ------------------------------- THE IAU-SOFA SOFTWARE LIBRARIES ------------------------------- SOFA stands for "Standards Of Fundamental Astronomy". The SOFA software libraries are a collection of subprograms, in source- code form, which implement official IAU algorithms for fundamental- astronomy computations. The subprograms at present comprise 176 "astronomy" routines supported by 55 "vector/matrix" routines, available in both Fortran77 and C implementations. THE SOFA INITIATIVE SOFA is an IAU Service which operates as a Standing Working Group under Division A (Fundamental Astronomy). The IAU set up the SOFA initiative at the 1994 General Assembly, to promulgate an authoritative set of fundamental-astronomy constants and algorithms. At the subsequent General Assembly, in 1997, the appointment of a review board and the selection of a site for the SOFA Center (the outlet for SOFA products) were announced. The SOFA initiative was originally proposed by the IAU Working Group on Astronomical Standards (WGAS), under the chairmanship of Toshio Fukushima. The proposal was for "...new arrangements to establish and maintain an accessible and authoritative set of constants, algorithms and procedures that implement standard models used in fundamental astronomy". The SOFA Software Libraries implement the "algorithms" part of the SOFA initiative. They were developed under the supervision of an international panel called the SOFA Board. The current membership of this panel is listed in an appendix. A feature of the original SOFA software proposals was that the products would be self-contained and not depend on other software. This includes basic documentation, which, like the present file, will mostly be plain ASCII text. It should also be noted that there is no assumption that the software will be used on a particular computer and Operating System. Although OS-related facilities may be present (Unix make files for instance, use by the SOFA Center of automatic code management systems, HTML versions of some documentation), the routines themselves will be visible as individual text files and will run on a variety of platforms. ALGORITHMS The SOFA Board's initial goal has been to create a set of callable subprograms. Whether "subroutines" or "functions", they are all referred to simply as "routines". They are designed for use by software developers wishing to write complete applications; no runnable, free- standing applications are included in SOFA's present plans. The algorithms are drawn from a variety of sources. Because most of the routines so far developed have either been standard "text-book" operations or implement well-documented standard algorithms, it has not been necessary to invite the whole community to submit algorithms, though consultation with authorities has occurred where necessary. It should also be noted that consistency with the conventions published by the International Earth Rotation Service was a stipulation in the original SOFA proposals, further constraining the software designs. This state of affairs will continue to exist for some time, as there is a large backlog of agreed extensions to work on. However, in the future the Board may decide to call for proposals, and is in the meantime willing to look into any suggestions that are received by the SOFA Center. SCOPE The routines currently available are listed in the next two chapters of this document. The "astronomy" library comprises 176 routines (plus one obsolete Fortran routine that now appears under a revised name). The areas addressed include calendars, astrometry, time scales, Earth rotation, ephemerides, precession-nutation, star catalog transformations, and geodetic/geocentric transformations. The "vector-matrix" library, comprising 55 routines, contains a collection of simple tools for manipulating the vectors, matrices and angles used by the astronomy routines. There is no explicit commitment by SOFA to support historical models, though as time goes on a legacy of superseded models will naturally accumulate. There is, for example, no support of B1950/FK4 star coordinates, or pre-1976 precession models, though these capabilities could be added were there significant demand. Though the SOFA software libraries are rather limited in scope, and are likely to remain so for a considerable time, they do offer distinct advantages to prospective users. In particular, the routines are: * authoritative: they are IAU-backed and have been constructed with great care; * practical: they are straightforward to use in spite of being precise and rigorous (to some stated degree); * accessible and supported: they are downloadable from an easy-to- find place, they are in an integrated and consistent form, they come with adequate internal documentation, and help for users is available. VERSIONS Once it has been published, an issue is never revised or updated, and remains accessible indefinitely. Subsequent issues may, however, include corrected versions under the original routine name and filenames. However, where a different model is introduced, it will have a different name. The issues will be referred to by the date when they were announced. The frequency of re-issue will be decided by the Board, taking into account the importance of the changes and the impact on the user community. DOCUMENTATION At present there is little free-standing documentation about individual routines. However, each routine has preamble comments which specify in detail what the routine does and how it is used. The files sofa_pn_f.pdf and sofa_pn_c.pdf (for Fortran and C users respectively) describe the SOFA tools for precession-nutation and other aspects of Earth attitude, and include example code and, in an appendix, diagrams showing the interrelationships between the routines supporting the latest (IAU 2006/2000A) models. Two other pairs of documents introduce time scale transformations (sofa_ts_f.pdf and sofa_ts_c.pdf ) and astrometric transformations (sofa_ast_f.pdf and sofa_ast_c.pdf). PROGRAMMING LANGUAGES AND STANDARDS The SOFA routines are available in two programming languages at present: Fortran77 and ANSI C. Related software in other languages is under consideration. The Fortran code conforms to ANSI X3.9-1978 in all but two minor respects: each has an IMPLICIT NONE declaration, and its name has a prefix of "iau_" and may be longer than 6 characters. A global edit to erase both of these will produce ANSI-compliant code with no change in its function. Coding style, and restrictions on the range of language features, have been much debated by the Board, and the results comply with the majority view. There is (at present) no document that defines the standards, but the code itself offers a wide range of examples of what is acceptable. The Fortran routines contain explicit numerical constants (the INCLUDE statement is not part of ANSI Fortran77). These are drawn from the file consts.lis, which is listed in an appendix. Constants for the SOFA/C functions are defined in a header file sofam.h. The naming convention is such that a SOFA routine referred to generically as "EXAMPL" exists as a Fortran subprogram iau_EXAMPL and a C function iauExampl. The calls for the two versions are very similar, with the same arguments in the same order. In a few cases, the C equivalent of a Fortran SUBROUTINE subprogram uses a return value rather than an argument. Each language version includes a "testbed" main-program that can be used to verify that the SOFA routines have been correctly compiled on the end user's system. The Fortran and C versions are called t_sofa_f.for and t_sofa_c.c respectively. The testbeds execute every SOFA routine and check that the results are within expected accuracy margins. It is not possible to guarantee that all platforms will meet the rather stringent criteria that have been used, and an occasional warning message may be encountered on some systems. COPYRIGHT ISSUES Copyright for all of the SOFA software and documentation is owned by the IAU SOFA Board. The Software is made available free of charge for all classes of user, including commercial. However, there are strict rules designed to avoid unauthorized variants coming into circulation. It is permissible to distribute derived works and other modifications, but they must be clearly marked to avoid confusion with the SOFA originals. Further details are included in the block of comments which concludes every routine. The text is also set out in an appendix to the present document. ACCURACY The SOFA policy is to organize the calculations so that the machine accuracy is fully exploited. The gap between the precision of the underlying model or theory and the computational resolution has to be kept as large as possible, hopefully leaving several orders of magnitude of headroom. The SOFA routines in some cases involve design compromises between rigor and ease of use (and also speed, though nowadays this is seldom a major concern). ACKNOWLEDGEMENTS The Board is indebted to a number of contributors, who are acknowledged in the preamble comments of the routines concerned. The Board's effort is provided by the members' individual institutes. Resources for operating the SOFA Center are provided by Her Majesty's Nautical Almanac Office, operated by the United Kingdom Hydrographic Office. sofa/20160503_c/c/doc/manual.lis0000644000113000011300000234116213027221063015136 0ustar bellsbells T H E SSSSS OOOOOO FFFFFFFFFFFFF AAAAAAA SSSSSSSSSS OOOOOOOOOOOO FFFFFFFFFFFF AAAAAAAA SSSSSSSSSSS OOOOOOOOOOOOOO FFFFFFFFFFFF AAAA AAAA SSSS S OOOOOO OOOOO FFFF AAAA AAAA SSSSS OOOOO OOOO FFFFF AAAA AAAA SSSSSSSSSS OOOO OOOOO FFFFFFFFFFFF AAAA AAAA SSSSSSSSS OOOOO OOOO FFFFFFFFFFFF AAAAAAAAAAAAA SSSSS OOOO OOOO FFFF AAAAAAAAAAAAAA S SSSS OOOOO OOOOO FFFF AAAAAAAAAAAAAAA SSSSSSSSSSS OOOOOOOOOOOOO FFFF AAAA AAAAA SSSSSSSSS OOOOOOOOOO FFFF AAAA AAAAA SSSS OOOOO FFFF AAAA AAAAA S O F T W A R E L I B R A R I E S International Astronomical Union Division A: Fundamental Astronomy Standards Of Fundamental Astronomy Board Release 12 2016 April 1 contents.lis 2008 October 8 -------- CONTENTS -------- 1) Introduction 2) The SOFA Astronomy Library 3) The SOFA Vector/Matrix Library 4) The individual routines A1 The SOFA copyright notice A2 Constants A3 SOFA Board membership intro.lis 2016 March 14 ------------------------------- THE IAU-SOFA SOFTWARE LIBRARIES ------------------------------- SOFA stands for "Standards Of Fundamental Astronomy". The SOFA software libraries are a collection of subprograms, in source- code form, which implement official IAU algorithms for fundamental- astronomy computations. The subprograms at present comprise 176 "astronomy" routines supported by 55 "vector/matrix" routines, available in both Fortran77 and C implementations. THE SOFA INITIATIVE SOFA is an IAU Service which operates as a Standing Working Group under Division A (Fundamental Astronomy). The IAU set up the SOFA initiative at the 1994 General Assembly, to promulgate an authoritative set of fundamental-astronomy constants and algorithms. At the subsequent General Assembly, in 1997, the appointment of a review board and the selection of a site for the SOFA Center (the outlet for SOFA products) were announced. The SOFA initiative was originally proposed by the IAU Working Group on Astronomical Standards (WGAS), under the chairmanship of Toshio Fukushima. The proposal was for "...new arrangements to establish and maintain an accessible and authoritative set of constants, algorithms and procedures that implement standard models used in fundamental astronomy". The SOFA Software Libraries implement the "algorithms" part of the SOFA initiative. They were developed under the supervision of an international panel called the SOFA Board. The current membership of this panel is listed in an appendix. A feature of the original SOFA software proposals was that the products would be self-contained and not depend on other software. This includes basic documentation, which, like the present file, will mostly be plain ASCII text. It should also be noted that there is no assumption that the software will be used on a particular computer and Operating System. Although OS-related facilities may be present (Unix make files for instance, use by the SOFA Center of automatic code management systems, HTML versions of some documentation), the routines themselves will be visible as individual text files and will run on a variety of platforms. ALGORITHMS The SOFA Board's initial goal has been to create a set of callable subprograms. Whether "subroutines" or "functions", they are all referred to simply as "routines". They are designed for use by software developers wishing to write complete applications; no runnable, free- standing applications are included in SOFA's present plans. The algorithms are drawn from a variety of sources. Because most of the routines so far developed have either been standard "text-book" operations or implement well-documented standard algorithms, it has not been necessary to invite the whole community to submit algorithms, though consultation with authorities has occurred where necessary. It should also be noted that consistency with the conventions published by the International Earth Rotation Service was a stipulation in the original SOFA proposals, further constraining the software designs. This state of affairs will continue to exist for some time, as there is a large backlog of agreed extensions to work on. However, in the future the Board may decide to call for proposals, and is in the meantime willing to look into any suggestions that are received by the SOFA Center. SCOPE The routines currently available are listed in the next two chapters of this document. The "astronomy" library comprises 176 routines (plus one obsolete Fortran routine that now appears under a revised name). The areas addressed include calendars, astrometry, time scales, Earth rotation, ephemerides, precession-nutation, star catalog transformations, and geodetic/geocentric transformations. The "vector-matrix" library, comprising 55 routines, contains a collection of simple tools for manipulating the vectors, matrices and angles used by the astronomy routines. There is no explicit commitment by SOFA to support historical models, though as time goes on a legacy of superseded models will naturally accumulate. There is, for example, no support of B1950/FK4 star coordinates, or pre-1976 precession models, though these capabilities could be added were there significant demand. Though the SOFA software libraries are rather limited in scope, and are likely to remain so for a considerable time, they do offer distinct advantages to prospective users. In particular, the routines are: * authoritative: they are IAU-backed and have been constructed with great care; * practical: they are straightforward to use in spite of being precise and rigorous (to some stated degree); * accessible and supported: they are downloadable from an easy-to- find place, they are in an integrated and consistent form, they come with adequate internal documentation, and help for users is available. VERSIONS Once it has been published, an issue is never revised or updated, and remains accessible indefinitely. Subsequent issues may, however, include corrected versions under the original routine name and filenames. However, where a different model is introduced, it will have a different name. The issues will be referred to by the date when they were announced. The frequency of re-issue will be decided by the Board, taking into account the importance of the changes and the impact on the user community. DOCUMENTATION At present there is little free-standing documentation about individual routines. However, each routine has preamble comments which specify in detail what the routine does and how it is used. The files sofa_pn_f.pdf and sofa_pn_c.pdf (for Fortran and C users respectively) describe the SOFA tools for precession-nutation and other aspects of Earth attitude, and include example code and, in an appendix, diagrams showing the interrelationships between the routines supporting the latest (IAU 2006/2000A) models. Two other pairs of documents introduce time scale transformations (sofa_ts_f.pdf and sofa_ts_c.pdf ) and astrometric transformations (sofa_ast_f.pdf and sofa_ast_c.pdf). PROGRAMMING LANGUAGES AND STANDARDS The SOFA routines are available in two programming languages at present: Fortran77 and ANSI C. Related software in other languages is under consideration. The Fortran code conforms to ANSI X3.9-1978 in all but two minor respects: each has an IMPLICIT NONE declaration, and its name has a prefix of "iau_" and may be longer than 6 characters. A global edit to erase both of these will produce ANSI-compliant code with no change in its function. Coding style, and restrictions on the range of language features, have been much debated by the Board, and the results comply with the majority view. There is (at present) no document that defines the standards, but the code itself offers a wide range of examples of what is acceptable. The Fortran routines contain explicit numerical constants (the INCLUDE statement is not part of ANSI Fortran77). These are drawn from the file consts.lis, which is listed in an appendix. Constants for the SOFA/C functions are defined in a header file sofam.h. The naming convention is such that a SOFA routine referred to generically as "EXAMPL" exists as a Fortran subprogram iau_EXAMPL and a C function iauExampl. The calls for the two versions are very similar, with the same arguments in the same order. In a few cases, the C equivalent of a Fortran SUBROUTINE subprogram uses a return value rather than an argument. Each language version includes a "testbed" main-program that can be used to verify that the SOFA routines have been correctly compiled on the end user's system. The Fortran and C versions are called t_sofa_f.for and t_sofa_c.c respectively. The testbeds execute every SOFA routine and check that the results are within expected accuracy margins. It is not possible to guarantee that all platforms will meet the rather stringent criteria that have been used, and an occasional warning message may be encountered on some systems. COPYRIGHT ISSUES Copyright for all of the SOFA software and documentation is owned by the IAU SOFA Board. The Software is made available free of charge for all classes of user, including commercial. However, there are strict rules designed to avoid unauthorized variants coming into circulation. It is permissible to distribute derived works and other modifications, but they must be clearly marked to avoid confusion with the SOFA originals. Further details are included in the block of comments which concludes every routine. The text is also set out in an appendix to the present document. ACCURACY The SOFA policy is to organize the calculations so that the machine accuracy is fully exploited. The gap between the precision of the underlying model or theory and the computational resolution has to be kept as large as possible, hopefully leaving several orders of magnitude of headroom. The SOFA routines in some cases involve design compromises between rigor and ease of use (and also speed, though nowadays this is seldom a major concern). ACKNOWLEDGEMENTS The Board is indebted to a number of contributors, who are acknowledged in the preamble comments of the routines concerned. The Board's effort is provided by the members' individual institutes. Resources for operating the SOFA Center are provided by Her Majesty's Nautical Almanac Office, operated by the United Kingdom Hydrographic Office. sofa_lib.lis 2016 March 10 ---------------------- SOFA Astronomy Library ---------------------- PREFACE The routines described here comprise the SOFA astronomy library. Their general appearance and coding style conforms to conventions agreed by the SOFA Board, and their functions, names and algorithms have been ratified by the Board. Procedures for soliciting and agreeing additions to the library are still evolving. PROGRAMMING LANGUAGES The SOFA routines are available in two programming languages at present: Fortran 77 and ANSI C. Except for a single obsolete Fortran routine, which has no C equivalent, there is a one-to-one relationship between the two language versions. The naming convention is such that a SOFA routine referred to generically as "EXAMPL" exists as a Fortran subprogram iau_EXAMPL and a C function iauExampl. The calls for the two versions are very similar, with the same arguments in the same order. In a few cases, the C equivalent of a Fortran SUBROUTINE subprogram uses a return value rather than an argument. GENERAL PRINCIPLES The principal function of the SOFA Astronomy Library is to provide definitive algorithms. A secondary function is to provide software suitable for convenient direct use by writers of astronomical applications. The astronomy routines call on the SOFA vector/matrix library routines, which are separately listed. The routines are designed to exploit the full floating-point accuracy of the machines on which they run, and not to rely on compiler optimizations. Within these constraints, the intention is that the code corresponds to the published formulation (if any). Dates are always Julian Dates (except in calendar conversion routines) and are expressed as two double precision numbers which sum to the required value. A distinction is made between routines that implement IAU-approved models and those that use those models to create other results. The former are referred to as "canonical models" in the preamble comments; the latter are described as "support routines". Using the library requires knowledge of positional astronomy and time-scales. These topics are covered in "Explanatory Supplement to the Astronomical Almanac", 3rd Edition, Sean E. Urban & P. Kenneth Seidelmann (eds.), University Science Books, 2013. Recent developments are documented in the scientific journals, and references to the relevant papers are given in the SOFA code as required. The IERS Conventions are also an essential reference. The routines concerned with Earth attitude (precession-nutation etc.) are described in the SOFA document sofa_pn.pdf. Those concerned with transformations between different time scales are described in sofa_ts_f.pdf (Fortran) and sofa_ts_c.pdf (C). Those concerned with astrometric transformations are described in sofa_ast_f.pdf (Fortran) and sofa_ast_c (C). ROUTINES Calendars CAL2JD Gregorian calendar to Julian Day number EPB Julian Date to Besselian Epoch EPB2JD Besselian Epoch to Julian Date EPJ Julian Date to Julian Epoch EPJ2JD Julian Epoch to Julian Date JD2CAL Julian Date to Gregorian year, month, day, fraction JDCALF Julian Date to Gregorian date for formatted output Astrometry AB apply stellar aberration APCG prepare for ICRS <-> GCRS, geocentric, special APCG13 prepare for ICRS <-> GCRS, geocentric APCI prepare for ICRS <-> CIRS, terrestrial, special APCI13 prepare for ICRS <-> CIRS, terrestrial APCO prepare for ICRS <-> observed, terrestrial, special APCO13 prepare for ICRS <-> observed, terrestrial APCS prepare for ICRS <-> CIRS, space, special APCS13 prepare for ICRS <-> CIRS, space APER insert ERA into context APER13 update context for Earth rotation APIO prepare for CIRS <-> observed, terrestrial, special APIO13 prepare for CIRS <-> observed, terrestrial ATCI13 catalog -> CIRS ATCIQ quick ICRS -> CIRS ATCIQN quick ICRS -> CIRS, multiple deflections ATCIQZ quick astrometric ICRS -> CIRS ATCO13 ICRS -> observed ATIC13 CIRS -> ICRS ATICQ quick CIRS -> ICRS ATCIQN quick CIRS -> ICRS, multiple deflections ATIO13 CIRS -> observed ATIOQ quick CIRS -> observed ATOC13 observed -> astrometric ICRS ATOI13 observed -> CIRS ATOIQ quick observed -> CIRS LD light deflection by a single solar-system body LDN light deflection by multiple solar-system bodies LDSUN light deflection by the Sun PMPX apply proper motion and parallax PMSAFE apply proper motion, with zero-parallax precautions PVTOB observatory position and velocity PVSTAR space motion pv-vector to star catalog data REFCO refraction constants STARPM apply proper motion STARPV star catalog data to space motion pv-vector Time scales D2DTF format 2-part JD for output DAT Delta(AT) (=TAI-UTC) for a given UTC date DTDB TDB-TT DTF2D encode time and date fields into 2-part JD TAITT TAI to TT TAIUT1 TAI to UT1 TAIUTC TAI to UTC TCBTDB TCB to TDB TCGTT TCG to TT TDBTCB TDB to TCB TDBTT TDB to TT TTTAI TT to TAI TTTCG TT to TCG TTTDB TT to TDB TTUT1 TT to UT1 UT1TAI UT1 to TAI UT1TT UT1 to TT UT1UTC UT1 to UTC UTCTAI UTC to TAI UTCUT1 UTC to UT1 Earth rotation angle and sidereal time EE00 equation of the equinoxes, IAU 2000 EE00A equation of the equinoxes, IAU 2000A EE00B equation of the equinoxes, IAU 2000B EE06A equation of the equinoxes, IAU 2006/2000A EECT00 equation of the equinoxes complementary terms, IAU 2000 EQEQ94 equation of the equinoxes, IAU 1994 ERA00 Earth rotation angle, IAU 2000 GMST00 Greenwich mean sidereal time, IAU 2000 GMST06 Greenwich mean sidereal time, IAU 2006 GMST82 Greenwich mean sidereal time, IAU 1982 GST00A Greenwich apparent sidereal time, IAU 2000A GST00B Greenwich apparent sidereal time, IAU 2000B GST06 Greenwich apparent ST, IAU 2006, given NPB matrix GST06A Greenwich apparent sidereal time, IAU 2006/2000A GST94 Greenwich apparent sidereal time, IAU 1994 Ephemerides (limited precision) EPV00 Earth position and velocity PLAN94 major-planet position and velocity Precession, nutation, polar motion BI00 frame bias components, IAU 2000 BP00 frame bias and precession matrices, IAU 2000 BP06 frame bias and precession matrices, IAU 2006 BPN2XY extract CIP X,Y coordinates from NPB matrix C2I00A celestial-to-intermediate matrix, IAU 2000A C2I00B celestial-to-intermediate matrix, IAU 2000B C2I06A celestial-to-intermediate matrix, IAU 2006/2000A C2IBPN celestial-to-intermediate matrix, given NPB matrix, IAU 2000 C2IXY celestial-to-intermediate matrix, given X,Y, IAU 2000 C2IXYS celestial-to-intermediate matrix, given X,Y and s C2T00A celestial-to-terrestrial matrix, IAU 2000A C2T00B celestial-to-terrestrial matrix, IAU 2000B C2T06A celestial-to-terrestrial matrix, IAU 2006/2000A C2TCIO form CIO-based celestial-to-terrestrial matrix C2TEQX form equinox-based celestial-to-terrestrial matrix C2TPE celestial-to-terrestrial matrix given nutation, IAU 2000 C2TXY celestial-to-terrestrial matrix given CIP, IAU 2000 EO06A equation of the origins, IAU 2006/2000A EORS equation of the origins, given NPB matrix and s FW2M Fukushima-Williams angles to r-matrix FW2XY Fukushima-Williams angles to X,Y LTP long-term precession matrix LTPB long-term precession matrix, including ICRS frame bias LTPECL long-term precession of the ecliptic LTPEQU long-term precession of the equator NUM00A nutation matrix, IAU 2000A NUM00B nutation matrix, IAU 2000B NUM06A nutation matrix, IAU 2006/2000A NUMAT form nutation matrix NUT00A nutation, IAU 2000A NUT00B nutation, IAU 2000B NUT06A nutation, IAU 2006/2000A NUT80 nutation, IAU 1980 NUTM80 nutation matrix, IAU 1980 OBL06 mean obliquity, IAU 2006 OBL80 mean obliquity, IAU 1980 PB06 zeta,z,theta precession angles, IAU 2006, including bias PFW06 bias-precession Fukushima-Williams angles, IAU 2006 PMAT00 precession matrix (including frame bias), IAU 2000 PMAT06 PB matrix, IAU 2006 PMAT76 precession matrix, IAU 1976 PN00 bias/precession/nutation results, IAU 2000 PN00A bias/precession/nutation, IAU 2000A PN00B bias/precession/nutation, IAU 2000B PN06 bias/precession/nutation results, IAU 2006 PN06A bias/precession/nutation results, IAU 2006/2000A PNM00A classical NPB matrix, IAU 2000A PNM00B classical NPB matrix, IAU 2000B PNM06A classical NPB matrix, IAU 2006/2000A PNM80 precession/nutation matrix, IAU 1976/1980 P06E precession angles, IAU 2006, equinox based POM00 polar motion matrix PR00 IAU 2000 precession adjustments PREC76 accumulated precession angles, IAU 1976 S00 the CIO locator s, given X,Y, IAU 2000A S00A the CIO locator s, IAU 2000A S00B the CIO locator s, IAU 2000B S06 the CIO locator s, given X,Y, IAU 2006 S06A the CIO locator s, IAU 2006/2000A SP00 the TIO locator s', IERS 2003 XY06 CIP, IAU 2006/2000A, from series XYS00A CIP and s, IAU 2000A XYS00B CIP and s, IAU 2000B XYS06A CIP and s, IAU 2006/2000A Fundamental arguments for nutation etc. FAD03 mean elongation of the Moon from the Sun FAE03 mean longitude of Earth FAF03 mean argument of the latitude of the Moon FAJU03 mean longitude of Jupiter FAL03 mean anomaly of the Moon FALP03 mean anomaly of the Sun FAMA03 mean longitude of Mars FAME03 mean longitude of Mercury FANE03 mean longitude of Neptune FAOM03 mean longitude of the Moon's ascending node FAPA03 general accumulated precession in longitude FASA03 mean longitude of Saturn FAUR03 mean longitude of Uranus FAVE03 mean longitude of Venus Star catalog conversions FK52H transform FK5 star data into the Hipparcos system FK5HIP FK5 to Hipparcos rotation and spin FK5HZ FK5 to Hipparcos assuming zero Hipparcos proper motion H2FK5 transform Hipparcos star data into the FK5 system HFK5Z Hipparcos to FK5 assuming zero Hipparcos proper motion Ecliptic coordinates ECEQ06 ecliptic to ICRS, IAU 2006 ECM06 rotation matrix, ICRS to ecliptic, IAU 2006 EQEC06 ICRS to ecliptic, IAU 2006 LTECEQ ecliptic to ICRS, long term LTECM rotation matrix, ICRS to ecliptic, long-term LTEQEC ICRS to ecliptic, long term Galactic coordinates G2ICRS transform IAU 1958 galactic coordinates to ICRS ICRS2G transform ICRS coordinates to IAU 1958 Galactic Geodetic/geocentric EFORM a,f for a nominated Earth reference ellipsoid GC2GD geocentric to geodetic for a nominated ellipsoid GC2GDE geocentric to geodetic given ellipsoid a,f GD2GC geodetic to geocentric for a nominated ellipsoid GD2GCE geodetic to geocentric given ellipsoid a,f Obsolete C2TCEO former name of C2TCIO CALLS: FORTRAN VERSION CALL iau_AB ( PNAT, V, S, BM1, PPR ) CALL iau_APCG ( DATE1, DATE2, EB, EH, ASTROM ) CALL iau_APCG13 ( DATE1, DATE2, ASTROM ) CALL iau_APCI ( DATE1, DATE2, EB, EH, X, Y, S, ASTROM ) CALL iau_APCI13 ( DATE1, DATE2, ASTROM, EO ) CALL iau_APCO ( DATE1, DATE2, EB, EH, X, Y, S, : THETA, ELONG, PHI, HM, XP, YP, SP, : REFA, REFB, ASTROM ) CALL iau_APCO13 ( UTC1, UTC2, DUT1, ELONG, PHI, HM, XP, YP, : PHPA, TC, RH, WL, ASTROM, EO, J ) CALL iau_APCS ( DATE1, DATE2, PV, EB, EH, ASTROM ) CALL iau_APCS13 ( DATE1, DATE2, PV, ASTROM ) CALL iau_APER ( THETA, ASTROM ) CALL iau_APER13 ( UT11, UT12, ASTROM ) CALL iau_APIO ( SP, THETA, ELONG, PHI, HM, XP, YP, : REFA, REFB, ASTROM ) CALL iau_APIO13 ( UTC1, UTC2, DUT1, ELONG, PHI, HM, XP, YP, : PHPA, TC, RH, WL, ASTROM, J ) CALL iau_ATCI13 ( RC, DC, PR, PD, PX, RV, DATE1, DATE2, RI, DI, EO ) CALL iau_ATCIQ ( RC, DC, PR, PD, PX, RV, ASTROM, RI, DI ) CALL iau_ATCIQN ( RC, DC, PR, PD, PX, RV, ASTROM, N, B, RI, DI ) CALL iau_ATCIQZ ( RC, DC, ASTROM, RI, DI ) CALL iau_ATCO13 ( RC, DC, PR, PD, PX, RV, UTC1, UTC2, DUT1, ELONG, : PHI, HM, XP, YP, PHPA, TC, RH, WL, : AOB, ZOB, HOB, DOB, ROB, EO, J ) CALL iau_ATIC13 ( RI, DI, DATE1, DATE2, RC, DC, EO ) CALL iau_ATICQ ( RI, DI, ASTROM, RC, DC ) CALL iau_ATCIQN ( RI, DI, ASTROM, N, B, RC, DC ) CALL iau_ATIO13 ( RI, DI, UTC1, UTC2, DUT1, ELONG, PHI, HM, XP, YP, PHPA, TC, RH, WL, AOB, ZOB, HOB, DOB, ROB, J ) CALL iau_ATIOQ ( RI, DI, ASTROM, AOB, ZOB, HOB, DOB, ROB ) CALL iau_ATOC13 ( TYPE, OB1, OB2, UTC1, UTC2, DUT1, : ELONG, PHI, HM, XP, YP, PHPA, TC, RH, WL, : RC, DC, J ) CALL iau_ATOI13 ( TYPE, OB1, OB2, UTC1, UTC2, DUT1, : ELONG, PHI, HM, XP, YP, PHPA, TC, RH, WL, : RI, DI, J ) CALL iau_ATOIQ ( TYPE, OB1, OB2, ASTROM, RI, DI ) CALL iau_BI00 ( DPSIBI, DEPSBI, DRA ) CALL iau_BP00 ( DATE1, DATE2, RB, RP, RBP ) CALL iau_BP06 ( DATE1, DATE2, RB, RP, RBP ) CALL iau_BPN2XY ( RBPN, X, Y ) CALL iau_C2I00A ( DATE1, DATE2, RC2I ) CALL iau_C2I00B ( DATE1, DATE2, RC2I ) CALL iau_C2I06A ( DATE1, DATE2, RC2I ) CALL iau_C2IBPN ( DATE1, DATE2, RBPN, RC2I ) CALL iau_C2IXY ( DATE1, DATE2, X, Y, RC2I ) CALL iau_C2IXYS ( X, Y, S, RC2I ) CALL iau_C2T00A ( TTA, TTB, UTA, UTB, XP, YP, RC2T ) CALL iau_C2T00B ( TTA, TTB, UTA, UTB, XP, YP, RC2T ) CALL iau_C2T06A ( TTA, TTB, UTA, UTB, XP, YP, RC2T ) CALL iau_C2TCEO ( RC2I, ERA, RPOM, RC2T ) CALL iau_C2TCIO ( RC2I, ERA, RPOM, RC2T ) CALL iau_C2TEQX ( RBPN, GST, RPOM, RC2T ) CALL iau_C2TPE ( TTA, TTB, UTA, UTB, DPSI, DEPS, XP, YP, RC2T ) CALL iau_C2TXY ( TTA, TTB, UTA, UTB, X, Y, XP, YP, RC2T ) CALL iau_CAL2JD ( IY, IM, ID, DJM0, DJM, J ) CALL iau_D2DTF ( SCALE, NDP, D1, D2, IY, IM, ID, IHMSF, J ) CALL iau_DAT ( IY, IM, ID, FD, DELTAT, J ) D = iau_DTDB ( DATE1, DATE2, UT, ELONG, U, V ) CALL iau_DTF2D ( SCALE, IY, IM, ID, IHR, IMN, SEC, D1, D2, J ) CALL iau_ECEQ06 ( DATE1, DATE2, DL, DB, DR, DD ) CALL iau_ECM06 ( DATE1, DATE2, RM ); D = iau_EE00 ( DATE1, DATE2, EPSA, DPSI ) D = iau_EE00A ( DATE1, DATE2 ) D = iau_EE00B ( DATE1, DATE2 ) D = iau_EE06A ( DATE1, DATE2 ) D = iau_EECT00 ( DATE1, DATE2 ) CALL iau_EFORM ( N, A, F, J ) D = iau_EO06A ( DATE1, DATE2 ) D = iau_EORS ( RNPB, S ) D = iau_EPB ( DJ1, DJ2 ) CALL iau_EPB2JD ( EPB, DJM0, DJM ) D = iau_EPJ ( DJ1, DJ2 ) CALL iau_EPJ2JD ( EPJ, DJM0, DJM ) CALL iau_EPV00 ( DJ1, DJ2, PVH, PVB, J ) CALL iau_EQEC06 ( DATE1, DATE2, DR, DD, DL, DB ) D = iau_EQEQ94 ( DATE1, DATE2 ) D = iau_ERA00 ( DJ1, DJ2 ) D = iau_FAD03 ( T ) D = iau_FAE03 ( T ) D = iau_FAF03 ( T ) D = iau_FAJU03 ( T ) D = iau_FAL03 ( T ) D = iau_FALP03 ( T ) D = iau_FAMA03 ( T ) D = iau_FAME03 ( T ) D = iau_FANE03 ( T ) D = iau_FAOM03 ( T ) D = iau_FAPA03 ( T ) D = iau_FASA03 ( T ) D = iau_FAUR03 ( T ) D = iau_FAVE03 ( T ) CALL iau_FK52H ( R5, D5, DR5, DD5, PX5, RV5, : RH, DH, DRH, DDH, PXH, RVH ) CALL iau_FK5HIP ( R5H, S5H ) CALL iau_FK5HZ ( R5, D5, DATE1, DATE2, RH, DH ) CALL iau_FW2M ( GAMB, PHIB, PSI, EPS, R ) CALL iau_FW2XY ( GAMB, PHIB, PSI, EPS, X, Y ) CALL iau_G2ICRS ( DL, DB, DR, DD ) CALL iau_GC2GD ( N, XYZ, ELONG, PHI, HEIGHT, J ) CALL iau_GC2GDE ( A, F, XYZ, ELONG, PHI, HEIGHT, J ) CALL iau_GD2GC ( N, ELONG, PHI, HEIGHT, XYZ, J ) CALL iau_GD2GCE ( A, F, ELONG, PHI, HEIGHT, XYZ, J ) D = iau_GMST00 ( UTA, UTB, TTA, TTB ) D = iau_GMST06 ( UTA, UTB, TTA, TTB ) D = iau_GMST82 ( UTA, UTB ) D = iau_GST00A ( UTA, UTB, TTA, TTB ) D = iau_GST00B ( UTA, UTB ) D = iau_GST06 ( UTA, UTB, TTA, TTB, RNPB ) D = iau_GST06A ( UTA, UTB, TTA, TTB ) D = iau_GST94 ( UTA, UTB ) CALL iau_H2FK5 ( RH, DH, DRH, DDH, PXH, RVH, : R5, D5, DR5, DD5, PX5, RV5 ) CALL iau_HFK5Z ( RH, DH, DATE1, DATE2, R5, D5, DR5, DD5 ) CALL iau_ICRS2G ( DR, DD, DL, DB ) CALL iau_JD2CAL ( DJ1, DJ2, IY, IM, ID, FD, J ) CALL iau_JDCALF ( NDP, DJ1, DJ2, IYMDF, J ) CALL iau_LD ( BM, P, Q, E, EM, DLIM, P1 ) CALL iau_LDN ( N, B, OB, SC, SN ) CALL iau_LDSUN ( P, E, EM, P1 ) CALL iau_LTECEQ ( EPJ, DL, DB, DR, DD ) CALL iau_LTECM ( EPJ, RM] ) CALL iau_LTEQEC ( EPJ, DR, DD, DL, DB ) CALL iau_LTP ( EPJ, RP ) CALL iau_LTPB ( EPJ, RPB ) CALL iau_LTPECL ( EPJ, VEC ) CALL iau_LTPEQU ( EPJ, VEQ ) CALL iau_NUM00A ( DATE1, DATE2, RMATN ) CALL iau_NUM00B ( DATE1, DATE2, RMATN ) CALL iau_NUM06A ( DATE1, DATE2, RMATN ) CALL iau_NUMAT ( EPSA, DPSI, DEPS, RMATN ) CALL iau_NUT00A ( DATE1, DATE2, DPSI, DEPS ) CALL iau_NUT00B ( DATE1, DATE2, DPSI, DEPS ) CALL iau_NUT06A ( DATE1, DATE2, DPSI, DEPS ) CALL iau_NUT80 ( DATE1, DATE2, DPSI, DEPS ) CALL iau_NUTM80 ( DATE1, DATE2, RMATN ) D = iau_OBL06 ( DATE1, DATE2 ) D = iau_OBL80 ( DATE1, DATE2 ) CALL iau_PB06 ( DATE1, DATE2, BZETA, BZ, BTHETA ) CALL iau_PFW06 ( DATE1, DATE2, GAMB, PHIB, PSIB, EPSA ) CALL iau_PLAN94 ( DATE1, DATE2, NP, PV, J ) CALL iau_PMAT00 ( DATE1, DATE2, RBP ) CALL iau_PMAT06 ( DATE1, DATE2, RBP ) CALL iau_PMAT76 ( DATE1, DATE2, RMATP ) CALL iau_PMPX ( RC, DC, PR, PD, PX, RV, PMT, POB, PCO ) CALL iau_PMSAFE ( RA1, DEC1, PMR1, PMD1, PX1, RV1, : EP1A, EP1B, EP2A, EP2B, : RA2, DEC2, PMR2, PMD2, PX2, RV2, J ) CALL iau_PN00 ( DATE1, DATE2, DPSI, DEPS, : EPSA, RB, RP, RBP, RN, RBPN ) CALL iau_PN00A ( DATE1, DATE2, : DPSI, DEPS, EPSA, RB, RP, RBP, RN, RBPN ) CALL iau_PN00B ( DATE1, DATE2, : DPSI, DEPS, EPSA, RB, RP, RBP, RN, RBPN ) CALL iau_PN06 ( DATE1, DATE2, DPSI, DEPS, : EPSA, RB, RP, RBP, RN, RBPN ) CALL iau_PN06A ( DATE1, DATE2, : DPSI, DEPS, RB, RP, RBP, RN, RBPN ) CALL iau_PNM00A ( DATE1, DATE2, RBPN ) CALL iau_PNM00B ( DATE1, DATE2, RBPN ) CALL iau_PNM06A ( DATE1, DATE2, RNPB ) CALL iau_PNM80 ( DATE1, DATE2, RMATPN ) CALL iau_P06E ( DATE1, DATE2, : EPS0, PSIA, OMA, BPA, BQA, PIA, BPIA, : EPSA, CHIA, ZA, ZETAA, THETAA, PA, GAM, PHI, PSI ) CALL iau_POM00 ( XP, YP, SP, RPOM ) CALL iau_PR00 ( DATE1, DATE2, DPSIPR, DEPSPR ) CALL iau_PREC76 ( DATE01, DATE02, DATE11, DATE12, ZETA, Z, THETA ) CALL iau_PVSTAR ( PV, RA, DEC, PMR, PMD, PX, RV, J ) CALL iau_PVTOB ( ELONG, PHI, HM, XP, YP, SP, THETA, PV ) CALL iau_REFCO ( PHPA, TC, RH, WL, REFA, REFB ) D = iau_S00 ( DATE1, DATE2, X, Y ) D = iau_S00A ( DATE1, DATE2 ) D = iau_S00B ( DATE1, DATE2 ) D = iau_S06 ( DATE1, DATE2, X, Y ) D = iau_S06A ( DATE1, DATE2 ) D = iau_SP00 ( DATE1, DATE2 ) CALL iau_STARPM ( RA1, DEC1, PMR1, PMD1, PX1, RV1, : EP1A, EP1B, EP2A, EP2B, : RA2, DEC2, PMR2, PMD2, PX2, RV2, J ) CALL iau_STARPV ( RA, DEC, PMR, PMD, PX, RV, PV, J ) CALL iau_TAITT ( TAI1, TAI2, TT1, TT2, J ) CALL iau_TAIUT1 ( TAI1, TAI2, DTA, UT11, UT12, J ) CALL iau_TAIUTC ( TAI1, TAI2, UTC1, UTC2, J ) CALL iau_TCBTDB ( TCB1, TCB2, TDB1, TDB2, J ) CALL iau_TCGTT ( TCG1, TCG2, TT1, TT2, J ) CALL iau_TDBTCB ( TDB1, TDB2, TCB1, TCB2, J ) CALL iau_TDBTT ( TDB1, TDB2, DTR, TT1, TT2, J ) CALL iau_TTTAI ( TT1, TT2, TAI1, TAI2, J ) CALL iau_TTTCG ( TT1, TT2, TCG1, TCG2, J ) CALL iau_TTTDB ( TT1, TT2, DTR, TDB1, TDB2, J ) CALL iau_TTUT1 ( TT1, TT2, DT, UT11, UT12, J ) CALL iau_UT1TAI ( UT11, UT12, TAI1, TAI2, J ) CALL iau_UT1TT ( UT11, UT12, DT, TT1, TT2, J ) CALL iau_UT1UTC ( UT11, UT12, DUT, UTC1, UTC2, J ) CALL iau_UTCTAI ( UTC1, UTC2, DTA, TAI1, TAI2, J ) CALL iau_UTCUT1 ( UTC1, UTC2, DUT, UT11, UT12, J ) CALL iau_XY06 ( DATE1, DATE2, X, Y ) CALL iau_XYS00A ( DATE1, DATE2, X, Y, S ) CALL iau_XYS00B ( DATE1, DATE2, X, Y, S ) CALL iau_XYS06A ( DATE1, DATE2, X, Y, S ) CALLS: C VERSION iauAb ( pnat, v, s, bm1, ppr ); iauApcg ( date1, date2, eb, eh, &astrom ); iauApcg13 ( date1, date2, &astrom ); iauApci ( date1, date2, eb, eh, x, y, s, &astrom ); iauApci13 ( date1, date2, &astrom, &eo ); iauApco ( date1, date2, eb, eh, x, y, s, theta, elong, phi, hm, xp, yp, sp, refa, refb, &astrom ); i = iauApco13 ( utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom, &eo ); iauApcs ( date1, date2, pv, eb, eh, &astrom ); iauApcs13 ( date1, date2, pv, &astrom ); iauAper ( theta, &astrom ); iauAper13 ( ut11, ut12, &astrom ); iauApio ( sp, theta, elong, phi, hm, xp, yp, refa, refb, &astrom ); i = iauApio13 ( utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom ); iauAtci13 ( rc, dc, pr, pd, px, rv, date1, date2, &ri, &di, &eo ); iauAtciq ( rc, dc, pr, pd, px, rv, &astrom, &ri, &di ); iauAtciqn ( rc, dc, pr, pd, px, rv, astrom, n, b, &ri, &di ); iauAtciqz ( rc, dc, &astrom, &ri, &di ); i = iauAtco13 ( rc, dc, pr, pd, px, rv, utc1, utc2, dut1, elong phi, hm, xp, yp, phpa, tc, rh, wl, aob, zob, hob, dob, rob, eo ); iauAtic13 ( ri, di, date1, date2, &rc, &dc, &eo ); iauAticq ( ri, di, &astrom, &rc, &dc ); iauAtciqn ( ri, di, astrom, n, b, &rc, &dc ); i = iauAtio13 ( ri, di, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, aob, zob, hob, dob, rob ); iauAtioq ( ri, di, &astrom, &aob, &zob, &hob, &dob, &rob ); i = iauAtoc13 ( type, ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &rc, &dc ); i = iauAtoi13 ( type, ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &ri, &di ); iauAtoiq ( type, ob1, ob2, &astrom, &ri, &di ); iauBi00 ( &dpsibi, &depsbi, &dra ); iauBp00 ( date1, date2, rb, rp, rbp ); iauBp06 ( date1, date2, rb, rp, rbp ); iauBpn2xy ( rbpn, &x, &y ); iauC2i00a ( date1, date2, rc2i ); iauC2i00b ( date1, date2, rc2i ); iauC2i06a ( date1, date2, rc2i ); iauC2ibpn ( date1, date2, rbpn, rc2i ); iauC2ixy ( date1, date2, x, y, rc2i ); iauC2ixys ( x, y, s, rc2i ); iauC2t00a ( tta, ttb, uta, utb, xp, yp, rc2t ); iauC2t00b ( tta, ttb, uta, utb, xp, yp, rc2t ); iauC2t06a ( tta, ttb, uta, utb, xp, yp, rc2t ); iauC2tcio ( rc2i, era, rpom, rc2t ); iauC2teqx ( rbpn, gst, rpom, rc2t ); iauC2tpe ( tta, ttb, uta, utb, dpsi, deps, xp, yp, rc2t ); iauC2txy ( tta, ttb, uta, utb, x, y, xp, yp, rc2t ); i = iauCal2jd ( iy, im, id, &djm0, &djm ); i = iauD2dtf ( scale, ndp, d1, d2, &iy, &im, &id, ihmsf ); i = iauDat ( iy, im, id, fd, &deltat ); d = iauDtdb ( date1, date2, ut, elong, u, v ); i = iauDtf2d ( scale, iy, im, id, ihr, imn, sec, &d1, &d2 ); iauEceq06 ( date1, date2, dl, db, &dr, &dd ); iauEcm06 ( date1, date2, rm ); d = iauEe00 ( date1, date2, epsa, dpsi ); d = iauEe00a ( date1, date2 ); d = iauEe00b ( date1, date2 ); d = iauEe06 ( date1, date2 ); d = iauEect00 ( date1, date2 ); i = iauEform ( n, &a, &f ); d = iauEo06 ( date1, date2 ); d = iauEors ( rnpb, s ); d = iauEpb ( dj1, dj2 ); iauEpb2jd ( epb, &djm0, &djm ); d = iauEpj ( dj1, dj2 ); iauEpj2jd ( epj, &djm0, &djm ); i = iauEpv00 ( dj1, dj2, pvh, pvb ); iauEqec06 ( date1, date2, dr, dd, &dl, &db ); d = iauEqeq94 ( date1, date2 ); d = iauEra00 ( dj1, dj2 ); d = iauFad03 ( t ); d = iauFae03 ( t ); d = iauFaf03 ( t ); d = iauFaju03 ( t ); d = iauFal03 ( t ); d = iauFalp03 ( t ); d = iauFama03 ( t ); d = iauFame03 ( t ); d = iauFane03 ( t ); d = iauFaom03 ( t ); d = iauFapa03 ( t ); d = iauFasa03 ( t ); d = iauFaur03 ( t ); d = iauFave03 ( t ); iauFk52h ( r5, d5, dr5, dd5, px5, rv5, &rh, &dh, &drh, &ddh, &pxh, &rvh ); iauFk5hip ( r5h, s5h ); iauFk5hz ( r5, d5, date1, date2, &rh, &dh ); iauFw2m ( gamb, phib, psi, eps, r ); iauFw2xy ( gamb, phib, psi, eps, &x, &y ); iauG2icrs ( dl, db, &dr, &dd ); i = iauGc2gd ( n, xyz, &elong, &phi, &height ); i = iauGc2gde ( a, f, xyz, &elong, &phi, &height ); i = iauGd2gc ( n, elong, phi, height, xyz ); i = iauGd2gce ( a, f, elong, phi, height, xyz ); d = iauGmst00 ( uta, utb, tta, ttb ); d = iauGmst06 ( uta, utb, tta, ttb ); d = iauGmst82 ( uta, utb ); d = iauGst00a ( uta, utb, tta, ttb ); d = iauGst00b ( uta, utb ); d = iauGst06 ( uta, utb, tta, ttb, rnpb ); d = iauGst06a ( uta, utb, tta, ttb ); d = iauGst94 ( uta, utb ); iauH2fk5 ( rh, dh, drh, ddh, pxh, rvh, &r5, &d5, &dr5, &dd5, &px5, &rv5 ); iauHfk5z ( rh, dh, date1, date2, &r5, &d5, &dr5, &dd5 ); iauIcrs2g ( dr, dd, &dl, &db ); i = iauJd2cal ( dj1, dj2, &iy, &im, &id, &fd ); i = iauJdcalf ( ndp, dj1, dj2, iymdf ); iauLd ( bm, p, q, e, em, dlim, p1 ); iauLdn ( n, b, ob, sc, sn ); iauLdsun ( p, e, em, p1 ); iauLteceq ( epj, dl, db, &dr, &dd ); iauLtecm ( epj, rm ); iauLteqec ( epj, dr, dd, &dl, &db ); iauLtp ( epj, rp ); iauLtpb ( epj, rpb ); iauLtpecl ( epj, vec ); iauLtpequ ( epj, veq ); iauNum00a ( date1, date2, rmatn ); iauNum00b ( date1, date2, rmatn ); iauNum06a ( date1, date2, rmatn ); iauNumat ( epsa, dpsi, deps, rmatn ); iauNut00a ( date1, date2, &dpsi, &deps ); iauNut00b ( date1, date2, &dpsi, &deps ); iauNut06a ( date1, date2, &dpsi, &deps ); iauNut80 ( date1, date2, &dpsi, &deps ); iauNutm80 ( date1, date2, rmatn ); d = iauObl06 ( date1, date2 ); d = iauObl80 ( date1, date2 ); iauPb06 ( date1, date2, &bzeta, &bz, &btheta ); iauPfw06 ( date1, date2, &gamb, &phib, &psib, &epsa ); i = iauPlan94 ( date1, date2, np, pv ); iauPmat00 ( date1, date2, rbp ); iauPmat06 ( date1, date2, rbp ); iauPmat76 ( date1, date2, rmatp ); iauPmpx ( rc, dc, pr, pd, px, rv, pmt, pob, pco ); i = iauPmsafe ( ra1, dec1, pmr1, pmd1, px1, rv1, ep1a, ep1b, ep2a, ep2b, &ra2, &dec2, &pmr2, &pmd2, &px2, &rv2); iauPn00 ( date1, date2, dpsi, deps, &epsa, rb, rp, rbp, rn, rbpn ); iauPn00a ( date1, date2, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn ); iauPn00b ( date1, date2, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn ); iauPn06 ( date1, date2, dpsi, deps, &epsa, rb, rp, rbp, rn, rbpn ); iauPn06a ( date1, date2, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn ); iauPnm00a ( date1, date2, rbpn ); iauPnm00b ( date1, date2, rbpn ); iauPnm06a ( date1, date2, rnpb ); iauPnm80 ( date1, date2, rmatpn ); iauP06e ( date1, date2, &eps0, &psia, &oma, &bpa, &bqa, &pia, &bpia, &epsa, &chia, &za, &zetaa, &thetaa, &pa, &gam, &phi, &psi ); iauPom00 ( xp, yp, sp, rpom ); iauPr00 ( date1, date2, &dpsipr, &depspr ); iauPrec76 ( date01, date02, date11, date12, &zeta, &z, &theta ); i = iauPvstar ( pv, &ra, &dec, &pmr, &pmd, &px, &rv ); iauPvtob ( elong, phi, hm, xp, yp, sp, theta, pv ); iauRefco ( phpa, tc, rh, wl, refa, refb ); d = iauS00 ( date1, date2, x, y ); d = iauS00a ( date1, date2 ); d = iauS00b ( date1, date2 ); d = iauS06 ( date1, date2, x, y ); d = iauS06a ( date1, date2 ); d = iauSp00 ( date1, date2 ); i = iauStarpm ( ra1, dec1, pmr1, pmd1, px1, rv1, ep1a, ep1b, ep2a, ep2b, &ra2, &dec2, &pmr2, &pmd2, &px2, &rv2 ); i = iauStarpv ( ra, dec, pmr, pmd, px, rv, pv ); i = iauTaitt ( tai1, tai2, &tt1, &tt2 ); i = iauTaiut1 ( tai1, tai2, dta, &ut11, &ut12 ); i = iauTaiutc ( tai1, tai2, &utc1, &utc2 ); i = iauTcbtdb ( tcb1, tcb2, &tdb1, &tdb2 ); i = iauTcgtt ( tcg1, tcg2, &tt1, &tt2 ); i = iauTdbtcb ( tdb1, tdb2, &tcb1, &tcb2 ); i = iauTdbtt ( tdb1, tdb2, dtr, &tt1, &tt2 ); i = iauTttai ( tt1, tt2, &tai1, &tai2 ); i = iauTttcg ( tt1, tt2, &tcg1, &tcg2 ); i = iauTttdb ( tt1, tt2, dtr, &tdb1, &tdb2 ); i = iauTtut1 ( tt1, tt2, dt, &ut11, &ut12 ); i = iauUt1tai ( ut11, ut12, &tai1, &tai2 ); i = iauUt1tt ( ut11, ut12, dt, &tt1, &tt2 ); i = iauUt1utc ( ut11, ut12, dut, &utc1, &utc2 ); i = iauUtctai ( utc1, utc2, dta, &tai1, &tai2 ); i = iauUtcut1 ( utc1, utc2, dut, &ut11, &ut12 ); iauXy06 ( date1, date2, &x, &y ); iauXys00a ( date1, date2, &x, &y, &s ); iauXys00b ( date1, date2, &x, &y, &s ); iauXys06a ( date1, date2, &x, &y, &s ); sofa_vml.lis 2013 October 8 -------------------------- SOFA Vector/Matrix Library -------------------------- PREFACE The routines described here comprise the SOFA vector/matrix library. Their general appearance and coding style conforms to conventions agreed by the SOFA Board, and their functions, names and algorithms have been ratified by the Board. Procedures for soliciting and agreeing additions to the library are still evolving. PROGRAMMING LANGUAGES The SOFA routines are available in two programming languages at present: Fortran 77 and ANSI C. There is a one-to-one relationship between the two language versions. The naming convention is such that a SOFA routine referred to generically as "EXAMPL" exists as a Fortran subprogram iau_EXAMPL and a C function iauExampl. The calls for the two versions are very similar, with the same arguments in the same order. In a few cases, the C equivalent of a Fortran SUBROUTINE subprogram uses a return value rather than an argument. GENERAL PRINCIPLES The library consists mostly of routines which operate on ordinary Cartesian vectors (x,y,z) and 3x3 rotation matrices. However, there is also support for vectors which represent velocity as well as position and vectors which represent rotation instead of position. The vectors which represent both position and velocity may be considered still to have dimensions (3), but to comprise elements each of which is two numbers, representing the value itself and the time derivative. Thus: * "Position" or "p" vectors (or just plain 3-vectors) have dimension (3) in Fortran and [3] in C. * "Position/velocity" or "pv" vectors have dimensions (3,2) in Fortran and [2][3] in C. * "Rotation" or "r" matrices have dimensions (3,3) in Fortran and [3][3] in C. When used for rotation, they are "orthogonal"; the inverse of such a matrix is equal to the transpose. Most of the routines in this library do not assume that r-matrices are necessarily orthogonal and in fact work on any 3x3 matrix. * "Rotation" or "r" vectors have dimensions (3) in Fortran and [3] in C. Such vectors are a combination of the Euler axis and angle and are convertible to and from r-matrices. The direction is the axis of rotation and the magnitude is the angle of rotation, in radians. Because the amount of rotation can be scaled up and down simply by multiplying the vector by a scalar, r-vectors are useful for representing spins about an axis which is fixed. * The above rules mean that in terms of memory address, the three velocity components of a pv-vector follow the three position components. Application code is permitted to exploit this and all other knowledge of the internal layouts: that x, y and z appear in that order and are in a right-handed Cartesian coordinate system etc. For example, the cp function (copy a p-vector) can be used to copy the velocity component of a pv-vector (indeed, this is how the CPV routine is coded). * The routines provided do not completely fill the range of operations that link all the various vector and matrix options, but are confined to functions that are required by other parts of the SOFA software or which are likely to prove useful. In addition to the vector/matrix routines, the library contains some routines related to spherical angles, including conversions to and from sexagesimal format. Using the library requires knowledge of vector/matrix methods, spherical trigonometry, and methods of attitude representation. These topics are covered in many textbooks, including "Spacecraft Attitude Determination and Control", James R. Wertz (ed.), Astrophysics and Space Science Library, Vol. 73, D. Reidel Publishing Company, 1986. OPERATIONS INVOLVING P-VECTORS AND R-MATRICES Initialize ZP zero p-vector ZR initialize r-matrix to null IR initialize r-matrix to identity Copy/extend/extract CP copy p-vector CR copy r-matrix Build rotations RX rotate r-matrix about x RY rotate r-matrix about y RZ rotate r-matrix about z Spherical/Cartesian conversions S2C spherical to unit vector C2S unit vector to spherical S2P spherical to p-vector P2S p-vector to spherical Operations on vectors PPP p-vector plus p-vector PMP p-vector minus p-vector PPSP p-vector plus scaled p-vector PDP inner (=scalar=dot) product of two p-vectors PXP outer (=vector=cross) product of two p-vectors PM modulus of p-vector PN normalize p-vector returning modulus SXP multiply p-vector by scalar Operations on matrices RXR r-matrix multiply TR transpose r-matrix Matrix-vector products RXP product of r-matrix and p-vector TRXP product of transpose of r-matrix and p-vector Separation and position-angle SEPP angular separation from p-vectors SEPS angular separation from spherical coordinates PAP position-angle from p-vectors PAS position-angle from spherical coordinates Rotation vectors RV2M r-vector to r-matrix RM2V r-matrix to r-vector OPERATIONS INVOLVING PV-VECTORS Initialize ZPV zero pv-vector Copy/extend/extract CPV copy pv-vector P2PV append zero velocity to p-vector PV2P discard velocity component of pv-vector Spherical/Cartesian conversions S2PV spherical to pv-vector PV2S pv-vector to spherical Operations on vectors PVPPV pv-vector plus pv-vector PVMPV pv-vector minus pv-vector PVDPV inner (=scalar=dot) product of two pv-vectors PVXPV outer (=vector=cross) product of two pv-vectors PVM modulus of pv-vector SXPV multiply pv-vector by scalar S2XPV multiply pv-vector by two scalars PVU update pv-vector PVUP update pv-vector discarding velocity Matrix-vector products RXPV product of r-matrix and pv-vector TRXPV product of transpose of r-matrix and pv-vector OPERATIONS ON ANGLES ANP normalize radians to range 0 to 2pi ANPM normalize radians to range -pi to +pi A2TF decompose radians into hours, minutes, seconds A2AF decompose radians into degrees, arcminutes, arcseconds AF2A degrees, arcminutes, arcseconds to radians D2TF decompose days into hours, minutes, seconds TF2A hours, minutes, seconds to radians TF2D hours, minutes, seconds to days CALLS: FORTRAN VERSION CALL iau_A2AF ( NDP, ANGLE, SIGN, IDMSF ) CALL iau_A2TF ( NDP, ANGLE, SIGN, IHMSF ) CALL iau_AF2A ( S, IDEG, IAMIN, ASEC, RAD, J ) D = iau_ANP ( A ) D = iau_ANPM ( A ) CALL iau_C2S ( P, THETA, PHI ) CALL iau_CP ( P, C ) CALL iau_CPV ( PV, C ) CALL iau_CR ( R, C ) CALL iau_D2TF ( NDP, DAYS, SIGN, IHMSF ) CALL iau_IR ( R ) CALL iau_P2PV ( P, PV ) CALL iau_P2S ( P, THETA, PHI, R ) CALL iau_PAP ( A, B, THETA ) CALL iau_PAS ( AL, AP, BL, BP, THETA ) CALL iau_PDP ( A, B, ADB ) CALL iau_PM ( P, R ) CALL iau_PMP ( A, B, AMB ) CALL iau_PN ( P, R, U ) CALL iau_PPP ( A, B, APB ) CALL iau_PPSP ( A, S, B, APSB ) CALL iau_PV2P ( PV, P ) CALL iau_PV2S ( PV, THETA, PHI, R, TD, PD, RD ) CALL iau_PVDPV ( A, B, ADB ) CALL iau_PVM ( PV, R, S ) CALL iau_PVMPV ( A, B, AMB ) CALL iau_PVPPV ( A, B, APB ) CALL iau_PVU ( DT, PV, UPV ) CALL iau_PVUP ( DT, PV, P ) CALL iau_PVXPV ( A, B, AXB ) CALL iau_PXP ( A, B, AXB ) CALL iau_RM2V ( R, P ) CALL iau_RV2M ( P, R ) CALL iau_RX ( PHI, R ) CALL iau_RXP ( R, P, RP ) CALL iau_RXPV ( R, PV, RPV ) CALL iau_RXR ( A, B, ATB ) CALL iau_RY ( THETA, R ) CALL iau_RZ ( PSI, R ) CALL iau_S2C ( THETA, PHI, C ) CALL iau_S2P ( THETA, PHI, R, P ) CALL iau_S2PV ( THETA, PHI, R, TD, PD, RD, PV ) CALL iau_S2XPV ( S1, S2, PV ) CALL iau_SEPP ( A, B, S ) CALL iau_SEPS ( AL, AP, BL, BP, S ) CALL iau_SXP ( S, P, SP ) CALL iau_SXPV ( S, PV, SPV ) CALL iau_TF2A ( S, IHOUR, IMIN, SEC, RAD, J ) CALL iau_TF2D ( S, IHOUR, IMIN, SEC, DAYS, J ) CALL iau_TR ( R, RT ) CALL iau_TRXP ( R, P, TRP ) CALL iau_TRXPV ( R, PV, TRPV ) CALL iau_ZP ( P ) CALL iau_ZPV ( PV ) CALL iau_ZR ( R ) CALLS: C VERSION iauA2af ( ndp, angle, &sign, idmsf ); iauA2tf ( ndp, angle, &sign, ihmsf ); i = iauAf2a ( s, ideg, iamin, asec, &rad ); d = iauAnp ( a ); d = iauAnpm ( a ); iauC2s ( p, &theta, &phi ); iauCp ( p, c ); iauCpv ( pv, c ); iauCr ( r, c ); iauD2tf ( ndp, days, &sign, ihmsf ); iauIr ( r ); iauP2pv ( p, pv ); iauP2s ( p, &theta, &phi, &r ); d = iauPap ( a, b ); d = iauPas ( al, ap, bl, bp ); d = iauPdp ( a, b ); d = iauPm ( p ); iauPmp ( a, b, amb ); iauPn ( p, &r, u ); iauPpp ( a, b, apb ); iauPpsp ( a, s, b, apsb ); iauPv2p ( pv, p ); iauPv2s ( pv, &theta, &phi, &r, &td, &pd, &rd ); iauPvdpv ( a, b, adb ); iauPvm ( pv, &r, &s ); iauPvmpv ( a, b, amb ); iauPvppv ( a, b, apb ); iauPvu ( dt, pv, upv ); iauPvup ( dt, pv, p ); iauPvxpv ( a, b, axb ); iauPxp ( a, b, axb ); iauRm2v ( r, p ); iauRv2m ( p, r ); iauRx ( phi, r ); iauRxp ( r, p, rp ); iauRxpv ( r, pv, rpv ); iauRxr ( a, b, atb ); iauRy ( theta, r ); iauRz ( psi, r ); iauS2c ( theta, phi, c ); iauS2p ( theta, phi, r, p ); iauS2pv ( theta, phi, r, td, pd, rd, pV ); iauS2xpv ( s1, s2, pv ); d = iauSepp ( a, b ); d = iauSeps ( al, ap, bl, bp ); iauSxp ( s, p, sp ); iauSxpv ( s, pv, spv ); i = iauTf2a ( s, ihour, imin, sec, &rad ); i = iauTf2d ( s, ihour, imin, sec, &days ); iauTr ( r, rt ); iauTrxp ( r, p, trp ); iauTrxpv ( r, pv, trpv ); iauZp ( p ); iauZpv ( pv ); iauZr ( r ); void iauA2af(int ndp, double angle, char *sign, int idmsf[4]) /* ** - - - - - - - - ** i a u A 2 a f ** - - - - - - - - ** ** Decompose radians into degrees, arcminutes, arcseconds, fraction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** ndp int resolution (Note 1) ** angle double angle in radians ** ** Returned: ** sign char '+' or '-' ** idmsf int[4] degrees, arcminutes, arcseconds, fraction ** ** Called: ** iauD2tf decompose days to hms ** ** Notes: ** ** 1) The argument ndp is interpreted as follows: ** ** ndp resolution ** : ...0000 00 00 ** -7 1000 00 00 ** -6 100 00 00 ** -5 10 00 00 ** -4 1 00 00 ** -3 0 10 00 ** -2 0 01 00 ** -1 0 00 10 ** 0 0 00 01 ** 1 0 00 00.1 ** 2 0 00 00.01 ** 3 0 00 00.001 ** : 0 00 00.000... ** ** 2) The largest positive useful value for ndp is determined by the ** size of angle, the format of doubles on the target platform, and ** the risk of overflowing idmsf[3]. On a typical platform, for ** angle up to 2pi, the available floating-point precision might ** correspond to ndp=12. However, the practical limit is typically ** ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is ** only 16 bits. ** ** 3) The absolute value of angle may exceed 2pi. In cases where it ** does not, it is up to the caller to test for and handle the ** case where angle is very nearly 2pi and rounds up to 360 degrees, ** by testing for idmsf[0]=360 and setting idmsf[0-3] to zero. ** */ void iauA2tf(int ndp, double angle, char *sign, int ihmsf[4]) /* ** - - - - - - - - ** i a u A 2 t f ** - - - - - - - - ** ** Decompose radians into hours, minutes, seconds, fraction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** ndp int resolution (Note 1) ** angle double angle in radians ** ** Returned: ** sign char '+' or '-' ** ihmsf int[4] hours, minutes, seconds, fraction ** ** Called: ** iauD2tf decompose days to hms ** ** Notes: ** ** 1) The argument ndp is interpreted as follows: ** ** ndp resolution ** : ...0000 00 00 ** -7 1000 00 00 ** -6 100 00 00 ** -5 10 00 00 ** -4 1 00 00 ** -3 0 10 00 ** -2 0 01 00 ** -1 0 00 10 ** 0 0 00 01 ** 1 0 00 00.1 ** 2 0 00 00.01 ** 3 0 00 00.001 ** : 0 00 00.000... ** ** 2) The largest positive useful value for ndp is determined by the ** size of angle, the format of doubles on the target platform, and ** the risk of overflowing ihmsf[3]. On a typical platform, for ** angle up to 2pi, the available floating-point precision might ** correspond to ndp=12. However, the practical limit is typically ** ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is ** only 16 bits. ** ** 3) The absolute value of angle may exceed 2pi. In cases where it ** does not, it is up to the caller to test for and handle the ** case where angle is very nearly 2pi and rounds up to 24 hours, ** by testing for ihmsf[0]=24 and setting ihmsf[0-3] to zero. ** */ void iauAb(double pnat[3], double v[3], double s, double bm1, double ppr[3]) /* ** - - - - - - ** i a u A b ** - - - - - - ** ** Apply aberration to transform natural direction into proper ** direction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** pnat double[3] natural direction to the source (unit vector) ** v double[3] observer barycentric velocity in units of c ** s double distance between the Sun and the observer (au) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** ** Returned: ** ppr double[3] proper direction to source (unit vector) ** ** Notes: ** ** 1) The algorithm is based on Expr. (7.40) in the Explanatory ** Supplement (Urban & Seidelmann 2013), but with the following ** changes: ** ** o Rigorous rather than approximate normalization is applied. ** ** o The gravitational potential term from Expr. (7) in ** Klioner (2003) is added, taking into account only the Sun's ** contribution. This has a maximum effect of about ** 0.4 microarcsecond. ** ** 2) In almost all cases, the maximum accuracy will be limited by the ** supplied velocity. For example, if the SOFA iauEpv00 function is ** used, errors of up to 5 microarcseconds could occur. ** ** References: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013). ** ** Klioner, Sergei A., "A practical relativistic model for micro- ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). ** ** Called: ** iauPdp scalar product of two p-vectors ** */ int iauAf2a(char s, int ideg, int iamin, double asec, double *rad) /* ** - - - - - - - - ** i a u A f 2 a ** - - - - - - - - ** ** Convert degrees, arcminutes, arcseconds to radians. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** s char sign: '-' = negative, otherwise positive ** ideg int degrees ** iamin int arcminutes ** asec double arcseconds ** ** Returned: ** rad double angle in radians ** ** Returned (function value): ** int status: 0 = OK ** 1 = ideg outside range 0-359 ** 2 = iamin outside range 0-59 ** 3 = asec outside range 0-59.999... ** ** Notes: ** ** 1) The result is computed even if any of the range checks fail. ** ** 2) Negative ideg, iamin and/or asec produce a warning status, but ** the absolute value is used in the conversion. ** ** 3) If there are multiple errors, the status value reflects only the ** first, the smallest taking precedence. ** */ double iauAnp(double a) /* ** - - - - - - - ** i a u A n p ** - - - - - - - ** ** Normalize angle into the range 0 <= a < 2pi. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double angle (radians) ** ** Returned (function value): ** double angle in range 0-2pi ** */ double iauAnpm(double a) /* ** - - - - - - - - ** i a u A n p m ** - - - - - - - - ** ** Normalize angle into the range -pi <= a < +pi. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double angle (radians) ** ** Returned (function value): ** double angle in range +/-pi ** */ void iauApcg(double date1, double date2, double ebpv[2][3], double ehp[3], iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p c g ** - - - - - - - - ** ** For a geocentric observer, prepare star-independent astrometry ** parameters for transformations between ICRS and GCRS coordinates. ** The Earth ephemeris is supplied by the caller. ** ** The parameters produced by this function are required in the ** parallax, light deflection and aberration parts of the astrometric ** transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ebpv double[2][3] Earth barycentric pos/vel (au, au/day) ** ehp double[3] Earth heliocentric position (au) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 4) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauApcs astrometry parameters, ICRS-GCRS, space observer ** */ void iauApcg13(double date1, double date2, iauASTROM *astrom) /* ** - - - - - - - - - - ** i a u A p c g 1 3 ** - - - - - - - - - - ** ** For a geocentric observer, prepare star-independent astrometry ** parameters for transformations between ICRS and GCRS coordinates. ** The caller supplies the date, and SOFA models are used to predict ** the Earth ephemeris. ** ** The parameters produced by this function are required in the ** parallax, light deflection and aberration parts of the astrometric ** transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) In cases where the caller wishes to supply his own Earth ** ephemeris, the function iauApcg can be used instead of the present ** function. ** ** 4) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 5) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauEpv00 Earth position and velocity ** iauApcg astrometry parameters, ICRS-GCRS, geocenter ** */ void iauApci(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p c i ** - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between ICRS and geocentric CIRS ** coordinates. The Earth ephemeris and CIP/CIO are supplied by the ** caller. ** ** The parameters produced by this function are required in the ** parallax, light deflection, aberration, and bias-precession-nutation ** parts of the astrometric transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ebpv double[2][3] Earth barycentric position/velocity (au, au/day) ** ehp double[3] Earth heliocentric position (au) ** x,y double CIP X,Y (components of unit vector) ** s double the CIO locator s (radians) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) In cases where the caller does not wish to provide the Earth ** ephemeris and CIP/CIO, the function iauApci13 can be used instead ** of the present function. This computes the required quantities ** using other SOFA functions. ** ** 4) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 5) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauApcg astrometry parameters, ICRS-GCRS, geocenter ** iauC2ixys celestial-to-intermediate matrix, given X,Y and s ** */ void iauApci13(double date1, double date2, iauASTROM *astrom, double *eo) /* ** - - - - - - - - - - ** i a u A p c i 1 3 ** - - - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between ICRS and geocentric CIRS ** coordinates. The caller supplies the date, and SOFA models are used ** to predict the Earth ephemeris and CIP/CIO. ** ** The parameters produced by this function are required in the ** parallax, light deflection, aberration, and bias-precession-nutation ** parts of the astrometric transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** eo double* equation of the origins (ERA-GST) ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) In cases where the caller wishes to supply his own Earth ** ephemeris and CIP/CIO, the function iauApci can be used instead ** of the present function. ** ** 4) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 5) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauEpv00 Earth position and velocity ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** iauApci astrometry parameters, ICRS-CIRS ** iauEors equation of the origins, given NPB matrix and s ** */ void iauApco(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, double theta, double elong, double phi, double hm, double xp, double yp, double sp, double refa, double refb, iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p c o ** - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between ICRS and observed ** coordinates. The caller supplies the Earth ephemeris, the Earth ** rotation information and the refraction constants as well as the ** site coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ebpv double[2][3] Earth barycentric PV (au, au/day, Note 2) ** ehp double[3] Earth heliocentric P (au, Note 2) ** x,y double CIP X,Y (components of unit vector) ** s double the CIO locator s (radians) ** theta double Earth rotation angle (radians) ** elong double longitude (radians, east +ve, Note 3) ** phi double latitude (geodetic, radians, Note 3) ** hm double height above ellipsoid (m, geodetic, Note 3) ** xp,yp double polar motion coordinates (radians, Note 4) ** sp double the TIO locator s' (radians, Note 4) ** refa double refraction constant A (radians, Note 5) ** refb double refraction constant B (radians, Note 5) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) The vectors eb, eh, and all the astrom vectors, are with respect ** to BCRS axes. ** ** 3) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN ** CONVENTION: the longitude required by the present function is ** right-handed, i.e. east-positive, in accordance with geographical ** convention. ** ** 4) xp and yp are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions), measured along the ** meridians 0 and 90 deg west respectively. sp is the TIO locator ** s', in radians, which positions the Terrestrial Intermediate ** Origin on the equator. For many applications, xp, yp and ** (especially) sp can be set to zero. ** ** Internally, the polar motion is stored in a form rotated onto the ** local meridian. ** ** 5) The refraction constants refa and refb are for use in a ** dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed ** (i.e. refracted) zenith distance and dZ is the amount of ** refraction. ** ** 6) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 7) In cases where the caller does not wish to provide the Earth ** Ephemeris, the Earth rotation information and refraction ** constants, the function iauApco13 can be used instead of the ** present function. This starts from UTC and weather readings etc. ** and computes suitable values using other SOFA functions. ** ** 8) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 9) The context structure astrom produced by this function is used by ** iauAtioq, iauAtoiq, iauAtciq* and iauAticq*. ** ** Called: ** iauAper astrometry parameters: update ERA ** iauC2ixys celestial-to-intermediate matrix, given X,Y and s ** iauPvtob position/velocity of terrestrial station ** iauTrxpv product of transpose of r-matrix and pv-vector ** iauApcs astrometry parameters, ICRS-GCRS, space observer ** iauCr copy r-matrix ** */ int iauApco13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom, double *eo) /* ** - - - - - - - - - - ** i a u A p c o 1 3 ** - - - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between ICRS and observed ** coordinates. The caller supplies UTC, site coordinates, ambient air ** conditions and observing wavelength, and SOFA models are used to ** obtain the Earth ephemeris, CIP/CIO and refraction constants. ** ** The parameters produced by this function are required in the ** parallax, light deflection, aberration, and bias-precession-nutation ** parts of the ICRS/CIRS transformations. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 1,2) ** dut1 double UT1-UTC (seconds, Note 3) ** elong double longitude (radians, east +ve, Note 4) ** phi double latitude (geodetic, radians, Note 4) ** hm double height above ellipsoid (m, geodetic, Notes 4,6) ** xp,yp double polar motion coordinates (radians, Note 5) ** phpa double pressure at the observer (hPa = mB, Note 6) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 7) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** eo double* equation of the origins (ERA-GST) ** ** Returned (function value): ** int status: +1 = dubious year (Note 2) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 2) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the ** future to be trusted. See iauDat for further details. ** ** 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 4) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 5) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many ** applications, xp and yp can be set to zero. ** ** Internally, the polar motion is stored in a form rotated onto ** the local meridian. ** ** 6) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to ** the pressure and that an accurate phpa value is important for ** precise work. ** ** 7) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 8) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 9) In cases where the caller wishes to supply his own Earth ** ephemeris, Earth rotation information and refraction constants, ** the function iauApco can be used instead of the present function. ** ** 10) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 11) The context structure astrom produced by this function is used ** by iauAtioq, iauAtoiq, iauAtciq* and iauAticq*. ** ** Called: ** iauUtctai UTC to TAI ** iauTaitt TAI to TT ** iauUtcut1 UTC to UT1 ** iauEpv00 Earth position and velocity ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** iauEra00 Earth rotation angle, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauRefco refraction constants for given ambient conditions ** iauApco astrometry parameters, ICRS-observed ** iauEors equation of the origins, given NPB matrix and s ** */ void iauApcs(double date1, double date2, double pv[2][3], double ebpv[2][3], double ehp[3], iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p c s ** - - - - - - - - ** ** For an observer whose geocentric position and velocity are known, ** prepare star-independent astrometry parameters for transformations ** between ICRS and GCRS. The Earth ephemeris is supplied by the ** caller. ** ** The parameters produced by this function are required in the space ** motion, parallax, light deflection and aberration parts of the ** astrometric transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** pv double[2][3] observer's geocentric pos/vel (m, m/s) ** ebpv double[2][3] Earth barycentric PV (au, au/day) ** ehp double[3] Earth heliocentric P (au) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) Providing separate arguments for (i) the observer's geocentric ** position and velocity and (ii) the Earth ephemeris is done for ** convenience in the geocentric, terrestrial and Earth orbit cases. ** For deep space applications it maybe more convenient to specify ** zero geocentric position and velocity and to supply the ** observer's position and velocity information directly instead of ** with respect to the Earth. However, note the different units: ** m and m/s for the geocentric vectors, au and au/day for the ** heliocentric and barycentric vectors. ** ** 4) In cases where the caller does not wish to provide the Earth ** ephemeris, the function iauApcs13 can be used instead of the ** present function. This computes the Earth ephemeris using the ** SOFA function iauEpv00. ** ** 5) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 6) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauCp copy p-vector ** iauPm modulus of p-vector ** iauPn decompose p-vector into modulus and direction ** iauIr initialize r-matrix to identity ** */ void iauApcs13(double date1, double date2, double pv[2][3], iauASTROM *astrom) /* ** - - - - - - - - - - ** i a u A p c s 1 3 ** - - - - - - - - - - ** ** For an observer whose geocentric position and velocity are known, ** prepare star-independent astrometry parameters for transformations ** between ICRS and GCRS. The Earth ephemeris is from SOFA models. ** ** The parameters produced by this function are required in the space ** motion, parallax, light deflection and aberration parts of the ** astrometric transformation chain. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** pv double[2][3] observer's geocentric pos/vel (Note 3) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) The observer's position and velocity pv are geocentric but with ** respect to BCRS axes, and in units of m and m/s. No assumptions ** are made about proximity to the Earth, and the function can be ** used for deep space applications as well as Earth orbit and ** terrestrial. ** ** 4) In cases where the caller wishes to supply his own Earth ** ephemeris, the function iauApcs can be used instead of the present ** function. ** ** 5) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 6) The context structure astrom produced by this function is used by ** iauAtciq* and iauAticq*. ** ** Called: ** iauEpv00 Earth position and velocity ** iauApcs astrometry parameters, ICRS-GCRS, space observer ** */ void iauAper(double theta, iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p e r ** - - - - - - - - ** ** In the star-independent astrometry parameters, update only the ** Earth rotation angle, supplied by the caller explicitly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** theta double Earth rotation angle (radians, Note 2) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double not used ** eb double[3] not used ** eh double[3] not used ** em double not used ** v double[3] not used ** bm1 double not used ** bpn double[3][3] not used ** along double longitude + s' (radians) ** xpl double not used ** ypl double not used ** sphi double not used ** cphi double not used ** diurab double not used ** eral double not used ** refa double not used ** refb double not used ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double unchanged ** eb double[3] unchanged ** eh double[3] unchanged ** em double unchanged ** v double[3] unchanged ** bm1 double unchanged ** bpn double[3][3] unchanged ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double "local" Earth rotation angle (radians) ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) This function exists to enable sidereal-tracking applications to ** avoid wasteful recomputation of the bulk of the astrometry ** parameters: only the Earth rotation is updated. ** ** 2) For targets expressed as equinox based positions, such as ** classical geocentric apparent (RA,Dec), the supplied theta can be ** Greenwich apparent sidereal time rather than Earth rotation ** angle. ** ** 3) The function iauAper13 can be used instead of the present ** function, and starts from UT1 rather than ERA itself. ** ** 4) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** */ void iauAper13(double ut11, double ut12, iauASTROM *astrom) /* ** - - - - - - - - - - ** i a u A p e r 1 3 ** - - - - - - - - - - ** ** In the star-independent astrometry parameters, update only the ** Earth rotation angle. The caller provides UT1, (n.b. not UTC). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ut11 double UT1 as a 2-part... ** ut12 double ...Julian Date (Note 1) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double not used ** eb double[3] not used ** eh double[3] not used ** em double not used ** v double[3] not used ** bm1 double not used ** bpn double[3][3] not used ** along double longitude + s' (radians) ** xpl double not used ** ypl double not used ** sphi double not used ** cphi double not used ** diurab double not used ** eral double not used ** refa double not used ** refb double not used ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double unchanged ** eb double[3] unchanged ** eh double[3] unchanged ** em double unchanged ** v double[3] unchanged ** bm1 double unchanged ** bpn double[3][3] unchanged ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double "local" Earth rotation angle (radians) ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The UT1 date (n.b. not UTC) ut11+ut12 is a Julian Date, ** apportioned in any convenient way between the arguments ut11 and ** ut12. For example, JD(UT1)=2450123.7 could be expressed in any ** of these ways, among others: ** ** ut11 ut12 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. The date & time method is ** best matched to the algorithm used: maximum precision is ** delivered when the ut11 argument is for 0hrs UT1 on the day in ** question and the ut12 argument lies in the range 0 to 1, or vice ** versa. ** ** 2) If the caller wishes to provide the Earth rotation angle itself, ** the function iauAper can be used instead. One use of this ** technique is to substitute Greenwich apparent sidereal time and ** thereby to support equinox based transformations directly. ** ** 3) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** Called: ** iauAper astrometry parameters: update ERA ** iauEra00 Earth rotation angle, IAU 2000 ** */ void iauApio(double sp, double theta, double elong, double phi, double hm, double xp, double yp, double refa, double refb, iauASTROM *astrom) /* ** - - - - - - - - ** i a u A p i o ** - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between CIRS and observed ** coordinates. The caller supplies the Earth orientation information ** and the refraction constants as well as the site coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** sp double the TIO locator s' (radians, Note 1) ** theta double Earth rotation angle (radians) ** elong double longitude (radians, east +ve, Note 2) ** phi double geodetic latitude (radians, Note 2) ** hm double height above ellipsoid (m, geodetic Note 2) ** xp,yp double polar motion coordinates (radians, Note 3) ** refa double refraction constant A (radians, Note 4) ** refb double refraction constant B (radians, Note 4) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double unchanged ** eb double[3] unchanged ** eh double[3] unchanged ** em double unchanged ** v double[3] unchanged ** bm1 double unchanged ** bpn double[3][3] unchanged ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Notes: ** ** 1) sp, the TIO locator s', is a tiny quantity needed only by the ** most precise applications. It can either be set to zero or ** predicted using the SOFA function iauSp00. ** ** 2) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 3) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many applications, ** xp and yp can be set to zero. ** ** Internally, the polar motion is stored in a form rotated onto the ** local meridian. ** ** 4) The refraction constants refa and refb are for use in a ** dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed ** (i.e. refracted) zenith distance and dZ is the amount of ** refraction. ** ** 5) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 6) In cases where the caller does not wish to provide the Earth ** rotation information and refraction constants, the function ** iauApio13 can be used instead of the present function. This ** starts from UTC and weather readings etc. and computes suitable ** values using other SOFA functions. ** ** 7) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 8) The context structure astrom produced by this function is used by ** iauAtioq and iauAtoiq. ** ** Called: ** iauPvtob position/velocity of terrestrial station ** iauAper astrometry parameters: update ERA ** */ int iauApio13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom) /* ** - - - - - - - - - - ** i a u A p i o 1 3 ** - - - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between CIRS and observed ** coordinates. The caller supplies UTC, site coordinates, ambient air ** conditions and observing wavelength. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 1,2) ** dut1 double UT1-UTC (seconds) ** elong double longitude (radians, east +ve, Note 3) ** phi double geodetic latitude (radians, Note 3) ** hm double height above ellipsoid (m, geodetic Notes 4,6) ** xp,yp double polar motion coordinates (radians, Note 5) ** phpa double pressure at the observer (hPa = mB, Note 6) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 7) ** ** Returned: ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double unchanged ** eb double[3] unchanged ** eh double[3] unchanged ** em double unchanged ** v double[3] unchanged ** bm1 double unchanged ** bpn double[3][3] unchanged ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned (function value): ** int status: +1 = dubious year (Note 2) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 2) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 4) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 5) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many applications, ** xp and yp can be set to zero. ** ** Internally, the polar motion is stored in a form rotated onto ** the local meridian. ** ** 6) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to the ** pressure and that an accurate phpa value is important for ** precise work. ** ** 7) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 8) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 9) In cases where the caller wishes to supply his own Earth ** rotation information and refraction constants, the function ** iauApc can be used instead of the present function. ** ** 10) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** iauApcg iauApcg13 geocentric ICRS <-> GCRS ** iauApci iauApci13 terrestrial ICRS <-> CIRS ** iauApco iauApco13 terrestrial ICRS <-> observed ** iauApcs iauApcs13 space ICRS <-> GCRS ** iauAper iauAper13 terrestrial update Earth rotation ** iauApio iauApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary SOFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 11) The context structure astrom produced by this function is used ** by iauAtioq and iauAtoiq. ** ** Called: ** iauUtctai UTC to TAI ** iauTaitt TAI to TT ** iauUtcut1 UTC to UT1 ** iauSp00 the TIO locator s', IERS 2000 ** iauEra00 Earth rotation angle, IAU 2000 ** iauRefco refraction constants for given ambient conditions ** iauApio astrometry parameters, CIRS-observed ** */ void iauAtci13(double rc, double dc, double pr, double pd, double px, double rv, double date1, double date2, double *ri, double *di, double *eo) /* ** - - - - - - - - - - ** i a u A t c i 1 3 ** - - - - - - - - - - ** ** Transform ICRS star data, epoch J2000.0, to CIRS. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc double ICRS right ascension at J2000.0 (radians, Note 1) ** dc double ICRS declination at J2000.0 (radians, Note 1) ** pr double RA proper motion (radians/year; Note 2) ** pd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, +ve if receding) ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 3) ** ** Returned: ** ri,di double* CIRS geocentric RA,Dec (radians) ** eo double* equation of the origins (ERA-GST, Note 5) ** ** Notes: ** ** 1) Star data for an epoch other than J2000.0 (for example from the ** Hipparcos catalog, which has an epoch of J1991.25) will require a ** preliminary call to iauPmsafe before use. ** ** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 3) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.8g could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.8g 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 4) The available accuracy is better than 1 milliarcsecond, limited ** mainly by the precession-nutation model that is used, namely ** IAU 2000A/2006. Very close to solar system bodies, additional ** errors of up to several milliarcseconds can occur because of ** unmodeled light deflection; however, the Sun's contribution is ** taken into account, to first order. The accuracy limitations of ** the SOFA function iauEpv00 (used to compute Earth position and ** velocity) can contribute aberration errors of up to ** 5 microarcseconds. Light deflection at the Sun's limb is ** uncertain at the 0.4 mas level. ** ** 5) Should the transformation to (equinox based) apparent place be ** required rather than (CIO based) intermediate place, subtract the ** equation of the origins from the returned right ascension: ** RA = RI - EO. (The iauAnp function can then be applied, as ** required, to keep the result in the conventional 0-2pi range.) ** ** Called: ** iauApci13 astrometry parameters, ICRS-CIRS, 2013 ** iauAtciq quick ICRS to CIRS ** */ void iauAtciq(double rc, double dc, double pr, double pd, double px, double rv, iauASTROM *astrom, double *ri, double *di) /* ** - - - - - - - - - ** i a u A t c i q ** - - - - - - - - - ** ** Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed ** star-independent astrometry parameters. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are to be transformed for one date. The ** star-independent parameters can be obtained by calling one of the ** functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13]. ** ** If the parallax and proper motions are zero the iauAtciqz function ** can be used instead. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc,dc double ICRS RA,Dec at J2000.0 (radians) ** pr double RA proper motion (radians/year; Note 3) ** pd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, +ve if receding) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** ri,di double CIRS RA,Dec (radians) ** ** Notes: ** ** 1) All the vectors are with respect to BCRS axes. ** ** 2) Star data for an epoch other than J2000.0 (for example from the ** Hipparcos catalog, which has an epoch of J1991.25) will require a ** preliminary call to iauPmsafe before use. ** ** 3) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** Called: ** iauPmpx proper motion and parallax ** iauLdsun light deflection by the Sun ** iauAb stellar aberration ** iauRxp product of r-matrix and pv-vector ** iauC2s p-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** */ void iauAtciqn(double rc, double dc, double pr, double pd, double px, double rv, iauASTROM *astrom, int n, iauLDBODY b[], double *ri, double *di) /* ** - - - - - - - - - - ** i a u A t c i q n ** - - - - - - - - - - ** ** Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed ** star-independent astrometry parameters plus a list of light- ** deflecting bodies. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are to be transformed for one date. The ** star-independent parameters can be obtained by calling one of the ** functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13]. ** ** ** If the only light-deflecting body to be taken into account is the ** Sun, the iauAtciq function can be used instead. If in addition the ** parallax and proper motions are zero, the iauAtciqz function can be ** used. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc,dc double ICRS RA,Dec at J2000.0 (radians) ** pr double RA proper motion (radians/year; Note 3) ** pd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, +ve if receding) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** n int number of bodies (Note 3) ** b iauLDBODY[n] data for each of the n bodies (Notes 3,4): ** bm double mass of the body (solar masses, Note 5) ** dl double deflection limiter (Note 6) ** pv [2][3] barycentric PV of the body (au, au/day) ** ** Returned: ** ri,di double CIRS RA,Dec (radians) ** ** Notes: ** ** 1) Star data for an epoch other than J2000.0 (for example from the ** Hipparcos catalog, which has an epoch of J1991.25) will require a ** preliminary call to iauPmsafe before use. ** ** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 3) The struct b contains n entries, one for each body to be ** considered. If n = 0, no gravitational light deflection will be ** applied, not even for the Sun. ** ** 4) The struct b should include an entry for the Sun as well as for ** any planet or other body to be taken into account. The entries ** should be in the order in which the light passes the body. ** ** 5) In the entry in the b struct for body i, the mass parameter ** b[i].bm can, as required, be adjusted in order to allow for such ** effects as quadrupole field. ** ** 6) The deflection limiter parameter b[i].dl is phi^2/2, where phi is ** the angular separation (in radians) between star and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. Example values suitable for a terrestrial ** observer, together with masses, are as follows: ** ** body i b[i].bm b[i].dl ** ** Sun 1.0 6e-6 ** Jupiter 0.00095435 3e-9 ** Saturn 0.00028574 3e-10 ** ** 7) For efficiency, validation of the contents of the b array is ** omitted. The supplied masses must be greater than zero, the ** position and velocity vectors must be right, and the deflection ** limiter greater than zero. ** ** Called: ** iauPmpx proper motion and parallax ** iauLdn light deflection by n bodies ** iauAb stellar aberration ** iauRxp product of r-matrix and pv-vector ** iauC2s p-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** */ void iauAtciqz(double rc, double dc, iauASTROM *astrom, double *ri, double *di) /* ** - - - - - - - - - - ** i a u A t c i q z ** - - - - - - - - - - ** ** Quick ICRS to CIRS transformation, given precomputed star- ** independent astrometry parameters, and assuming zero parallax and ** proper motion. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are to be transformed for one date. The ** star-independent parameters can be obtained by calling one of the ** functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13]. ** ** The corresponding function for the case of non-zero parallax and ** proper motion is iauAtciq. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc,dc double ICRS astrometric RA,Dec (radians) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** ri,di double CIRS RA,Dec (radians) ** ** Note: ** ** All the vectors are with respect to BCRS axes. ** ** References: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013). ** ** Klioner, Sergei A., "A practical relativistic model for micro- ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauLdsun light deflection due to Sun ** iauAb stellar aberration ** iauRxp product of r-matrix and p-vector ** iauC2s p-vector to spherical ** iauAnp normalize angle into range +/- pi ** */ int iauAtco13(double rc, double dc, double pr, double pd, double px, double rv, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *aob, double *zob, double *hob, double *dob, double *rob, double *eo) /* ** - - - - - - - - - - ** i a u A t c o 1 3 ** - - - - - - - - - - ** ** ICRS RA,Dec to observed place. The caller supplies UTC, site ** coordinates, ambient air conditions and observing wavelength. ** ** SOFA models are used for the Earth ephemeris, bias-precession- ** nutation, Earth orientation and refraction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc,dc double ICRS right ascension at J2000.0 (radians, Note 1) ** pr double RA proper motion (radians/year; Note 2) ** pd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, +ve if receding) ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 3-4) ** dut1 double UT1-UTC (seconds, Note 5) ** elong double longitude (radians, east +ve, Note 6) ** phi double latitude (geodetic, radians, Note 6) ** hm double height above ellipsoid (m, geodetic, Notes 6,8) ** xp,yp double polar motion coordinates (radians, Note 7) ** phpa double pressure at the observer (hPa = mB, Note 8) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 9) ** ** Returned: ** aob double* observed azimuth (radians: N=0,E=90) ** zob double* observed zenith distance (radians) ** hob double* observed hour angle (radians) ** dob double* observed declination (radians) ** rob double* observed right ascension (CIO-based, radians) ** eo double* equation of the origins (ERA-GST) ** ** Returned (function value): ** int status: +1 = dubious year (Note 4) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) Star data for an epoch other than J2000.0 (for example from the ** Hipparcos catalog, which has an epoch of J1991.25) will require ** a preliminary call to iauPmsafe before use. ** ** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 3) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 4) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the ** future to be trusted. See iauDat for further details. ** ** 5) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 6) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 7) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many ** applications, xp and yp can be set to zero. ** ** 8) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), ** is available, an adequate estimate of hm can be obtained from ** the expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to ** the pressure and that an accurate phpa value is important for ** precise work. ** ** 9) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 10) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted observed ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better ** than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions iauAtco13 and ** iauAtoc13 are self-consistent to better than 1 microarcsecond ** all over the celestial sphere. With refraction included, ** consistency falls off at high zenith distances, but is still ** better than 0.05 arcsec at 85 degrees. ** ** 11) "Observed" Az,ZD means the position that would be seen by a ** perfect geodetically aligned theodolite. (Zenith distance is ** used rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) This is ** related to the observed HA,Dec via the standard rotation, using ** the geodetic latitude (corrected for polar motion), while the ** observed HA and RA are related simply through the Earth rotation ** angle and the site longitude. "Observed" RA,Dec or HA,Dec thus ** means the position that would be seen by a perfect equatorial ** with its polar axis aligned to the Earth's axis of rotation. ** ** 12) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** iauApco13 astrometry parameters, ICRS-observed, 2013 ** iauAtciq quick ICRS to CIRS ** iauAtioq quick CIRS to observed ** */ void iauAtic13(double ri, double di, double date1, double date2, double *rc, double *dc, double *eo) /* ** - - - - - - - - - - ** i a u A t i c 1 3 ** - - - - - - - - - - ** ** Transform star RA,Dec from geocentric CIRS to ICRS astrometric. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri,di double CIRS geocentric RA,Dec (radians) ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ** Returned: ** rc,dc double ICRS astrometric RA,Dec (radians) ** eo double equation of the origins (ERA-GST, Note 4) ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) Iterative techniques are used for the aberration and light ** deflection corrections so that the functions iauAtic13 (or ** iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses; ** even at the edge of the Sun's disk the discrepancy is only about ** 1 nanoarcsecond. ** ** 3) The available accuracy is better than 1 milliarcsecond, limited ** mainly by the precession-nutation model that is used, namely ** IAU 2000A/2006. Very close to solar system bodies, additional ** errors of up to several milliarcseconds can occur because of ** unmodeled light deflection; however, the Sun's contribution is ** taken into account, to first order. The accuracy limitations of ** the SOFA function iauEpv00 (used to compute Earth position and ** velocity) can contribute aberration errors of up to ** 5 microarcseconds. Light deflection at the Sun's limb is ** uncertain at the 0.4 mas level. ** ** 4) Should the transformation to (equinox based) J2000.0 mean place ** be required rather than (CIO based) ICRS coordinates, subtract the ** equation of the origins from the returned right ascension: ** RA = RI - EO. (The iauAnp function can then be applied, as ** required, to keep the result in the conventional 0-2pi range.) ** ** Called: ** iauApci13 astrometry parameters, ICRS-CIRS, 2013 ** iauAticq quick CIRS to ICRS astrometric ** */ void iauAticq(double ri, double di, iauASTROM *astrom, double *rc, double *dc) /* ** - - - - - - - - - ** i a u A t i c q ** - - - - - - - - - ** ** Quick CIRS RA,Dec to ICRS astrometric place, given the star- ** independent astrometry parameters. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are all to be transformed for one date. ** The star-independent astrometry parameters can be obtained by ** calling one of the functions iauApci[13], iauApcg[13], iauApco[13] ** or iauApcs[13]. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri,di double CIRS RA,Dec (radians) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** rc,dc double ICRS astrometric RA,Dec (radians) ** ** Notes: ** ** 1) Only the Sun is taken into account in the light deflection ** correction. ** ** 2) Iterative techniques are used for the aberration and light ** deflection corrections so that the functions iauAtic13 (or ** iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses; ** even at the edge of the Sun's disk the discrepancy is only about ** 1 nanoarcsecond. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauTrxp product of transpose of r-matrix and p-vector ** iauZp zero p-vector ** iauAb stellar aberration ** iauLdsun light deflection by the Sun ** iauC2s p-vector to spherical ** iauAnp normalize angle into range +/- pi ** */ void iauAticqn(double ri, double di, iauASTROM *astrom, int n, iauLDBODY b[], double *rc, double *dc) /* ** - - - - - - - - - ** i a u A t i c q n ** - - - - - - - - - ** ** Quick CIRS to ICRS astrometric place transformation, given the star- ** independent astrometry parameters plus a list of light-deflecting ** bodies. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are all to be transformed for one date. ** The star-independent astrometry parameters can be obtained by ** calling one of the functions iauApci[13], iauApcg[13], iauApco[13] ** or iauApcs[13]. * * If the only light-deflecting body to be taken into account is the * Sun, the iauAticq function can be used instead. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri,di double CIRS RA,Dec (radians) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** n int number of bodies (Note 3) ** b iauLDBODY[n] data for each of the n bodies (Notes 3,4): ** bm double mass of the body (solar masses, Note 5) ** dl double deflection limiter (Note 6) ** pv [2][3] barycentric PV of the body (au, au/day) ** ** Returned: ** rc,dc double ICRS astrometric RA,Dec (radians) ** ** Notes: ** ** 1) Iterative techniques are used for the aberration and light ** deflection corrections so that the functions iauAticqn and ** iauAtciqn are accurate inverses; even at the edge of the Sun's ** disk the discrepancy is only about 1 nanoarcsecond. ** ** 2) If the only light-deflecting body to be taken into account is the ** Sun, the iauAticq function can be used instead. ** ** 3) The struct b contains n entries, one for each body to be ** considered. If n = 0, no gravitational light deflection will be ** applied, not even for the Sun. ** ** 4) The struct b should include an entry for the Sun as well as for ** any planet or other body to be taken into account. The entries ** should be in the order in which the light passes the body. ** ** 5) In the entry in the b struct for body i, the mass parameter ** b[i].bm can, as required, be adjusted in order to allow for such ** effects as quadrupole field. ** ** 6) The deflection limiter parameter b[i].dl is phi^2/2, where phi is ** the angular separation (in radians) between star and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. Example values suitable for a terrestrial ** observer, together with masses, are as follows: ** ** body i b[i].bm b[i].dl ** ** Sun 1.0 6e-6 ** Jupiter 0.00095435 3e-9 ** Saturn 0.00028574 3e-10 ** ** 7) For efficiency, validation of the contents of the b array is ** omitted. The supplied masses must be greater than zero, the ** position and velocity vectors must be right, and the deflection ** limiter greater than zero. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauTrxp product of transpose of r-matrix and p-vector ** iauZp zero p-vector ** iauAb stellar aberration ** iauLdn light deflection by n bodies ** iauC2s p-vector to spherical ** iauAnp normalize angle into range +/- pi ** */ int iauAtio13(double ri, double di, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *aob, double *zob, double *hob, double *dob, double *rob) /* ** - - - - - - - - - - ** i a u A t i o 1 3 ** - - - - - - - - - - ** ** CIRS RA,Dec to observed place. The caller supplies UTC, site ** coordinates, ambient air conditions and observing wavelength. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri double CIRS right ascension (CIO-based, radians) ** di double CIRS declination (radians) ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 1,2) ** dut1 double UT1-UTC (seconds, Note 3) ** elong double longitude (radians, east +ve, Note 4) ** phi double geodetic latitude (radians, Note 4) ** hm double height above ellipsoid (m, geodetic Notes 4,6) ** xp,yp double polar motion coordinates (radians, Note 5) ** phpa double pressure at the observer (hPa = mB, Note 6) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 7) ** ** Returned: ** aob double* observed azimuth (radians: N=0,E=90) ** zob double* observed zenith distance (radians) ** hob double* observed hour angle (radians) ** dob double* observed declination (radians) ** rob double* observed right ascension (CIO-based, radians) ** ** Returned (function value): ** int status: +1 = dubious year (Note 2) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 2) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the ** future to be trusted. See iauDat for further details. ** ** 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 4) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 5) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many ** applications, xp and yp can be set to zero. ** ** 6) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to ** the pressure and that an accurate phpa value is important for ** precise work. ** ** 7) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 8) "Observed" Az,ZD means the position that would be seen by a ** perfect geodetically aligned theodolite. (Zenith distance is ** used rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) This is ** related to the observed HA,Dec via the standard rotation, using ** the geodetic latitude (corrected for polar motion), while the ** observed HA and RA are related simply through the Earth rotation ** angle and the site longitude. "Observed" RA,Dec or HA,Dec thus ** means the position that would be seen by a perfect equatorial ** with its polar axis aligned to the Earth's axis of rotation. ** ** 9) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted astrometric ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better ** than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** 10) The complementary functions iauAtio13 and iauAtoi13 are self- ** consistent to better than 1 microarcsecond all over the ** celestial sphere. ** ** 11) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** iauApio13 astrometry parameters, CIRS-observed, 2013 ** iauAtioq quick CIRS to observed ** */ void iauAtioq(double ri, double di, iauASTROM *astrom, double *aob, double *zob, double *hob, double *dob, double *rob) /* ** - - - - - - - - - ** i a u A t i o q ** - - - - - - - - - ** ** Quick CIRS to observed place transformation. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are all to be transformed for one date. ** The star-independent astrometry parameters can be obtained by ** calling iauApio[13] or iauApco[13]. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri double CIRS right ascension ** di double CIRS declination ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** aob double* observed azimuth (radians: N=0,E=90) ** zob double* observed zenith distance (radians) ** hob double* observed hour angle (radians) ** dob double* observed declination (radians) ** rob double* observed right ascension (CIO-based, radians) ** ** Notes: ** ** 1) This function returns zenith distance rather than altitude in ** order to reflect the fact that no allowance is made for ** depression of the horizon. ** ** 2) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted observed ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better ** than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions iauAtioq and ** iauAtoiq are self-consistent to better than 1 microarcsecond all ** over the celestial sphere. With refraction included, consistency ** falls off at high zenith distances, but is still better than ** 0.05 arcsec at 85 degrees. ** ** 3) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 4) The CIRS RA,Dec is obtained from a star catalog mean place by ** allowing for space motion, parallax, the Sun's gravitational lens ** effect, annual aberration and precession-nutation. For star ** positions in the ICRS, these effects can be applied by means of ** the iauAtci13 (etc.) functions. Starting from classical "mean ** place" systems, additional transformations will be needed first. ** ** 5) "Observed" Az,El means the position that would be seen by a ** perfect geodetically aligned theodolite. This is obtained from ** the CIRS RA,Dec by allowing for Earth orientation and diurnal ** aberration, rotating from equator to horizon coordinates, and ** then adjusting for refraction. The HA,Dec is obtained by ** rotating back into equatorial coordinates, and is the position ** that would be seen by a perfect equatorial with its polar axis ** aligned to the Earth's axis of rotation. Finally, the RA is ** obtained by subtracting the HA from the local ERA. ** ** 6) The star-independent CIRS-to-observed-place parameters in ASTROM ** may be computed with iauApio[13] or iauApco[13]. If nothing has ** changed significantly except the time, iauAper[13] may be used to ** perform the requisite adjustment to the astrom structure. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauC2s p-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** */ int iauAtoc13(const char *type, double ob1, double ob2, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *rc, double *dc) /* ** - - - - - - - - - - ** i a u A t o c 1 3 ** - - - - - - - - - - ** ** Observed place at a groundbased site to to ICRS astrometric RA,Dec. ** The caller supplies UTC, site coordinates, ambient air conditions ** and observing wavelength. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** type char[] type of coordinates - "R", "H" or "A" (Notes 1,2) ** ob1 double observed Az, HA or RA (radians; Az is N=0,E=90) ** ob2 double observed ZD or Dec (radians) ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 3,4) ** dut1 double UT1-UTC (seconds, Note 5) ** elong double longitude (radians, east +ve, Note 6) ** phi double geodetic latitude (radians, Note 6) ** hm double height above ellipsoid (m, geodetic Notes 6,8) ** xp,yp double polar motion coordinates (radians, Note 7) ** phpa double pressure at the observer (hPa = mB, Note 8) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 9) ** ** Returned: ** rc,dc double ICRS astrometric RA,Dec (radians) ** ** Returned (function value): ** int status: +1 = dubious year (Note 4) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) "Observed" Az,ZD means the position that would be seen by a ** perfect geodetically aligned theodolite. (Zenith distance is ** used rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) This is ** related to the observed HA,Dec via the standard rotation, using ** the geodetic latitude (corrected for polar motion), while the ** observed HA and RA are related simply through the Earth rotation ** angle and the site longitude. "Observed" RA,Dec or HA,Dec thus ** means the position that would be seen by a perfect equatorial ** with its polar axis aligned to the Earth's axis of rotation. ** ** 2) Only the first character of the type argument is significant. ** "R" or "r" indicates that ob1 and ob2 are the observed right ** ascension and declination; "H" or "h" indicates that they are ** hour angle (west +ve) and declination; anything else ("A" or ** "a" is recommended) indicates that ob1 and ob2 are azimuth ** (north zero, east 90 deg) and zenith distance. ** ** 3) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 4) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the ** future to be trusted. See iauDat for further details. ** ** 5) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 6) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 7) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many ** applications, xp and yp can be set to zero. ** ** 8) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to ** the pressure and that an accurate phpa value is important for ** precise work. ** ** 9) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 10) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted astrometric ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better ** than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions iauAtco13 and ** iauAtoc13 are self-consistent to better than 1 microarcsecond ** all over the celestial sphere. With refraction included, ** consistency falls off at high zenith distances, but is still ** better than 0.05 arcsec at 85 degrees. ** ** 11) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** iauApco13 astrometry parameters, ICRS-observed ** iauAtoiq quick observed to CIRS ** iauAticq quick CIRS to ICRS ** */ int iauAtoi13(const char *type, double ob1, double ob2, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *ri, double *di) /* ** - - - - - - - - - - ** i a u A t o i 1 3 ** - - - - - - - - - - ** ** Observed place to CIRS. The caller supplies UTC, site coordinates, ** ambient air conditions and observing wavelength. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** type char[] type of coordinates - "R", "H" or "A" (Notes 1,2) ** ob1 double observed Az, HA or RA (radians; Az is N=0,E=90) ** ob2 double observed ZD or Dec (radians) ** utc1 double UTC as a 2-part... ** utc2 double ...quasi Julian Date (Notes 3,4) ** dut1 double UT1-UTC (seconds, Note 5) ** elong double longitude (radians, east +ve, Note 6) ** phi double geodetic latitude (radians, Note 6) ** hm double height above the ellipsoid (meters, Notes 6,8) ** xp,yp double polar motion coordinates (radians, Note 7) ** phpa double pressure at the observer (hPa = mB, Note 8) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers, Note 9) ** ** Returned: ** ri double* CIRS right ascension (CIO-based, radians) ** di double* CIRS declination (radians) ** ** Returned (function value): ** int status: +1 = dubious year (Note 2) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) "Observed" Az,ZD means the position that would be seen by a ** perfect geodetically aligned theodolite. (Zenith distance is ** used rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) This is ** related to the observed HA,Dec via the standard rotation, using ** the geodetic latitude (corrected for polar motion), while the ** observed HA and RA are related simply through the Earth rotation ** angle and the site longitude. "Observed" RA,Dec or HA,Dec thus ** means the position that would be seen by a perfect equatorial ** with its polar axis aligned to the Earth's axis of rotation. ** ** 2) Only the first character of the type argument is significant. ** "R" or "r" indicates that ob1 and ob2 are the observed right ** ascension and declination; "H" or "h" indicates that they are ** hour angle (west +ve) and declination; anything else ("A" or ** "a" is recommended) indicates that ob1 and ob2 are azimuth ** (north zero, east 90 deg) and zenith distance. ** ** 3) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** However, JD cannot unambiguously represent UTC during a leap ** second unless special measures are taken. The convention in the ** present function is that the JD day represents UTC days whether ** the length is 86399, 86400 or 86401 SI seconds. ** ** Applications should use the function iauDtf2d to convert from ** calendar date and time of day into 2-part quasi Julian Date, as ** it implements the leap-second-ambiguity convention just ** described. ** ** 4) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the ** future to be trusted. See iauDat for further details. ** ** 5) UT1-UTC is tabulated in IERS bulletins. It increases by exactly ** one second at the end of each positive UTC leap second, ** introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This ** practice is under review, and in the future UT1-UTC may grow ** essentially without limit. ** ** 6) The geographical coordinates are with respect to the WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the ** longitude required by the present function is east-positive ** (i.e. right-handed), in accordance with geographical convention. ** ** 7) The polar motion xp,yp can be obtained from IERS bulletins. The ** values are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions 2003), measured along the ** meridians 0 and 90 deg west respectively. For many ** applications, xp and yp can be set to zero. ** ** 8) If hm, the height above the ellipsoid of the observing station ** in meters, is not known but phpa, the pressure in hPa (=mB), is ** available, an adequate estimate of hm can be obtained from the ** expression ** ** hm = -29.3 * tsl * log ( phpa / 1013.25 ); ** ** where tsl is the approximate sea-level air temperature in K ** (See Astrophysical Quantities, C.W.Allen, 3rd edition, section ** 52). Similarly, if the pressure phpa is not known, it can be ** estimated from the height of the observing station, hm, as ** follows: ** ** phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); ** ** Note, however, that the refraction is nearly proportional to ** the pressure and that an accurate phpa value is important for ** precise work. ** ** 9) The argument wl specifies the observing wavelength in ** micrometers. The transition from optical to radio is assumed to ** occur at 100 micrometers (about 3000 GHz). ** ** 10) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted astrometric ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better ** than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions iauAtio13 and ** iauAtoi13 are self-consistent to better than 1 microarcsecond ** all over the celestial sphere. With refraction included, ** consistency falls off at high zenith distances, but is still ** better than 0.05 arcsec at 85 degrees. ** ** 12) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** iauApio13 astrometry parameters, CIRS-observed, 2013 ** iauAtoiq quick observed to CIRS ** */ void iauAtoiq(const char *type, double ob1, double ob2, iauASTROM *astrom, double *ri, double *di) /* ** - - - - - - - - - ** i a u A t o i q ** - - - - - - - - - ** ** Quick observed place to CIRS, given the star-independent astrometry ** parameters. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are all to be transformed for one date. ** The star-independent astrometry parameters can be obtained by ** calling iauApio[13] or iauApco[13]. ** ** Status: support function. ** ** Given: ** type char[] type of coordinates: "R", "H" or "A" (Note 1) ** ob1 double observed Az, HA or RA (radians; Az is N=0,E=90) ** ob2 double observed ZD or Dec (radians) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** ri double* CIRS right ascension (CIO-based, radians) ** di double* CIRS declination (radians) ** ** Notes: ** ** 1) "Observed" Az,El means the position that would be seen by a ** perfect geodetically aligned theodolite. This is related to ** the observed HA,Dec via the standard rotation, using the geodetic ** latitude (corrected for polar motion), while the observed HA and ** RA are related simply through the Earth rotation angle and the ** site longitude. "Observed" RA,Dec or HA,Dec thus means the ** position that would be seen by a perfect equatorial with its ** polar axis aligned to the Earth's axis of rotation. By removing ** from the observed place the effects of atmospheric refraction and ** diurnal aberration, the CIRS RA,Dec is obtained. ** ** 2) Only the first character of the type argument is significant. ** "R" or "r" indicates that ob1 and ob2 are the observed right ** ascension and declination; "H" or "h" indicates that they are ** hour angle (west +ve) and declination; anything else ("A" or ** "a" is recommended) indicates that ob1 and ob2 are azimuth (north ** zero, east 90 deg) and zenith distance. (Zenith distance is used ** rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) ** ** 3) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted observed ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better than ** 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions iauAtioq and ** iauAtoiq are self-consistent to better than 1 microarcsecond all ** over the celestial sphere. With refraction included, consistency ** falls off at high zenith distances, but is still better than ** 0.05 arcsec at 85 degrees. ** ** 4) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauC2s p-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** */ void iauBi00(double *dpsibi, double *depsbi, double *dra) /* ** - - - - - - - - ** i a u B i 0 0 ** - - - - - - - - ** ** Frame bias components of IAU 2000 precession-nutation models (part ** of MHB2000 with additions). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Returned: ** dpsibi,depsbi double longitude and obliquity corrections ** dra double the ICRS RA of the J2000.0 mean equinox ** ** Notes: ** ** 1) The frame bias corrections in longitude and obliquity (radians) ** are required in order to correct for the offset between the GCRS ** pole and the mean J2000.0 pole. They define, with respect to the ** GCRS frame, a J2000.0 mean pole that is consistent with the rest ** of the IAU 2000A precession-nutation model. ** ** 2) In addition to the displacement of the pole, the complete ** description of the frame bias requires also an offset in right ** ascension. This is not part of the IAU 2000A model, and is from ** Chapront et al. (2002). It is returned in radians. ** ** 3) This is a supplemented implementation of one aspect of the IAU ** 2000A nutation model, formally adopted by the IAU General ** Assembly in 2000, namely MHB2000 (Mathews et al. 2002). ** ** References: ** ** Chapront, J., Chapront-Touze, M. & Francou, G., Astron. ** Astrophys., 387, 700, 2002. ** ** Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation ** and precession New nutation series for nonrigid Earth and ** insights into the Earth's interior", J.Geophys.Res., 107, B4, ** 2002. The MHB2000 code itself was obtained on 9th September 2002 ** from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A. ** */ void iauBp00(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]) /* ** - - - - - - - - ** i a u B p 0 0 ** - - - - - - - - ** ** Frame bias and precession, IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rb double[3][3] frame bias matrix (Note 2) ** rp double[3][3] precession matrix (Note 3) ** rbp double[3][3] bias-precession matrix (Note 4) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rb transforms vectors from GCRS to mean J2000.0 by ** applying frame bias. ** ** 3) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 4) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 5) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the order given. ** ** Called: ** iauBi00 frame bias components, IAU 2000 ** iauPr00 IAU 2000 precession adjustments ** iauIr initialize r-matrix to identity ** iauRx rotate around X-axis ** iauRy rotate around Y-axis ** iauRz rotate around Z-axis ** iauCr copy r-matrix ** iauRxr product of two r-matrices ** ** Reference: ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** */ void iauBp06(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]) /* ** - - - - - - - - ** i a u B p 0 6 ** - - - - - - - - ** ** Frame bias and precession, IAU 2006. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rb double[3][3] frame bias matrix (Note 2) ** rp double[3][3] precession matrix (Note 3) ** rbp double[3][3] bias-precession matrix (Note 4) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rb transforms vectors from GCRS to mean J2000.0 by ** applying frame bias. ** ** 3) The matrix rp transforms vectors from mean J2000.0 to mean of ** date by applying precession. ** ** 4) The matrix rbp transforms vectors from GCRS to mean of date by ** applying frame bias then precession. It is the product rp x rb. ** ** 5) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the order given. ** ** Called: ** iauPfw06 bias-precession F-W angles, IAU 2006 ** iauFw2m F-W angles to r-matrix ** iauPmat06 PB matrix, IAU 2006 ** iauTr transpose r-matrix ** iauRxr product of two r-matrices ** iauCr copy r-matrix ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** */ void iauBpn2xy(double rbpn[3][3], double *x, double *y) /* ** - - - - - - - - - - ** i a u B p n 2 x y ** - - - - - - - - - - ** ** Extract from the bias-precession-nutation matrix the X,Y coordinates ** of the Celestial Intermediate Pole. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rbpn double[3][3] celestial-to-true matrix (Note 1) ** ** Returned: ** x,y double Celestial Intermediate Pole (Note 2) ** ** Notes: ** ** 1) The matrix rbpn transforms vectors from GCRS to true equator (and ** CIO or equinox) of date, and therefore the Celestial Intermediate ** Pole unit vector is the bottom row of the matrix. ** ** 2) The arguments x,y are components of the Celestial Intermediate ** Pole unit vector in the Geocentric Celestial Reference System. ** ** Reference: ** ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 ** (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** */ void iauC2i00a(double date1, double date2, double rc2i[3][3]) /* ** - - - - - - - - - - ** i a u C 2 i 0 0 a ** - - - - - - - - - - ** ** Form the celestial-to-intermediate matrix for a given date using the ** IAU 2000A precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 3) A faster, but slightly less accurate result (about 1 mas), can be ** obtained by using instead the iauC2i00b function. ** ** Called: ** iauPnm00a classical NPB matrix, IAU 2000A ** iauC2ibpn celestial-to-intermediate matrix, given NPB matrix ** ** References: ** ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 ** (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauC2i00b(double date1, double date2, double rc2i[3][3]) /* ** - - - - - - - - - - ** i a u C 2 i 0 0 b ** - - - - - - - - - - ** ** Form the celestial-to-intermediate matrix for a given date using the ** IAU 2000B precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 3) The present function is faster, but slightly less accurate (about ** 1 mas), than the iauC2i00a function. ** ** Called: ** iauPnm00b classical NPB matrix, IAU 2000B ** iauC2ibpn celestial-to-intermediate matrix, given NPB matrix ** ** References: ** ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 ** (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauC2i06a(double date1, double date2, double rc2i[3][3]) /* ** - - - - - - - - - - ** i a u C 2 i 0 6 a ** - - - - - - - - - - ** ** Form the celestial-to-intermediate matrix for a given date using the ** IAU 2006 precession and IAU 2000A nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = RC2T * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** Called: ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** iauC2ixys celestial-to-intermediate matrix, given X,Y and s ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** */ void iauC2ibpn(double date1, double date2, double rbpn[3][3], double rc2i[3][3]) /* ** - - - - - - - - - - ** i a u C 2 i b p n ** - - - - - - - - - - ** ** Form the celestial-to-intermediate matrix for a given date given ** the bias-precession-nutation matrix. IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** rbpn double[3][3] celestial-to-true matrix (Note 2) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 3) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rbpn transforms vectors from GCRS to true equator (and ** CIO or equinox) of date. Only the CIP (bottom row) is used. ** ** 3) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = RC2T * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 4) Although its name does not include "00", This function is in fact ** specific to the IAU 2000 models. ** ** Called: ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauC2ixy celestial-to-intermediate matrix, given X,Y ** ** References: ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauC2ixy(double date1, double date2, double x, double y, double rc2i[3][3]) /* ** - - - - - - - - - ** i a u C 2 i x y ** - - - - - - - - - ** ** Form the celestial to intermediate-frame-of-date matrix for a given ** date when the CIP X,Y coordinates are known. IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** x,y double Celestial Intermediate Pole (Note 2) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 3) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y components ** of the unit vector in the Geocentric Celestial Reference System. ** ** 3) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = RC2T * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 4) Although its name does not include "00", This function is in fact ** specific to the IAU 2000 models. ** ** Called: ** iauC2ixys celestial-to-intermediate matrix, given X,Y and s ** iauS00 the CIO locator s, given X,Y, IAU 2000A ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauC2ixys(double x, double y, double s, double rc2i[3][3]) /* ** - - - - - - - - - - ** i a u C 2 i x y s ** - - - - - - - - - - ** ** Form the celestial to intermediate-frame-of-date matrix given the CIP ** X,Y and the CIO locator s. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** x,y double Celestial Intermediate Pole (Note 1) ** s double the CIO locator s (Note 2) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 3) ** ** Notes: ** ** 1) The Celestial Intermediate Pole coordinates are the x,y ** components of the unit vector in the Geocentric Celestial ** Reference System. ** ** 2) The CIO locator s (in radians) positions the Celestial ** Intermediate Origin on the equator of the CIP. ** ** 3) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = RC2T * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** Called: ** iauIr initialize r-matrix to identity ** iauRz rotate around Z-axis ** iauRy rotate around Y-axis ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauC2s(double p[3], double *theta, double *phi) /* ** - - - - - - - ** i a u C 2 s ** - - - - - - - ** ** P-vector to spherical coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector ** ** Returned: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** ** Notes: ** ** 1) The vector p can have any magnitude; only its direction is used. ** ** 2) If p is null, zero theta and phi are returned. ** ** 3) At either pole, zero theta is returned. ** */ void iauC2t00a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t 0 0 a ** - - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1 and ** the polar motion, using the IAU 2000A nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** xp,yp double coordinates of the pole (radians, Note 2) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any of ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 3) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), RC2I is the ** celestial-to-intermediate matrix, ERA is the Earth rotation ** angle and RPOM is the polar motion matrix. ** ** 4) A faster, but slightly less accurate result (about 1 mas), can ** be obtained by using instead the iauC2t00b function. ** ** Called: ** iauC2i00a celestial-to-intermediate matrix, IAU 2000A ** iauEra00 Earth rotation angle, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauPom00 polar motion matrix ** iauC2tcio form CIO-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauC2t00b(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t 0 0 b ** - - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1 and ** the polar motion, using the IAU 2000B nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** xp,yp double coordinates of the pole (radians, Note 2) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any of ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 3) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), RC2I is the ** celestial-to-intermediate matrix, ERA is the Earth rotation ** angle and RPOM is the polar motion matrix. ** ** 4) The present function is faster, but slightly less accurate (about ** 1 mas), than the iauC2t00a function. ** ** Called: ** iauC2i00b celestial-to-intermediate matrix, IAU 2000B ** iauEra00 Earth rotation angle, IAU 2000 ** iauPom00 polar motion matrix ** iauC2tcio form CIO-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauC2t06a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t 0 6 a ** - - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1 and ** the polar motion, using the IAU 2006 precession and IAU 2000A ** nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** xp,yp double coordinates of the pole (radians, Note 2) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any of ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 3) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), RC2I is the ** celestial-to-intermediate matrix, ERA is the Earth rotation ** angle and RPOM is the polar motion matrix. ** ** Called: ** iauC2i06a celestial-to-intermediate matrix, IAU 2006/2000A ** iauEra00 Earth rotation angle, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauPom00 polar motion matrix ** iauC2tcio form CIO-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** */ void iauC2tcio(double rc2i[3][3], double era, double rpom[3][3], double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t c i o ** - - - - - - - - - - ** ** Assemble the celestial to terrestrial matrix from CIO-based ** components (the celestial-to-intermediate matrix, the Earth Rotation ** Angle and the polar motion matrix). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc2i double[3][3] celestial-to-intermediate matrix ** era double Earth rotation angle (radians) ** rpom double[3][3] polar-motion matrix ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix ** ** Notes: ** ** 1) This function constructs the rotation matrix that transforms ** vectors in the celestial system into vectors in the terrestrial ** system. It does so starting from precomputed components, namely ** the matrix which rotates from celestial coordinates to the ** intermediate frame, the Earth rotation angle and the polar motion ** matrix. One use of the present function is when generating a ** series of celestial-to-terrestrial matrices where only the Earth ** Rotation Angle changes, avoiding the considerable overhead of ** recomputing the precession-nutation more often than necessary to ** achieve given accuracy objectives. ** ** 2) The relationship between the arguments is as follows: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003). ** ** Called: ** iauCr copy r-matrix ** iauRz rotate around Z-axis ** iauRxr product of two r-matrices ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** */ void iauC2teqx(double rbpn[3][3], double gst, double rpom[3][3], double rc2t[3][3]) /* ** - - - - - - - - - - ** i a u C 2 t e q x ** - - - - - - - - - - ** ** Assemble the celestial to terrestrial matrix from equinox-based ** components (the celestial-to-true matrix, the Greenwich Apparent ** Sidereal Time and the polar motion matrix). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rbpn double[3][3] celestial-to-true matrix ** gst double Greenwich (apparent) Sidereal Time (radians) ** rpom double[3][3] polar-motion matrix ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 2) ** ** Notes: ** ** 1) This function constructs the rotation matrix that transforms ** vectors in the celestial system into vectors in the terrestrial ** system. It does so starting from precomputed components, namely ** the matrix which rotates from celestial coordinates to the ** true equator and equinox of date, the Greenwich Apparent Sidereal ** Time and the polar motion matrix. One use of the present function ** is when generating a series of celestial-to-terrestrial matrices ** where only the Sidereal Time changes, avoiding the considerable ** overhead of recomputing the precession-nutation more often than ** necessary to achieve given accuracy objectives. ** ** 2) The relationship between the arguments is as follows: ** ** [TRS] = rpom * R_3(gst) * rbpn * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003). ** ** Called: ** iauCr copy r-matrix ** iauRz rotate around Z-axis ** iauRxr product of two r-matrices ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauC2tpe(double tta, double ttb, double uta, double utb, double dpsi, double deps, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - ** i a u C 2 t p e ** - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1, ** the nutation and the polar motion. IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** dpsi,deps double nutation (Note 2) ** xp,yp double coordinates of the pole (radians, Note 3) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 4) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any of ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The caller is responsible for providing the nutation components; ** they are in longitude and obliquity, in radians and are with ** respect to the equinox and ecliptic of date. For high-accuracy ** applications, free core nutation should be included as well as ** any other relevant corrections to the position of the CIP. ** ** 3) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 4) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(GST) * RBPN * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), RBPN is the ** bias-precession-nutation matrix, GST is the Greenwich (apparent) ** Sidereal Time and RPOM is the polar motion matrix. ** ** 5) Although its name does not include "00", This function is in fact ** specific to the IAU 2000 models. ** ** Called: ** iauPn00 bias/precession/nutation results, IAU 2000 ** iauGmst00 Greenwich mean sidereal time, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauEe00 equation of the equinoxes, IAU 2000 ** iauPom00 polar motion matrix ** iauC2teqx form equinox-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauC2txy(double tta, double ttb, double uta, double utb, double x, double y, double xp, double yp, double rc2t[3][3]) /* ** - - - - - - - - - ** i a u C 2 t x y ** - - - - - - - - - ** ** Form the celestial to terrestrial matrix given the date, the UT1, ** the CIP coordinates and the polar motion. IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** tta,ttb double TT as a 2-part Julian Date (Note 1) ** uta,utb double UT1 as a 2-part Julian Date (Note 1) ** x,y double Celestial Intermediate Pole (Note 2) ** xp,yp double coordinates of the pole (radians, Note 3) ** ** Returned: ** rc2t double[3][3] celestial-to-terrestrial matrix (Note 4) ** ** Notes: ** ** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, ** apportioned in any convenient way between the arguments uta and ** utb. For example, JD(UT1)=2450123.7 could be expressed in any o ** these ways, among others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. In the case of uta,utb, the ** date & time method is best matched to the Earth rotation angle ** algorithm used: maximum precision is delivered when the uta ** argument is for 0hrs UT1 on the day in question and the utb ** argument lies in the range 0 to 1, or vice versa. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y ** components of the unit vector in the Geocentric Celestial ** Reference System. ** ** 3) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 4) The matrix rc2t transforms from celestial to terrestrial ** coordinates: ** ** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] ** ** = rc2t * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** 5) Although its name does not include "00", This function is in fact ** specific to the IAU 2000 models. ** ** Called: ** iauC2ixy celestial-to-intermediate matrix, given X,Y ** iauEra00 Earth rotation angle, IAU 2000 ** iauSp00 the TIO locator s', IERS 2000 ** iauPom00 polar motion matrix ** iauC2tcio form CIO-based celestial-to-terrestrial matrix ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ int iauCal2jd(int iy, int im, int id, double *djm0, double *djm) /* ** - - - - - - - - - - ** i a u C a l 2 j d ** - - - - - - - - - - ** ** Gregorian Calendar to Julian Date. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** iy,im,id int year, month, day in Gregorian calendar (Note 1) ** ** Returned: ** djm0 double MJD zero-point: always 2400000.5 ** djm double Modified Julian Date for 0 hrs ** ** Returned (function value): ** int status: ** 0 = OK ** -1 = bad year (Note 3: JD not computed) ** -2 = bad month (JD not computed) ** -3 = bad day (JD computed) ** ** Notes: ** ** 1) The algorithm used is valid from -4800 March 1, but this ** implementation rejects dates before -4799 January 1. ** ** 2) The Julian Date is returned in two pieces, in the usual SOFA ** manner, which is designed to preserve time resolution. The ** Julian Date is available as a single number by adding djm0 and ** djm. ** ** 3) In early eras the conversion is from the "Proleptic Gregorian ** Calendar"; no account is taken of the date(s) of adoption of ** the Gregorian Calendar, nor is the AD/BC numbering convention ** observed. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 12.92 (p604). ** */ void iauCp(double p[3], double c[3]) /* ** - - - - - - ** i a u C p ** - - - - - - ** ** Copy a p-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector to be copied ** ** Returned: ** c double[3] copy ** */ void iauCpv(double pv[2][3], double c[2][3]) /* ** - - - - - - - ** i a u C p v ** - - - - - - - ** ** Copy a position/velocity vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** pv double[2][3] position/velocity vector to be copied ** ** Returned: ** c double[2][3] copy ** ** Called: ** iauCp copy p-vector ** */ void iauCr(double r[3][3], double c[3][3]) /* ** - - - - - - ** i a u C r ** - - - - - - ** ** Copy an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix to be copied ** ** Returned: ** c double[3][3] copy ** ** Called: ** iauCp copy p-vector ** */ int iauD2dtf(const char *scale, int ndp, double d1, double d2, int *iy, int *im, int *id, int ihmsf[4]) /* ** - - - - - - - - - ** i a u D 2 d t f ** - - - - - - - - - ** ** Format for output a 2-part Julian Date (or in the case of UTC a ** quasi-JD form that includes special provision for leap seconds). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** scale char[] time scale ID (Note 1) ** ndp int resolution (Note 2) ** d1,d2 double time as a 2-part Julian Date (Notes 3,4) ** ** Returned: ** iy,im,id int year, month, day in Gregorian calendar (Note 5) ** ihmsf int[4] hours, minutes, seconds, fraction (Note 1) ** ** Returned (function value): ** int status: +1 = dubious year (Note 5) ** 0 = OK ** -1 = unacceptable date (Note 6) ** ** Notes: ** ** 1) scale identifies the time scale. Only the value "UTC" (in upper ** case) is significant, and enables handling of leap seconds (see ** Note 4). ** ** 2) ndp is the number of decimal places in the seconds field, and can ** have negative as well as positive values, such as: ** ** ndp resolution ** -4 1 00 00 ** -3 0 10 00 ** -2 0 01 00 ** -1 0 00 10 ** 0 0 00 01 ** 1 0 00 00.1 ** 2 0 00 00.01 ** 3 0 00 00.001 ** ** The limits are platform dependent, but a safe range is -5 to +9. ** ** 3) d1+d2 is Julian Date, apportioned in any convenient way between ** the two arguments, for example where d1 is the Julian Day Number ** and d2 is the fraction of a day. In the case of UTC, where the ** use of JD is problematical, special conventions apply: see the ** next note. ** ** 4) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The SOFA internal convention is that ** the quasi-JD day represents UTC days whether the length is 86399, ** 86400 or 86401 SI seconds. In the 1960-1972 era there were ** smaller jumps (in either direction) each time the linear UTC(TAI) ** expression was changed, and these "mini-leaps" are also included ** in the SOFA convention. ** ** 5) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 6) For calendar conventions and limitations, see iauCal2jd. ** ** Called: ** iauJd2cal JD to Gregorian calendar ** iauD2tf decompose days to hms ** iauDat delta(AT) = TAI-UTC ** */ void iauD2tf(int ndp, double days, char *sign, int ihmsf[4]) /* ** - - - - - - - - ** i a u D 2 t f ** - - - - - - - - ** ** Decompose days to hours, minutes, seconds, fraction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** ndp int resolution (Note 1) ** days double interval in days ** ** Returned: ** sign char '+' or '-' ** ihmsf int[4] hours, minutes, seconds, fraction ** ** Notes: ** ** 1) The argument ndp is interpreted as follows: ** ** ndp resolution ** : ...0000 00 00 ** -7 1000 00 00 ** -6 100 00 00 ** -5 10 00 00 ** -4 1 00 00 ** -3 0 10 00 ** -2 0 01 00 ** -1 0 00 10 ** 0 0 00 01 ** 1 0 00 00.1 ** 2 0 00 00.01 ** 3 0 00 00.001 ** : 0 00 00.000... ** ** 2) The largest positive useful value for ndp is determined by the ** size of days, the format of double on the target platform, and ** the risk of overflowing ihmsf[3]. On a typical platform, for ** days up to 1.0, the available floating-point precision might ** correspond to ndp=12. However, the practical limit is typically ** ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is ** only 16 bits. ** ** 3) The absolute value of days may exceed 1.0. In cases where it ** does not, it is up to the caller to test for and handle the ** case where days is very nearly 1.0 and rounds up to 24 hours, ** by testing for ihmsf[0]=24 and setting ihmsf[0-3] to zero. ** */ int iauDat(int iy, int im, int id, double fd, double *deltat ) /* ** - - - - - - - ** i a u D a t ** - - - - - - - ** ** For a given UTC date, calculate delta(AT) = TAI-UTC. ** ** :------------------------------------------: ** : : ** : IMPORTANT : ** : : ** : A new version of this function must be : ** : produced whenever a new leap second is : ** : announced. There are four items to : ** : change on each such occasion: : ** : : ** : 1) A new line must be added to the set : ** : of statements that initialize the : ** : array "changes". : ** : : ** : 2) The constant IYV must be set to the : ** : current year. : ** : : ** : 3) The "Latest leap second" comment : ** : below must be set to the new leap : ** : second date. : ** : : ** : 4) The "This revision" comment, later, : ** : must be set to the current date. : ** : : ** : Change (2) must also be carried out : ** : whenever the function is re-issued, : ** : even if no leap seconds have been : ** : added. : ** : : ** : Latest leap second: 2016 December 31 : ** : : ** :__________________________________________: ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** iy int UTC: year (Notes 1 and 2) ** im int month (Note 2) ** id int day (Notes 2 and 3) ** fd double fraction of day (Note 4) ** ** Returned: ** deltat double TAI minus UTC, seconds ** ** Returned (function value): ** int status (Note 5): ** 1 = dubious year (Note 1) ** 0 = OK ** -1 = bad year ** -2 = bad month ** -3 = bad day (Note 3) ** -4 = bad fraction (Note 4) ** -5 = internal error (Note 5) ** ** Notes: ** ** 1) UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper ** to call the function with an earlier date. If this is attempted, ** zero is returned together with a warning status. ** ** Because leap seconds cannot, in principle, be predicted in ** advance, a reliable check for dates beyond the valid range is ** impossible. To guard against gross errors, a year five or more ** after the release year of the present function (see the constant ** IYV) is considered dubious. In this case a warning status is ** returned but the result is computed in the normal way. ** ** For both too-early and too-late years, the warning status is +1. ** This is distinct from the error status -1, which signifies a year ** so early that JD could not be computed. ** ** 2) If the specified date is for a day which ends with a leap second, ** the UTC-TAI value returned is for the period leading up to the ** leap second. If the date is for a day which begins as a leap ** second ends, the UTC-TAI returned is for the period following the ** leap second. ** ** 3) The day number must be in the normal calendar range, for example ** 1 through 30 for April. The "almanac" convention of allowing ** such dates as January 0 and December 32 is not supported in this ** function, in order to avoid confusion near leap seconds. ** ** 4) The fraction of day is used only for dates before the ** introduction of leap seconds, the first of which occurred at the ** end of 1971. It is tested for validity (0 to 1 is the valid ** range) even if not used; if invalid, zero is used and status -4 ** is returned. For many applications, setting fd to zero is ** acceptable; the resulting error is always less than 3 ms (and ** occurs only pre-1972). ** ** 5) The status value returned in the case where there are multiple ** errors refers to the first error detected. For example, if the ** month and day are 13 and 32 respectively, status -2 (bad month) ** will be returned. The "internal error" status refers to a ** case that is impossible but causes some compilers to issue a ** warning. ** ** 6) In cases where a valid result is not available, zero is returned. ** ** References: ** ** 1) For dates from 1961 January 1 onwards, the expressions from the ** file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used. ** ** 2) The 5ms timestep at 1961 January 1 is taken from 2.58.1 (p87) of ** the 1992 Explanatory Supplement. ** ** Called: ** iauCal2jd Gregorian calendar to JD ** */ double iauDtdb(double date1, double date2, double ut, double elong, double u, double v) /* ** - - - - - - - - ** i a u D t d b ** - - - - - - - - ** ** An approximation to TDB-TT, the difference between barycentric ** dynamical time and terrestrial time, for an observer on the Earth. ** ** The different time scales - proper, coordinate and realized - are ** related to each other: ** ** TAI <- physically realized ** : ** offset <- observed (nominally +32.184s) ** : ** TT <- terrestrial time ** : ** rate adjustment (L_G) <- definition of TT ** : ** TCG <- time scale for GCRS ** : ** "periodic" terms <- iauDtdb is an implementation ** : ** rate adjustment (L_C) <- function of solar-system ephemeris ** : ** TCB <- time scale for BCRS ** : ** rate adjustment (-L_B) <- definition of TDB ** : ** TDB <- TCB scaled to track TT ** : ** "periodic" terms <- -iauDtdb is an approximation ** : ** TT <- terrestrial time ** ** Adopted values for the various constants can be found in the IERS ** Conventions (McCarthy & Petit 2003). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support routine. ** ** Given: ** date1,date2 double date, TDB (Notes 1-3) ** ut double universal time (UT1, fraction of one day) ** elong double longitude (east positive, radians) ** u double distance from Earth spin axis (km) ** v double distance north of equatorial plane (km) ** ** Returned (function value): ** double TDB-TT (seconds) ** ** Notes: ** ** 1) The date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** Although the date is, formally, barycentric dynamical time (TDB), ** the terrestrial dynamical time (TT) can be used with no practical ** effect on the accuracy of the prediction. ** ** 2) TT can be regarded as a coordinate time that is realized as an ** offset of 32.184s from International Atomic Time, TAI. TT is a ** specific linear transformation of geocentric coordinate time TCG, ** which is the time scale for the Geocentric Celestial Reference ** System, GCRS. ** ** 3) TDB is a coordinate time, and is a specific linear transformation ** of barycentric coordinate time TCB, which is the time scale for ** the Barycentric Celestial Reference System, BCRS. ** ** 4) The difference TCG-TCB depends on the masses and positions of the ** bodies of the solar system and the velocity of the Earth. It is ** dominated by a rate difference, the residual being of a periodic ** character. The latter, which is modeled by the present function, ** comprises a main (annual) sinusoidal term of amplitude ** approximately 0.00166 seconds, plus planetary terms up to about ** 20 microseconds, and lunar and diurnal terms up to 2 microseconds. ** These effects come from the changing transverse Doppler effect ** and gravitational red-shift as the observer (on the Earth's ** surface) experiences variations in speed (with respect to the ** BCRS) and gravitational potential. ** ** 5) TDB can be regarded as the same as TCB but with a rate adjustment ** to keep it close to TT, which is convenient for many applications. ** The history of successive attempts to define TDB is set out in ** Resolution 3 adopted by the IAU General Assembly in 2006, which ** defines a fixed TDB(TCB) transformation that is consistent with ** contemporary solar-system ephemerides. Future ephemerides will ** imply slightly changed transformations between TCG and TCB, which ** could introduce a linear drift between TDB and TT; however, any ** such drift is unlikely to exceed 1 nanosecond per century. ** ** 6) The geocentric TDB-TT model used in the present function is that of ** Fairhead & Bretagnon (1990), in its full form. It was originally ** supplied by Fairhead (private communications with P.T.Wallace, ** 1990) as a Fortran subroutine. The present C function contains an ** adaptation of the Fairhead code. The numerical results are ** essentially unaffected by the changes, the differences with ** respect to the Fairhead & Bretagnon original being at the 1e-20 s ** level. ** ** The topocentric part of the model is from Moyer (1981) and ** Murray (1983), with fundamental arguments adapted from ** Simon et al. 1994. It is an approximation to the expression ** ( v / c ) . ( r / c ), where v is the barycentric velocity of ** the Earth, r is the geocentric position of the observer and ** c is the speed of light. ** ** By supplying zeroes for u and v, the topocentric part of the ** model can be nullified, and the function will return the Fairhead ** & Bretagnon result alone. ** ** 7) During the interval 1950-2050, the absolute accuracy is better ** than +/- 3 nanoseconds relative to time ephemerides obtained by ** direct numerical integrations based on the JPL DE405 solar system ** ephemeris. ** ** 8) It must be stressed that the present function is merely a model, ** and that numerical integration of solar-system ephemerides is the ** definitive method for predicting the relationship between TCG and ** TCB and hence between TT and TDB. ** ** References: ** ** Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247 ** (1990). ** ** IAU 2006 Resolution 3. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Moyer, T.D., Cel.Mech., 23, 33 (1981). ** ** Murray, C.A., Vectorial Astrometry, Adam Hilger (1983). ** ** Seidelmann, P.K. et al., Explanatory Supplement to the ** Astronomical Almanac, Chapter 2, University Science Books (1992). ** ** Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994). ** */ int iauDtf2d(const char *scale, int iy, int im, int id, int ihr, int imn, double sec, double *d1, double *d2) /* ** - - - - - - - - - ** i a u D t f 2 d ** - - - - - - - - - ** ** Encode date and time fields into 2-part Julian Date (or in the case ** of UTC a quasi-JD form that includes special provision for leap ** seconds). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** scale char[] time scale ID (Note 1) ** iy,im,id int year, month, day in Gregorian calendar (Note 2) ** ihr,imn int hour, minute ** sec double seconds ** ** Returned: ** d1,d2 double 2-part Julian Date (Notes 3,4) ** ** Returned (function value): ** int status: +3 = both of next two ** +2 = time is after end of day (Note 5) ** +1 = dubious year (Note 6) ** 0 = OK ** -1 = bad year ** -2 = bad month ** -3 = bad day ** -4 = bad hour ** -5 = bad minute ** -6 = bad second (<0) ** ** Notes: ** ** 1) scale identifies the time scale. Only the value "UTC" (in upper ** case) is significant, and enables handling of leap seconds (see ** Note 4). ** ** 2) For calendar conventions and limitations, see iauCal2jd. ** ** 3) The sum of the results, d1+d2, is Julian Date, where normally d1 ** is the Julian Day Number and d2 is the fraction of a day. In the ** case of UTC, where the use of JD is problematical, special ** conventions apply: see the next note. ** ** 4) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The SOFA internal convention is that ** the quasi-JD day represents UTC days whether the length is 86399, ** 86400 or 86401 SI seconds. In the 1960-1972 era there were ** smaller jumps (in either direction) each time the linear UTC(TAI) ** expression was changed, and these "mini-leaps" are also included ** in the SOFA convention. ** ** 5) The warning status "time is after end of day" usually means that ** the sec argument is greater than 60.0. However, in a day ending ** in a leap second the limit changes to 61.0 (or 59.0 in the case ** of a negative leap second). ** ** 6) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 7) Only in the case of continuous and regular time scales (TAI, TT, ** TCG, TCB and TDB) is the result d1+d2 a Julian Date, strictly ** speaking. In the other cases (UT1 and UTC) the result must be ** used with circumspection; in particular the difference between ** two such results cannot be interpreted as a precise time ** interval. ** ** Called: ** iauCal2jd Gregorian calendar to JD ** iauDat delta(AT) = TAI-UTC ** iauJd2cal JD to Gregorian calendar ** */ void iauEceq06(double date1, double date2, double dl, double db, double *dr, double *dd) /* ** - - - - - - - - - - ** i a u E c e q 0 6 ** - - - - - - - - - - ** ** Transformation from ecliptic coordinates (mean equinox and ecliptic ** of date) to ICRS RA,Dec, using the IAU 2006 precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian date (Note 1) ** dl,db double ecliptic longitude and latitude (radians) ** ** Returned: ** dr,dd double ICRS right ascension and declination (radians) ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) No assumptions are made about whether the coordinates represent ** starlight and embody astrometric effects such as parallax or ** aberration. ** ** 3) The transformation is approximately that from ecliptic longitude ** and latitude (mean equinox and ecliptic of date) to mean J2000.0 ** right ascension and declination, with only frame bias (always ** less than 25 mas) to disturb this classical picture. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauEcm06 J2000.0 to ecliptic rotation matrix, IAU 2006 ** iauTrxp product of transpose of r-matrix and p-vector ** iauC2s unit vector to spherical coordinates ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** */ void iauEcm06(double date1, double date2, double rm[3][3]) /* ** - - - - - - - - - ** i a u E c m 0 6 ** - - - - - - - - - ** ** ICRS equatorial to ecliptic rotation matrix, IAU 2006. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian date (Note 1) ** ** Returned: ** rm double[3][3] ICRS to ecliptic rotation matrix ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 1) The matrix is in the sense ** ** E_ep = rm x P_ICRS, ** ** where P_ICRS is a vector with respect to ICRS right ascension ** and declination axes and E_ep is the same vector with respect to ** the (inertial) ecliptic and equinox of date. ** ** 2) P_ICRS is a free vector, merely a direction, typically of unit ** magnitude, and not bound to any particular spatial origin, such ** as the Earth, Sun or SSB. No assumptions are made about whether ** it represents starlight and embodies astrometric effects such as ** parallax or aberration. The transformation is approximately that ** between mean J2000.0 right ascension and declination and ecliptic ** longitude and latitude, with only frame bias (always less than ** 25 mas) to disturb this classical picture. ** ** Called: ** iauObl06 mean obliquity, IAU 2006 ** iauPmat06 PB matrix, IAU 2006 ** iauIr initialize r-matrix to identity ** iauRx rotate around X-axis ** iauRxr product of two r-matrices ** */ double iauEe00(double date1, double date2, double epsa, double dpsi) /* ** - - - - - - - - ** i a u E e 0 0 ** - - - - - - - - ** ** The equation of the equinoxes, compatible with IAU 2000 resolutions, ** given the nutation in longitude and the mean obliquity. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** epsa double mean obliquity (Note 2) ** dpsi double nutation in longitude (Note 3) ** ** Returned (function value): ** double equation of the equinoxes (Note 4) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The obliquity, in radians, is mean of date. ** ** 3) The result, which is in radians, operates in the following sense: ** ** Greenwich apparent ST = GMST + equation of the equinoxes ** ** 4) The result is compatible with the IAU 2000 resolutions. For ** further details, see IERS Conventions 2003 and Capitaine et al. ** (2002). ** ** Called: ** iauEect00 equation of the equinoxes complementary terms ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ double iauEe00a(double date1, double date2) /* ** - - - - - - - - - ** i a u E e 0 0 a ** - - - - - - - - - ** ** Equation of the equinoxes, compatible with IAU 2000 resolutions. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double equation of the equinoxes (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result, which is in radians, operates in the following sense: ** ** Greenwich apparent ST = GMST + equation of the equinoxes ** ** 3) The result is compatible with the IAU 2000 resolutions. For ** further details, see IERS Conventions 2003 and Capitaine et al. ** (2002). ** ** Called: ** iauPr00 IAU 2000 precession adjustments ** iauObl80 mean obliquity, IAU 1980 ** iauNut00a nutation, IAU 2000A ** iauEe00 equation of the equinoxes, IAU 2000 ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003). ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004). ** */ double iauEe00b(double date1, double date2) /* ** - - - - - - - - - ** i a u E e 0 0 b ** - - - - - - - - - ** ** Equation of the equinoxes, compatible with IAU 2000 resolutions but ** using the truncated nutation model IAU 2000B. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double equation of the equinoxes (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result, which is in radians, operates in the following sense: ** ** Greenwich apparent ST = GMST + equation of the equinoxes ** ** 3) The result is compatible with the IAU 2000 resolutions except ** that accuracy has been compromised for the sake of speed. For ** further details, see McCarthy & Luzum (2001), IERS Conventions ** 2003 and Capitaine et al. (2003). ** ** Called: ** iauPr00 IAU 2000 precession adjustments ** iauObl80 mean obliquity, IAU 1980 ** iauNut00b nutation, IAU 2000B ** iauEe00 equation of the equinoxes, IAU 2000 ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** McCarthy, D.D. & Luzum, B.J., "An abridged model of the ** precession-nutation of the celestial pole", Celestial Mechanics & ** Dynamical Astronomy, 85, 37-49 (2003) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ double iauEe06a(double date1, double date2) /* ** - - - - - - - - - ** i a u E e 0 6 a ** - - - - - - - - - ** ** Equation of the equinoxes, compatible with IAU 2000 resolutions and ** IAU 2006/2000A precession-nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double equation of the equinoxes (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result, which is in radians, operates in the following sense: ** ** Greenwich apparent ST = GMST + equation of the equinoxes ** ** Called: ** iauAnpm normalize angle into range +/- pi ** iauGst06a Greenwich apparent sidereal time, IAU 2006/2000A ** iauGmst06 Greenwich mean sidereal time, IAU 2006 ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** */ double iauEect00(double date1, double date2) /* ** - - - - - - - - - - ** i a u E e c t 0 0 ** - - - - - - - - - - ** ** Equation of the equinoxes complementary terms, consistent with ** IAU 2000 resolutions. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double complementary terms (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The "complementary terms" are part of the equation of the ** equinoxes (EE), classically the difference between apparent and ** mean Sidereal Time: ** ** GAST = GMST + EE ** ** with: ** ** EE = dpsi * cos(eps) ** ** where dpsi is the nutation in longitude and eps is the obliquity ** of date. However, if the rotation of the Earth were constant in ** an inertial frame the classical formulation would lead to ** apparent irregularities in the UT1 timescale traceable to side- ** effects of precession-nutation. In order to eliminate these ** effects from UT1, "complementary terms" were introduced in 1994 ** (IAU, 1994) and took effect from 1997 (Capitaine and Gontier, ** 1993): ** ** GAST = GMST + CT + EE ** ** By convention, the complementary terms are included as part of ** the equation of the equinoxes rather than as part of the mean ** Sidereal Time. This slightly compromises the "geometrical" ** interpretation of mean sidereal time but is otherwise ** inconsequential. ** ** The present function computes CT in the above expression, ** compatible with IAU 2000 resolutions (Capitaine et al., 2002, and ** IERS Conventions 2003). ** ** Called: ** iauFal03 mean anomaly of the Moon ** iauFalp03 mean anomaly of the Sun ** iauFaf03 mean argument of the latitude of the Moon ** iauFad03 mean elongation of the Moon from the Sun ** iauFaom03 mean longitude of the Moon's ascending node ** iauFave03 mean longitude of Venus ** iauFae03 mean longitude of Earth ** iauFapa03 general accumulated precession in longitude ** ** References: ** ** Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275, ** 645-650 (1993) ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** IAU Resolution C7, Recommendation 3 (1994) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ int iauEform ( int n, double *a, double *f ) /* ** - - - - - - - - - ** i a u E f o r m ** - - - - - - - - - ** ** Earth reference ellipsoids. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** n int ellipsoid identifier (Note 1) ** ** Returned: ** a double equatorial radius (meters, Note 2) ** f double flattening (Note 2) ** ** Returned (function value): ** int status: 0 = OK ** -1 = illegal identifier (Note 3) ** ** Notes: ** ** 1) The identifier n is a number that specifies the choice of ** reference ellipsoid. The following are supported: ** ** n ellipsoid ** ** 1 WGS84 ** 2 GRS80 ** 3 WGS72 ** ** The n value has no significance outside the SOFA software. For ** convenience, symbols WGS84 etc. are defined in sofam.h. ** ** 2) The ellipsoid parameters are returned in the form of equatorial ** radius in meters (a) and flattening (f). The latter is a number ** around 0.00335, i.e. around 1/298. ** ** 3) For the case where an unsupported n value is supplied, zero a and ** f are returned, as well as error status. ** ** References: ** ** Department of Defense World Geodetic System 1984, National ** Imagery and Mapping Agency Technical Report 8350.2, Third ** Edition, p3-2. ** ** Moritz, H., Bull. Geodesique 66-2, 187 (1992). ** ** The Department of Defense World Geodetic System 1972, World ** Geodetic System Committee, May 1974. ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** p220. ** */ double iauEo06a(double date1, double date2) /* ** - - - - - - - - - ** i a u E o 0 6 a ** - - - - - - - - - ** ** Equation of the origins, IAU 2006 precession and IAU 2000A nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double equation of the origins in radians ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The equation of the origins is the distance between the true ** equinox and the celestial intermediate origin and, equivalently, ** the difference between Earth rotation angle and Greenwich ** apparent sidereal time (ERA-GST). It comprises the precession ** (since J2000.0) in right ascension plus the equation of the ** equinoxes (including the small correction terms). ** ** Called: ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** iauEors equation of the origins, given NPB matrix and s ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** */ double iauEors(double rnpb[3][3], double s) /* ** - - - - - - - - ** i a u E o r s ** - - - - - - - - ** ** Equation of the origins, given the classical NPB matrix and the ** quantity s. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rnpb double[3][3] classical nutation x precession x bias matrix ** s double the quantity s (the CIO locator) ** ** Returned (function value): ** double the equation of the origins in radians. ** ** Notes: ** ** 1) The equation of the origins is the distance between the true ** equinox and the celestial intermediate origin and, equivalently, ** the difference between Earth rotation angle and Greenwich ** apparent sidereal time (ERA-GST). It comprises the precession ** (since J2000.0) in right ascension plus the equation of the ** equinoxes (including the small correction terms). ** ** 2) The algorithm is from Wallace & Capitaine (2006). ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** */ double iauEpb(double dj1, double dj2) /* ** - - - - - - - ** i a u E p b ** - - - - - - - ** ** Julian Date to Besselian Epoch. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** dj1,dj2 double Julian Date (see note) ** ** Returned (function value): ** double Besselian Epoch. ** ** Note: ** ** The Julian Date is supplied in two pieces, in the usual SOFA ** manner, which is designed to preserve time resolution. The ** Julian Date is available as a single number by adding dj1 and ** dj2. The maximum resolution is achieved if dj1 is 2451545.0 ** (J2000.0). ** ** Reference: ** ** Lieske, J.H., 1979. Astron.Astrophys., 73, 282. ** */ void iauEpb2jd(double epb, double *djm0, double *djm) /* ** - - - - - - - - - - ** i a u E p b 2 j d ** - - - - - - - - - - ** ** Besselian Epoch to Julian Date. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epb double Besselian Epoch (e.g. 1957.3) ** ** Returned: ** djm0 double MJD zero-point: always 2400000.5 ** djm double Modified Julian Date ** ** Note: ** ** The Julian Date is returned in two pieces, in the usual SOFA ** manner, which is designed to preserve time resolution. The ** Julian Date is available as a single number by adding djm0 and ** djm. ** ** Reference: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282. ** */ double iauEpj(double dj1, double dj2) /* ** - - - - - - - ** i a u E p j ** - - - - - - - ** ** Julian Date to Julian Epoch. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** dj1,dj2 double Julian Date (see note) ** ** Returned (function value): ** double Julian Epoch ** ** Note: ** ** The Julian Date is supplied in two pieces, in the usual SOFA ** manner, which is designed to preserve time resolution. The ** Julian Date is available as a single number by adding dj1 and ** dj2. The maximum resolution is achieved if dj1 is 2451545.0 ** (J2000.0). ** ** Reference: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282. ** */ void iauEpj2jd(double epj, double *djm0, double *djm) /* ** - - - - - - - - - - ** i a u E p j 2 j d ** - - - - - - - - - - ** ** Julian Epoch to Julian Date. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian Epoch (e.g. 1996.8) ** ** Returned: ** djm0 double MJD zero-point: always 2400000.5 ** djm double Modified Julian Date ** ** Note: ** ** The Julian Date is returned in two pieces, in the usual SOFA ** manner, which is designed to preserve time resolution. The ** Julian Date is available as a single number by adding djm0 and ** djm. ** ** Reference: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282. ** */ int iauEpv00(double date1, double date2, double pvh[2][3], double pvb[2][3]) /* ** - - - - - - - - - ** i a u E p v 0 0 ** - - - - - - - - - ** ** Earth position and velocity, heliocentric and barycentric, with ** respect to the Barycentric Celestial Reference System. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TDB date (Note 1) ** ** Returned: ** pvh double[2][3] heliocentric Earth position/velocity ** pvb double[2][3] barycentric Earth position/velocity ** ** Returned (function value): ** int status: 0 = OK ** +1 = warning: date outside ** the range 1900-2100 AD ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. However, ** the accuracy of the result is more likely to be limited by the ** algorithm itself than the way the date has been expressed. ** ** n.b. TT can be used instead of TDB in most applications. ** ** 2) On return, the arrays pvh and pvb contain the following: ** ** pvh[0][0] x } ** pvh[0][1] y } heliocentric position, AU ** pvh[0][2] z } ** ** pvh[1][0] xdot } ** pvh[1][1] ydot } heliocentric velocity, AU/d ** pvh[1][2] zdot } ** ** pvb[0][0] x } ** pvb[0][1] y } barycentric position, AU ** pvb[0][2] z } ** ** pvb[1][0] xdot } ** pvb[1][1] ydot } barycentric velocity, AU/d ** pvb[1][2] zdot } ** ** The vectors are with respect to the Barycentric Celestial ** Reference System. The time unit is one day in TDB. ** ** 3) The function is a SIMPLIFIED SOLUTION from the planetary theory ** VSOP2000 (X. Moisson, P. Bretagnon, 2001, Celes. Mechanics & ** Dyn. Astron., 80, 3/4, 205-213) and is an adaptation of original ** Fortran code supplied by P. Bretagnon (private comm., 2000). ** ** 4) Comparisons over the time span 1900-2100 with this simplified ** solution and the JPL DE405 ephemeris give the following results: ** ** RMS max ** Heliocentric: ** position error 3.7 11.2 km ** velocity error 1.4 5.0 mm/s ** ** Barycentric: ** position error 4.6 13.4 km ** velocity error 1.4 4.9 mm/s ** ** Comparisons with the JPL DE406 ephemeris show that by 1800 and ** 2200 the position errors are approximately double their 1900-2100 ** size. By 1500 and 2500 the deterioration is a factor of 10 and ** by 1000 and 3000 a factor of 60. The velocity accuracy falls off ** at about half that rate. ** ** 5) It is permissible to use the same array for pvh and pvb, which ** will receive the barycentric values. ** */ void iauEqec06(double date1, double date2, double dr, double dd, double *dl, double *db) /* ** - - - - - - - - - - ** i a u E q e c 0 6 ** - - - - - - - - - - ** ** Transformation from ICRS equatorial coordinates to ecliptic ** coordinates (mean equinox and ecliptic of date) using IAU 2006 ** precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian date (Note 1) ** dr,dd double ICRS right ascension and declination (radians) ** ** Returned: ** dl,db double ecliptic longitude and latitude (radians) ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) No assumptions are made about whether the coordinates represent ** starlight and embody astrometric effects such as parallax or ** aberration. ** ** 3) The transformation is approximately that from mean J2000.0 right ** ascension and declination to ecliptic longitude and latitude ** (mean equinox and ecliptic of date), with only frame bias (always ** less than 25 mas) to disturb this classical picture. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauEcm06 J2000.0 to ecliptic rotation matrix, IAU 2006 ** iauRxp product of r-matrix and p-vector ** iauC2s unit vector to spherical coordinates ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** */ double iauEqeq94(double date1, double date2) /* ** - - - - - - - - - - ** i a u E q e q 9 4 ** - - - - - - - - - - ** ** Equation of the equinoxes, IAU 1994 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TDB date (Note 1) ** ** Returned (function value): ** double equation of the equinoxes (Note 2) ** ** Notes: ** ** 1) The date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result, which is in radians, operates in the following sense: ** ** Greenwich apparent ST = GMST + equation of the equinoxes ** ** Called: ** iauAnpm normalize angle into range +/- pi ** iauNut80 nutation, IAU 1980 ** iauObl80 mean obliquity, IAU 1980 ** ** References: ** ** IAU Resolution C7, Recommendation 3 (1994). ** ** Capitaine, N. & Gontier, A.-M., 1993, Astron. Astrophys., 275, ** 645-650. ** */ double iauEra00(double dj1, double dj2) /* ** - - - - - - - - - ** i a u E r a 0 0 ** - - - - - - - - - ** ** Earth rotation angle (IAU 2000 model). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** dj1,dj2 double UT1 as a 2-part Julian Date (see note) ** ** Returned (function value): ** double Earth rotation angle (radians), range 0-2pi ** ** Notes: ** ** 1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any ** convenient way between the arguments dj1 and dj2. For example, ** JD(UT1)=2450123.7 could be expressed in any of these ways, ** among others: ** ** dj1 dj2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. The date & time method is ** best matched to the algorithm used: maximum precision is ** delivered when the dj1 argument is for 0hrs UT1 on the day in ** question and the dj2 argument lies in the range 0 to 1, or vice ** versa. ** ** 2) The algorithm is adapted from Expression 22 of Capitaine et al. ** 2000. The time argument has been expressed in days directly, ** and, to retain precision, integer contributions have been ** eliminated. The same formulation is given in IERS Conventions ** (2003), Chap. 5, Eq. 14. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Capitaine N., Guinot B. and McCarthy D.D, 2000, Astron. ** Astrophys., 355, 398-405. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ double iauFad03(double t) /* ** - - - - - - - - - ** i a u F a d 0 3 ** - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean elongation of the Moon from the Sun. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double D, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** */ double iauFae03(double t) /* ** - - - - - - - - - ** i a u F a e 0 3 ** - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Earth. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Earth, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** */ double iauFaf03(double t) /* ** - - - - - - - - - ** i a u F a f 0 3 ** - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of the Moon minus mean longitude of the ascending ** node. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double F, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** */ double iauFaju03(double t) /* ** - - - - - - - - - - ** i a u F a j u 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Jupiter. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Jupiter, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** */ double iauFal03(double t) /* ** - - - - - - - - - ** i a u F a l 0 3 ** - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean anomaly of the Moon. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double l, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** */ double iauFalp03(double t) /* ** - - - - - - - - - - ** i a u F a l p 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean anomaly of the Sun. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double l', radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** */ double iauFama03(double t) /* ** - - - - - - - - - - ** i a u F a m a 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Mars. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Mars, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** */ double iauFame03(double t) /* ** - - - - - - - - - - ** i a u F a m e 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Mercury. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Mercury, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** */ double iauFane03(double t) /* ** - - - - - - - - - - ** i a u F a n e 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Neptune. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Neptune, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is adapted from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** */ double iauFaom03(double t) /* ** - - - - - - - - - - ** i a u F a o m 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of the Moon's ascending node. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double Omega, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** */ double iauFapa03(double t) /* ** - - - - - - - - - - ** i a u F a p a 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** general accumulated precession in longitude. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double general precession in longitude, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003). It ** is taken from Kinoshita & Souchay (1990) and comes originally ** from Lieske et al. (1977). ** ** References: ** ** Kinoshita, H. and Souchay J. 1990, Celest.Mech. and Dyn.Astron. ** 48, 187 ** ** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, ** Astron.Astrophys. 58, 1-16 ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ double iauFasa03(double t) /* ** - - - - - - - - - - ** i a u F a s a 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Saturn. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Saturn, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** */ double iauFaur03(double t) /* ** - - - - - - - - - - ** i a u F a u r 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Uranus. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Uranus, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** is adapted from Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** */ double iauFave03(double t) /* ** - - - - - - - - - - ** i a u F a v e 0 3 ** - - - - - - - - - - ** ** Fundamental argument, IERS Conventions (2003): ** mean longitude of Venus. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** t double TDB, Julian centuries since J2000.0 (Note 1) ** ** Returned (function value): ** double mean longitude of Venus, radians (Note 2) ** ** Notes: ** ** 1) Though t is strictly TDB, it is usually more convenient to use ** TT, which makes no significant difference. ** ** 2) The expression used is as adopted in IERS Conventions (2003) and ** comes from Souchay et al. (1999) after Simon et al. (1994). ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** */ void iauFk52h(double r5, double d5, double dr5, double dd5, double px5, double rv5, double *rh, double *dh, double *drh, double *ddh, double *pxh, double *rvh) /* ** - - - - - - - - - ** i a u F k 5 2 h ** - - - - - - - - - ** ** Transform FK5 (J2000.0) star data into the Hipparcos system. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given (all FK5, equinox J2000.0, epoch J2000.0): ** r5 double RA (radians) ** d5 double Dec (radians) ** dr5 double proper motion in RA (dRA/dt, rad/Jyear) ** dd5 double proper motion in Dec (dDec/dt, rad/Jyear) ** px5 double parallax (arcsec) ** rv5 double radial velocity (km/s, positive = receding) ** ** Returned (all Hipparcos, epoch J2000.0): ** rh double RA (radians) ** dh double Dec (radians) ** drh double proper motion in RA (dRA/dt, rad/Jyear) ** ddh double proper motion in Dec (dDec/dt, rad/Jyear) ** pxh double parallax (arcsec) ** rvh double radial velocity (km/s, positive = receding) ** ** Notes: ** ** 1) This function transforms FK5 star positions and proper motions ** into the system of the Hipparcos catalog. ** ** 2) The proper motions in RA are dRA/dt rather than ** cos(Dec)*dRA/dt, and are per year rather than per century. ** ** 3) The FK5 to Hipparcos transformation is modeled as a pure ** rotation and spin; zonal errors in the FK5 catalog are not ** taken into account. ** ** 4) See also iauH2fk5, iauFk5hz, iauHfk5z. ** ** Called: ** iauStarpv star catalog data to space motion pv-vector ** iauFk5hip FK5 to Hipparcos rotation and spin ** iauRxp product of r-matrix and p-vector ** iauPxp vector product of two p-vectors ** iauPpp p-vector plus p-vector ** iauPvstar space motion pv-vector to star catalog data ** ** Reference: ** ** F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000). ** */ void iauFk5hip(double r5h[3][3], double s5h[3]) /* ** - - - - - - - - - - ** i a u F k 5 h i p ** - - - - - - - - - - ** ** FK5 to Hipparcos rotation and spin. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Returned: ** r5h double[3][3] r-matrix: FK5 rotation wrt Hipparcos (Note 2) ** s5h double[3] r-vector: FK5 spin wrt Hipparcos (Note 3) ** ** Notes: ** ** 1) This function models the FK5 to Hipparcos transformation as a ** pure rotation and spin; zonal errors in the FK5 catalogue are ** not taken into account. ** ** 2) The r-matrix r5h operates in the sense: ** ** P_Hipparcos = r5h x P_FK5 ** ** where P_FK5 is a p-vector in the FK5 frame, and P_Hipparcos is ** the equivalent Hipparcos p-vector. ** ** 3) The r-vector s5h represents the time derivative of the FK5 to ** Hipparcos rotation. The units are radians per year (Julian, ** TDB). ** ** Called: ** iauRv2m r-vector to r-matrix ** ** Reference: ** ** F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000). ** */ void iauFk5hz(double r5, double d5, double date1, double date2, double *rh, double *dh) /* ** - - - - - - - - - ** i a u F k 5 h z ** - - - - - - - - - ** ** Transform an FK5 (J2000.0) star position into the system of the ** Hipparcos catalogue, assuming zero Hipparcos proper motion. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** r5 double FK5 RA (radians), equinox J2000.0, at date ** d5 double FK5 Dec (radians), equinox J2000.0, at date ** date1,date2 double TDB date (Notes 1,2) ** ** Returned: ** rh double Hipparcos RA (radians) ** dh double Hipparcos Dec (radians) ** ** Notes: ** ** 1) This function converts a star position from the FK5 system to ** the Hipparcos system, in such a way that the Hipparcos proper ** motion is zero. Because such a star has, in general, a non-zero ** proper motion in the FK5 system, the function requires the date ** at which the position in the FK5 system was determined. ** ** 2) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 3) The FK5 to Hipparcos transformation is modeled as a pure ** rotation and spin; zonal errors in the FK5 catalogue are not ** taken into account. ** ** 4) The position returned by this function is in the Hipparcos ** reference system but at date date1+date2. ** ** 5) See also iauFk52h, iauH2fk5, iauHfk5z. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauFk5hip FK5 to Hipparcos rotation and spin ** iauSxp multiply p-vector by scalar ** iauRv2m r-vector to r-matrix ** iauTrxp product of transpose of r-matrix and p-vector ** iauPxp vector product of two p-vectors ** iauC2s p-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739. ** */ void iauFw2m(double gamb, double phib, double psi, double eps, double r[3][3]) /* ** - - - - - - - - ** i a u F w 2 m ** - - - - - - - - ** ** Form rotation matrix given the Fukushima-Williams angles. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** gamb double F-W angle gamma_bar (radians) ** phib double F-W angle phi_bar (radians) ** psi double F-W angle psi (radians) ** eps double F-W angle epsilon (radians) ** ** Returned: ** r double[3][3] rotation matrix ** ** Notes: ** ** 1) Naming the following points: ** ** e = J2000.0 ecliptic pole, ** p = GCRS pole, ** E = ecliptic pole of date, ** and P = CIP, ** ** the four Fukushima-Williams angles are as follows: ** ** gamb = gamma = epE ** phib = phi = pE ** psi = psi = pEP ** eps = epsilon = EP ** ** 2) The matrix representing the combined effects of frame bias, ** precession and nutation is: ** ** NxPxB = R_1(-eps).R_3(-psi).R_1(phib).R_3(gamb) ** ** 3) Three different matrices can be constructed, depending on the ** supplied angles: ** ** o To obtain the nutation x precession x frame bias matrix, ** generate the four precession angles, generate the nutation ** components and add them to the psi_bar and epsilon_A angles, ** and call the present function. ** ** o To obtain the precession x frame bias matrix, generate the ** four precession angles and call the present function. ** ** o To obtain the frame bias matrix, generate the four precession ** angles for date J2000.0 and call the present function. ** ** The nutation-only and precession-only matrices can if necessary ** be obtained by combining these three appropriately. ** ** Called: ** iauIr initialize r-matrix to identity ** iauRz rotate around Z-axis ** iauRx rotate around X-axis ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** */ void iauFw2xy(double gamb, double phib, double psi, double eps, double *x, double *y) /* ** - - - - - - - - - ** i a u F w 2 x y ** - - - - - - - - - ** ** CIP X,Y given Fukushima-Williams bias-precession-nutation angles. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** gamb double F-W angle gamma_bar (radians) ** phib double F-W angle phi_bar (radians) ** psi double F-W angle psi (radians) ** eps double F-W angle epsilon (radians) ** ** Returned: ** x,y double CIP unit vector X,Y ** ** Notes: ** ** 1) Naming the following points: ** ** e = J2000.0 ecliptic pole, ** p = GCRS pole ** E = ecliptic pole of date, ** and P = CIP, ** ** the four Fukushima-Williams angles are as follows: ** ** gamb = gamma = epE ** phib = phi = pE ** psi = psi = pEP ** eps = epsilon = EP ** ** 2) The matrix representing the combined effects of frame bias, ** precession and nutation is: ** ** NxPxB = R_1(-epsA).R_3(-psi).R_1(phib).R_3(gamb) ** ** The returned values x,y are elements [2][0] and [2][1] of the ** matrix. Near J2000.0, they are essentially angles in radians. ** ** Called: ** iauFw2m F-W angles to r-matrix ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** */ void iauG2icrs ( double dl, double db, double *dr, double *dd ) /* ** - - - - - - - - - - ** i a u G 2 i c r s ** - - - - - - - - - - ** ** Transformation from Galactic Coordinates to ICRS. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support routine. ** ** Given: ** dl double galactic longitude (radians) ** db double galactic latitude (radians) ** ** Returned: ** dr double ICRS right ascension (radians) ** dd double ICRS declination (radians) ** ** Notes: ** ** 1) The IAU 1958 system of Galactic coordinates was defined with ** respect to the now obsolete reference system FK4 B1950.0. When ** interpreting the system in a modern context, several factors have ** to be taken into account: ** ** . The inclusion in FK4 positions of the E-terms of aberration. ** ** . The distortion of the FK4 proper motion system by differential ** Galactic rotation. ** ** . The use of the B1950.0 equinox rather than the now-standard ** J2000.0. ** ** . The frame bias between ICRS and the J2000.0 mean place system. ** ** The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation ** matrix that transforms directly between ICRS and Galactic ** coordinates with the above factors taken into account. The ** matrix is derived from three angles, namely the ICRS coordinates ** of the Galactic pole and the longitude of the ascending node of ** the galactic equator on the ICRS equator. They are given in ** degrees to five decimal places and for canonical purposes are ** regarded as exact. In the Hipparcos Catalogue the matrix ** elements are given to 10 decimal places (about 20 microarcsec). ** In the present SOFA function the matrix elements have been ** recomputed from the canonical three angles and are given to 30 ** decimal places. ** ** 2) The inverse transformation is performed by the function iauIcrs2g. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** iauS2c spherical coordinates to unit vector ** iauTrxp product of transpose of r-matrix and p-vector ** iauC2s p-vector to spherical ** ** Reference: ** Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho ** catalogues. Astrometric and photometric star catalogues ** derived from the ESA Hipparcos Space Astrometry Mission. ESA ** Publications Division, Noordwijk, Netherlands. ** */ int iauGc2gd ( int n, double xyz[3], double *elong, double *phi, double *height ) /* ** - - - - - - - - - ** i a u G c 2 g d ** - - - - - - - - - ** ** Transform geocentric coordinates to geodetic using the specified ** reference ellipsoid. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical transformation. ** ** Given: ** n int ellipsoid identifier (Note 1) ** xyz double[3] geocentric vector (Note 2) ** ** Returned: ** elong double longitude (radians, east +ve, Note 3) ** phi double latitude (geodetic, radians, Note 3) ** height double height above ellipsoid (geodetic, Notes 2,3) ** ** Returned (function value): ** int status: 0 = OK ** -1 = illegal identifier (Note 3) ** -2 = internal error (Note 3) ** ** Notes: ** ** 1) The identifier n is a number that specifies the choice of ** reference ellipsoid. The following are supported: ** ** n ellipsoid ** ** 1 WGS84 ** 2 GRS80 ** 3 WGS72 ** ** The n value has no significance outside the SOFA software. For ** convenience, symbols WGS84 etc. are defined in sofam.h. ** ** 2) The geocentric vector (xyz, given) and height (height, returned) ** are in meters. ** ** 3) An error status -1 means that the identifier n is illegal. An ** error status -2 is theoretically impossible. In all error cases, ** all three results are set to -1e9. ** ** 4) The inverse transformation is performed in the function iauGd2gc. ** ** Called: ** iauEform Earth reference ellipsoids ** iauGc2gde geocentric to geodetic transformation, general ** */ int iauGc2gde ( double a, double f, double xyz[3], double *elong, double *phi, double *height ) /* ** - - - - - - - - - - ** i a u G c 2 g d e ** - - - - - - - - - - ** ** Transform geocentric coordinates to geodetic for a reference ** ellipsoid of specified form. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** a double equatorial radius (Notes 2,4) ** f double flattening (Note 3) ** xyz double[3] geocentric vector (Note 4) ** ** Returned: ** elong double longitude (radians, east +ve) ** phi double latitude (geodetic, radians) ** height double height above ellipsoid (geodetic, Note 4) ** ** Returned (function value): ** int status: 0 = OK ** -1 = illegal f ** -2 = illegal a ** ** Notes: ** ** 1) This function is based on the GCONV2H Fortran subroutine by ** Toshio Fukushima (see reference). ** ** 2) The equatorial radius, a, can be in any units, but meters is ** the conventional choice. ** ** 3) The flattening, f, is (for the Earth) a value around 0.00335, ** i.e. around 1/298. ** ** 4) The equatorial radius, a, and the geocentric vector, xyz, ** must be given in the same units, and determine the units of ** the returned height, height. ** ** 5) If an error occurs (status < 0), elong, phi and height are ** unchanged. ** ** 6) The inverse transformation is performed in the function ** iauGd2gce. ** ** 7) The transformation for a standard ellipsoid (such as WGS84) can ** more conveniently be performed by calling iauGc2gd, which uses a ** numerical code to identify the required A and F values. ** ** Reference: ** ** Fukushima, T., "Transformation from Cartesian to geodetic ** coordinates accelerated by Halley's method", J.Geodesy (2006) ** 79: 689-693 ** */ int iauGd2gc ( int n, double elong, double phi, double height, double xyz[3] ) /* ** - - - - - - - - - ** i a u G d 2 g c ** - - - - - - - - - ** ** Transform geodetic coordinates to geocentric using the specified ** reference ellipsoid. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical transformation. ** ** Given: ** n int ellipsoid identifier (Note 1) ** elong double longitude (radians, east +ve) ** phi double latitude (geodetic, radians, Note 3) ** height double height above ellipsoid (geodetic, Notes 2,3) ** ** Returned: ** xyz double[3] geocentric vector (Note 2) ** ** Returned (function value): ** int status: 0 = OK ** -1 = illegal identifier (Note 3) ** -2 = illegal case (Note 3) ** ** Notes: ** ** 1) The identifier n is a number that specifies the choice of ** reference ellipsoid. The following are supported: ** ** n ellipsoid ** ** 1 WGS84 ** 2 GRS80 ** 3 WGS72 ** ** The n value has no significance outside the SOFA software. For ** convenience, symbols WGS84 etc. are defined in sofam.h. ** ** 2) The height (height, given) and the geocentric vector (xyz, ** returned) are in meters. ** ** 3) No validation is performed on the arguments elong, phi and ** height. An error status -1 means that the identifier n is ** illegal. An error status -2 protects against cases that would ** lead to arithmetic exceptions. In all error cases, xyz is set ** to zeros. ** ** 4) The inverse transformation is performed in the function iauGc2gd. ** ** Called: ** iauEform Earth reference ellipsoids ** iauGd2gce geodetic to geocentric transformation, general ** iauZp zero p-vector ** */ int iauGd2gce ( double a, double f, double elong, double phi, double height, double xyz[3] ) /* ** - - - - - - - - - - ** i a u G d 2 g c e ** - - - - - - - - - - ** ** Transform geodetic coordinates to geocentric for a reference ** ellipsoid of specified form. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** a double equatorial radius (Notes 1,4) ** f double flattening (Notes 2,4) ** elong double longitude (radians, east +ve) ** phi double latitude (geodetic, radians, Note 4) ** height double height above ellipsoid (geodetic, Notes 3,4) ** ** Returned: ** xyz double[3] geocentric vector (Note 3) ** ** Returned (function value): ** int status: 0 = OK ** -1 = illegal case (Note 4) ** Notes: ** ** 1) The equatorial radius, a, can be in any units, but meters is ** the conventional choice. ** ** 2) The flattening, f, is (for the Earth) a value around 0.00335, ** i.e. around 1/298. ** ** 3) The equatorial radius, a, and the height, height, must be ** given in the same units, and determine the units of the ** returned geocentric vector, xyz. ** ** 4) No validation is performed on individual arguments. The error ** status -1 protects against (unrealistic) cases that would lead ** to arithmetic exceptions. If an error occurs, xyz is unchanged. ** ** 5) The inverse transformation is performed in the function ** iauGc2gde. ** ** 6) The transformation for a standard ellipsoid (such as WGS84) can ** more conveniently be performed by calling iauGd2gc, which uses a ** numerical code to identify the required a and f values. ** ** References: ** ** Green, R.M., Spherical Astronomy, Cambridge University Press, ** (1985) Section 4.5, p96. ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 4.22, p202. ** */ double iauGmst00(double uta, double utb, double tta, double ttb) /* ** - - - - - - - - - - ** i a u G m s t 0 0 ** - - - - - - - - - - ** ** Greenwich mean sidereal time (model consistent with IAU 2000 ** resolutions). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** tta,ttb double TT as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich mean sidereal time (radians) ** ** Notes: ** ** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both ** Julian Dates, apportioned in any convenient way between the ** argument pairs. For example, JD=2450123.7 could be expressed in ** any of these ways, among others: ** ** Part A Part B ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable (in the case of UT; the TT is not at all critical ** in this respect). The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** Rotation Angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation ** and TT to predict the effects of precession. If UT1 is used for ** both purposes, errors of order 100 microarcseconds result. ** ** 3) This GMST is compatible with the IAU 2000 resolutions and must be ** used only in conjunction with other IAU 2000 compatible ** components such as precession-nutation and equation of the ** equinoxes. ** ** 4) The result is returned in the range 0 to 2pi. ** ** 5) The algorithm is from Capitaine et al. (2003) and IERS ** Conventions 2003. ** ** Called: ** iauEra00 Earth rotation angle, IAU 2000 ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ double iauGmst06(double uta, double utb, double tta, double ttb) /* ** - - - - - - - - - - ** i a u G m s t 0 6 ** - - - - - - - - - - ** ** Greenwich mean sidereal time (consistent with IAU 2006 precession). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** tta,ttb double TT as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich mean sidereal time (radians) ** ** Notes: ** ** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both ** Julian Dates, apportioned in any convenient way between the ** argument pairs. For example, JD=2450123.7 could be expressed in ** any of these ways, among others: ** ** Part A Part B ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable (in the case of UT; the TT is not at all critical ** in this respect). The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** rotation angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation ** and TT to predict the effects of precession. If UT1 is used for ** both purposes, errors of order 100 microarcseconds result. ** ** 3) This GMST is compatible with the IAU 2006 precession and must not ** be used with other precession models. ** ** 4) The result is returned in the range 0 to 2pi. ** ** Called: ** iauEra00 Earth rotation angle, IAU 2000 ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** Capitaine, N., Wallace, P.T. & Chapront, J., 2005, ** Astron.Astrophys. 432, 355 ** */ double iauGmst82(double dj1, double dj2) /* ** - - - - - - - - - - ** i a u G m s t 8 2 ** - - - - - - - - - - ** ** Universal Time to Greenwich mean sidereal time (IAU 1982 model). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** dj1,dj2 double UT1 Julian Date (see note) ** ** Returned (function value): ** double Greenwich mean sidereal time (radians) ** ** Notes: ** ** 1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any ** convenient way between the arguments dj1 and dj2. For example, ** JD(UT1)=2450123.7 could be expressed in any of these ways, ** among others: ** ** dj1 dj2 ** ** 2450123.7 0 (JD method) ** 2451545 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. The date & time method is ** best matched to the algorithm used: maximum accuracy (or, at ** least, minimum noise) is delivered when the dj1 argument is for ** 0hrs UT1 on the day in question and the dj2 argument lies in the ** range 0 to 1, or vice versa. ** ** 2) The algorithm is based on the IAU 1982 expression. This is ** always described as giving the GMST at 0 hours UT1. In fact, it ** gives the difference between the GMST and the UT, the steady ** 4-minutes-per-day drawing-ahead of ST with respect to UT. When ** whole days are ignored, the expression happens to equal the GMST ** at 0 hours UT1 each day. ** ** 3) In this function, the entire UT1 (the sum of the two arguments ** dj1 and dj2) is used directly as the argument for the standard ** formula, the constant term of which is adjusted by 12 hours to ** take account of the noon phasing of Julian Date. The UT1 is then ** added, but omitting whole days to conserve accuracy. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Transactions of the International Astronomical Union, ** XVIII B, 67 (1983). ** ** Aoki et al., Astron. Astrophys. 105, 359-361 (1982). ** */ double iauGst00a(double uta, double utb, double tta, double ttb) /* ** - - - - - - - - - - ** i a u G s t 0 0 a ** - - - - - - - - - - ** ** Greenwich apparent sidereal time (consistent with IAU 2000 ** resolutions). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** tta,ttb double TT as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich apparent sidereal time (radians) ** ** Notes: ** ** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both ** Julian Dates, apportioned in any convenient way between the ** argument pairs. For example, JD=2450123.7 could be expressed in ** any of these ways, among others: ** ** Part A Part B ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable (in the case of UT; the TT is not at all critical ** in this respect). The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** Rotation Angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation ** and TT to predict the effects of precession-nutation. If UT1 is ** used for both purposes, errors of order 100 microarcseconds ** result. ** ** 3) This GAST is compatible with the IAU 2000 resolutions and must be ** used only in conjunction with other IAU 2000 compatible ** components such as precession-nutation. ** ** 4) The result is returned in the range 0 to 2pi. ** ** 5) The algorithm is from Capitaine et al. (2003) and IERS ** Conventions 2003. ** ** Called: ** iauGmst00 Greenwich mean sidereal time, IAU 2000 ** iauEe00a equation of the equinoxes, IAU 2000A ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ double iauGst00b(double uta, double utb) /* ** - - - - - - - - - - ** i a u G s t 0 0 b ** - - - - - - - - - - ** ** Greenwich apparent sidereal time (consistent with IAU 2000 ** resolutions but using the truncated nutation model IAU 2000B). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich apparent sidereal time (radians) ** ** Notes: ** ** 1) The UT1 date uta+utb is a Julian Date, apportioned in any ** convenient way between the argument pair. For example, ** JD=2450123.7 could be expressed in any of these ways, among ** others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** Rotation Angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) The result is compatible with the IAU 2000 resolutions, except ** that accuracy has been compromised for the sake of speed and ** convenience in two respects: ** ** . UT is used instead of TDB (or TT) to compute the precession ** component of GMST and the equation of the equinoxes. This ** results in errors of order 0.1 mas at present. ** ** . The IAU 2000B abridged nutation model (McCarthy & Luzum, 2001) ** is used, introducing errors of up to 1 mas. ** ** 3) This GAST is compatible with the IAU 2000 resolutions and must be ** used only in conjunction with other IAU 2000 compatible ** components such as precession-nutation. ** ** 4) The result is returned in the range 0 to 2pi. ** ** 5) The algorithm is from Capitaine et al. (2003) and IERS ** Conventions 2003. ** ** Called: ** iauGmst00 Greenwich mean sidereal time, IAU 2000 ** iauEe00b equation of the equinoxes, IAU 2000B ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to ** implement the IAU 2000 definition of UT1", Astronomy & ** Astrophysics, 406, 1135-1149 (2003) ** ** McCarthy, D.D. & Luzum, B.J., "An abridged model of the ** precession-nutation of the celestial pole", Celestial Mechanics & ** Dynamical Astronomy, 85, 37-49 (2003) ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ double iauGst06(double uta, double utb, double tta, double ttb, double rnpb[3][3]) /* ** - - - - - - - - - ** i a u G s t 0 6 ** - - - - - - - - - ** ** Greenwich apparent sidereal time, IAU 2006, given the NPB matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** tta,ttb double TT as a 2-part Julian Date (Notes 1,2) ** rnpb double[3][3] nutation x precession x bias matrix ** ** Returned (function value): ** double Greenwich apparent sidereal time (radians) ** ** Notes: ** ** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both ** Julian Dates, apportioned in any convenient way between the ** argument pairs. For example, JD=2450123.7 could be expressed in ** any of these ways, among others: ** ** Part A Part B ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable (in the case of UT; the TT is not at all critical ** in this respect). The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** rotation angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation ** and TT to predict the effects of precession-nutation. If UT1 is ** used for both purposes, errors of order 100 microarcseconds ** result. ** ** 3) Although the function uses the IAU 2006 series for s+XY/2, it is ** otherwise independent of the precession-nutation model and can in ** practice be used with any equinox-based NPB matrix. ** ** 4) The result is returned in the range 0 to 2pi. ** ** Called: ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** iauAnp normalize angle into range 0 to 2pi ** iauEra00 Earth rotation angle, IAU 2000 ** iauEors equation of the origins, given NPB matrix and s ** ** Reference: ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** */ double iauGst06a(double uta, double utb, double tta, double ttb) /* ** - - - - - - - - - - ** i a u G s t 0 6 a ** - - - - - - - - - - ** ** Greenwich apparent sidereal time (consistent with IAU 2000 and 2006 ** resolutions). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** tta,ttb double TT as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich apparent sidereal time (radians) ** ** Notes: ** ** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both ** Julian Dates, apportioned in any convenient way between the ** argument pairs. For example, JD=2450123.7 could be expressed in ** any of these ways, among others: ** ** Part A Part B ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable (in the case of UT; the TT is not at all critical ** in this respect). The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** rotation angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation ** and TT to predict the effects of precession-nutation. If UT1 is ** used for both purposes, errors of order 100 microarcseconds ** result. ** ** 3) This GAST is compatible with the IAU 2000/2006 resolutions and ** must be used only in conjunction with IAU 2006 precession and ** IAU 2000A nutation. ** ** 4) The result is returned in the range 0 to 2pi. ** ** Called: ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauGst06 Greenwich apparent ST, IAU 2006, given NPB matrix ** ** Reference: ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** */ double iauGst94(double uta, double utb) /* ** - - - - - - - - - ** i a u G s t 9 4 ** - - - - - - - - - ** ** Greenwich apparent sidereal time (consistent with IAU 1982/94 ** resolutions). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) ** ** Returned (function value): ** double Greenwich apparent sidereal time (radians) ** ** Notes: ** ** 1) The UT1 date uta+utb is a Julian Date, apportioned in any ** convenient way between the argument pair. For example, ** JD=2450123.7 could be expressed in any of these ways, among ** others: ** ** uta utb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 and MJD methods are good compromises ** between resolution and convenience. For UT, the date & time ** method is best matched to the algorithm that is used by the Earth ** Rotation Angle function, called internally: maximum precision is ** delivered when the uta argument is for 0hrs UT1 on the day in ** question and the utb argument lies in the range 0 to 1, or vice ** versa. ** ** 2) The result is compatible with the IAU 1982 and 1994 resolutions, ** except that accuracy has been compromised for the sake of ** convenience in that UT is used instead of TDB (or TT) to compute ** the equation of the equinoxes. ** ** 3) This GAST must be used only in conjunction with contemporaneous ** IAU standards such as 1976 precession, 1980 obliquity and 1982 ** nutation. It is not compatible with the IAU 2000 resolutions. ** ** 4) The result is returned in the range 0 to 2pi. ** ** Called: ** iauGmst82 Greenwich mean sidereal time, IAU 1982 ** iauEqeq94 equation of the equinoxes, IAU 1994 ** iauAnp normalize angle into range 0 to 2pi ** ** References: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** IAU Resolution C7, Recommendation 3 (1994) ** */ void iauH2fk5(double rh, double dh, double drh, double ddh, double pxh, double rvh, double *r5, double *d5, double *dr5, double *dd5, double *px5, double *rv5) /* ** - - - - - - - - - ** i a u H 2 f k 5 ** - - - - - - - - - ** ** Transform Hipparcos star data into the FK5 (J2000.0) system. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given (all Hipparcos, epoch J2000.0): ** rh double RA (radians) ** dh double Dec (radians) ** drh double proper motion in RA (dRA/dt, rad/Jyear) ** ddh double proper motion in Dec (dDec/dt, rad/Jyear) ** pxh double parallax (arcsec) ** rvh double radial velocity (km/s, positive = receding) ** ** Returned (all FK5, equinox J2000.0, epoch J2000.0): ** r5 double RA (radians) ** d5 double Dec (radians) ** dr5 double proper motion in RA (dRA/dt, rad/Jyear) ** dd5 double proper motion in Dec (dDec/dt, rad/Jyear) ** px5 double parallax (arcsec) ** rv5 double radial velocity (km/s, positive = receding) ** ** Notes: ** ** 1) This function transforms Hipparcos star positions and proper ** motions into FK5 J2000.0. ** ** 2) The proper motions in RA are dRA/dt rather than ** cos(Dec)*dRA/dt, and are per year rather than per century. ** ** 3) The FK5 to Hipparcos transformation is modeled as a pure ** rotation and spin; zonal errors in the FK5 catalog are not ** taken into account. ** ** 4) See also iauFk52h, iauFk5hz, iauHfk5z. ** ** Called: ** iauStarpv star catalog data to space motion pv-vector ** iauFk5hip FK5 to Hipparcos rotation and spin ** iauRv2m r-vector to r-matrix ** iauRxp product of r-matrix and p-vector ** iauTrxp product of transpose of r-matrix and p-vector ** iauPxp vector product of two p-vectors ** iauPmp p-vector minus p-vector ** iauPvstar space motion pv-vector to star catalog data ** ** Reference: ** ** F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000). ** */ void iauHfk5z(double rh, double dh, double date1, double date2, double *r5, double *d5, double *dr5, double *dd5) /* ** - - - - - - - - - ** i a u H f k 5 z ** - - - - - - - - - ** ** Transform a Hipparcos star position into FK5 J2000.0, assuming ** zero Hipparcos proper motion. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rh double Hipparcos RA (radians) ** dh double Hipparcos Dec (radians) ** date1,date2 double TDB date (Note 1) ** ** Returned (all FK5, equinox J2000.0, date date1+date2): ** r5 double RA (radians) ** d5 double Dec (radians) ** dr5 double FK5 RA proper motion (rad/year, Note 4) ** dd5 double Dec proper motion (rad/year, Note 4) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 3) The FK5 to Hipparcos transformation is modeled as a pure rotation ** and spin; zonal errors in the FK5 catalogue are not taken into ** account. ** ** 4) It was the intention that Hipparcos should be a close ** approximation to an inertial frame, so that distant objects have ** zero proper motion; such objects have (in general) non-zero ** proper motion in FK5, and this function returns those fictitious ** proper motions. ** ** 5) The position returned by this function is in the FK5 J2000.0 ** reference system but at date date1+date2. ** ** 6) See also iauFk52h, iauH2fk5, iauFk5zhz. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauFk5hip FK5 to Hipparcos rotation and spin ** iauRxp product of r-matrix and p-vector ** iauSxp multiply p-vector by scalar ** iauRxr product of two r-matrices ** iauTrxp product of transpose of r-matrix and p-vector ** iauPxp vector product of two p-vectors ** iauPv2s pv-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739. ** */ void iauIcrs2g ( double dr, double dd, double *dl, double *db ) /* ** - - - - - - - - - - ** i a u I c r s 2 g ** - - - - - - - - - - ** ** Transformation from ICRS to Galactic Coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support routine. ** ** Given: ** dr double ICRS right ascension (radians) ** dd double ICRS declination (radians) ** ** Returned: ** dl double galactic longitude (radians) ** db double galactic latitude (radians) ** ** Notes: ** ** 1) The IAU 1958 system of Galactic coordinates was defined with ** respect to the now obsolete reference system FK4 B1950.0. When ** interpreting the system in a modern context, several factors have ** to be taken into account: ** ** . The inclusion in FK4 positions of the E-terms of aberration. ** ** . The distortion of the FK4 proper motion system by differential ** Galactic rotation. ** ** . The use of the B1950.0 equinox rather than the now-standard ** J2000.0. ** ** . The frame bias between ICRS and the J2000.0 mean place system. ** ** The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation ** matrix that transforms directly between ICRS and Galactic ** coordinates with the above factors taken into account. The ** matrix is derived from three angles, namely the ICRS coordinates ** of the Galactic pole and the longitude of the ascending node of ** the galactic equator on the ICRS equator. They are given in ** degrees to five decimal places and for canonical purposes are ** regarded as exact. In the Hipparcos Catalogue the matrix ** elements are given to 10 decimal places (about 20 microarcsec). ** In the present SOFA function the matrix elements have been ** recomputed from the canonical three angles and are given to 30 ** decimal places. ** ** 2) The inverse transformation is performed by the function iauG2icrs. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** iauS2c spherical coordinates to unit vector ** iauRxp product of r-matrix and p-vector ** iauC2s p-vector to spherical ** ** Reference: ** Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho ** catalogues. Astrometric and photometric star catalogues ** derived from the ESA Hipparcos Space Astrometry Mission. ESA ** Publications Division, Noordwijk, Netherlands. ** */ void iauIr(double r[3][3]) /* ** - - - - - - ** i a u I r ** - - - - - - ** ** Initialize an r-matrix to the identity matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Returned: ** r double[3][3] r-matrix ** */ int iauJd2cal(double dj1, double dj2, int *iy, int *im, int *id, double *fd) /* ** - - - - - - - - - - ** i a u J d 2 c a l ** - - - - - - - - - - ** ** Julian Date to Gregorian year, month, day, and fraction of a day. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** dj1,dj2 double Julian Date (Notes 1, 2) ** ** Returned (arguments): ** iy int year ** im int month ** id int day ** fd double fraction of day ** ** Returned (function value): ** int status: ** 0 = OK ** -1 = unacceptable date (Note 3) ** ** Notes: ** ** 1) The earliest valid date is -68569.5 (-4900 March 1). The ** largest value accepted is 1e9. ** ** 2) The Julian Date is apportioned in any convenient way between ** the arguments dj1 and dj2. For example, JD=2450123.7 could ** be expressed in any of these ways, among others: ** ** dj1 dj2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** 3) In early eras the conversion is from the "proleptic Gregorian ** calendar"; no account is taken of the date(s) of adoption of ** the Gregorian calendar, nor is the AD/BC numbering convention ** observed. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 12.92 (p604). ** */ int iauJdcalf(int ndp, double dj1, double dj2, int iymdf[4]) /* ** - - - - - - - - - - ** i a u J d c a l f ** - - - - - - - - - - ** ** Julian Date to Gregorian Calendar, expressed in a form convenient ** for formatting messages: rounded to a specified precision. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ndp int number of decimal places of days in fraction ** dj1,dj2 double dj1+dj2 = Julian Date (Note 1) ** ** Returned: ** iymdf int[4] year, month, day, fraction in Gregorian ** calendar ** ** Returned (function value): ** int status: ** -1 = date out of range ** 0 = OK ** +1 = NDP not 0-9 (interpreted as 0) ** ** Notes: ** ** 1) The Julian Date is apportioned in any convenient way between ** the arguments dj1 and dj2. For example, JD=2450123.7 could ** be expressed in any of these ways, among others: ** ** dj1 dj2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** 2) In early eras the conversion is from the "Proleptic Gregorian ** Calendar"; no account is taken of the date(s) of adoption of ** the Gregorian Calendar, nor is the AD/BC numbering convention ** observed. ** ** 3) Refer to the function iauJd2cal. ** ** 4) NDP should be 4 or less if internal overflows are to be ** avoided on machines which use 16-bit integers. ** ** Called: ** iauJd2cal JD to Gregorian calendar ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 12.92 (p604). ** */ void iauLd(double bm, double p[3], double q[3], double e[3], double em, double dlim, double p1[3]) /* ** - - - - - - ** i a u L d ** - - - - - - ** ** Apply light deflection by a solar-system body, as part of ** transforming coordinate direction into natural direction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** bm double mass of the gravitating body (solar masses) ** p double[3] direction from observer to source (unit vector) ** q double[3] direction from body to source (unit vector) ** e double[3] direction from body to observer (unit vector) ** em double distance from body to observer (au) ** dlim double deflection limiter (Note 4) ** ** Returned: ** p1 double[3] observer to deflected source (unit vector) ** ** Notes: ** ** 1) The algorithm is based on Expr. (70) in Klioner (2003) and ** Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann ** 2013), with some rearrangement to minimize the effects of machine ** precision. ** ** 2) The mass parameter bm can, as required, be adjusted in order to ** allow for such effects as quadrupole field. ** ** 3) The barycentric position of the deflecting body should ideally ** correspond to the time of closest approach of the light ray to ** the body. ** ** 4) The deflection limiter parameter dlim is phi^2/2, where phi is ** the angular separation (in radians) between source and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. ** ** 5) The returned vector p1 is not normalized, but the consequential ** departure from unit magnitude is always negligible. ** ** 6) The arguments p and p1 can be the same array. ** ** 7) To accumulate total light deflection taking into account the ** contributions from several bodies, call the present function for ** each body in succession, in decreasing order of distance from the ** observer. ** ** 8) For efficiency, validation is omitted. The supplied vectors must ** be of unit magnitude, and the deflection limiter non-zero and ** positive. ** ** References: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013). ** ** Klioner, Sergei A., "A practical relativistic model for micro- ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). ** ** Called: ** iauPdp scalar product of two p-vectors ** iauPxp vector product of two p-vectors ** */ void iauLdn(int n, iauLDBODY b[], double ob[3], double sc[3], double sn[3]) /*+ ** - - - - - - - ** i a u L d n ** - - - - - - - ** ** For a star, apply light deflection by multiple solar-system bodies, ** as part of transforming coordinate direction into natural direction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** n int number of bodies (note 1) ** b iauLDBODY[n] data for each of the n bodies (Notes 1,2): ** bm double mass of the body (solar masses, Note 3) ** dl double deflection limiter (Note 4) ** pv [2][3] barycentric PV of the body (au, au/day) ** ob double[3] barycentric position of the observer (au) ** sc double[3] observer to star coord direction (unit vector) ** ** Returned: ** sn double[3] observer to deflected star (unit vector) ** ** 1) The array b contains n entries, one for each body to be ** considered. If n = 0, no gravitational light deflection will be ** applied, not even for the Sun. ** ** 2) The array b should include an entry for the Sun as well as for ** any planet or other body to be taken into account. The entries ** should be in the order in which the light passes the body. ** ** 3) In the entry in the b array for body i, the mass parameter ** b[i].bm can, as required, be adjusted in order to allow for such ** effects as quadrupole field. ** ** 4) The deflection limiter parameter b[i].dl is phi^2/2, where phi is ** the angular separation (in radians) between star and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. Example values suitable for a terrestrial ** observer, together with masses, are as follows: ** ** body i b[i].bm b[i].dl ** ** Sun 1.0 6e-6 ** Jupiter 0.00095435 3e-9 ** Saturn 0.00028574 3e-10 ** ** 5) For cases where the starlight passes the body before reaching the ** observer, the body is placed back along its barycentric track by ** the light time from that point to the observer. For cases where ** the body is "behind" the observer no such shift is applied. If ** a different treatment is preferred, the user has the option of ** instead using the iauLd function. Similarly, iauLd can be used ** for cases where the source is nearby, not a star. ** ** 6) The returned vector sn is not normalized, but the consequential ** departure from unit magnitude is always negligible. ** ** 7) The arguments sc and sn can be the same array. ** ** 8) For efficiency, validation is omitted. The supplied masses must ** be greater than zero, the position and velocity vectors must be ** right, and the deflection limiter greater than zero. ** ** Reference: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013), Section 7.2.4. ** ** Called: ** iauCp copy p-vector ** iauPdp scalar product of two p-vectors ** iauPmp p-vector minus p-vector ** iauPpsp p-vector plus scaled p-vector ** iauPn decompose p-vector into modulus and direction ** iauLd light deflection by a solar-system body ** */ void iauLdsun(double p[3], double e[3], double em, double p1[3]) /* ** - - - - - - - - - ** i a u L d s u n ** - - - - - - - - - ** ** Deflection of starlight by the Sun. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** p double[3] direction from observer to star (unit vector) ** e double[3] direction from Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** ** Returned: ** p1 double[3] observer to deflected star (unit vector) ** ** Notes: ** ** 1) The source is presumed to be sufficiently distant that its ** directions seen from the Sun and the observer are essentially ** the same. ** ** 2) The deflection is restrained when the angle between the star and ** the center of the Sun is less than a threshold value, falling to ** zero deflection for zero separation. The chosen threshold value ** is within the solar limb for all solar-system applications, and ** is about 5 arcminutes for the case of a terrestrial observer. ** ** 3) The arguments p and p1 can be the same array. ** ** Called: ** iauLd light deflection by a solar-system body ** */ void iauLteceq(double epj, double dl, double db, double *dr, double *dd) /* ** - - - - - - - - - - ** i a u L t e c e q ** - - - - - - - - - - ** ** Transformation from ecliptic coordinates (mean equinox and ecliptic ** of date) to ICRS RA,Dec, using a long-term precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** dl,db double ecliptic longitude and latitude (radians) ** ** Returned: ** dr,dd double ICRS right ascension and declination (radians) ** ** 1) No assumptions are made about whether the coordinates represent ** starlight and embody astrometric effects such as parallax or ** aberration. ** ** 2) The transformation is approximately that from ecliptic longitude ** and latitude (mean equinox and ecliptic of date) to mean J2000.0 ** right ascension and declination, with only frame bias (always ** less than 25 mas) to disturb this classical picture. ** ** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauLtecm J2000.0 to ecliptic rotation matrix, long term ** iauTrxp product of transpose of r-matrix and p-vector ** iauC2s unit vector to spherical coordinates ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** */ void iauLtecm(double epj, double rm[3][3]) /* ** - - - - - - - - - ** i a u L t e c m ** - - - - - - - - - ** ** ICRS equatorial to ecliptic rotation matrix, long-term. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** ** Returned: ** rm double[3][3] ICRS to ecliptic rotation matrix ** ** Notes: ** ** 1) The matrix is in the sense ** ** E_ep = rm x P_ICRS, ** ** where P_ICRS is a vector with respect to ICRS right ascension ** and declination axes and E_ep is the same vector with respect to ** the (inertial) ecliptic and equinox of epoch epj. ** ** 2) P_ICRS is a free vector, merely a direction, typically of unit ** magnitude, and not bound to any particular spatial origin, such ** as the Earth, Sun or SSB. No assumptions are made about whether ** it represents starlight and embodies astrometric effects such as ** parallax or aberration. The transformation is approximately that ** between mean J2000.0 right ascension and declination and ecliptic ** longitude and latitude, with only frame bias (always less than ** 25 mas) to disturb this classical picture. ** ** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** Called: ** iauLtpequ equator pole, long term ** iauLtpecl ecliptic pole, long term ** iauPxp vector product ** iauPn normalize vector ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** */ void iauLteqec(double epj, double dr, double dd, double *dl, double *db) /* ** - - - - - - - - - - ** i a u L t e q e c ** - - - - - - - - - - ** ** Transformation from ICRS equatorial coordinates to ecliptic ** coordinates (mean equinox and ecliptic of date) using a long-term ** precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** dr,dd double ICRS right ascension and declination (radians) ** ** Returned: ** dl,db double ecliptic longitude and latitude (radians) ** ** 1) No assumptions are made about whether the coordinates represent ** starlight and embody astrometric effects such as parallax or ** aberration. ** ** 2) The transformation is approximately that from mean J2000.0 right ** ascension and declination to ecliptic longitude and latitude ** (mean equinox and ecliptic of date), with only frame bias (always ** less than 25 mas) to disturb this classical picture. ** ** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauLtecm J2000.0 to ecliptic rotation matrix, long term ** iauRxp product of r-matrix and p-vector ** iauC2s unit vector to spherical coordinates ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** */ void iauLtp(double epj, double rp[3][3]) /* ** - - - - - - - ** i a u L t p ** - - - - - - - ** ** Long-term precession matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** ** Returned: ** rp double[3][3] precession matrix, J2000.0 to date ** ** Notes: ** ** 1) The matrix is in the sense ** ** P_date = rp x P_J2000, ** ** where P_J2000 is a vector with respect to the J2000.0 mean ** equator and equinox and P_date is the same vector with respect to ** the equator and equinox of epoch epj. ** ** 2) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** Called: ** iauLtpequ equator pole, long term ** iauLtpecl ecliptic pole, long term ** iauPxp vector product ** iauPn normalize vector ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** */ void iauLtpb(double epj, double rpb[3][3]) /* ** - - - - - - - - ** i a u L t p b ** - - - - - - - - ** ** Long-term precession matrix, including ICRS frame bias. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** ** Returned: ** rpb double[3][3] precession-bias matrix, J2000.0 to date ** ** Notes: ** ** 1) The matrix is in the sense ** ** P_date = rpb x P_ICRS, ** ** where P_ICRS is a vector in the Geocentric Celestial Reference ** System, and P_date is the vector with respect to the Celestial ** Intermediate Reference System at that date but with nutation ** neglected. ** ** 2) A first order frame bias formulation is used, of sub- ** microarcsecond accuracy compared with a full 3D rotation. ** ** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** */ void iauLtpecl(double epj, double vec[3]) /* ** - - - - - - - - - - ** i a u L t p e c l ** - - - - - - - - - - ** ** Long-term precession of the ecliptic. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** ** Returned: ** vec double[3] ecliptic pole unit vector ** ** Notes: ** ** 1) The returned vector is with respect to the J2000.0 mean equator ** and equinox. ** ** 2) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** */ void iauLtpequ(double epj, double veq[3]) /* ** - - - - - - - - - - ** i a u L t p e q u ** - - - - - - - - - - ** ** Long-term precession of the equator. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** ** Returned: ** veq double[3] equator pole unit vector ** ** Notes: ** ** 1) The returned vector is with respect to the J2000.0 mean equator ** and equinox. ** ** 2) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** */ void iauNum00a(double date1, double date2, double rmatn[3][3]) /* ** - - - - - - - - - - ** i a u N u m 0 0 a ** - - - - - - - - - - ** ** Form the matrix of nutation for a given date, IAU 2000A model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rmatn double[3][3] nutation matrix ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(true) = rmatn * V(mean), where ** the p-vector V(true) is with respect to the true equatorial triad ** of date and the p-vector V(mean) is with respect to the mean ** equatorial triad of date. ** ** 3) A faster, but slightly less accurate result (about 1 mas), can be ** obtained by using instead the iauNum00b function. ** ** Called: ** iauPn00a bias/precession/nutation, IAU 2000A ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222-3 (p114). ** */ void iauNum00b(double date1, double date2, double rmatn[3][3]) /* ** - - - - - - - - - - ** i a u N u m 0 0 b ** - - - - - - - - - - ** ** Form the matrix of nutation for a given date, IAU 2000B model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rmatn double[3][3] nutation matrix ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(true) = rmatn * V(mean), where ** the p-vector V(true) is with respect to the true equatorial triad ** of date and the p-vector V(mean) is with respect to the mean ** equatorial triad of date. ** ** 3) The present function is faster, but slightly less accurate (about ** 1 mas), than the iauNum00a function. ** ** Called: ** iauPn00b bias/precession/nutation, IAU 2000B ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222-3 (p114). ** */ void iauNum06a(double date1, double date2, double rmatn[3][3]) /* ** - - - - - - - - - - ** i a u N u m 0 6 a ** - - - - - - - - - - ** ** Form the matrix of nutation for a given date, IAU 2006/2000A model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rmatn double[3][3] nutation matrix ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(true) = rmatn * V(mean), where ** the p-vector V(true) is with respect to the true equatorial triad ** of date and the p-vector V(mean) is with respect to the mean ** equatorial triad of date. ** ** Called: ** iauObl06 mean obliquity, IAU 2006 ** iauNut06a nutation, IAU 2006/2000A ** iauNumat form nutation matrix ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222-3 (p114). ** */ void iauNumat(double epsa, double dpsi, double deps, double rmatn[3][3]) /* ** - - - - - - - - - ** i a u N u m a t ** - - - - - - - - - ** ** Form the matrix of nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epsa double mean obliquity of date (Note 1) ** dpsi,deps double nutation (Note 2) ** ** Returned: ** rmatn double[3][3] nutation matrix (Note 3) ** ** Notes: ** ** ** 1) The supplied mean obliquity epsa, must be consistent with the ** precession-nutation models from which dpsi and deps were obtained. ** ** 2) The caller is responsible for providing the nutation components; ** they are in longitude and obliquity, in radians and are with ** respect to the equinox and ecliptic of date. ** ** 3) The matrix operates in the sense V(true) = rmatn * V(mean), ** where the p-vector V(true) is with respect to the true ** equatorial triad of date and the p-vector V(mean) is with ** respect to the mean equatorial triad of date. ** ** Called: ** iauIr initialize r-matrix to identity ** iauRx rotate around X-axis ** iauRz rotate around Z-axis ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222-3 (p114). ** */ void iauNut00a(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - - ** i a u N u t 0 0 a ** - - - - - - - - - - ** ** Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation ** with free core nutation omitted). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation, luni-solar + planetary (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components in longitude and obliquity are in radians ** and with respect to the equinox and ecliptic of date. The ** obliquity at J2000.0 is assumed to be the Lieske et al. (1977) ** value of 84381.448 arcsec. ** ** Both the luni-solar and planetary nutations are included. The ** latter are due to direct planetary nutations and the ** perturbations of the lunar and terrestrial orbits. ** ** 3) The function computes the MHB2000 nutation series with the ** associated corrections for planetary nutations. It is an ** implementation of the nutation part of the IAU 2000A precession- ** nutation model, formally adopted by the IAU General Assembly in ** 2000, namely MHB2000 (Mathews et al. 2002), but with the free ** core nutation (FCN - see Note 4) omitted. ** ** 4) The full MHB2000 model also contains contributions to the ** nutations in longitude and obliquity due to the free-excitation ** of the free-core-nutation during the period 1979-2000. These FCN ** terms, which are time-dependent and unpredictable, are NOT ** included in the present function and, if required, must be ** independently computed. With the FCN corrections included, the ** present function delivers a pole which is at current epochs ** accurate to a few hundred microarcseconds. The omission of FCN ** introduces further errors of about that size. ** ** 5) The present function provides classical nutation. The MHB2000 ** algorithm, from which it is adapted, deals also with (i) the ** offsets between the GCRS and mean poles and (ii) the adjustments ** in longitude and obliquity due to the changed precession rates. ** These additional functions, namely frame bias and precession ** adjustments, are supported by the SOFA functions iauBi00 and ** iauPr00. ** ** 6) The MHB2000 algorithm also provides "total" nutations, comprising ** the arithmetic sum of the frame bias, precession adjustments, ** luni-solar nutation and planetary nutation. These total ** nutations can be used in combination with an existing IAU 1976 ** precession implementation, such as iauPmat76, to deliver GCRS- ** to-true predictions of sub-mas accuracy at current dates. ** However, there are three shortcomings in the MHB2000 model that ** must be taken into account if more accurate or definitive results ** are required (see Wallace 2002): ** ** (i) The MHB2000 total nutations are simply arithmetic sums, ** yet in reality the various components are successive Euler ** rotations. This slight lack of rigor leads to cross terms ** that exceed 1 mas after a century. The rigorous procedure ** is to form the GCRS-to-true rotation matrix by applying the ** bias, precession and nutation in that order. ** ** (ii) Although the precession adjustments are stated to be with ** respect to Lieske et al. (1977), the MHB2000 model does ** not specify which set of Euler angles are to be used and ** how the adjustments are to be applied. The most literal ** and straightforward procedure is to adopt the 4-rotation ** epsilon_0, psi_A, omega_A, xi_A option, and to add DPSIPR ** to psi_A and DEPSPR to both omega_A and eps_A. ** ** (iii) The MHB2000 model predates the determination by Chapront ** et al. (2002) of a 14.6 mas displacement between the ** J2000.0 mean equinox and the origin of the ICRS frame. It ** should, however, be noted that neglecting this displacement ** when calculating star coordinates does not lead to a ** 14.6 mas change in right ascension, only a small second- ** order distortion in the pattern of the precession-nutation ** effect. ** ** For these reasons, the SOFA functions do not generate the "total ** nutations" directly, though they can of course easily be ** generated by calling iauBi00, iauPr00 and the present function ** and adding the results. ** ** 7) The MHB2000 model contains 41 instances where the same frequency ** appears multiple times, of which 38 are duplicates and three are ** triplicates. To keep the present code close to the original MHB ** algorithm, this small inefficiency has not been corrected. ** ** Called: ** iauFal03 mean anomaly of the Moon ** iauFaf03 mean argument of the latitude of the Moon ** iauFaom03 mean longitude of the Moon's ascending node ** iauFame03 mean longitude of Mercury ** iauFave03 mean longitude of Venus ** iauFae03 mean longitude of Earth ** iauFama03 mean longitude of Mars ** iauFaju03 mean longitude of Jupiter ** iauFasa03 mean longitude of Saturn ** iauFaur03 mean longitude of Uranus ** iauFapa03 general accumulated precession in longitude ** ** References: ** ** Chapront, J., Chapront-Touze, M. & Francou, G. 2002, ** Astron.Astrophys. 387, 700 ** ** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, ** Astron.Astrophys. 58, 1-16 ** ** Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. ** 107, B4. The MHB_2000 code itself was obtained on 9th September ** 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A. ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** Wallace, P.T., "Software for Implementing the IAU 2000 ** Resolutions", in IERS Workshop 5.1 (2002) ** */ void iauNut00b(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - - ** i a u N u t 0 0 b ** - - - - - - - - - - ** ** Nutation, IAU 2000B model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation, luni-solar + planetary (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components in longitude and obliquity are in radians ** and with respect to the equinox and ecliptic of date. The ** obliquity at J2000.0 is assumed to be the Lieske et al. (1977) ** value of 84381.448 arcsec. (The errors that result from using ** this function with the IAU 2006 value of 84381.406 arcsec can be ** neglected.) ** ** The nutation model consists only of luni-solar terms, but ** includes also a fixed offset which compensates for certain long- ** period planetary terms (Note 7). ** ** 3) This function is an implementation of the IAU 2000B abridged ** nutation model formally adopted by the IAU General Assembly in ** 2000. The function computes the MHB_2000_SHORT luni-solar ** nutation series (Luzum 2001), but without the associated ** corrections for the precession rate adjustments and the offset ** between the GCRS and J2000.0 mean poles. ** ** 4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400 ** terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only ** 77 terms, plus additional simplifications, yet still delivers ** results of 1 mas accuracy at present epochs. This combination of ** accuracy and size makes the IAU 2000B abridged nutation model ** suitable for most practical applications. ** ** The function delivers a pole accurate to 1 mas from 1900 to 2100 ** (usually better than 1 mas, very occasionally just outside ** 1 mas). The full IAU 2000A model, which is implemented in the ** function iauNut00a (q.v.), delivers considerably greater accuracy ** at current dates; however, to realize this improved accuracy, ** corrections for the essentially unpredictable free-core-nutation ** (FCN) must also be included. ** ** 5) The present function provides classical nutation. The ** MHB_2000_SHORT algorithm, from which it is adapted, deals also ** with (i) the offsets between the GCRS and mean poles and (ii) the ** adjustments in longitude and obliquity due to the changed ** precession rates. These additional functions, namely frame bias ** and precession adjustments, are supported by the SOFA functions ** iauBi00 and iauPr00. ** ** 6) The MHB_2000_SHORT algorithm also provides "total" nutations, ** comprising the arithmetic sum of the frame bias, precession ** adjustments, and nutation (luni-solar + planetary). These total ** nutations can be used in combination with an existing IAU 1976 ** precession implementation, such as iauPmat76, to deliver GCRS- ** to-true predictions of mas accuracy at current epochs. However, ** for symmetry with the iauNut00a function (q.v. for the reasons), ** the SOFA functions do not generate the "total nutations" ** directly. Should they be required, they could of course easily ** be generated by calling iauBi00, iauPr00 and the present function ** and adding the results. ** ** 7) The IAU 2000B model includes "planetary bias" terms that are ** fixed in size but compensate for long-period nutations. The ** amplitudes quoted in McCarthy & Luzum (2003), namely ** Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for ** the "total nutations" method described in Note 6. The Luzum ** (2001) values used in this SOFA implementation, namely -0.135 mas ** and +0.388 mas, are optimized for the "rigorous" method, where ** frame bias, precession and nutation are applied separately and in ** that order. During the interval 1995-2050, the SOFA ** implementation delivers a maximum error of 1.001 mas (not ** including FCN). ** ** References: ** ** Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions ** for the precession quantities based upon the IAU /1976/ system of ** astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977) ** ** Luzum, B., private communication, 2001 (Fortran code ** MHB_2000_SHORT) ** ** McCarthy, D.D. & Luzum, B.J., "An abridged model of the ** precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron. ** 85, 37-49 (2003) ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994) ** */ void iauNut06a(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - - ** i a u N u t 0 6 a ** - - - - - - - - - - ** ** IAU 2000A nutation with adjustments to match the IAU 2006 ** precession. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation, luni-solar + planetary (Note 2) ** ** Status: canonical model. ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components in longitude and obliquity are in radians ** and with respect to the mean equinox and ecliptic of date, ** IAU 2006 precession model (Hilton et al. 2006, Capitaine et al. ** 2005). ** ** 3) The function first computes the IAU 2000A nutation, then applies ** adjustments for (i) the consequences of the change in obliquity ** from the IAU 1980 ecliptic to the IAU 2006 ecliptic and (ii) the ** secular variation in the Earth's dynamical form factor J2. ** ** 4) The present function provides classical nutation, complementing ** the IAU 2000 frame bias and IAU 2006 precession. It delivers a ** pole which is at current epochs accurate to a few tens of ** microarcseconds, apart from the free core nutation. ** ** Called: ** iauNut00a nutation, IAU 2000A ** ** References: ** ** Chapront, J., Chapront-Touze, M. & Francou, G. 2002, ** Astron.Astrophys. 387, 700 ** ** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, ** Astron.Astrophys. 58, 1-16 ** ** Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. ** 107, B4. The MHB_2000 code itself was obtained on 9th September ** 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A. ** ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** Wallace, P.T., "Software for Implementing the IAU 2000 ** Resolutions", in IERS Workshop 5.1 (2002) ** */ void iauNut80(double date1, double date2, double *dpsi, double *deps) /* ** - - - - - - - - - ** i a u N u t 8 0 ** - - - - - - - - - ** ** Nutation, IAU 1980 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi double nutation in longitude (radians) ** deps double nutation in obliquity (radians) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components are with respect to the ecliptic of ** date. ** ** Called: ** iauAnpm normalize angle into range +/- pi ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.222 (p111). ** */ void iauNutm80(double date1, double date2, double rmatn[3][3]) /* ** - - - - - - - - - - ** i a u N u t m 8 0 ** - - - - - - - - - - ** ** Form the matrix of nutation for a given date, IAU 1980 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TDB date (Note 1) ** ** Returned: ** rmatn double[3][3] nutation matrix ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(true) = rmatn * V(mean), ** where the p-vector V(true) is with respect to the true ** equatorial triad of date and the p-vector V(mean) is with ** respect to the mean equatorial triad of date. ** ** Called: ** iauNut80 nutation, IAU 1980 ** iauObl80 mean obliquity, IAU 1980 ** iauNumat form nutation matrix ** */ double iauObl06(double date1, double date2) /* ** - - - - - - - - - ** i a u O b l 0 6 ** - - - - - - - - - ** ** Mean obliquity of the ecliptic, IAU 2006 precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double obliquity of the ecliptic (radians, Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result is the angle between the ecliptic and mean equator of ** date date1+date2. ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** */ double iauObl80(double date1, double date2) /* ** - - - - - - - - - ** i a u O b l 8 0 ** - - - - - - - - - ** ** Mean obliquity of the ecliptic, IAU 1980 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double obliquity of the ecliptic (radians, Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The result is the angle between the ecliptic and mean equator of ** date date1+date2. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Expression 3.222-1 (p114). ** */ void iauP06e(double date1, double date2, double *eps0, double *psia, double *oma, double *bpa, double *bqa, double *pia, double *bpia, double *epsa, double *chia, double *za, double *zetaa, double *thetaa, double *pa, double *gam, double *phi, double *psi) /* ** - - - - - - - - ** i a u P 0 6 e ** - - - - - - - - ** ** Precession angles, IAU 2006, equinox based. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical models. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (see Note 2): ** eps0 double epsilon_0 ** psia double psi_A ** oma double omega_A ** bpa double P_A ** bqa double Q_A ** pia double pi_A ** bpia double Pi_A ** epsa double obliquity epsilon_A ** chia double chi_A ** za double z_A ** zetaa double zeta_A ** thetaa double theta_A ** pa double p_A ** gam double F-W angle gamma_J2000 ** phi double F-W angle phi_J2000 ** psi double F-W angle psi_J2000 ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) This function returns the set of equinox based angles for the ** Capitaine et al. "P03" precession theory, adopted by the IAU in ** 2006. The angles are set out in Table 1 of Hilton et al. (2006): ** ** eps0 epsilon_0 obliquity at J2000.0 ** psia psi_A luni-solar precession ** oma omega_A inclination of equator wrt J2000.0 ecliptic ** bpa P_A ecliptic pole x, J2000.0 ecliptic triad ** bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad ** pia pi_A angle between moving and J2000.0 ecliptics ** bpia Pi_A longitude of ascending node of the ecliptic ** epsa epsilon_A obliquity of the ecliptic ** chia chi_A planetary precession ** za z_A equatorial precession: -3rd 323 Euler angle ** zetaa zeta_A equatorial precession: -1st 323 Euler angle ** thetaa theta_A equatorial precession: 2nd 323 Euler angle ** pa p_A general precession ** gam gamma_J2000 J2000.0 RA difference of ecliptic poles ** phi phi_J2000 J2000.0 codeclination of ecliptic pole ** psi psi_J2000 longitude difference of equator poles, J2000.0 ** ** The returned values are all radians. ** ** 3) Hilton et al. (2006) Table 1 also contains angles that depend on ** models distinct from the P03 precession theory itself, namely the ** IAU 2000A frame bias and nutation. The quoted polynomials are ** used in other SOFA functions: ** ** . iauXy06 contains the polynomial parts of the X and Y series. ** ** . iauS06 contains the polynomial part of the s+XY/2 series. ** ** . iauPfw06 implements the series for the Fukushima-Williams ** angles that are with respect to the GCRS pole (i.e. the variants ** that include frame bias). ** ** 4) The IAU resolution stipulated that the choice of parameterization ** was left to the user, and so an IAU compliant precession ** implementation can be constructed using various combinations of ** the angles returned by the present function. ** ** 5) The parameterization used by SOFA is the version of the Fukushima- ** Williams angles that refers directly to the GCRS pole. These ** angles may be calculated by calling the function iauPfw06. SOFA ** also supports the direct computation of the CIP GCRS X,Y by ** series, available by calling iauXy06. ** ** 6) The agreement between the different parameterizations is at the ** 1 microarcsecond level in the present era. ** ** 7) When constructing a precession formulation that refers to the GCRS ** pole rather than the dynamical pole, it may (depending on the ** choice of angles) be necessary to introduce the frame bias ** explicitly. ** ** 8) It is permissible to re-use the same variable in the returned ** arguments. The quantities are stored in the stated order. ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** ** Called: ** iauObl06 mean obliquity, IAU 2006 ** */ void iauP2pv(double p[3], double pv[2][3]) /* ** - - - - - - - - ** i a u P 2 p v ** - - - - - - - - ** ** Extend a p-vector to a pv-vector by appending a zero velocity. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector ** ** Returned: ** pv double[2][3] pv-vector ** ** Called: ** iauCp copy p-vector ** iauZp zero p-vector ** */ void iauP2s(double p[3], double *theta, double *phi, double *r) /* ** - - - - - - - ** i a u P 2 s ** - - - - - - - ** ** P-vector to spherical polar coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector ** ** Returned: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** r double radial distance ** ** Notes: ** ** 1) If P is null, zero theta, phi and r are returned. ** ** 2) At either pole, zero theta is returned. ** ** Called: ** iauC2s p-vector to spherical ** iauPm modulus of p-vector ** */ double iauPap(double a[3], double b[3]) /* ** - - - - - - - ** i a u P a p ** - - - - - - - ** ** Position-angle from two p-vectors. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] direction of reference point ** b double[3] direction of point whose PA is required ** ** Returned (function value): ** double position angle of b with respect to a (radians) ** ** Notes: ** ** 1) The result is the position angle, in radians, of direction b with ** respect to direction a. It is in the range -pi to +pi. The ** sense is such that if b is a small distance "north" of a the ** position angle is approximately zero, and if b is a small ** distance "east" of a the position angle is approximately +pi/2. ** ** 2) The vectors a and b need not be of unit length. ** ** 3) Zero is returned if the two directions are the same or if either ** vector is null. ** ** 4) If vector a is at a pole, the result is ill-defined. ** ** Called: ** iauPn decompose p-vector into modulus and direction ** iauPm modulus of p-vector ** iauPxp vector product of two p-vectors ** iauPmp p-vector minus p-vector ** iauPdp scalar product of two p-vectors ** */ double iauPas(double al, double ap, double bl, double bp) /* ** - - - - - - - ** i a u P a s ** - - - - - - - ** ** Position-angle from spherical coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** al double longitude of point A (e.g. RA) in radians ** ap double latitude of point A (e.g. Dec) in radians ** bl double longitude of point B ** bp double latitude of point B ** ** Returned (function value): ** double position angle of B with respect to A ** ** Notes: ** ** 1) The result is the bearing (position angle), in radians, of point ** B with respect to point A. It is in the range -pi to +pi. The ** sense is such that if B is a small distance "east" of point A, ** the bearing is approximately +pi/2. ** ** 2) Zero is returned if the two points are coincident. ** */ void iauPb06(double date1, double date2, double *bzeta, double *bz, double *btheta) /* ** - - - - - - - - ** i a u P b 0 6 ** - - - - - - - - ** ** This function forms three Euler angles which implement general ** precession from epoch J2000.0, using the IAU 2006 model. Frame ** bias (the offset between ICRS and mean J2000.0) is included. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** bzeta double 1st rotation: radians cw around z ** bz double 3rd rotation: radians cw around z ** btheta double 2nd rotation: radians ccw around y ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The traditional accumulated precession angles zeta_A, z_A, ** theta_A cannot be obtained in the usual way, namely through ** polynomial expressions, because of the frame bias. The latter ** means that two of the angles undergo rapid changes near this ** date. They are instead the results of decomposing the ** precession-bias matrix obtained by using the Fukushima-Williams ** method, which does not suffer from the problem. The ** decomposition returns values which can be used in the ** conventional formulation and which include frame bias. ** ** 3) The three angles are returned in the conventional order, which ** is not the same as the order of the corresponding Euler ** rotations. The precession-bias matrix is ** R_3(-z) x R_2(+theta) x R_3(-zeta). ** ** 4) Should zeta_A, z_A, theta_A angles be required that do not ** contain frame bias, they are available by calling the SOFA ** function iauP06e. ** ** Called: ** iauPmat06 PB matrix, IAU 2006 ** iauRz rotate around Z-axis ** */ double iauPdp(double a[3], double b[3]) /* ** - - - - - - - ** i a u P d p ** - - - - - - - ** ** p-vector inner (=scalar=dot) product. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector ** b double[3] second p-vector ** ** Returned (function value): ** double a . b ** */ void iauPfw06(double date1, double date2, double *gamb, double *phib, double *psib, double *epsa) /* ** - - - - - - - - - ** i a u P f w 0 6 ** - - - - - - - - - ** ** Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** gamb double F-W angle gamma_bar (radians) ** phib double F-W angle phi_bar (radians) ** psib double F-W angle psi_bar (radians) ** epsa double F-W angle epsilon_A (radians) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) Naming the following points: ** ** e = J2000.0 ecliptic pole, ** p = GCRS pole, ** E = mean ecliptic pole of date, ** and P = mean pole of date, ** ** the four Fukushima-Williams angles are as follows: ** ** gamb = gamma_bar = epE ** phib = phi_bar = pE ** psib = psi_bar = pEP ** epsa = epsilon_A = EP ** ** 3) The matrix representing the combined effects of frame bias and ** precession is: ** ** PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb) ** ** 4) The matrix representing the combined effects of frame bias, ** precession and nutation is simply: ** ** NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb) ** ** where dP and dE are the nutation components with respect to the ** ecliptic of date. ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** ** Called: ** iauObl06 mean obliquity, IAU 2006 ** */ int iauPlan94(double date1, double date2, int np, double pv[2][3]) /* ** - - - - - - - - - - ** i a u P l a n 9 4 ** - - - - - - - - - - ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Approximate heliocentric position and velocity of a nominated major ** planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or ** Neptune (but not the Earth itself). ** ** Given: ** date1 double TDB date part A (Note 1) ** date2 double TDB date part B (Note 1) ** np int planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars, ** 5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune) ** ** Returned (argument): ** pv double[2][3] planet p,v (heliocentric, J2000.0, AU,AU/d) ** ** Returned (function value): ** int status: -1 = illegal NP (outside 1-8) ** 0 = OK ** +1 = warning: year outside 1000-3000 ** +2 = warning: failed to converge ** ** Notes: ** ** 1) The date date1+date2 is in the TDB time scale (in practice TT can ** be used) and is a Julian Date, apportioned in any convenient way ** between the two arguments. For example, JD(TDB)=2450123.7 could ** be expressed in any of these ways, among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. The limited ** accuracy of the present algorithm is such that any of the methods ** is satisfactory. ** ** 2) If an np value outside the range 1-8 is supplied, an error status ** (function value -1) is returned and the pv vector set to zeroes. ** ** 3) For np=3 the result is for the Earth-Moon Barycenter. To obtain ** the heliocentric position and velocity of the Earth, use instead ** the SOFA function iauEpv00. ** ** 4) On successful return, the array pv contains the following: ** ** pv[0][0] x } ** pv[0][1] y } heliocentric position, AU ** pv[0][2] z } ** ** pv[1][0] xdot } ** pv[1][1] ydot } heliocentric velocity, AU/d ** pv[1][2] zdot } ** ** The reference frame is equatorial and is with respect to the ** mean equator and equinox of epoch J2000.0. ** ** 5) The algorithm is due to J.L. Simon, P. Bretagnon, J. Chapront, ** M. Chapront-Touze, G. Francou and J. Laskar (Bureau des ** Longitudes, Paris, France). From comparisons with JPL ** ephemeris DE102, they quote the following maximum errors ** over the interval 1800-2050: ** ** L (arcsec) B (arcsec) R (km) ** ** Mercury 4 1 300 ** Venus 5 1 800 ** EMB 6 1 1000 ** Mars 17 1 7700 ** Jupiter 71 5 76000 ** Saturn 81 13 267000 ** Uranus 86 7 712000 ** Neptune 11 1 253000 ** ** Over the interval 1000-3000, they report that the accuracy is no ** worse than 1.5 times that over 1800-2050. Outside 1000-3000 the ** accuracy declines. ** ** Comparisons of the present function with the JPL DE200 ephemeris ** give the following RMS errors over the interval 1960-2025: ** ** position (km) velocity (m/s) ** ** Mercury 334 0.437 ** Venus 1060 0.855 ** EMB 2010 0.815 ** Mars 7690 1.98 ** Jupiter 71700 7.70 ** Saturn 199000 19.4 ** Uranus 564000 16.4 ** Neptune 158000 14.4 ** ** Comparisons against DE200 over the interval 1800-2100 gave the ** following maximum absolute differences. (The results using ** DE406 were essentially the same.) ** ** L (arcsec) B (arcsec) R (km) Rdot (m/s) ** ** Mercury 7 1 500 0.7 ** Venus 7 1 1100 0.9 ** EMB 9 1 1300 1.0 ** Mars 26 1 9000 2.5 ** Jupiter 78 6 82000 8.2 ** Saturn 87 14 263000 24.6 ** Uranus 86 7 661000 27.4 ** Neptune 11 2 248000 21.4 ** ** 6) The present SOFA re-implementation of the original Simon et al. ** Fortran code differs from the original in the following respects: ** ** * C instead of Fortran. ** ** * The date is supplied in two parts. ** ** * The result is returned only in equatorial Cartesian form; ** the ecliptic longitude, latitude and radius vector are not ** returned. ** ** * The result is in the J2000.0 equatorial frame, not ecliptic. ** ** * More is done in-line: there are fewer calls to subroutines. ** ** * Different error/warning status values are used. ** ** * A different Kepler's-equation-solver is used (avoiding ** use of double precision complex). ** ** * Polynomials in t are nested to minimize rounding errors. ** ** * Explicit double constants are used to avoid mixed-mode ** expressions. ** ** None of the above changes affects the result significantly. ** ** 7) The returned status indicates the most serious condition ** encountered during execution of the function. Illegal np is ** considered the most serious, overriding failure to converge, ** which in turn takes precedence over the remote date warning. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: Simon, J.L, Bretagnon, P., Chapront, J., ** Chapront-Touze, M., Francou, G., and Laskar, J., ** Astron. Astrophys. 282, 663 (1994). ** */ double iauPm(double p[3]) /* ** - - - - - - ** i a u P m ** - - - - - - ** ** Modulus of p-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector ** ** Returned (function value): ** double modulus ** */ void iauPmat00(double date1, double date2, double rbp[3][3]) /* ** - - - - - - - - - - ** i a u P m a t 0 0 ** - - - - - - - - - - ** ** Precession matrix (including frame bias) from GCRS to a specified ** date, IAU 2000 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rbp double[3][3] bias-precession matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rbp * V(GCRS), where ** the p-vector V(GCRS) is with respect to the Geocentric Celestial ** Reference System (IAU, 2000) and the p-vector V(date) is with ** respect to the mean equatorial triad of the given date. ** ** Called: ** iauBp00 frame bias and precession matrices, IAU 2000 ** ** Reference: ** ** IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. ** 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. ** (2000) ** */ void iauPmat06(double date1, double date2, double rbp[3][3]) /* ** - - - - - - - - - - ** i a u P m a t 0 6 ** - - - - - - - - - - ** ** Precession matrix (including frame bias) from GCRS to a specified ** date, IAU 2006 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rbp double[3][3] bias-precession matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rbp * V(GCRS), where ** the p-vector V(GCRS) is with respect to the Geocentric Celestial ** Reference System (IAU, 2000) and the p-vector V(date) is with ** respect to the mean equatorial triad of the given date. ** ** Called: ** iauPfw06 bias-precession F-W angles, IAU 2006 ** iauFw2m F-W angles to r-matrix ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** */ void iauPmat76(double date1, double date2, double rmatp[3][3]) /* ** - - - - - - - - - - ** i a u P m a t 7 6 ** - - - - - - - - - - ** ** Precession matrix from J2000.0 to a specified date, IAU 1976 model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double ending date, TT (Note 1) ** ** Returned: ** rmatp double[3][3] precession matrix, J2000.0 -> date1+date2 ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = RMATP * V(J2000), ** where the p-vector V(J2000) is with respect to the mean ** equatorial triad of epoch J2000.0 and the p-vector V(date) ** is with respect to the mean equatorial triad of the given ** date. ** ** 3) Though the matrix method itself is rigorous, the precession ** angles are expressed through canonical polynomials which are ** valid only for a limited time span. In addition, the IAU 1976 ** precession rate is known to be imperfect. The absolute accuracy ** of the present formulation is better than 0.1 arcsec from ** 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD, ** and remains below 3 arcsec for the whole of the period ** 500BC to 3000AD. The errors exceed 10 arcsec outside the ** range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to ** 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD. ** ** Called: ** iauPrec76 accumulated precession angles, IAU 1976 ** iauIr initialize r-matrix to identity ** iauRz rotate around Z-axis ** iauRy rotate around Y-axis ** iauCr copy r-matrix ** ** References: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282. ** equations (6) & (7), p283. ** ** Kaplan,G.H., 1981. USNO circular no. 163, pA2. ** */ void iauPmp(double a[3], double b[3], double amb[3]) /* ** - - - - - - - ** i a u P m p ** - - - - - - - ** ** P-vector subtraction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector ** b double[3] second p-vector ** ** Returned: ** amb double[3] a - b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** */ void iauPmpx(double rc, double dc, double pr, double pd, double px, double rv, double pmt, double pob[3], double pco[3]) /* ** - - - - - - - - ** i a u P m p x ** - - - - - - - - ** ** Proper motion and parallax. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rc,dc double ICRS RA,Dec at catalog epoch (radians) ** pr double RA proper motion (radians/year; Note 1) ** pd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, +ve if receding) ** pmt double proper motion time interval (SSB, Julian years) ** pob double[3] SSB to observer vector (au) ** ** Returned: ** pco double[3] coordinate direction (BCRS unit vector) ** ** Notes: ** ** 1) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 2) The proper motion time interval is for when the starlight ** reaches the solar system barycenter. ** ** 3) To avoid the need for iteration, the Roemer effect (i.e. the ** small annual modulation of the proper motion coming from the ** changing light time) is applied approximately, using the ** direction of the star at the catalog epoch. ** ** References: ** ** 1984 Astronomical Almanac, pp B39-B41. ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013), Section 7.2. ** ** Called: ** iauPdp scalar product of two p-vectors ** iauPn decompose p-vector into modulus and direction ** */ int iauPmsafe(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2) /* ** - - - - - - - - - - ** i a u P m s a f e ** - - - - - - - - - - ** ** Star proper motion: update star catalog data for space motion, with ** special handling to handle the zero parallax case. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ra1 double right ascension (radians), before ** dec1 double declination (radians), before ** pmr1 double RA proper motion (radians/year), before ** pmd1 double Dec proper motion (radians/year), before ** px1 double parallax (arcseconds), before ** rv1 double radial velocity (km/s, +ve = receding), before ** ep1a double "before" epoch, part A (Note 1) ** ep1b double "before" epoch, part B (Note 1) ** ep2a double "after" epoch, part A (Note 1) ** ep2b double "after" epoch, part B (Note 1) ** ** Returned: ** ra2 double right ascension (radians), after ** dec2 double declination (radians), after ** pmr2 double RA proper motion (radians/year), after ** pmd2 double Dec proper motion (radians/year), after ** px2 double parallax (arcseconds), after ** rv2 double radial velocity (km/s, +ve = receding), after ** ** Returned (function value): ** int status: ** -1 = system error (should not occur) ** 0 = no warnings or errors ** 1 = distance overridden (Note 6) ** 2 = excessive velocity (Note 7) ** 4 = solution didn't converge (Note 8) ** else = binary logical OR of the above warnings ** ** Notes: ** ** 1) The starting and ending TDB epochs ep1a+ep1b and ep2a+ep2b are ** Julian Dates, apportioned in any convenient way between the two ** parts (A and B). For example, JD(TDB)=2450123.7 could be ** expressed in any of these ways, among others: ** ** epNa epNb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. ** ** 2) In accordance with normal star-catalog conventions, the object's ** right ascension and declination are freed from the effects of ** secular aberration. The frame, which is aligned to the catalog ** equator and equinox, is Lorentzian and centered on the SSB. ** ** The proper motions are the rate of change of the right ascension ** and declination at the catalog epoch and are in radians per TDB ** Julian year. ** ** The parallax and radial velocity are in the same frame. ** ** 3) Care is needed with units. The star coordinates are in radians ** and the proper motions in radians per Julian year, but the ** parallax is in arcseconds. ** ** 4) The RA proper motion is in terms of coordinate angle, not true ** angle. If the catalog uses arcseconds for both RA and Dec proper ** motions, the RA proper motion will need to be divided by cos(Dec) ** before use. ** ** 5) Straight-line motion at constant speed, in the inertial frame, is ** assumed. ** ** 6) An extremely small (or zero or negative) parallax is overridden ** to ensure that the object is at a finite but very large distance, ** but not so large that the proper motion is equivalent to a large ** but safe speed (about 0.1c using the chosen constant). A warning ** status of 1 is added to the status if this action has been taken. ** ** 7) If the space velocity is a significant fraction of c (see the ** constant VMAX in the function iauStarpv), it is arbitrarily set ** to zero. When this action occurs, 2 is added to the status. ** ** 8) The relativistic adjustment carried out in the iauStarpv function ** involves an iterative calculation. If the process fails to ** converge within a set number of iterations, 4 is added to the ** status. ** ** Called: ** iauSeps angle between two points ** iauStarpm update star catalog data for space motion ** */ void iauPn(double p[3], double *r, double u[3]) /* ** - - - - - - ** i a u P n ** - - - - - - ** ** Convert a p-vector into modulus and unit vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** p double[3] p-vector ** ** Returned: ** r double modulus ** u double[3] unit vector ** ** Notes: ** ** 1) If p is null, the result is null. Otherwise the result is a unit ** vector. ** ** 2) It is permissible to re-use the same array for any of the ** arguments. ** ** Called: ** iauPm modulus of p-vector ** iauZp zero p-vector ** iauSxp multiply p-vector by scalar ** */ void iauPn00(double date1, double date2, double dpsi, double deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - ** i a u P n 0 0 ** - - - - - - - - ** ** Precession-nutation, IAU 2000 model: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based ** use indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** dpsi,deps double nutation (Note 2) ** ** Returned: ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Note 8) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The caller is responsible for providing the nutation components; ** they are in longitude and obliquity, in radians and are with ** respect to the equinox and ecliptic of date. For high-accuracy ** applications, free core nutation should be included as well as ** any other relevant corrections to the position of the CIP. ** ** 3) The returned mean obliquity is consistent with the IAU 2000 ** precession-nutation models. ** ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean ** equator and equinox by applying frame bias. ** ** 5) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean equator and equinox of ** date to true equator and equinox of date by applying the nutation ** (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true equator and ** equinox of date. It is the product rn x rbp, applying frame ** bias, precession and nutation in that order. ** ** 9) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the order given. ** ** Called: ** iauPr00 IAU 2000 precession adjustments ** iauObl80 mean obliquity, IAU 1980 ** iauBp00 frame bias and precession matrices, IAU 2000 ** iauCr copy r-matrix ** iauNumat form nutation matrix ** iauRxr product of two r-matrices ** ** Reference: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** */ void iauPn00a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - - ** i a u P n 0 0 a ** - - - - - - - - - ** ** Precession-nutation, IAU 2000A model: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based ** use indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation (Note 2) ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components (luni-solar + planetary, IAU 2000A) in ** longitude and obliquity are in radians and with respect to the ** equinox and ecliptic of date. Free core nutation is omitted; ** for the utmost accuracy, use the iauPn00 function, where the ** nutation components are caller-specified. For faster but ** slightly less accurate results, use the iauPn00b function. ** ** 3) The mean obliquity is consistent with the IAU 2000 precession. ** ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean ** equator and equinox by applying frame bias. ** ** 5) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean equator and equinox ** of date to true equator and equinox of date by applying the ** nutation (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true equator and ** equinox of date. It is the product rn x rbp, applying frame ** bias, precession and nutation in that order. ** ** 9) The X,Y,Z coordinates of the IAU 2000A Celestial Intermediate ** Pole are elements (3,1-3) of the GCRS-to-true matrix, ** i.e. rbpn[2][0-2]. ** ** 10) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the order given. ** ** Called: ** iauNut00a nutation, IAU 2000A ** iauPn00 bias/precession/nutation results, IAU 2000 ** ** Reference: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** */ void iauPn00b(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - - ** i a u P n 0 0 b ** - - - - - - - - - ** ** Precession-nutation, IAU 2000B model: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based ** use indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation (Note 2) ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components (luni-solar + planetary, IAU 2000B) in ** longitude and obliquity are in radians and with respect to the ** equinox and ecliptic of date. For more accurate results, but ** at the cost of increased computation, use the iauPn00a function. ** For the utmost accuracy, use the iauPn00 function, where the ** nutation components are caller-specified. ** ** 3) The mean obliquity is consistent with the IAU 2000 precession. ** ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean ** equator and equinox by applying frame bias. ** ** 5) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean equator and equinox ** of date to true equator and equinox of date by applying the ** nutation (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true equator and ** equinox of date. It is the product rn x rbp, applying frame ** bias, precession and nutation in that order. ** ** 9) The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate ** Pole are elements (3,1-3) of the GCRS-to-true matrix, ** i.e. rbpn[2][0-2]. ** ** 10) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the stated order. ** ** Called: ** iauNut00b nutation, IAU 2000B ** iauPn00 bias/precession/nutation results, IAU 2000 ** ** Reference: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003). ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** */ void iauPn06(double date1, double date2, double dpsi, double deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - ** i a u P n 0 6 ** - - - - - - - - ** ** Precession-nutation, IAU 2006 model: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based use ** indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** dpsi,deps double nutation (Note 2) ** ** Returned: ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Note 8) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The caller is responsible for providing the nutation components; ** they are in longitude and obliquity, in radians and are with ** respect to the equinox and ecliptic of date. For high-accuracy ** applications, free core nutation should be included as well as ** any other relevant corrections to the position of the CIP. ** ** 3) The returned mean obliquity is consistent with the IAU 2006 ** precession. ** ** 4) The matrix rb transforms vectors from GCRS to J2000.0 mean ** equator and equinox by applying frame bias. ** ** 5) The matrix rp transforms vectors from J2000.0 mean equator and ** equinox to mean equator and equinox of date by applying ** precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean equator and ** equinox of date by applying frame bias then precession. It is ** the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean equator and equinox ** of date to true equator and equinox of date by applying the ** nutation (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true equator and ** equinox of date. It is the product rn x rbp, applying frame ** bias, precession and nutation in that order. ** ** 9) The X,Y,Z coordinates of the Celestial Intermediate Pole are ** elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2]. ** ** 10) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the stated order. ** ** Called: ** iauPfw06 bias-precession F-W angles, IAU 2006 ** iauFw2m F-W angles to r-matrix ** iauCr copy r-matrix ** iauTr transpose r-matrix ** iauRxr product of two r-matrices ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** */ void iauPn06a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) /* ** - - - - - - - - - ** i a u P n 0 6 a ** - - - - - - - - - ** ** Precession-nutation, IAU 2006/2000A models: a multi-purpose function, ** supporting classical (equinox-based) use directly and CIO-based use ** indirectly. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsi,deps double nutation (Note 2) ** epsa double mean obliquity (Note 3) ** rb double[3][3] frame bias matrix (Note 4) ** rp double[3][3] precession matrix (Note 5) ** rbp double[3][3] bias-precession matrix (Note 6) ** rn double[3][3] nutation matrix (Note 7) ** rbpn double[3][3] GCRS-to-true matrix (Notes 8,9) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The nutation components (luni-solar + planetary, IAU 2000A) in ** longitude and obliquity are in radians and with respect to the ** equinox and ecliptic of date. Free core nutation is omitted; ** for the utmost accuracy, use the iauPn06 function, where the ** nutation components are caller-specified. ** ** 3) The mean obliquity is consistent with the IAU 2006 precession. ** ** 4) The matrix rb transforms vectors from GCRS to mean J2000.0 by ** applying frame bias. ** ** 5) The matrix rp transforms vectors from mean J2000.0 to mean of ** date by applying precession. ** ** 6) The matrix rbp transforms vectors from GCRS to mean of date by ** applying frame bias then precession. It is the product rp x rb. ** ** 7) The matrix rn transforms vectors from mean of date to true of ** date by applying the nutation (luni-solar + planetary). ** ** 8) The matrix rbpn transforms vectors from GCRS to true of date ** (CIP/equinox). It is the product rn x rbp, applying frame bias, ** precession and nutation in that order. ** ** 9) The X,Y,Z coordinates of the IAU 2006/2000A Celestial ** Intermediate Pole are elements (3,1-3) of the GCRS-to-true ** matrix, i.e. rbpn[2][0-2]. ** ** 10) It is permissible to re-use the same array in the returned ** arguments. The arrays are filled in the stated order. ** ** Called: ** iauNut06a nutation, IAU 2006/2000A ** iauPn06 bias/precession/nutation results, IAU 2006 ** ** Reference: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** */ void iauPnm00a(double date1, double date2, double rbpn[3][3]) /* ** - - - - - - - - - - ** i a u P n m 0 0 a ** - - - - - - - - - - ** ** Form the matrix of precession-nutation for a given date (including ** frame bias), equinox-based, IAU 2000A model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rbpn double[3][3] classical NPB matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where ** the p-vector V(date) is with respect to the true equatorial triad ** of date date1+date2 and the p-vector V(GCRS) is with respect to ** the Geocentric Celestial Reference System (IAU, 2000). ** ** 3) A faster, but slightly less accurate result (about 1 mas), can be ** obtained by using instead the iauPnm00b function. ** ** Called: ** iauPn00a bias/precession/nutation, IAU 2000A ** ** Reference: ** ** IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. ** 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. ** (2000) ** */ void iauPnm00b(double date1, double date2, double rbpn[3][3]) /* ** - - - - - - - - - - ** i a u P n m 0 0 b ** - - - - - - - - - - ** ** Form the matrix of precession-nutation for a given date (including ** frame bias), equinox-based, IAU 2000B model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rbpn double[3][3] bias-precession-nutation matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where ** the p-vector V(date) is with respect to the true equatorial triad ** of date date1+date2 and the p-vector V(GCRS) is with respect to ** the Geocentric Celestial Reference System (IAU, 2000). ** ** 3) The present function is faster, but slightly less accurate (about ** 1 mas), than the iauPnm00a function. ** ** Called: ** iauPn00b bias/precession/nutation, IAU 2000B ** ** Reference: ** ** IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. ** 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. ** (2000) ** */ void iauPnm06a(double date1, double date2, double rnpb[3][3]) /* ** - - - - - - - - - - ** i a u P n m 0 6 a ** - - - - - - - - - - ** ** Form the matrix of precession-nutation for a given date (including ** frame bias), IAU 2006 precession and IAU 2000A nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rnpb double[3][3] bias-precession-nutation matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rnpb * V(GCRS), where ** the p-vector V(date) is with respect to the true equatorial triad ** of date date1+date2 and the p-vector V(GCRS) is with respect to ** the Geocentric Celestial Reference System (IAU, 2000). ** ** Called: ** iauPfw06 bias-precession F-W angles, IAU 2006 ** iauNut06a nutation, IAU 2006/2000A ** iauFw2m F-W angles to r-matrix ** ** Reference: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855. ** */ void iauPnm80(double date1, double date2, double rmatpn[3][3]) /* ** - - - - - - - - - ** i a u P n m 8 0 ** - - - - - - - - - ** ** Form the matrix of precession/nutation for a given date, IAU 1976 ** precession model, IAU 1980 nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TDB date (Note 1) ** ** Returned: ** rmatpn double[3][3] combined precession/nutation matrix ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix operates in the sense V(date) = rmatpn * V(J2000), ** where the p-vector V(date) is with respect to the true equatorial ** triad of date date1+date2 and the p-vector V(J2000) is with ** respect to the mean equatorial triad of epoch J2000.0. ** ** Called: ** iauPmat76 precession matrix, IAU 1976 ** iauNutm80 nutation matrix, IAU 1980 ** iauRxr product of two r-matrices ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992), ** Section 3.3 (p145). ** */ void iauPom00(double xp, double yp, double sp, double rpom[3][3]) /* ** - - - - - - - - - - ** i a u P o m 0 0 ** - - - - - - - - - - ** ** Form the matrix of polar motion for a given date, IAU 2000. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** xp,yp double coordinates of the pole (radians, Note 1) ** sp double the TIO locator s' (radians, Note 2) ** ** Returned: ** rpom double[3][3] polar-motion matrix (Note 3) ** ** Notes: ** ** 1) The arguments xp and yp are the coordinates (in radians) of the ** Celestial Intermediate Pole with respect to the International ** Terrestrial Reference System (see IERS Conventions 2003), ** measured along the meridians to 0 and 90 deg west respectively. ** ** 2) The argument sp is the TIO locator s', in radians, which ** positions the Terrestrial Intermediate Origin on the equator. It ** is obtained from polar motion observations by numerical ** integration, and so is in essence unpredictable. However, it is ** dominated by a secular drift of about 47 microarcseconds per ** century, and so can be taken into account by using s' = -47*t, ** where t is centuries since J2000.0. The function iauSp00 ** implements this approximation. ** ** 3) The matrix operates in the sense V(TRS) = rpom * V(CIP), meaning ** that it is the final rotation when computing the pointing ** direction to a celestial source. ** ** Called: ** iauIr initialize r-matrix to identity ** iauRz rotate around Z-axis ** iauRy rotate around Y-axis ** iauRx rotate around X-axis ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauPpp(double a[3], double b[3], double apb[3]) /* ** - - - - - - - ** i a u P p p ** - - - - - - - ** ** P-vector addition. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector ** b double[3] second p-vector ** ** Returned: ** apb double[3] a + b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** */ void iauPpsp(double a[3], double s, double b[3], double apsb[3]) /* ** - - - - - - - - ** i a u P p s p ** - - - - - - - - ** ** P-vector plus scaled p-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector ** s double scalar (multiplier for b) ** b double[3] second p-vector ** ** Returned: ** apsb double[3] a + s*b ** ** Note: ** It is permissible for any of a, b and apsb to be the same array. ** ** Called: ** iauSxp multiply p-vector by scalar ** iauPpp p-vector plus p-vector ** */ void iauPr00(double date1, double date2, double *dpsipr, double *depspr) /* ** - - - - - - - - ** i a u P r 0 0 ** - - - - - - - - ** ** Precession-rate part of the IAU 2000 precession-nutation models ** (part of MHB2000). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** dpsipr,depspr double precession corrections (Notes 2,3) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The precession adjustments are expressed as "nutation ** components", corrections in longitude and obliquity with respect ** to the J2000.0 equinox and ecliptic. ** ** 3) Although the precession adjustments are stated to be with respect ** to Lieske et al. (1977), the MHB2000 model does not specify which ** set of Euler angles are to be used and how the adjustments are to ** be applied. The most literal and straightforward procedure is to ** adopt the 4-rotation epsilon_0, psi_A, omega_A, xi_A option, and ** to add dpsipr to psi_A and depspr to both omega_A and eps_A. ** ** 4) This is an implementation of one aspect of the IAU 2000A nutation ** model, formally adopted by the IAU General Assembly in 2000, ** namely MHB2000 (Mathews et al. 2002). ** ** References: ** ** Lieske, J.H., Lederle, T., Fricke, W. & Morando, B., "Expressions ** for the precession quantities based upon the IAU (1976) System of ** Astronomical Constants", Astron.Astrophys., 58, 1-16 (1977) ** ** Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation ** and precession New nutation series for nonrigid Earth and ** insights into the Earth's interior", J.Geophys.Res., 107, B4, ** 2002. The MHB2000 code itself was obtained on 9th September 2002 ** from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A. ** ** Wallace, P.T., "Software for Implementing the IAU 2000 ** Resolutions", in IERS Workshop 5.1 (2002). ** */ void iauPrec76(double date01, double date02, double date11, double date12, double *zeta, double *z, double *theta) /* ** - - - - - - - - - - ** i a u P r e c 7 6 ** - - - - - - - - - - ** ** IAU 1976 precession model. ** ** This function forms the three Euler angles which implement general ** precession between two dates, using the IAU 1976 model (as for the ** FK5 catalog). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date01,date02 double TDB starting date (Note 1) ** date11,date12 double TDB ending date (Note 1) ** ** Returned: ** zeta double 1st rotation: radians cw around z ** z double 3rd rotation: radians cw around z ** theta double 2nd rotation: radians ccw around y ** ** Notes: ** ** 1) The dates date01+date02 and date11+date12 are Julian Dates, ** apportioned in any convenient way between the arguments daten1 ** and daten2. For example, JD(TDB)=2450123.7 could be expressed in ** any of these ways, among others: ** ** daten1 daten2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** The two dates may be expressed using different methods, but at ** the risk of losing some resolution. ** ** 2) The accumulated precession angles zeta, z, theta are expressed ** through canonical polynomials which are valid only for a limited ** time span. In addition, the IAU 1976 precession rate is known to ** be imperfect. The absolute accuracy of the present formulation ** is better than 0.1 arcsec from 1960AD to 2040AD, better than ** 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for ** the whole of the period 500BC to 3000AD. The errors exceed ** 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec ** outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to ** 8200AD. ** ** 3) The three angles are returned in the conventional order, which ** is not the same as the order of the corresponding Euler ** rotations. The precession matrix is ** R_3(-z) x R_2(+theta) x R_3(-zeta). ** ** Reference: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations ** (6) & (7), p283. ** */ void iauPv2p(double pv[2][3], double p[3]) /* ** - - - - - - - - ** i a u P v 2 p ** - - - - - - - - ** ** Discard velocity component of a pv-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** pv double[2][3] pv-vector ** ** Returned: ** p double[3] p-vector ** ** Called: ** iauCp copy p-vector ** */ void iauPv2s(double pv[2][3], double *theta, double *phi, double *r, double *td, double *pd, double *rd) /* ** - - - - - - - - ** i a u P v 2 s ** - - - - - - - - ** ** Convert position/velocity from Cartesian to spherical coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** pv double[2][3] pv-vector ** ** Returned: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** r double radial distance ** td double rate of change of theta ** pd double rate of change of phi ** rd double rate of change of r ** ** Notes: ** ** 1) If the position part of pv is null, theta, phi, td and pd ** are indeterminate. This is handled by extrapolating the ** position through unit time by using the velocity part of ** pv. This moves the origin without changing the direction ** of the velocity component. If the position and velocity ** components of pv are both null, zeroes are returned for all ** six results. ** ** 2) If the position is a pole, theta, td and pd are indeterminate. ** In such cases zeroes are returned for all three. ** */ void iauPvdpv(double a[2][3], double b[2][3], double adb[2]) /* ** - - - - - - - - - ** i a u P v d p v ** - - - - - - - - - ** ** Inner (=scalar=dot) product of two pv-vectors. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[2][3] first pv-vector ** b double[2][3] second pv-vector ** ** Returned: ** adb double[2] a . b (see note) ** ** Note: ** ** If the position and velocity components of the two pv-vectors are ** ( ap, av ) and ( bp, bv ), the result, a . b, is the pair of ** numbers ( ap . bp , ap . bv + av . bp ). The two numbers are the ** dot-product of the two p-vectors and its derivative. ** ** Called: ** iauPdp scalar product of two p-vectors ** */ void iauPvm(double pv[2][3], double *r, double *s) /* ** - - - - - - - ** i a u P v m ** - - - - - - - ** ** Modulus of pv-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** pv double[2][3] pv-vector ** ** Returned: ** r double modulus of position component ** s double modulus of velocity component ** ** Called: ** iauPm modulus of p-vector ** */ void iauPvmpv(double a[2][3], double b[2][3], double amb[2][3]) /* ** - - - - - - - - - ** i a u P v m p v ** - - - - - - - - - ** ** Subtract one pv-vector from another. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[2][3] first pv-vector ** b double[2][3] second pv-vector ** ** Returned: ** amb double[2][3] a - b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** ** Called: ** iauPmp p-vector minus p-vector ** */ void iauPvppv(double a[2][3], double b[2][3], double apb[2][3]) /* ** - - - - - - - - - ** i a u P v p p v ** - - - - - - - - - ** ** Add one pv-vector to another. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[2][3] first pv-vector ** b double[2][3] second pv-vector ** ** Returned: ** apb double[2][3] a + b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** ** Called: ** iauPpp p-vector plus p-vector ** */ int iauPvstar(double pv[2][3], double *ra, double *dec, double *pmr, double *pmd, double *px, double *rv) /* ** - - - - - - - - - - ** i a u P v s t a r ** - - - - - - - - - - ** ** Convert star position+velocity vector to catalog coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given (Note 1): ** pv double[2][3] pv-vector (AU, AU/day) ** ** Returned (Note 2): ** ra double right ascension (radians) ** dec double declination (radians) ** pmr double RA proper motion (radians/year) ** pmd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, positive = receding) ** ** Returned (function value): ** int status: ** 0 = OK ** -1 = superluminal speed (Note 5) ** -2 = null position vector ** ** Notes: ** ** 1) The specified pv-vector is the coordinate direction (and its rate ** of change) for the date at which the light leaving the star ** reached the solar-system barycenter. ** ** 2) The star data returned by this function are "observables" for an ** imaginary observer at the solar-system barycenter. Proper motion ** and radial velocity are, strictly, in terms of barycentric ** coordinate time, TCB. For most practical applications, it is ** permissible to neglect the distinction between TCB and ordinary ** "proper" time on Earth (TT/TAI). The result will, as a rule, be ** limited by the intrinsic accuracy of the proper-motion and ** radial-velocity data; moreover, the supplied pv-vector is likely ** to be merely an intermediate result (for example generated by the ** function iauStarpv), so that a change of time unit will cancel ** out overall. ** ** In accordance with normal star-catalog conventions, the object's ** right ascension and declination are freed from the effects of ** secular aberration. The frame, which is aligned to the catalog ** equator and equinox, is Lorentzian and centered on the SSB. ** ** Summarizing, the specified pv-vector is for most stars almost ** identical to the result of applying the standard geometrical ** "space motion" transformation to the catalog data. The ** differences, which are the subject of the Stumpff paper cited ** below, are: ** ** (i) In stars with significant radial velocity and proper motion, ** the constantly changing light-time distorts the apparent proper ** motion. Note that this is a classical, not a relativistic, ** effect. ** ** (ii) The transformation complies with special relativity. ** ** 3) Care is needed with units. The star coordinates are in radians ** and the proper motions in radians per Julian year, but the ** parallax is in arcseconds; the radial velocity is in km/s, but ** the pv-vector result is in AU and AU/day. ** ** 4) The proper motions are the rate of change of the right ascension ** and declination at the catalog epoch and are in radians per Julian ** year. The RA proper motion is in terms of coordinate angle, not ** true angle, and will thus be numerically larger at high ** declinations. ** ** 5) Straight-line motion at constant speed in the inertial frame is ** assumed. If the speed is greater than or equal to the speed of ** light, the function aborts with an error status. ** ** 6) The inverse transformation is performed by the function iauStarpv. ** ** Called: ** iauPn decompose p-vector into modulus and direction ** iauPdp scalar product of two p-vectors ** iauSxp multiply p-vector by scalar ** iauPmp p-vector minus p-vector ** iauPm modulus of p-vector ** iauPpp p-vector plus p-vector ** iauPv2s pv-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240. ** */ void iauPvtob(double elong, double phi, double hm, double xp, double yp, double sp, double theta, double pv[2][3]) /* ** - - - - - - - - - ** i a u P v t o b ** - - - - - - - - - ** ** Position and velocity of a terrestrial observing station. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** elong double longitude (radians, east +ve, Note 1) ** phi double latitude (geodetic, radians, Note 1) ** hm double height above ref. ellipsoid (geodetic, m) ** xp,yp double coordinates of the pole (radians, Note 2) ** sp double the TIO locator s' (radians, Note 2) ** theta double Earth rotation angle (radians, Note 3) ** ** Returned: ** pv double[2][3] position/velocity vector (m, m/s, CIRS) ** ** Notes: ** ** 1) The terrestrial coordinates are with respect to the WGS84 ** reference ellipsoid. ** ** 2) xp and yp are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions), measured along the ** meridians 0 and 90 deg west respectively. sp is the TIO locator ** s', in radians, which positions the Terrestrial Intermediate ** Origin on the equator. For many applications, xp, yp and ** (especially) sp can be set to zero. ** ** 3) If theta is Greenwich apparent sidereal time instead of Earth ** rotation angle, the result is with respect to the true equator ** and equinox of date, i.e. with the x-axis at the equinox rather ** than the celestial intermediate origin. ** ** 4) The velocity units are meters per UT1 second, not per SI second. ** This is unlikely to have any practical consequences in the modern ** era. ** ** 5) No validation is performed on the arguments. Error cases that ** could lead to arithmetic exceptions are trapped by the iauGd2gc ** function, and the result set to zeros. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013), Section 7.4.3.3. ** ** Called: ** iauGd2gc geodetic to geocentric transformation ** iauPom00 polar motion matrix ** iauTrxp product of transpose of r-matrix and p-vector ** */ void iauPvu(double dt, double pv[2][3], double upv[2][3]) /* ** - - - - - - - ** i a u P v u ** - - - - - - - ** ** Update a pv-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** dt double time interval ** pv double[2][3] pv-vector ** ** Returned: ** upv double[2][3] p updated, v unchanged ** ** Notes: ** ** 1) "Update" means "refer the position component of the vector ** to a new date dt time units from the existing date". ** ** 2) The time units of dt must match those of the velocity. ** ** 3) It is permissible for pv and upv to be the same array. ** ** Called: ** iauPpsp p-vector plus scaled p-vector ** iauCp copy p-vector ** */ void iauPvup(double dt, double pv[2][3], double p[3]) /* ** - - - - - - - - ** i a u P v u p ** - - - - - - - - ** ** Update a pv-vector, discarding the velocity component. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** dt double time interval ** pv double[2][3] pv-vector ** ** Returned: ** p double[3] p-vector ** ** Notes: ** ** 1) "Update" means "refer the position component of the vector to a ** new date dt time units from the existing date". ** ** 2) The time units of dt must match those of the velocity. ** */ void iauPvxpv(double a[2][3], double b[2][3], double axb[2][3]) /* ** - - - - - - - - - ** i a u P v x p v ** - - - - - - - - - ** ** Outer (=vector=cross) product of two pv-vectors. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[2][3] first pv-vector ** b double[2][3] second pv-vector ** ** Returned: ** axb double[2][3] a x b ** ** Notes: ** ** 1) If the position and velocity components of the two pv-vectors are ** ( ap, av ) and ( bp, bv ), the result, a x b, is the pair of ** vectors ( ap x bp, ap x bv + av x bp ). The two vectors are the ** cross-product of the two p-vectors and its derivative. ** ** 2) It is permissible to re-use the same array for any of the ** arguments. ** ** Called: ** iauCpv copy pv-vector ** iauPxp vector product of two p-vectors ** iauPpp p-vector plus p-vector ** */ void iauPxp(double a[3], double b[3], double axb[3]) /* ** - - - - - - - ** i a u P x p ** - - - - - - - ** ** p-vector outer (=vector=cross) product. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector ** b double[3] second p-vector ** ** Returned: ** axb double[3] a x b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** */ void iauRefco(double phpa, double tc, double rh, double wl, double *refa, double *refb) /* ** - - - - - - - - - ** i a u R e f c o ** - - - - - - - - - ** ** Determine the constants A and B in the atmospheric refraction model ** dZ = A tan Z + B tan^3 Z. ** ** Z is the "observed" zenith distance (i.e. affected by refraction) ** and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo) ** zenith distance. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** phpa double pressure at the observer (hPa = millibar) ** tc double ambient temperature at the observer (deg C) ** rh double relative humidity at the observer (range 0-1) ** wl double wavelength (micrometers) ** ** Returned: ** refa double* tan Z coefficient (radians) ** refb double* tan^3 Z coefficient (radians) ** ** Notes: ** ** 1) The model balances speed and accuracy to give good results in ** applications where performance at low altitudes is not paramount. ** Performance is maintained across a range of conditions, and ** applies to both optical/IR and radio. ** ** 2) The model omits the effects of (i) height above sea level (apart ** from the reduced pressure itself), (ii) latitude (i.e. the ** flattening of the Earth), (iii) variations in tropospheric lapse ** rate and (iv) dispersive effects in the radio. ** ** The model was tested using the following range of conditions: ** ** lapse rates 0.0055, 0.0065, 0.0075 deg/meter ** latitudes 0, 25, 50, 75 degrees ** heights 0, 2500, 5000 meters ASL ** pressures mean for height -10% to +5% in steps of 5% ** temperatures -10 deg to +20 deg with respect to 280 deg at SL ** relative humidity 0, 0.5, 1 ** wavelengths 0.4, 0.6, ... 2 micron, + radio ** zenith distances 15, 45, 75 degrees ** ** The accuracy with respect to raytracing through a model ** atmosphere was as follows: ** ** worst RMS ** ** optical/IR 62 mas 8 mas ** radio 319 mas 49 mas ** ** For this particular set of conditions: ** ** lapse rate 0.0065 K/meter ** latitude 50 degrees ** sea level ** pressure 1005 mb ** temperature 280.15 K ** humidity 80% ** wavelength 5740 Angstroms ** ** the results were as follows: ** ** ZD raytrace iauRefco Saastamoinen ** ** 10 10.27 10.27 10.27 ** 20 21.19 21.20 21.19 ** 30 33.61 33.61 33.60 ** 40 48.82 48.83 48.81 ** 45 58.16 58.18 58.16 ** 50 69.28 69.30 69.27 ** 55 82.97 82.99 82.95 ** 60 100.51 100.54 100.50 ** 65 124.23 124.26 124.20 ** 70 158.63 158.68 158.61 ** 72 177.32 177.37 177.31 ** 74 200.35 200.38 200.32 ** 76 229.45 229.43 229.42 ** 78 267.44 267.29 267.41 ** 80 319.13 318.55 319.10 ** ** deg arcsec arcsec arcsec ** ** The values for Saastamoinen's formula (which includes terms ** up to tan^5) are taken from Hohenkerk and Sinclair (1985). ** ** 3) A wl value in the range 0-100 selects the optical/IR case and is ** wavelength in micrometers. Any value outside this range selects ** the radio case. ** ** 4) Outlandish input parameters are silently limited to ** mathematically safe values. Zero pressure is permissible, and ** causes zeroes to be returned. ** ** 5) The algorithm draws on several sources, as follows: ** ** a) The formula for the saturation vapour pressure of water as ** a function of temperature and temperature is taken from ** Equations (A4.5-A4.7) of Gill (1982). ** ** b) The formula for the water vapour pressure, given the ** saturation pressure and the relative humidity, is from ** Crane (1976), Equation (2.5.5). ** ** c) The refractivity of air is a function of temperature, ** total pressure, water-vapour pressure and, in the case ** of optical/IR, wavelength. The formulae for the two cases are ** developed from Hohenkerk & Sinclair (1985) and Rueger (2002). ** ** d) The formula for beta, the ratio of the scale height of the ** atmosphere to the geocentric distance of the observer, is ** an adaption of Equation (9) from Stone (1996). The ** adaptations, arrived at empirically, consist of (i) a small ** adjustment to the coefficient and (ii) a humidity term for the ** radio case only. ** ** e) The formulae for the refraction constants as a function of ** n-1 and beta are from Green (1987), Equation (4.31). ** ** References: ** ** Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral ** Atmosphere", Methods of Experimental Physics: Astrophysics 12B, ** Academic Press, 1976. ** ** Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press, ** 1982. ** ** Green, R.M., "Spherical Astronomy", Cambridge University Press, ** 1987. ** ** Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63, ** 1985. ** ** Rueger, J.M., "Refractive Index Formulae for Electronic Distance ** Measurement with Radio and Millimetre Waves", in Unisurv Report ** S-68, School of Surveying and Spatial Information Systems, ** University of New South Wales, Sydney, Australia, 2002. ** ** Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996. ** */ void iauRm2v(double r[3][3], double w[3]) /* ** - - - - - - - - ** i a u R m 2 v ** - - - - - - - - ** ** Express an r-matrix as an r-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] rotation matrix ** ** Returned: ** w double[3] rotation vector (Note 1) ** ** Notes: ** ** 1) A rotation matrix describes a rotation through some angle about ** some arbitrary axis called the Euler axis. The "rotation vector" ** returned by this function has the same direction as the Euler axis, ** and its magnitude is the angle in radians. (The magnitude and ** direction can be separated by means of the function iauPn.) ** ** 2) If r is null, so is the result. If r is not a rotation matrix ** the result is undefined; r must be proper (i.e. have a positive ** determinant) and real orthogonal (inverse = transpose). ** ** 3) The reference frame rotates clockwise as seen looking along ** the rotation vector from the origin. ** */ void iauRv2m(double w[3], double r[3][3]) /* ** - - - - - - - - ** i a u R v 2 m ** - - - - - - - - ** ** Form the r-matrix corresponding to a given r-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** w double[3] rotation vector (Note 1) ** ** Returned: ** r double[3][3] rotation matrix ** ** Notes: ** ** 1) A rotation matrix describes a rotation through some angle about ** some arbitrary axis called the Euler axis. The "rotation vector" ** supplied to This function has the same direction as the Euler ** axis, and its magnitude is the angle in radians. ** ** 2) If w is null, the unit matrix is returned. ** ** 3) The reference frame rotates clockwise as seen looking along the ** rotation vector from the origin. ** */ void iauRx(double phi, double r[3][3]) /* ** - - - - - - ** i a u R x ** - - - - - - ** ** Rotate an r-matrix about the x-axis. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** phi double angle (radians) ** ** Given and returned: ** r double[3][3] r-matrix, rotated ** ** Notes: ** ** 1) Calling this function with positive phi incorporates in the ** supplied r-matrix r an additional rotation, about the x-axis, ** anticlockwise as seen looking towards the origin from positive x. ** ** 2) The additional rotation can be represented by this matrix: ** ** ( 1 0 0 ) ** ( ) ** ( 0 + cos(phi) + sin(phi) ) ** ( ) ** ( 0 - sin(phi) + cos(phi) ) ** */ void iauRxp(double r[3][3], double p[3], double rp[3]) /* ** - - - - - - - ** i a u R x p ** - - - - - - - ** ** Multiply a p-vector by an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix ** p double[3] p-vector ** ** Returned: ** rp double[3] r * p ** ** Note: ** It is permissible for p and rp to be the same array. ** ** Called: ** iauCp copy p-vector ** */ void iauRxpv(double r[3][3], double pv[2][3], double rpv[2][3]) /* ** - - - - - - - - ** i a u R x p v ** - - - - - - - - ** ** Multiply a pv-vector by an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix ** pv double[2][3] pv-vector ** ** Returned: ** rpv double[2][3] r * pv ** ** Note: ** It is permissible for pv and rpv to be the same array. ** ** Called: ** iauRxp product of r-matrix and p-vector ** */ void iauRxr(double a[3][3], double b[3][3], double atb[3][3]) /* ** - - - - - - - ** i a u R x r ** - - - - - - - ** ** Multiply two r-matrices. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3][3] first r-matrix ** b double[3][3] second r-matrix ** ** Returned: ** atb double[3][3] a * b ** ** Note: ** It is permissible to re-use the same array for any of the ** arguments. ** ** Called: ** iauCr copy r-matrix ** */ void iauRy(double theta, double r[3][3]) /* ** - - - - - - ** i a u R y ** - - - - - - ** ** Rotate an r-matrix about the y-axis. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** theta double angle (radians) ** ** Given and returned: ** r double[3][3] r-matrix, rotated ** ** Notes: ** ** 1) Calling this function with positive theta incorporates in the ** supplied r-matrix r an additional rotation, about the y-axis, ** anticlockwise as seen looking towards the origin from positive y. ** ** 2) The additional rotation can be represented by this matrix: ** ** ( + cos(theta) 0 - sin(theta) ) ** ( ) ** ( 0 1 0 ) ** ( ) ** ( + sin(theta) 0 + cos(theta) ) ** */ void iauRz(double psi, double r[3][3]) /* ** - - - - - - ** i a u R z ** - - - - - - ** ** Rotate an r-matrix about the z-axis. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** psi double angle (radians) ** ** Given and returned: ** r double[3][3] r-matrix, rotated ** ** Notes: ** ** 1) Calling this function with positive psi incorporates in the ** supplied r-matrix r an additional rotation, about the z-axis, ** anticlockwise as seen looking towards the origin from positive z. ** ** 2) The additional rotation can be represented by this matrix: ** ** ( + cos(psi) + sin(psi) 0 ) ** ( ) ** ( - sin(psi) + cos(psi) 0 ) ** ( ) ** ( 0 0 1 ) ** */ double iauS00(double date1, double date2, double x, double y) /* ** - - - - - - - ** i a u S 0 0 ** - - - - - - - ** ** The CIO locator s, positioning the Celestial Intermediate Origin on ** the equator of the Celestial Intermediate Pole, given the CIP's X,Y ** coordinates. Compatible with IAU 2000A precession-nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** x,y double CIP coordinates (Note 3) ** ** Returned (function value): ** double the CIO locator s in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The CIO locator s is the difference between the right ascensions ** of the same point in two systems: the two systems are the GCRS ** and the CIP,CIO, and the point is the ascending node of the ** CIP equator. The quantity s remains below 0.1 arcsecond ** throughout 1900-2100. ** ** 3) The series used to compute s is in fact for s+XY/2, where X and Y ** are the x and y components of the CIP unit vector; this series ** is more compact than a direct series for s would be. This ** function requires X,Y to be supplied by the caller, who is ** responsible for providing values that are consistent with the ** supplied date. ** ** 4) The model is consistent with the IAU 2000A precession-nutation. ** ** Called: ** iauFal03 mean anomaly of the Moon ** iauFalp03 mean anomaly of the Sun ** iauFaf03 mean argument of the latitude of the Moon ** iauFad03 mean elongation of the Moon from the Sun ** iauFaom03 mean longitude of the Moon's ascending node ** iauFave03 mean longitude of Venus ** iauFae03 mean longitude of Earth ** iauFapa03 general accumulated precession in longitude ** ** References: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ double iauS00a(double date1, double date2) /* ** - - - - - - - - ** i a u S 0 0 a ** - - - - - - - - ** ** The CIO locator s, positioning the Celestial Intermediate Origin on ** the equator of the Celestial Intermediate Pole, using the IAU 2000A ** precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double the CIO locator s in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The CIO locator s is the difference between the right ascensions ** of the same point in two systems. The two systems are the GCRS ** and the CIP,CIO, and the point is the ascending node of the ** CIP equator. The CIO locator s remains a small fraction of ** 1 arcsecond throughout 1900-2100. ** ** 3) The series used to compute s is in fact for s+XY/2, where X and Y ** are the x and y components of the CIP unit vector; this series ** is more compact than a direct series for s would be. The present ** function uses the full IAU 2000A nutation model when predicting ** the CIP position. Faster results, with no significant loss of ** accuracy, can be obtained via the function iauS00b, which uses ** instead the IAU 2000B truncated model. ** ** Called: ** iauPnm00a classical NPB matrix, IAU 2000A ** iauBnp2xy extract CIP X,Y from the BPN matrix ** iauS00 the CIO locator s, given X,Y, IAU 2000A ** ** References: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ double iauS00b(double date1, double date2) /* ** - - - - - - - - ** i a u S 0 0 b ** - - - - - - - - ** ** The CIO locator s, positioning the Celestial Intermediate Origin on ** the equator of the Celestial Intermediate Pole, using the IAU 2000B ** precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double the CIO locator s in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The CIO locator s is the difference between the right ascensions ** of the same point in two systems. The two systems are the GCRS ** and the CIP,CIO, and the point is the ascending node of the ** CIP equator. The CIO locator s remains a small fraction of ** 1 arcsecond throughout 1900-2100. ** ** 3) The series used to compute s is in fact for s+XY/2, where X and Y ** are the x and y components of the CIP unit vector; this series ** is more compact than a direct series for s would be. The present ** function uses the IAU 2000B truncated nutation model when ** predicting the CIP position. The function iauS00a uses instead ** the full IAU 2000A model, but with no significant increase in ** accuracy and at some cost in speed. ** ** Called: ** iauPnm00b classical NPB matrix, IAU 2000B ** iauBnp2xy extract CIP X,Y from the BPN matrix ** iauS00 the CIO locator s, given X,Y, IAU 2000A ** ** References: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ double iauS06(double date1, double date2, double x, double y) /* ** - - - - - - - ** i a u S 0 6 ** - - - - - - - ** ** The CIO locator s, positioning the Celestial Intermediate Origin on ** the equator of the Celestial Intermediate Pole, given the CIP's X,Y ** coordinates. Compatible with IAU 2006/2000A precession-nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** x,y double CIP coordinates (Note 3) ** ** Returned (function value): ** double the CIO locator s in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The CIO locator s is the difference between the right ascensions ** of the same point in two systems: the two systems are the GCRS ** and the CIP,CIO, and the point is the ascending node of the ** CIP equator. The quantity s remains below 0.1 arcsecond ** throughout 1900-2100. ** ** 3) The series used to compute s is in fact for s+XY/2, where X and Y ** are the x and y components of the CIP unit vector; this series ** is more compact than a direct series for s would be. This ** function requires X,Y to be supplied by the caller, who is ** responsible for providing values that are consistent with the ** supplied date. ** ** 4) The model is consistent with the "P03" precession (Capitaine et ** al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the ** IAU 2000A nutation (with P03 adjustments). ** ** Called: ** iauFal03 mean anomaly of the Moon ** iauFalp03 mean anomaly of the Sun ** iauFaf03 mean argument of the latitude of the Moon ** iauFad03 mean elongation of the Moon from the Sun ** iauFaom03 mean longitude of the Moon's ascending node ** iauFave03 mean longitude of Venus ** iauFae03 mean longitude of Earth ** iauFapa03 general accumulated precession in longitude ** ** References: ** ** Capitaine, N., Wallace, P.T. & Chapront, J., 2003, Astron. ** Astrophys. 432, 355 ** ** McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** */ double iauS06a(double date1, double date2) /* ** - - - - - - - - ** i a u S 0 6 a ** - - - - - - - - ** ** The CIO locator s, positioning the Celestial Intermediate Origin on ** the equator of the Celestial Intermediate Pole, using the IAU 2006 ** precession and IAU 2000A nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double the CIO locator s in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The CIO locator s is the difference between the right ascensions ** of the same point in two systems. The two systems are the GCRS ** and the CIP,CIO, and the point is the ascending node of the ** CIP equator. The CIO locator s remains a small fraction of ** 1 arcsecond throughout 1900-2100. ** ** 3) The series used to compute s is in fact for s+XY/2, where X and Y ** are the x and y components of the CIP unit vector; this series is ** more compact than a direct series for s would be. The present ** function uses the full IAU 2000A nutation model when predicting ** the CIP position. ** ** Called: ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** ** References: ** ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., ** "Expressions for the Celestial Intermediate Pole and Celestial ** Ephemeris Origin consistent with the IAU 2000A precession- ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003) ** ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial ** intermediate origin" (CIO) by IAU 2006 Resolution 2. ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** */ void iauS2c(double theta, double phi, double c[3]) /* ** - - - - - - - ** i a u S 2 c ** - - - - - - - ** ** Convert spherical coordinates to Cartesian. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** ** Returned: ** c double[3] direction cosines ** */ void iauS2p(double theta, double phi, double r, double p[3]) /* ** - - - - - - - ** i a u S 2 p ** - - - - - - - ** ** Convert spherical polar coordinates to p-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** r double radial distance ** ** Returned: ** p double[3] Cartesian coordinates ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauSxp multiply p-vector by scalar ** */ void iauS2pv(double theta, double phi, double r, double td, double pd, double rd, double pv[2][3]) /* ** - - - - - - - - ** i a u S 2 p v ** - - - - - - - - ** ** Convert position/velocity from spherical to Cartesian coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** theta double longitude angle (radians) ** phi double latitude angle (radians) ** r double radial distance ** td double rate of change of theta ** pd double rate of change of phi ** rd double rate of change of r ** ** Returned: ** pv double[2][3] pv-vector ** */ void iauS2xpv(double s1, double s2, double pv[2][3], double spv[2][3]) /* ** - - - - - - - - - ** i a u S 2 x p v ** - - - - - - - - - ** ** Multiply a pv-vector by two scalars. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** s1 double scalar to multiply position component by ** s2 double scalar to multiply velocity component by ** pv double[2][3] pv-vector ** ** Returned: ** spv double[2][3] pv-vector: p scaled by s1, v scaled by s2 ** ** Note: ** It is permissible for pv and spv to be the same array. ** ** Called: ** iauSxp multiply p-vector by scalar ** */ double iauSepp(double a[3], double b[3]) /* ** - - - - - - - - ** i a u S e p p ** - - - - - - - - ** ** Angular separation between two p-vectors. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector (not necessarily unit length) ** b double[3] second p-vector (not necessarily unit length) ** ** Returned (function value): ** double angular separation (radians, always positive) ** ** Notes: ** ** 1) If either vector is null, a zero result is returned. ** ** 2) The angular separation is most simply formulated in terms of ** scalar product. However, this gives poor accuracy for angles ** near zero and pi. The present algorithm uses both cross product ** and dot product, to deliver full accuracy whatever the size of ** the angle. ** ** Called: ** iauPxp vector product of two p-vectors ** iauPm modulus of p-vector ** iauPdp scalar product of two p-vectors ** */ double iauSeps(double al, double ap, double bl, double bp) /* ** - - - - - - - - ** i a u S e p s ** - - - - - - - - ** ** Angular separation between two sets of spherical coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** al double first longitude (radians) ** ap double first latitude (radians) ** bl double second longitude (radians) ** bp double second latitude (radians) ** ** Returned (function value): ** double angular separation (radians) ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauSepp angular separation between two p-vectors ** */ double iauSp00(double date1, double date2) /* ** - - - - - - - - ** i a u S p 0 0 ** - - - - - - - - ** ** The TIO locator s', positioning the Terrestrial Intermediate Origin ** on the equator of the Celestial Intermediate Pole. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (function value): ** double the TIO locator s' in radians (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The TIO locator s' is obtained from polar motion observations by ** numerical integration, and so is in essence unpredictable. ** However, it is dominated by a secular drift of about ** 47 microarcseconds per century, which is the approximation ** evaluated by the present function. ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ int iauStarpm(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2) /* ** - - - - - - - - - - ** i a u S t a r p m ** - - - - - - - - - - ** ** Star proper motion: update star catalog data for space motion. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ra1 double right ascension (radians), before ** dec1 double declination (radians), before ** pmr1 double RA proper motion (radians/year), before ** pmd1 double Dec proper motion (radians/year), before ** px1 double parallax (arcseconds), before ** rv1 double radial velocity (km/s, +ve = receding), before ** ep1a double "before" epoch, part A (Note 1) ** ep1b double "before" epoch, part B (Note 1) ** ep2a double "after" epoch, part A (Note 1) ** ep2b double "after" epoch, part B (Note 1) ** ** Returned: ** ra2 double right ascension (radians), after ** dec2 double declination (radians), after ** pmr2 double RA proper motion (radians/year), after ** pmd2 double Dec proper motion (radians/year), after ** px2 double parallax (arcseconds), after ** rv2 double radial velocity (km/s, +ve = receding), after ** ** Returned (function value): ** int status: ** -1 = system error (should not occur) ** 0 = no warnings or errors ** 1 = distance overridden (Note 6) ** 2 = excessive velocity (Note 7) ** 4 = solution didn't converge (Note 8) ** else = binary logical OR of the above warnings ** ** Notes: ** ** 1) The starting and ending TDB dates ep1a+ep1b and ep2a+ep2b are ** Julian Dates, apportioned in any convenient way between the two ** parts (A and B). For example, JD(TDB)=2450123.7 could be ** expressed in any of these ways, among others: ** ** epna epnb ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) In accordance with normal star-catalog conventions, the object's ** right ascension and declination are freed from the effects of ** secular aberration. The frame, which is aligned to the catalog ** equator and equinox, is Lorentzian and centered on the SSB. ** ** The proper motions are the rate of change of the right ascension ** and declination at the catalog epoch and are in radians per TDB ** Julian year. ** ** The parallax and radial velocity are in the same frame. ** ** 3) Care is needed with units. The star coordinates are in radians ** and the proper motions in radians per Julian year, but the ** parallax is in arcseconds. ** ** 4) The RA proper motion is in terms of coordinate angle, not true ** angle. If the catalog uses arcseconds for both RA and Dec proper ** motions, the RA proper motion will need to be divided by cos(Dec) ** before use. ** ** 5) Straight-line motion at constant speed, in the inertial frame, ** is assumed. ** ** 6) An extremely small (or zero or negative) parallax is interpreted ** to mean that the object is on the "celestial sphere", the radius ** of which is an arbitrary (large) value (see the iauStarpv ** function for the value used). When the distance is overridden in ** this way, the status, initially zero, has 1 added to it. ** ** 7) If the space velocity is a significant fraction of c (see the ** constant VMAX in the function iauStarpv), it is arbitrarily set ** to zero. When this action occurs, 2 is added to the status. ** ** 8) The relativistic adjustment carried out in the iauStarpv function ** involves an iterative calculation. If the process fails to ** converge within a set number of iterations, 4 is added to the ** status. ** ** Called: ** iauStarpv star catalog data to space motion pv-vector ** iauPvu update a pv-vector ** iauPdp scalar product of two p-vectors ** iauPvstar space motion pv-vector to star catalog data ** */ int iauStarpv(double ra, double dec, double pmr, double pmd, double px, double rv, double pv[2][3]) /* ** - - - - - - - - - - ** i a u S t a r p v ** - - - - - - - - - - ** ** Convert star catalog coordinates to position+velocity vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given (Note 1): ** ra double right ascension (radians) ** dec double declination (radians) ** pmr double RA proper motion (radians/year) ** pmd double Dec proper motion (radians/year) ** px double parallax (arcseconds) ** rv double radial velocity (km/s, positive = receding) ** ** Returned (Note 2): ** pv double[2][3] pv-vector (AU, AU/day) ** ** Returned (function value): ** int status: ** 0 = no warnings ** 1 = distance overridden (Note 6) ** 2 = excessive speed (Note 7) ** 4 = solution didn't converge (Note 8) ** else = binary logical OR of the above ** ** Notes: ** ** 1) The star data accepted by this function are "observables" for an ** imaginary observer at the solar-system barycenter. Proper motion ** and radial velocity are, strictly, in terms of barycentric ** coordinate time, TCB. For most practical applications, it is ** permissible to neglect the distinction between TCB and ordinary ** "proper" time on Earth (TT/TAI). The result will, as a rule, be ** limited by the intrinsic accuracy of the proper-motion and ** radial-velocity data; moreover, the pv-vector is likely to be ** merely an intermediate result, so that a change of time unit ** would cancel out overall. ** ** In accordance with normal star-catalog conventions, the object's ** right ascension and declination are freed from the effects of ** secular aberration. The frame, which is aligned to the catalog ** equator and equinox, is Lorentzian and centered on the SSB. ** ** 2) The resulting position and velocity pv-vector is with respect to ** the same frame and, like the catalog coordinates, is freed from ** the effects of secular aberration. Should the "coordinate ** direction", where the object was located at the catalog epoch, be ** required, it may be obtained by calculating the magnitude of the ** position vector pv[0][0-2] dividing by the speed of light in ** AU/day to give the light-time, and then multiplying the space ** velocity pv[1][0-2] by this light-time and adding the result to ** pv[0][0-2]. ** ** Summarizing, the pv-vector returned is for most stars almost ** identical to the result of applying the standard geometrical ** "space motion" transformation. The differences, which are the ** subject of the Stumpff paper referenced below, are: ** ** (i) In stars with significant radial velocity and proper motion, ** the constantly changing light-time distorts the apparent proper ** motion. Note that this is a classical, not a relativistic, ** effect. ** ** (ii) The transformation complies with special relativity. ** ** 3) Care is needed with units. The star coordinates are in radians ** and the proper motions in radians per Julian year, but the ** parallax is in arcseconds; the radial velocity is in km/s, but ** the pv-vector result is in AU and AU/day. ** ** 4) The RA proper motion is in terms of coordinate angle, not true ** angle. If the catalog uses arcseconds for both RA and Dec proper ** motions, the RA proper motion will need to be divided by cos(Dec) ** before use. ** ** 5) Straight-line motion at constant speed, in the inertial frame, ** is assumed. ** ** 6) An extremely small (or zero or negative) parallax is interpreted ** to mean that the object is on the "celestial sphere", the radius ** of which is an arbitrary (large) value (see the constant PXMIN). ** When the distance is overridden in this way, the status, ** initially zero, has 1 added to it. ** ** 7) If the space velocity is a significant fraction of c (see the ** constant VMAX), it is arbitrarily set to zero. When this action ** occurs, 2 is added to the status. ** ** 8) The relativistic adjustment involves an iterative calculation. ** If the process fails to converge within a set number (IMAX) of ** iterations, 4 is added to the status. ** ** 9) The inverse transformation is performed by the function ** iauPvstar. ** ** Called: ** iauS2pv spherical coordinates to pv-vector ** iauPm modulus of p-vector ** iauZp zero p-vector ** iauPn decompose p-vector into modulus and direction ** iauPdp scalar product of two p-vectors ** iauSxp multiply p-vector by scalar ** iauPmp p-vector minus p-vector ** iauPpp p-vector plus p-vector ** ** Reference: ** ** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240. ** */ void iauSxp(double s, double p[3], double sp[3]) /* ** - - - - - - - ** i a u S x p ** - - - - - - - ** ** Multiply a p-vector by a scalar. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** s double scalar ** p double[3] p-vector ** ** Returned: ** sp double[3] s * p ** ** Note: ** It is permissible for p and sp to be the same array. ** */ void iauSxpv(double s, double pv[2][3], double spv[2][3]) /* ** - - - - - - - - ** i a u S x p v ** - - - - - - - - ** ** Multiply a pv-vector by a scalar. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** s double scalar ** pv double[2][3] pv-vector ** ** Returned: ** spv double[2][3] s * pv ** ** Note: ** It is permissible for pv and spv to be the same array ** ** Called: ** iauS2xpv multiply pv-vector by two scalars ** */ int iauTaitt(double tai1, double tai2, double *tt1, double *tt2) /* ** - - - - - - - - - ** i a u T a i t t ** - - - - - - - - - ** ** Time scale transformation: International Atomic Time, TAI, to ** Terrestrial Time, TT. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tai1,tai2 double TAI as a 2-part Julian Date ** ** Returned: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Note: ** ** tai1+tai2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tai1 is the Julian ** Day Number and tai2 is the fraction of a day. The returned ** tt1,tt2 follow suit. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** */ int iauTaiut1(double tai1, double tai2, double dta, double *ut11, double *ut12) /* ** - - - - - - - - - - ** i a u T a i u t 1 ** - - - - - - - - - - ** ** Time scale transformation: International Atomic Time, TAI, to ** Universal Time, UT1. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tai1,tai2 double TAI as a 2-part Julian Date ** dta double UT1-TAI in seconds ** ** Returned: ** ut11,ut12 double UT1 as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tai1+tai2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tai1 is the Julian ** Day Number and tai2 is the fraction of a day. The returned ** UT11,UT12 follow suit. ** ** 2) The argument dta, i.e. UT1-TAI, is an observed quantity, and is ** available from IERS tabulations. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** */ int iauTaiutc(double tai1, double tai2, double *utc1, double *utc2) /* ** - - - - - - - - - - ** i a u T a i u t c ** - - - - - - - - - - ** ** Time scale transformation: International Atomic Time, TAI, to ** Coordinated Universal Time, UTC. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tai1,tai2 double TAI as a 2-part Julian Date (Note 1) ** ** Returned: ** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-3) ** ** Returned (function value): ** int status: +1 = dubious year (Note 4) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) tai1+tai2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tai1 is the Julian ** Day Number and tai2 is the fraction of a day. The returned utc1 ** and utc2 form an analogous pair, except that a special convention ** is used, to deal with the problem of leap seconds - see the next ** note. ** ** 2) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The convention in the present ** function is that the JD day represents UTC days whether the ** length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era ** there were smaller jumps (in either direction) each time the ** linear UTC(TAI) expression was changed, and these "mini-leaps" ** are also included in the SOFA convention. ** ** 3) The function iauD2dtf can be used to transform the UTC quasi-JD ** into calendar date and clock time, including UTC leap second ** handling. ** ** 4) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** Called: ** iauUtctai UTC to TAI ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** */ int iauTcbtdb(double tcb1, double tcb2, double *tdb1, double *tdb2) /* ** - - - - - - - - - - ** i a u T c b t d b ** - - - - - - - - - - ** ** Time scale transformation: Barycentric Coordinate Time, TCB, to ** Barycentric Dynamical Time, TDB. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tcb1,tcb2 double TCB as a 2-part Julian Date ** ** Returned: ** tdb1,tdb2 double TDB as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tcb1+tcb2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tcb1 is the Julian ** Day Number and tcb2 is the fraction of a day. The returned ** tdb1,tdb2 follow suit. ** ** 2) The 2006 IAU General Assembly introduced a conventional linear ** transformation between TDB and TCB. This transformation ** compensates for the drift between TCB and terrestrial time TT, ** and keeps TDB approximately centered on TT. Because the ** relationship between TT and TCB depends on the adopted solar ** system ephemeris, the degree of alignment between TDB and TT over ** long intervals will vary according to which ephemeris is used. ** Former definitions of TDB attempted to avoid this problem by ** stipulating that TDB and TT should differ only by periodic ** effects. This is a good description of the nature of the ** relationship but eluded precise mathematical formulation. The ** conventional linear relationship adopted in 2006 sidestepped ** these difficulties whilst delivering a TDB that in practice was ** consistent with values before that date. ** ** 3) TDB is essentially the same as Teph, the time argument for the ** JPL solar system ephemerides. ** ** Reference: ** ** IAU 2006 Resolution B3 ** */ int iauTcgtt(double tcg1, double tcg2, double *tt1, double *tt2) /* ** - - - - - - - - - ** i a u T c g t t ** - - - - - - - - - ** ** Time scale transformation: Geocentric Coordinate Time, TCG, to ** Terrestrial Time, TT. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tcg1,tcg2 double TCG as a 2-part Julian Date ** ** Returned: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Note: ** ** tcg1+tcg2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tcg1 is the Julian ** Day Number and tcg22 is the fraction of a day. The returned ** tt1,tt2 follow suit. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),. ** IERS Technical Note No. 32, BKG (2004) ** ** IAU 2000 Resolution B1.9 ** */ int iauTdbtcb(double tdb1, double tdb2, double *tcb1, double *tcb2) /* ** - - - - - - - - - - ** i a u T d b t c b ** - - - - - - - - - - ** ** Time scale transformation: Barycentric Dynamical Time, TDB, to ** Barycentric Coordinate Time, TCB. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tdb1,tdb2 double TDB as a 2-part Julian Date ** ** Returned: ** tcb1,tcb2 double TCB as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tdb1+tdb2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tdb1 is the Julian ** Day Number and tdb2 is the fraction of a day. The returned ** tcb1,tcb2 follow suit. ** ** 2) The 2006 IAU General Assembly introduced a conventional linear ** transformation between TDB and TCB. This transformation ** compensates for the drift between TCB and terrestrial time TT, ** and keeps TDB approximately centered on TT. Because the ** relationship between TT and TCB depends on the adopted solar ** system ephemeris, the degree of alignment between TDB and TT over ** long intervals will vary according to which ephemeris is used. ** Former definitions of TDB attempted to avoid this problem by ** stipulating that TDB and TT should differ only by periodic ** effects. This is a good description of the nature of the ** relationship but eluded precise mathematical formulation. The ** conventional linear relationship adopted in 2006 sidestepped ** these difficulties whilst delivering a TDB that in practice was ** consistent with values before that date. ** ** 3) TDB is essentially the same as Teph, the time argument for the ** JPL solar system ephemerides. ** ** Reference: ** ** IAU 2006 Resolution B3 ** */ int iauTdbtt(double tdb1, double tdb2, double dtr, double *tt1, double *tt2 ) /* ** - - - - - - - - - ** i a u T d b t t ** - - - - - - - - - ** ** Time scale transformation: Barycentric Dynamical Time, TDB, to ** Terrestrial Time, TT. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tdb1,tdb2 double TDB as a 2-part Julian Date ** dtr double TDB-TT in seconds ** ** Returned: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tdb1+tdb2 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where tdb1 is the Julian ** Day Number and tdb2 is the fraction of a day. The returned ** tt1,tt2 follow suit. ** ** 2) The argument dtr represents the quasi-periodic component of the ** GR transformation between TT and TCB. It is dependent upon the ** adopted solar-system ephemeris, and can be obtained by numerical ** integration, by interrogating a precomputed time ephemeris or by ** evaluating a model such as that implemented in the SOFA function ** iauDtdb. The quantity is dominated by an annual term of 1.7 ms ** amplitude. ** ** 3) TDB is essentially the same as Teph, the time argument for the ** JPL solar system ephemerides. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** IAU 2006 Resolution 3 ** */ int iauTf2a(char s, int ihour, int imin, double sec, double *rad) /* ** - - - - - - - - ** i a u T f 2 a ** - - - - - - - - ** ** Convert hours, minutes, seconds to radians. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** s char sign: '-' = negative, otherwise positive ** ihour int hours ** imin int minutes ** sec double seconds ** ** Returned: ** rad double angle in radians ** ** Returned (function value): ** int status: 0 = OK ** 1 = ihour outside range 0-23 ** 2 = imin outside range 0-59 ** 3 = sec outside range 0-59.999... ** ** Notes: ** ** 1) The result is computed even if any of the range checks fail. ** ** 2) Negative ihour, imin and/or sec produce a warning status, but ** the absolute value is used in the conversion. ** ** 3) If there are multiple errors, the status value reflects only the ** first, the smallest taking precedence. ** */ int iauTf2d(char s, int ihour, int imin, double sec, double *days) /* ** - - - - - - - - ** i a u T f 2 d ** - - - - - - - - ** ** Convert hours, minutes, seconds to days. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** s char sign: '-' = negative, otherwise positive ** ihour int hours ** imin int minutes ** sec double seconds ** ** Returned: ** days double interval in days ** ** Returned (function value): ** int status: 0 = OK ** 1 = ihour outside range 0-23 ** 2 = imin outside range 0-59 ** 3 = sec outside range 0-59.999... ** ** Notes: ** ** 1) The result is computed even if any of the range checks fail. ** ** 2) Negative ihour, imin and/or sec produce a warning status, but ** the absolute value is used in the conversion. ** ** 3) If there are multiple errors, the status value reflects only the ** first, the smallest taking precedence. ** */ void iauTr(double r[3][3], double rt[3][3]) /* ** - - - - - - ** i a u T r ** - - - - - - ** ** Transpose an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix ** ** Returned: ** rt double[3][3] transpose ** ** Note: ** It is permissible for r and rt to be the same array. ** ** Called: ** iauCr copy r-matrix ** */ void iauTrxp(double r[3][3], double p[3], double trp[3]) /* ** - - - - - - - - ** i a u T r x p ** - - - - - - - - ** ** Multiply a p-vector by the transpose of an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix ** p double[3] p-vector ** ** Returned: ** trp double[3] r * p ** ** Note: ** It is permissible for p and trp to be the same array. ** ** Called: ** iauTr transpose r-matrix ** iauRxp product of r-matrix and p-vector ** */ void iauTrxpv(double r[3][3], double pv[2][3], double trpv[2][3]) /* ** - - - - - - - - - ** i a u T r x p v ** - - - - - - - - - ** ** Multiply a pv-vector by the transpose of an r-matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** r double[3][3] r-matrix ** pv double[2][3] pv-vector ** ** Returned: ** trpv double[2][3] r * pv ** ** Note: ** It is permissible for pv and trpv to be the same array. ** ** Called: ** iauTr transpose r-matrix ** iauRxpv product of r-matrix and pv-vector ** */ int iauTttai(double tt1, double tt2, double *tai1, double *tai2) /* ** - - - - - - - - - ** i a u T t t a i ** - - - - - - - - - ** ** Time scale transformation: Terrestrial Time, TT, to International ** Atomic Time, TAI. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned: ** tai1,tai2 double TAI as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Note: ** ** tt1+tt2 is Julian Date, apportioned in any convenient way between ** the two arguments, for example where tt1 is the Julian Day Number ** and tt2 is the fraction of a day. The returned tai1,tai2 follow ** suit. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** */ int iauTttcg(double tt1, double tt2, double *tcg1, double *tcg2) /* ** - - - - - - - - - ** i a u T t t c g ** - - - - - - - - - ** ** Time scale transformation: Terrestrial Time, TT, to Geocentric ** Coordinate Time, TCG. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned: ** tcg1,tcg2 double TCG as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Note: ** ** tt1+tt2 is Julian Date, apportioned in any convenient way between ** the two arguments, for example where tt1 is the Julian Day Number ** and tt2 is the fraction of a day. The returned tcg1,tcg2 follow ** suit. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** IAU 2000 Resolution B1.9 ** */ int iauTttdb(double tt1, double tt2, double dtr, double *tdb1, double *tdb2) /* ** - - - - - - - - - ** i a u T t t d b ** - - - - - - - - - ** ** Time scale transformation: Terrestrial Time, TT, to Barycentric ** Dynamical Time, TDB. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tt1,tt2 double TT as a 2-part Julian Date ** dtr double TDB-TT in seconds ** ** Returned: ** tdb1,tdb2 double TDB as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tt1+tt2 is Julian Date, apportioned in any convenient way between ** the two arguments, for example where tt1 is the Julian Day Number ** and tt2 is the fraction of a day. The returned tdb1,tdb2 follow ** suit. ** ** 2) The argument dtr represents the quasi-periodic component of the ** GR transformation between TT and TCB. It is dependent upon the ** adopted solar-system ephemeris, and can be obtained by numerical ** integration, by interrogating a precomputed time ephemeris or by ** evaluating a model such as that implemented in the SOFA function ** iauDtdb. The quantity is dominated by an annual term of 1.7 ms ** amplitude. ** ** 3) TDB is essentially the same as Teph, the time argument for the JPL ** solar system ephemerides. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** IAU 2006 Resolution 3 ** */ int iauTtut1(double tt1, double tt2, double dt, double *ut11, double *ut12) /* ** - - - - - - - - - ** i a u T t u t 1 ** - - - - - - - - - ** ** Time scale transformation: Terrestrial Time, TT, to Universal Time, ** UT1. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** tt1,tt2 double TT as a 2-part Julian Date ** dt double TT-UT1 in seconds ** ** Returned: ** ut11,ut12 double UT1 as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) tt1+tt2 is Julian Date, apportioned in any convenient way between ** the two arguments, for example where tt1 is the Julian Day Number ** and tt2 is the fraction of a day. The returned ut11,ut12 follow ** suit. ** ** 2) The argument dt is classical Delta T. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** */ int iauUt1tai(double ut11, double ut12, double dta, double *tai1, double *tai2) /* ** - - - - - - - - - - ** i a u U t 1 t a i ** - - - - - - - - - - ** ** Time scale transformation: Universal Time, UT1, to International ** Atomic Time, TAI. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** ut11,ut12 double UT1 as a 2-part Julian Date ** dta double UT1-TAI in seconds ** ** Returned: ** tai1,tai2 double TAI as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) ut11+ut12 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where ut11 is the Julian ** Day Number and ut12 is the fraction of a day. The returned ** tai1,tai2 follow suit. ** ** 2) The argument dta, i.e. UT1-TAI, is an observed quantity, and is ** available from IERS tabulations. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** */ int iauUt1tt(double ut11, double ut12, double dt, double *tt1, double *tt2) /* ** - - - - - - - - - ** i a u U t 1 t t ** - - - - - - - - - ** ** Time scale transformation: Universal Time, UT1, to Terrestrial ** Time, TT. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** ut11,ut12 double UT1 as a 2-part Julian Date ** dt double TT-UT1 in seconds ** ** Returned: ** tt1,tt2 double TT as a 2-part Julian Date ** ** Returned (function value): ** int status: 0 = OK ** ** Notes: ** ** 1) ut11+ut12 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where ut11 is the Julian ** Day Number and ut12 is the fraction of a day. The returned ** tt1,tt2 follow suit. ** ** 2) The argument dt is classical Delta T. ** ** Reference: ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** */ int iauUt1utc(double ut11, double ut12, double dut1, double *utc1, double *utc2) /* ** - - - - - - - - - - ** i a u U t 1 u t c ** - - - - - - - - - - ** ** Time scale transformation: Universal Time, UT1, to Coordinated ** Universal Time, UTC. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** ut11,ut12 double UT1 as a 2-part Julian Date (Note 1) ** dut1 double Delta UT1: UT1-UTC in seconds (Note 2) ** ** Returned: ** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 3,4) ** ** Returned (function value): ** int status: +1 = dubious year (Note 5) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) ut11+ut12 is Julian Date, apportioned in any convenient way ** between the two arguments, for example where ut11 is the Julian ** Day Number and ut12 is the fraction of a day. The returned utc1 ** and utc2 form an analogous pair, except that a special convention ** is used, to deal with the problem of leap seconds - see Note 3. ** ** 2) Delta UT1 can be obtained from tabulations provided by the ** International Earth Rotation and Reference Systems Service. The ** value changes abruptly by 1s at a leap second; however, close to ** a leap second the algorithm used here is tolerant of the "wrong" ** choice of value being made. ** ** 3) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The convention in the present ** function is that the returned quasi JD day UTC1+UTC2 represents ** UTC days whether the length is 86399, 86400 or 86401 SI seconds. ** ** 4) The function iauD2dtf can be used to transform the UTC quasi-JD ** into calendar date and clock time, including UTC leap second ** handling. ** ** 5) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** Called: ** iauJd2cal JD to Gregorian calendar ** iauDat delta(AT) = TAI-UTC ** iauCal2jd Gregorian calendar to JD ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** */ int iauUtctai(double utc1, double utc2, double *tai1, double *tai2) /* ** - - - - - - - - - - ** i a u U t c t a i ** - - - - - - - - - - ** ** Time scale transformation: Coordinated Universal Time, UTC, to ** International Atomic Time, TAI. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-4) ** ** Returned: ** tai1,tai2 double TAI as a 2-part Julian Date (Note 5) ** ** Returned (function value): ** int status: +1 = dubious year (Note 3) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** 2) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The convention in the present ** function is that the JD day represents UTC days whether the ** length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era ** there were smaller jumps (in either direction) each time the ** linear UTC(TAI) expression was changed, and these "mini-leaps" ** are also included in the SOFA convention. ** ** 3) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 4) The function iauDtf2d converts from calendar date and time of day ** into 2-part Julian Date, and in the case of UTC implements the ** leap-second-ambiguity convention described above. ** ** 5) The returned TAI1,TAI2 are such that their sum is the TAI Julian ** Date. ** ** Called: ** iauJd2cal JD to Gregorian calendar ** iauDat delta(AT) = TAI-UTC ** iauCal2jd Gregorian calendar to JD ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** */ int iauUtcut1(double utc1, double utc2, double dut1, double *ut11, double *ut12) /* ** - - - - - - - - - - ** i a u U t c u t 1 ** - - - - - - - - - - ** ** Time scale transformation: Coordinated Universal Time, UTC, to ** Universal Time, UT1. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: canonical. ** ** Given: ** utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-4) ** dut1 double Delta UT1 = UT1-UTC in seconds (Note 5) ** ** Returned: ** ut11,ut12 double UT1 as a 2-part Julian Date (Note 6) ** ** Returned (function value): ** int status: +1 = dubious year (Note 3) ** 0 = OK ** -1 = unacceptable date ** ** Notes: ** ** 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any ** convenient way between the two arguments, for example where utc1 ** is the Julian Day Number and utc2 is the fraction of a day. ** ** 2) JD cannot unambiguously represent UTC during a leap second unless ** special measures are taken. The convention in the present ** function is that the JD day represents UTC days whether the ** length is 86399, 86400 or 86401 SI seconds. ** ** 3) The warning status "dubious year" flags UTCs that predate the ** introduction of the time scale or that are too far in the future ** to be trusted. See iauDat for further details. ** ** 4) The function iauDtf2d converts from calendar date and time of ** day into 2-part Julian Date, and in the case of UTC implements ** the leap-second-ambiguity convention described above. ** ** 5) Delta UT1 can be obtained from tabulations provided by the ** International Earth Rotation and Reference Systems Service. ** It is the caller's responsibility to supply a dut1 argument ** containing the UT1-UTC value that matches the given UTC. ** ** 6) The returned ut11,ut12 are such that their sum is the UT1 Julian ** Date. ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** ** Explanatory Supplement to the Astronomical Almanac, ** P. Kenneth Seidelmann (ed), University Science Books (1992) ** ** Called: ** iauJd2cal JD to Gregorian calendar ** iauDat delta(AT) = TAI-UTC ** iauUtctai UTC to TAI ** iauTaiut1 TAI to UT1 ** */ void iauXy06(double date1, double date2, double *x, double *y) /* ** - - - - - - - - ** i a u X y 0 6 ** - - - - - - - - ** ** X,Y coordinates of celestial intermediate pole from series based ** on IAU 2006 precession and IAU 2000A nutation. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** x,y double CIP X,Y coordinates (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The X,Y coordinates are those of the unit vector towards the ** celestial intermediate pole. They represent the combined effects ** of frame bias, precession and nutation. ** ** 3) The fundamental arguments used are as adopted in IERS Conventions ** (2003) and are from Simon et al. (1994) and Souchay et al. ** (1999). ** ** 4) This is an alternative to the angles-based method, via the SOFA ** function iauFw2xy and as used in iauXys06a for example. The two ** methods agree at the 1 microarcsecond level (at present), a ** negligible amount compared with the intrinsic accuracy of the ** models. However, it would be unwise to mix the two methods ** (angles-based and series-based) in a single application. ** ** Called: ** iauFal03 mean anomaly of the Moon ** iauFalp03 mean anomaly of the Sun ** iauFaf03 mean argument of the latitude of the Moon ** iauFad03 mean elongation of the Moon from the Sun ** iauFaom03 mean longitude of the Moon's ascending node ** iauFame03 mean longitude of Mercury ** iauFave03 mean longitude of Venus ** iauFae03 mean longitude of Earth ** iauFama03 mean longitude of Mars ** iauFaju03 mean longitude of Jupiter ** iauFasa03 mean longitude of Saturn ** iauFaur03 mean longitude of Uranus ** iauFane03 mean longitude of Neptune ** iauFapa03 general accumulated precession in longitude ** ** References: ** ** Capitaine, N., Wallace, P.T. & Chapront, J., 2003, ** Astron.Astrophys., 412, 567 ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M., ** Francou, G. & Laskar, J., Astron.Astrophys., 1994, 282, 663 ** ** Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M., 1999, ** Astron.Astrophys.Supp.Ser. 135, 111 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** */ void iauXys00a(double date1, double date2, double *x, double *y, double *s) /* ** - - - - - - - - - - ** i a u X y s 0 0 a ** - - - - - - - - - - ** ** For a given TT date, compute the X,Y coordinates of the Celestial ** Intermediate Pole and the CIO locator s, using the IAU 2000A ** precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** x,y double Celestial Intermediate Pole (Note 2) ** s double the CIO locator s (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y ** components of the unit vector in the Geocentric Celestial ** Reference System. ** ** 3) The CIO locator s (in radians) positions the Celestial ** Intermediate Origin on the equator of the CIP. ** ** 4) A faster, but slightly less accurate result (about 1 mas for ** X,Y), can be obtained by using instead the iauXys00b function. ** ** Called: ** iauPnm00a classical NPB matrix, IAU 2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS00 the CIO locator s, given X,Y, IAU 2000A ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauXys00b(double date1, double date2, double *x, double *y, double *s) /* ** - - - - - - - - - - ** i a u X y s 0 0 b ** - - - - - - - - - - ** ** For a given TT date, compute the X,Y coordinates of the Celestial ** Intermediate Pole and the CIO locator s, using the IAU 2000B ** precession-nutation model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** x,y double Celestial Intermediate Pole (Note 2) ** s double the CIO locator s (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y ** components of the unit vector in the Geocentric Celestial ** Reference System. ** ** 3) The CIO locator s (in radians) positions the Celestial ** Intermediate Origin on the equator of the CIP. ** ** 4) The present function is faster, but slightly less accurate (about ** 1 mas in X,Y), than the iauXys00a function. ** ** Called: ** iauPnm00b classical NPB matrix, IAU 2000B ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS00 the CIO locator s, given X,Y, IAU 2000A ** ** Reference: ** ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), ** IERS Technical Note No. 32, BKG (2004) ** */ void iauXys06a(double date1, double date2, double *x, double *y, double *s) /* ** - - - - - - - - - - ** i a u X y s 0 6 a ** - - - - - - - - - - ** ** For a given TT date, compute the X,Y coordinates of the Celestial ** Intermediate Pole and the CIO locator s, using the IAU 2006 ** precession and IAU 2000A nutation models. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** x,y double Celestial Intermediate Pole (Note 2) ** s double the CIO locator s (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The Celestial Intermediate Pole coordinates are the x,y components ** of the unit vector in the Geocentric Celestial Reference System. ** ** 3) The CIO locator s (in radians) positions the Celestial ** Intermediate Origin on the equator of the CIP. ** ** 4) Series-based solutions for generating X and Y are also available: ** see Capitaine & Wallace (2006) and iauXy06. ** ** Called: ** iauPnm06a classical NPB matrix, IAU 2006/2000A ** iauBpn2xy extract CIP X,Y coordinates from NPB matrix ** iauS06 the CIO locator s, given X,Y, IAU 2006 ** ** References: ** ** Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 ** ** Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 ** */ void iauZp(double p[3]) /* ** - - - - - - ** i a u Z p ** - - - - - - ** ** Zero a p-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Returned: ** p double[3] p-vector ** */ void iauZpv(double pv[2][3]) /* ** - - - - - - - ** i a u Z p v ** - - - - - - - ** ** Zero a pv-vector. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Returned: ** pv double[2][3] pv-vector ** ** Called: ** iauZp zero p-vector ** */ void iauZr(double r[3][3]) /* ** - - - - - - ** i a u Z r ** - - - - - - ** ** Initialize an r-matrix to the null matrix. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Returned: ** r double[3][3] r-matrix ** */ copyr.lis 2015 January 5 COPYRIGHT NOTICE Text equivalent to the following appears at the end of every SOFA routine. (There are small formatting differences between the Fortran and C versions.) *+---------------------------------------------------------------------- * * Copyright (C) 2016 * Standards Of Fundamental Astronomy Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND * CONDITIONS WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Board ("SOFA"). * * 2. Permission is granted to anyone to use the SOFA software for any * purpose, including commercial applications, free of charge and * without payment of royalties, subject to the conditions and * restrictions listed below. * * 3. You (the user) may copy and distribute SOFA source code to others, * and use and adapt its code and algorithms in your own software, * on a world-wide, royalty-free basis. That portion of your * distribution that does not consist of intact and unchanged copies * of SOFA source code files is a "derived work" that must comply * with the following requirements: * * a) Your work shall be marked or carry a statement that it * (i) uses routines and computations derived by you from * software provided by SOFA under license to you; and * (ii) does not itself constitute software provided by and/or * endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon, contains and/or differs * from the original SOFA software. * * c) The names of all routines in your derived work shall not * include the prefix "iau" or "sofa" or trivial modifications * thereof such as changes of case. * * d) The origin of the SOFA components of your derived work must * not be misrepresented; you must not claim that you wrote the * original software, nor file a patent application for SOFA * software or algorithms embedded in the SOFA software. * * e) These requirements must be reproduced intact in any source * distribution and shall apply to anyone to whom you have * granted a further right to modify the source code of your * derived work. * * Note that, as originally distributed, the SOFA software is * intended to be a definitive implementation of the IAU standards, * and consequently third-party modifications are discouraged. All * variations, no matter how minor, must be explicitly marked as * such, as explained above. * * 4. You shall not cause the SOFA software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or * by inappropriate modification. * * 5. The SOFA software is provided "as is" and SOFA makes no warranty * as to its use or performance. SOFA does not and cannot warrant * the performance or results which the user may obtain by using the * SOFA software. SOFA makes no warranties, express or implied, as * to non-infringement of third party rights, merchantability, or * fitness for any particular purpose. In no event will SOFA be * liable to the user for any consequential, incidental, or special * damages, including any lost profits or lost savings, even if a * SOFA representative has been advised of such damages, or for any * claim by any third party. * * 6. The provision of any version of the SOFA software under the terms * and conditions specified herein does not imply that future * versions will also be made available under the same terms and * conditions. * * In any published work or commercial product which uses the SOFA * software directly, acknowledgement (see www.iausofa.org) is * appreciated. * * Correspondence concerning SOFA software should be addressed as * follows: * * By email: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- consts.lis 2008 September 30 SOFA Fortran constants ---------------------- These must be used exactly as presented below. * Pi DOUBLE PRECISION DPI PARAMETER ( DPI = 3.141592653589793238462643D0 ) * 2Pi DOUBLE PRECISION D2PI PARAMETER ( D2PI = 6.283185307179586476925287D0 ) * Radians to hours DOUBLE PRECISION DR2H PARAMETER ( DR2H = 3.819718634205488058453210D0 ) * Radians to seconds DOUBLE PRECISION DR2S PARAMETER ( DR2S = 13750.98708313975701043156D0 ) * Radians to degrees DOUBLE PRECISION DR2D PARAMETER ( DR2D = 57.29577951308232087679815D0 ) * Radians to arc seconds DOUBLE PRECISION DR2AS PARAMETER ( DR2AS = 206264.8062470963551564734D0 ) * Hours to radians DOUBLE PRECISION DH2R PARAMETER ( DH2R = 0.2617993877991494365385536D0 ) * Seconds to radians DOUBLE PRECISION DS2R PARAMETER ( DS2R = 7.272205216643039903848712D-5 ) * Degrees to radians DOUBLE PRECISION DD2R PARAMETER ( DD2R = 1.745329251994329576923691D-2 ) * Arc seconds to radians DOUBLE PRECISION DAS2R PARAMETER ( DAS2R = 4.848136811095359935899141D-6 ) SOFA C constants ---------------- The constants used by the C version of SOFA are defined in the header file sofam.h. #ifndef SOFAHDEF #define SOFAHDEF /* ** - - - - - - - ** s o f a . h ** - - - - - - - ** ** Prototype function declarations for SOFA library. ** ** This file is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** This revision: 2016 March 10 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ #include "sofam.h" #include "math.h" #ifdef __cplusplus extern "C" { #endif /* Astronomy/Calendars */ int iauCal2jd(int iy, int im, int id, double *djm0, double *djm); double iauEpb(double dj1, double dj2); void iauEpb2jd(double epb, double *djm0, double *djm); double iauEpj(double dj1, double dj2); void iauEpj2jd(double epj, double *djm0, double *djm); int iauJd2cal(double dj1, double dj2, int *iy, int *im, int *id, double *fd); int iauJdcalf(int ndp, double dj1, double dj2, int iymdf[4]); /* Astronomy/Astrometry */ void iauAb(double pnat[3], double v[3], double s, double bm1, double ppr[3]); void iauApcg(double date1, double date2, double ebpv[2][3], double ehp[3], iauASTROM *astrom); void iauApcg13(double date1, double date2, iauASTROM *astrom); void iauApci(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, iauASTROM *astrom); void iauApci13(double date1, double date2, iauASTROM *astrom, double *eo); void iauApco(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, double theta, double elong, double phi, double hm, double xp, double yp, double sp, double refa, double refb, iauASTROM *astrom); int iauApco13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom, double *eo); void iauApcs(double date1, double date2, double pv[2][3], double ebpv[2][3], double ehp[3], iauASTROM *astrom); void iauApcs13(double date1, double date2, double pv[2][3], iauASTROM *astrom); void iauAper(double theta, iauASTROM *astrom); void iauAper13(double ut11, double ut12, iauASTROM *astrom); void iauApio(double sp, double theta, double elong, double phi, double hm, double xp, double yp, double refa, double refb, iauASTROM *astrom); int iauApio13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom); void iauAtci13(double rc, double dc, double pr, double pd, double px, double rv, double date1, double date2, double *ri, double *di, double *eo); void iauAtciq(double rc, double dc, double pr, double pd, double px, double rv, iauASTROM *astrom, double *ri, double *di); void iauAtciqn(double rc, double dc, double pr, double pd, double px, double rv, iauASTROM *astrom, int n, iauLDBODY b[], double *ri, double *di); void iauAtciqz(double rc, double dc, iauASTROM *astrom, double *ri, double *di); int iauAtco13(double rc, double dc, double pr, double pd, double px, double rv, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *aob, double *zob, double *hob, double *dob, double *rob, double *eo); void iauAtic13(double ri, double di, double date1, double date2, double *rc, double *dc, double *eo); void iauAticq(double ri, double di, iauASTROM *astrom, double *rc, double *dc); void iauAticqn(double ri, double di, iauASTROM *astrom, int n, iauLDBODY b[], double *rc, double *dc); int iauAtio13(double ri, double di, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *aob, double *zob, double *hob, double *dob, double *rob); void iauAtioq(double ri, double di, iauASTROM *astrom, double *aob, double *zob, double *hob, double *dob, double *rob); int iauAtoc13(const char *type, double ob1, double ob2, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *rc, double *dc); int iauAtoi13(const char *type, double ob1, double ob2, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *ri, double *di); void iauAtoiq(const char *type, double ob1, double ob2, iauASTROM *astrom, double *ri, double *di); void iauLd(double bm, double p[3], double q[3], double e[3], double em, double dlim, double p1[3]); void iauLdn(int n, iauLDBODY b[], double ob[3], double sc[3], double sn[3]); void iauLdsun(double p[3], double e[3], double em, double p1[3]); void iauPmpx(double rc, double dc, double pr, double pd, double px, double rv, double pmt, double pob[3], double pco[3]); int iauPmsafe(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2); void iauPvtob(double elong, double phi, double height, double xp, double yp, double sp, double theta, double pv[2][3]); void iauRefco(double phpa, double tc, double rh, double wl, double *refa, double *refb); /* Astronomy/Ephemerides */ int iauEpv00(double date1, double date2, double pvh[2][3], double pvb[2][3]); int iauPlan94(double date1, double date2, int np, double pv[2][3]); /* Astronomy/FundamentalArgs */ double iauFad03(double t); double iauFae03(double t); double iauFaf03(double t); double iauFaju03(double t); double iauFal03(double t); double iauFalp03(double t); double iauFama03(double t); double iauFame03(double t); double iauFane03(double t); double iauFaom03(double t); double iauFapa03(double t); double iauFasa03(double t); double iauFaur03(double t); double iauFave03(double t); /* Astronomy/PrecNutPolar */ void iauBi00(double *dpsibi, double *depsbi, double *dra); void iauBp00(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]); void iauBp06(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]); void iauBpn2xy(double rbpn[3][3], double *x, double *y); void iauC2i00a(double date1, double date2, double rc2i[3][3]); void iauC2i00b(double date1, double date2, double rc2i[3][3]); void iauC2i06a(double date1, double date2, double rc2i[3][3]); void iauC2ibpn(double date1, double date2, double rbpn[3][3], double rc2i[3][3]); void iauC2ixy(double date1, double date2, double x, double y, double rc2i[3][3]); void iauC2ixys(double x, double y, double s, double rc2i[3][3]); void iauC2t00a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]); void iauC2t00b(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]); void iauC2t06a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]); void iauC2tcio(double rc2i[3][3], double era, double rpom[3][3], double rc2t[3][3]); void iauC2teqx(double rbpn[3][3], double gst, double rpom[3][3], double rc2t[3][3]); void iauC2tpe(double tta, double ttb, double uta, double utb, double dpsi, double deps, double xp, double yp, double rc2t[3][3]); void iauC2txy(double tta, double ttb, double uta, double utb, double x, double y, double xp, double yp, double rc2t[3][3]); double iauEo06a(double date1, double date2); double iauEors(double rnpb[3][3], double s); void iauFw2m(double gamb, double phib, double psi, double eps, double r[3][3]); void iauFw2xy(double gamb, double phib, double psi, double eps, double *x, double *y); void iauLtp(double epj, double rp[3][3]); void iauLtpb(double epj, double rpb[3][3]); void iauLtpecl(double epj, double vec[3]); void iauLtpequ(double epj, double veq[3]); void iauNum00a(double date1, double date2, double rmatn[3][3]); void iauNum00b(double date1, double date2, double rmatn[3][3]); void iauNum06a(double date1, double date2, double rmatn[3][3]); void iauNumat(double epsa, double dpsi, double deps, double rmatn[3][3]); void iauNut00a(double date1, double date2, double *dpsi, double *deps); void iauNut00b(double date1, double date2, double *dpsi, double *deps); void iauNut06a(double date1, double date2, double *dpsi, double *deps); void iauNut80(double date1, double date2, double *dpsi, double *deps); void iauNutm80(double date1, double date2, double rmatn[3][3]); double iauObl06(double date1, double date2); double iauObl80(double date1, double date2); void iauP06e(double date1, double date2, double *eps0, double *psia, double *oma, double *bpa, double *bqa, double *pia, double *bpia, double *epsa, double *chia, double *za, double *zetaa, double *thetaa, double *pa, double *gam, double *phi, double *psi); void iauPb06(double date1, double date2, double *bzeta, double *bz, double *btheta); void iauPfw06(double date1, double date2, double *gamb, double *phib, double *psib, double *epsa); void iauPmat00(double date1, double date2, double rbp[3][3]); void iauPmat06(double date1, double date2, double rbp[3][3]); void iauPmat76(double date1, double date2, double rmatp[3][3]); void iauPn00(double date1, double date2, double dpsi, double deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]); void iauPn00a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]); void iauPn00b(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]); void iauPn06(double date1, double date2, double dpsi, double deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]); void iauPn06a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]); void iauPnm00a(double date1, double date2, double rbpn[3][3]); void iauPnm00b(double date1, double date2, double rbpn[3][3]); void iauPnm06a(double date1, double date2, double rnpb[3][3]); void iauPnm80(double date1, double date2, double rmatpn[3][3]); void iauPom00(double xp, double yp, double sp, double rpom[3][3]); void iauPr00(double date1, double date2, double *dpsipr, double *depspr); void iauPrec76(double date01, double date02, double date11, double date12, double *zeta, double *z, double *theta); double iauS00(double date1, double date2, double x, double y); double iauS00a(double date1, double date2); double iauS00b(double date1, double date2); double iauS06(double date1, double date2, double x, double y); double iauS06a(double date1, double date2); double iauSp00(double date1, double date2); void iauXy06(double date1, double date2, double *x, double *y); void iauXys00a(double date1, double date2, double *x, double *y, double *s); void iauXys00b(double date1, double date2, double *x, double *y, double *s); void iauXys06a(double date1, double date2, double *x, double *y, double *s); /* Astronomy/RotationAndTime */ double iauEe00(double date1, double date2, double epsa, double dpsi); double iauEe00a(double date1, double date2); double iauEe00b(double date1, double date2); double iauEe06a(double date1, double date2); double iauEect00(double date1, double date2); double iauEqeq94(double date1, double date2); double iauEra00(double dj1, double dj2); double iauGmst00(double uta, double utb, double tta, double ttb); double iauGmst06(double uta, double utb, double tta, double ttb); double iauGmst82(double dj1, double dj2); double iauGst00a(double uta, double utb, double tta, double ttb); double iauGst00b(double uta, double utb); double iauGst06(double uta, double utb, double tta, double ttb, double rnpb[3][3]); double iauGst06a(double uta, double utb, double tta, double ttb); double iauGst94(double uta, double utb); /* Astronomy/SpaceMotion */ int iauPvstar(double pv[2][3], double *ra, double *dec, double *pmr, double *pmd, double *px, double *rv); int iauStarpv(double ra, double dec, double pmr, double pmd, double px, double rv, double pv[2][3]); /* Astronomy/StarCatalogs */ void iauFk52h(double r5, double d5, double dr5, double dd5, double px5, double rv5, double *rh, double *dh, double *drh, double *ddh, double *pxh, double *rvh); void iauFk5hip(double r5h[3][3], double s5h[3]); void iauFk5hz(double r5, double d5, double date1, double date2, double *rh, double *dh); void iauH2fk5(double rh, double dh, double drh, double ddh, double pxh, double rvh, double *r5, double *d5, double *dr5, double *dd5, double *px5, double *rv5); void iauHfk5z(double rh, double dh, double date1, double date2, double *r5, double *d5, double *dr5, double *dd5); int iauStarpm(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2); /* Astronomy/EclipticCoordinates */ void iauEceq06(double date1, double date2, double dl, double db, double *dr, double *dd); void iauEcm06(double date1, double date2, double rm[3][3]); void iauEqec06(double date1, double date2, double dr, double dd, double *dl, double *db); void iauLteceq(double epj, double dl, double db, double *dr, double *dd); void iauLtecm(double epj, double rm[3][3]); void iauLteqec(double epj, double dr, double dd, double *dl, double *db); /* Astronomy/GalacticCoordinates */ void iauG2icrs(double dl, double db, double *dr, double *dd); void iauIcrs2g(double dr, double dd, double *dl, double *db); /* Astronomy/GeodeticGeocentric */ int iauEform(int n, double *a, double *f); int iauGc2gd(int n, double xyz[3], double *elong, double *phi, double *height); int iauGc2gde(double a, double f, double xyz[3], double *elong, double *phi, double *height); int iauGd2gc(int n, double elong, double phi, double height, double xyz[3]); int iauGd2gce(double a, double f, double elong, double phi, double height, double xyz[3]); /* Astronomy/Timescales */ int iauD2dtf(const char *scale, int ndp, double d1, double d2, int *iy, int *im, int *id, int ihmsf[4]); int iauDat(int iy, int im, int id, double fd, double *deltat); double iauDtdb(double date1, double date2, double ut, double elong, double u, double v); int iauDtf2d(const char *scale, int iy, int im, int id, int ihr, int imn, double sec, double *d1, double *d2); int iauTaitt(double tai1, double tai2, double *tt1, double *tt2); int iauTaiut1(double tai1, double tai2, double dta, double *ut11, double *ut12); int iauTaiutc(double tai1, double tai2, double *utc1, double *utc2); int iauTcbtdb(double tcb1, double tcb2, double *tdb1, double *tdb2); int iauTcgtt(double tcg1, double tcg2, double *tt1, double *tt2); int iauTdbtcb(double tdb1, double tdb2, double *tcb1, double *tcb2); int iauTdbtt(double tdb1, double tdb2, double dtr, double *tt1, double *tt2); int iauTttai(double tt1, double tt2, double *tai1, double *tai2); int iauTttcg(double tt1, double tt2, double *tcg1, double *tcg2); int iauTttdb(double tt1, double tt2, double dtr, double *tdb1, double *tdb2); int iauTtut1(double tt1, double tt2, double dt, double *ut11, double *ut12); int iauUt1tai(double ut11, double ut12, double dta, double *tai1, double *tai2); int iauUt1tt(double ut11, double ut12, double dt, double *tt1, double *tt2); int iauUt1utc(double ut11, double ut12, double dut1, double *utc1, double *utc2); int iauUtctai(double utc1, double utc2, double *tai1, double *tai2); int iauUtcut1(double utc1, double utc2, double dut1, double *ut11, double *ut12); /* VectorMatrix/AngleOps */ void iauA2af(int ndp, double angle, char *sign, int idmsf[4]); void iauA2tf(int ndp, double angle, char *sign, int ihmsf[4]); int iauAf2a(char s, int ideg, int iamin, double asec, double *rad); double iauAnp(double a); double iauAnpm(double a); void iauD2tf(int ndp, double days, char *sign, int ihmsf[4]); int iauTf2a(char s, int ihour, int imin, double sec, double *rad); int iauTf2d(char s, int ihour, int imin, double sec, double *days); /* VectorMatrix/BuildRotations */ void iauRx(double phi, double r[3][3]); void iauRy(double theta, double r[3][3]); void iauRz(double psi, double r[3][3]); /* VectorMatrix/CopyExtendExtract */ void iauCp(double p[3], double c[3]); void iauCpv(double pv[2][3], double c[2][3]); void iauCr(double r[3][3], double c[3][3]); void iauP2pv(double p[3], double pv[2][3]); void iauPv2p(double pv[2][3], double p[3]); /* VectorMatrix/Initialization */ void iauIr(double r[3][3]); void iauZp(double p[3]); void iauZpv(double pv[2][3]); void iauZr(double r[3][3]); /* VectorMatrix/MatrixOps */ void iauRxr(double a[3][3], double b[3][3], double atb[3][3]); void iauTr(double r[3][3], double rt[3][3]); /* VectorMatrix/MatrixVectorProducts */ void iauRxp(double r[3][3], double p[3], double rp[3]); void iauRxpv(double r[3][3], double pv[2][3], double rpv[2][3]); void iauTrxp(double r[3][3], double p[3], double trp[3]); void iauTrxpv(double r[3][3], double pv[2][3], double trpv[2][3]); /* VectorMatrix/RotationVectors */ void iauRm2v(double r[3][3], double w[3]); void iauRv2m(double w[3], double r[3][3]); /* VectorMatrix/SeparationAndAngle */ double iauPap(double a[3], double b[3]); double iauPas(double al, double ap, double bl, double bp); double iauSepp(double a[3], double b[3]); double iauSeps(double al, double ap, double bl, double bp); /* VectorMatrix/SphericalCartesian */ void iauC2s(double p[3], double *theta, double *phi); void iauP2s(double p[3], double *theta, double *phi, double *r); void iauPv2s(double pv[2][3], double *theta, double *phi, double *r, double *td, double *pd, double *rd); void iauS2c(double theta, double phi, double c[3]); void iauS2p(double theta, double phi, double r, double p[3]); void iauS2pv(double theta, double phi, double r, double td, double pd, double rd, double pv[2][3]); /* VectorMatrix/VectorOps */ double iauPdp(double a[3], double b[3]); double iauPm(double p[3]); void iauPmp(double a[3], double b[3], double amb[3]); void iauPn(double p[3], double *r, double u[3]); void iauPpp(double a[3], double b[3], double apb[3]); void iauPpsp(double a[3], double s, double b[3], double apsb[3]); void iauPvdpv(double a[2][3], double b[2][3], double adb[2]); void iauPvm(double pv[2][3], double *r, double *s); void iauPvmpv(double a[2][3], double b[2][3], double amb[2][3]); void iauPvppv(double a[2][3], double b[2][3], double apb[2][3]); void iauPvu(double dt, double pv[2][3], double upv[2][3]); void iauPvup(double dt, double pv[2][3], double p[3]); void iauPvxpv(double a[2][3], double b[2][3], double axb[2][3]); void iauPxp(double a[3], double b[3], double axb[3]); void iauS2xpv(double s1, double s2, double pv[2][3], double spv[2][3]); void iauSxp(double s, double p[3], double sp[3]); void iauSxpv(double s, double pv[2][3], double spv[2][3]); #ifdef __cplusplus } #endif #endif /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ #ifndef SOFAMHDEF #define SOFAMHDEF /* ** - - - - - - - - ** s o f a m . h ** - - - - - - - - ** ** Macros used by SOFA library. ** ** This file is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Please note that the constants defined below are to be used only in ** the context of the SOFA software, and have no other official IAU ** status. In addition, self consistency is not guaranteed. ** ** This revision: 2013 August 27 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ /* Star-independent astrometry parameters */ typedef struct { double pmt; /* PM time interval (SSB, Julian years) */ double eb[3]; /* SSB to observer (vector, au) */ double eh[3]; /* Sun to observer (unit vector) */ double em; /* distance from Sun to observer (au) */ double v[3]; /* barycentric observer velocity (vector, c) */ double bm1; /* sqrt(1-|v|^2): reciprocal of Lorenz factor */ double bpn[3][3]; /* bias-precession-nutation matrix */ double along; /* longitude + s' + dERA(DUT) (radians) */ double phi; /* geodetic latitude (radians) */ double xpl; /* polar motion xp wrt local meridian (radians) */ double ypl; /* polar motion yp wrt local meridian (radians) */ double sphi; /* sine of geodetic latitude */ double cphi; /* cosine of geodetic latitude */ double diurab; /* magnitude of diurnal aberration vector */ double eral; /* "local" Earth rotation angle (radians) */ double refa; /* refraction constant A (radians) */ double refb; /* refraction constant B (radians) */ } iauASTROM; /* (Vectors eb, eh, em and v are all with respect to BCRS axes.) */ /* Body parameters for light deflection */ typedef struct { double bm; /* mass of the body (solar masses) */ double dl; /* deflection limiter (radians^2/2) */ double pv[2][3]; /* barycentric PV of the body (au, au/day) */ } iauLDBODY; /* Pi */ #define DPI (3.141592653589793238462643) /* 2Pi */ #define D2PI (6.283185307179586476925287) /* Radians to degrees */ #define DR2D (57.29577951308232087679815) /* Degrees to radians */ #define DD2R (1.745329251994329576923691e-2) /* Radians to arcseconds */ #define DR2AS (206264.8062470963551564734) /* Arcseconds to radians */ #define DAS2R (4.848136811095359935899141e-6) /* Seconds of time to radians */ #define DS2R (7.272205216643039903848712e-5) /* Arcseconds in a full circle */ #define TURNAS (1296000.0) /* Milliarcseconds to radians */ #define DMAS2R (DAS2R / 1e3) /* Length of tropical year B1900 (days) */ #define DTY (365.242198781) /* Seconds per day. */ #define DAYSEC (86400.0) /* Days per Julian year */ #define DJY (365.25) /* Days per Julian century */ #define DJC (36525.0) /* Days per Julian millennium */ #define DJM (365250.0) /* Reference epoch (J2000.0), Julian Date */ #define DJ00 (2451545.0) /* Julian Date of Modified Julian Date zero */ #define DJM0 (2400000.5) /* Reference epoch (J2000.0), Modified Julian Date */ #define DJM00 (51544.5) /* 1977 Jan 1.0 as MJD */ #define DJM77 (43144.0) /* TT minus TAI (s) */ #define TTMTAI (32.184) /* Astronomical unit (m) */ #define DAU (149597870e3) /* Speed of light (m/s) */ #define CMPS 299792458.0 /* Light time for 1 au (s) */ #define AULT 499.004782 /* Speed of light (AU per day) */ #define DC (DAYSEC / AULT) /* L_G = 1 - d(TT)/d(TCG) */ #define ELG (6.969290134e-10) /* L_B = 1 - d(TDB)/d(TCB), and TDB (s) at TAI 1977/1/1.0 */ #define ELB (1.550519768e-8) #define TDB0 (-6.55e-5) /* Schwarzschild radius of the Sun (au) */ /* = 2 * 1.32712440041e20 / (2.99792458e8)^2 / 1.49597870700e11 */ #define SRS 1.97412574336e-8 /* dint(A) - truncate to nearest whole number towards zero (double) */ #define dint(A) ((A)<0.0?ceil(A):floor(A)) /* dnint(A) - round to nearest whole number (double) */ #define dnint(A) ((A)<0.0?ceil((A)-0.5):floor((A)+0.5)) /* dsign(A,B) - magnitude of A with sign of B (double) */ #define dsign(A,B) ((B)<0.0?-fabs(A):fabs(A)) /* max(A,B) - larger (most +ve) of two numbers (generic) */ #define gmax(A,B) (((A)>(B))?(A):(B)) /* min(A,B) - smaller (least +ve) of two numbers (generic) */ #define gmin(A,B) (((A)<(B))?(A):(B)) /* Reference ellipsoids */ #define WGS84 1 #define GRS80 2 #define WGS72 3 #endif /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ board.lis 2015 December 6 IAU STANDARDS OF FUNDAMENTAL ASTRONOMY BOARD Current Membership John Bangert - United States Naval Observatory, retired Steven Bell - Her Majesty's Nautical Almanac Office Nicole Capitaine - Paris Observatory William Folkner - Jet Propulsion Laboratory Mickal Gastineau - Paris Observatory, IMCCE Catherine Hohenkerk - Her Majesty's Nautical Almanac Office (Chair) Li Jinling - Shanghai Astronomical Observatory Brian Luzum - United States Naval Observatory (IERS) Zinovy Malkin - Pulkovo Observatory, St Petersburg Jeffrey Percival - University of Wisconsin Wendy Puatua - United States Naval Observatory Scott Ransom - National Radio Astronomy Observatory Patrick Wallace - RAL Space, retired Past Members Wim Brouw University of Groningen Mark Calabretta Australia Telescope National Facility Anne-Marie Gontier Paris Observatory George Hobbs Australia Telescope National Facility George Kaplan United States Naval Observatory Dennis McCarthy United States Naval Observatory Skip Newhall Jet Propulsion Laboratory Jin Wen-Jing Shanghai Observatory The e-mail for the Board chair is Catherine.Hohenkerk@ukho.gov.uk sofa/20160503_c/c/doc/sofa_lib.lis0000644000113000011300000007354113027221063015440 0ustar bellsbellssofa_lib.lis 2016 March 10 ---------------------- SOFA Astronomy Library ---------------------- PREFACE The routines described here comprise the SOFA astronomy library. Their general appearance and coding style conforms to conventions agreed by the SOFA Board, and their functions, names and algorithms have been ratified by the Board. Procedures for soliciting and agreeing additions to the library are still evolving. PROGRAMMING LANGUAGES The SOFA routines are available in two programming languages at present: Fortran 77 and ANSI C. Except for a single obsolete Fortran routine, which has no C equivalent, there is a one-to-one relationship between the two language versions. The naming convention is such that a SOFA routine referred to generically as "EXAMPL" exists as a Fortran subprogram iau_EXAMPL and a C function iauExampl. The calls for the two versions are very similar, with the same arguments in the same order. In a few cases, the C equivalent of a Fortran SUBROUTINE subprogram uses a return value rather than an argument. GENERAL PRINCIPLES The principal function of the SOFA Astronomy Library is to provide definitive algorithms. A secondary function is to provide software suitable for convenient direct use by writers of astronomical applications. The astronomy routines call on the SOFA vector/matrix library routines, which are separately listed. The routines are designed to exploit the full floating-point accuracy of the machines on which they run, and not to rely on compiler optimizations. Within these constraints, the intention is that the code corresponds to the published formulation (if any). Dates are always Julian Dates (except in calendar conversion routines) and are expressed as two double precision numbers which sum to the required value. A distinction is made between routines that implement IAU-approved models and those that use those models to create other results. The former are referred to as "canonical models" in the preamble comments; the latter are described as "support routines". Using the library requires knowledge of positional astronomy and time-scales. These topics are covered in "Explanatory Supplement to the Astronomical Almanac", 3rd Edition, Sean E. Urban & P. Kenneth Seidelmann (eds.), University Science Books, 2013. Recent developments are documented in the scientific journals, and references to the relevant papers are given in the SOFA code as required. The IERS Conventions are also an essential reference. The routines concerned with Earth attitude (precession-nutation etc.) are described in the SOFA document sofa_pn.pdf. Those concerned with transformations between different time scales are described in sofa_ts_f.pdf (Fortran) and sofa_ts_c.pdf (C). Those concerned with astrometric transformations are described in sofa_ast_f.pdf (Fortran) and sofa_ast_c (C). ROUTINES Calendars CAL2JD Gregorian calendar to Julian Day number EPB Julian Date to Besselian Epoch EPB2JD Besselian Epoch to Julian Date EPJ Julian Date to Julian Epoch EPJ2JD Julian Epoch to Julian Date JD2CAL Julian Date to Gregorian year, month, day, fraction JDCALF Julian Date to Gregorian date for formatted output Astrometry AB apply stellar aberration APCG prepare for ICRS <-> GCRS, geocentric, special APCG13 prepare for ICRS <-> GCRS, geocentric APCI prepare for ICRS <-> CIRS, terrestrial, special APCI13 prepare for ICRS <-> CIRS, terrestrial APCO prepare for ICRS <-> observed, terrestrial, special APCO13 prepare for ICRS <-> observed, terrestrial APCS prepare for ICRS <-> CIRS, space, special APCS13 prepare for ICRS <-> CIRS, space APER insert ERA into context APER13 update context for Earth rotation APIO prepare for CIRS <-> observed, terrestrial, special APIO13 prepare for CIRS <-> observed, terrestrial ATCI13 catalog -> CIRS ATCIQ quick ICRS -> CIRS ATCIQN quick ICRS -> CIRS, multiple deflections ATCIQZ quick astrometric ICRS -> CIRS ATCO13 ICRS -> observed ATIC13 CIRS -> ICRS ATICQ quick CIRS -> ICRS ATCIQN quick CIRS -> ICRS, multiple deflections ATIO13 CIRS -> observed ATIOQ quick CIRS -> observed ATOC13 observed -> astrometric ICRS ATOI13 observed -> CIRS ATOIQ quick observed -> CIRS LD light deflection by a single solar-system body LDN light deflection by multiple solar-system bodies LDSUN light deflection by the Sun PMPX apply proper motion and parallax PMSAFE apply proper motion, with zero-parallax precautions PVTOB observatory position and velocity PVSTAR space motion pv-vector to star catalog data REFCO refraction constants STARPM apply proper motion STARPV star catalog data to space motion pv-vector Time scales D2DTF format 2-part JD for output DAT Delta(AT) (=TAI-UTC) for a given UTC date DTDB TDB-TT DTF2D encode time and date fields into 2-part JD TAITT TAI to TT TAIUT1 TAI to UT1 TAIUTC TAI to UTC TCBTDB TCB to TDB TCGTT TCG to TT TDBTCB TDB to TCB TDBTT TDB to TT TTTAI TT to TAI TTTCG TT to TCG TTTDB TT to TDB TTUT1 TT to UT1 UT1TAI UT1 to TAI UT1TT UT1 to TT UT1UTC UT1 to UTC UTCTAI UTC to TAI UTCUT1 UTC to UT1 Earth rotation angle and sidereal time EE00 equation of the equinoxes, IAU 2000 EE00A equation of the equinoxes, IAU 2000A EE00B equation of the equinoxes, IAU 2000B EE06A equation of the equinoxes, IAU 2006/2000A EECT00 equation of the equinoxes complementary terms, IAU 2000 EQEQ94 equation of the equinoxes, IAU 1994 ERA00 Earth rotation angle, IAU 2000 GMST00 Greenwich mean sidereal time, IAU 2000 GMST06 Greenwich mean sidereal time, IAU 2006 GMST82 Greenwich mean sidereal time, IAU 1982 GST00A Greenwich apparent sidereal time, IAU 2000A GST00B Greenwich apparent sidereal time, IAU 2000B GST06 Greenwich apparent ST, IAU 2006, given NPB matrix GST06A Greenwich apparent sidereal time, IAU 2006/2000A GST94 Greenwich apparent sidereal time, IAU 1994 Ephemerides (limited precision) EPV00 Earth position and velocity PLAN94 major-planet position and velocity Precession, nutation, polar motion BI00 frame bias components, IAU 2000 BP00 frame bias and precession matrices, IAU 2000 BP06 frame bias and precession matrices, IAU 2006 BPN2XY extract CIP X,Y coordinates from NPB matrix C2I00A celestial-to-intermediate matrix, IAU 2000A C2I00B celestial-to-intermediate matrix, IAU 2000B C2I06A celestial-to-intermediate matrix, IAU 2006/2000A C2IBPN celestial-to-intermediate matrix, given NPB matrix, IAU 2000 C2IXY celestial-to-intermediate matrix, given X,Y, IAU 2000 C2IXYS celestial-to-intermediate matrix, given X,Y and s C2T00A celestial-to-terrestrial matrix, IAU 2000A C2T00B celestial-to-terrestrial matrix, IAU 2000B C2T06A celestial-to-terrestrial matrix, IAU 2006/2000A C2TCIO form CIO-based celestial-to-terrestrial matrix C2TEQX form equinox-based celestial-to-terrestrial matrix C2TPE celestial-to-terrestrial matrix given nutation, IAU 2000 C2TXY celestial-to-terrestrial matrix given CIP, IAU 2000 EO06A equation of the origins, IAU 2006/2000A EORS equation of the origins, given NPB matrix and s FW2M Fukushima-Williams angles to r-matrix FW2XY Fukushima-Williams angles to X,Y LTP long-term precession matrix LTPB long-term precession matrix, including ICRS frame bias LTPECL long-term precession of the ecliptic LTPEQU long-term precession of the equator NUM00A nutation matrix, IAU 2000A NUM00B nutation matrix, IAU 2000B NUM06A nutation matrix, IAU 2006/2000A NUMAT form nutation matrix NUT00A nutation, IAU 2000A NUT00B nutation, IAU 2000B NUT06A nutation, IAU 2006/2000A NUT80 nutation, IAU 1980 NUTM80 nutation matrix, IAU 1980 OBL06 mean obliquity, IAU 2006 OBL80 mean obliquity, IAU 1980 PB06 zeta,z,theta precession angles, IAU 2006, including bias PFW06 bias-precession Fukushima-Williams angles, IAU 2006 PMAT00 precession matrix (including frame bias), IAU 2000 PMAT06 PB matrix, IAU 2006 PMAT76 precession matrix, IAU 1976 PN00 bias/precession/nutation results, IAU 2000 PN00A bias/precession/nutation, IAU 2000A PN00B bias/precession/nutation, IAU 2000B PN06 bias/precession/nutation results, IAU 2006 PN06A bias/precession/nutation results, IAU 2006/2000A PNM00A classical NPB matrix, IAU 2000A PNM00B classical NPB matrix, IAU 2000B PNM06A classical NPB matrix, IAU 2006/2000A PNM80 precession/nutation matrix, IAU 1976/1980 P06E precession angles, IAU 2006, equinox based POM00 polar motion matrix PR00 IAU 2000 precession adjustments PREC76 accumulated precession angles, IAU 1976 S00 the CIO locator s, given X,Y, IAU 2000A S00A the CIO locator s, IAU 2000A S00B the CIO locator s, IAU 2000B S06 the CIO locator s, given X,Y, IAU 2006 S06A the CIO locator s, IAU 2006/2000A SP00 the TIO locator s', IERS 2003 XY06 CIP, IAU 2006/2000A, from series XYS00A CIP and s, IAU 2000A XYS00B CIP and s, IAU 2000B XYS06A CIP and s, IAU 2006/2000A Fundamental arguments for nutation etc. FAD03 mean elongation of the Moon from the Sun FAE03 mean longitude of Earth FAF03 mean argument of the latitude of the Moon FAJU03 mean longitude of Jupiter FAL03 mean anomaly of the Moon FALP03 mean anomaly of the Sun FAMA03 mean longitude of Mars FAME03 mean longitude of Mercury FANE03 mean longitude of Neptune FAOM03 mean longitude of the Moon's ascending node FAPA03 general accumulated precession in longitude FASA03 mean longitude of Saturn FAUR03 mean longitude of Uranus FAVE03 mean longitude of Venus Star catalog conversions FK52H transform FK5 star data into the Hipparcos system FK5HIP FK5 to Hipparcos rotation and spin FK5HZ FK5 to Hipparcos assuming zero Hipparcos proper motion H2FK5 transform Hipparcos star data into the FK5 system HFK5Z Hipparcos to FK5 assuming zero Hipparcos proper motion Ecliptic coordinates ECEQ06 ecliptic to ICRS, IAU 2006 ECM06 rotation matrix, ICRS to ecliptic, IAU 2006 EQEC06 ICRS to ecliptic, IAU 2006 LTECEQ ecliptic to ICRS, long term LTECM rotation matrix, ICRS to ecliptic, long-term LTEQEC ICRS to ecliptic, long term Galactic coordinates G2ICRS transform IAU 1958 galactic coordinates to ICRS ICRS2G transform ICRS coordinates to IAU 1958 Galactic Geodetic/geocentric EFORM a,f for a nominated Earth reference ellipsoid GC2GD geocentric to geodetic for a nominated ellipsoid GC2GDE geocentric to geodetic given ellipsoid a,f GD2GC geodetic to geocentric for a nominated ellipsoid GD2GCE geodetic to geocentric given ellipsoid a,f Obsolete C2TCEO former name of C2TCIO CALLS: FORTRAN VERSION CALL iau_AB ( PNAT, V, S, BM1, PPR ) CALL iau_APCG ( DATE1, DATE2, EB, EH, ASTROM ) CALL iau_APCG13 ( DATE1, DATE2, ASTROM ) CALL iau_APCI ( DATE1, DATE2, EB, EH, X, Y, S, ASTROM ) CALL iau_APCI13 ( DATE1, DATE2, ASTROM, EO ) CALL iau_APCO ( DATE1, DATE2, EB, EH, X, Y, S, : THETA, ELONG, PHI, HM, XP, YP, SP, : REFA, REFB, ASTROM ) CALL iau_APCO13 ( UTC1, UTC2, DUT1, ELONG, PHI, HM, XP, YP, : PHPA, TC, RH, WL, ASTROM, EO, J ) CALL iau_APCS ( DATE1, DATE2, PV, EB, EH, ASTROM ) CALL iau_APCS13 ( DATE1, DATE2, PV, ASTROM ) CALL iau_APER ( THETA, ASTROM ) CALL iau_APER13 ( UT11, UT12, ASTROM ) CALL iau_APIO ( SP, THETA, ELONG, PHI, HM, XP, YP, : REFA, REFB, ASTROM ) CALL iau_APIO13 ( UTC1, UTC2, DUT1, ELONG, PHI, HM, XP, YP, : PHPA, TC, RH, WL, ASTROM, J ) CALL iau_ATCI13 ( RC, DC, PR, PD, PX, RV, DATE1, DATE2, RI, DI, EO ) CALL iau_ATCIQ ( RC, DC, PR, PD, PX, RV, ASTROM, RI, DI ) CALL iau_ATCIQN ( RC, DC, PR, PD, PX, RV, ASTROM, N, B, RI, DI ) CALL iau_ATCIQZ ( RC, DC, ASTROM, RI, DI ) CALL iau_ATCO13 ( RC, DC, PR, PD, PX, RV, UTC1, UTC2, DUT1, ELONG, : PHI, HM, XP, YP, PHPA, TC, RH, WL, : AOB, ZOB, HOB, DOB, ROB, EO, J ) CALL iau_ATIC13 ( RI, DI, DATE1, DATE2, RC, DC, EO ) CALL iau_ATICQ ( RI, DI, ASTROM, RC, DC ) CALL iau_ATCIQN ( RI, DI, ASTROM, N, B, RC, DC ) CALL iau_ATIO13 ( RI, DI, UTC1, UTC2, DUT1, ELONG, PHI, HM, XP, YP, PHPA, TC, RH, WL, AOB, ZOB, HOB, DOB, ROB, J ) CALL iau_ATIOQ ( RI, DI, ASTROM, AOB, ZOB, HOB, DOB, ROB ) CALL iau_ATOC13 ( TYPE, OB1, OB2, UTC1, UTC2, DUT1, : ELONG, PHI, HM, XP, YP, PHPA, TC, RH, WL, : RC, DC, J ) CALL iau_ATOI13 ( TYPE, OB1, OB2, UTC1, UTC2, DUT1, : ELONG, PHI, HM, XP, YP, PHPA, TC, RH, WL, : RI, DI, J ) CALL iau_ATOIQ ( TYPE, OB1, OB2, ASTROM, RI, DI ) CALL iau_BI00 ( DPSIBI, DEPSBI, DRA ) CALL iau_BP00 ( DATE1, DATE2, RB, RP, RBP ) CALL iau_BP06 ( DATE1, DATE2, RB, RP, RBP ) CALL iau_BPN2XY ( RBPN, X, Y ) CALL iau_C2I00A ( DATE1, DATE2, RC2I ) CALL iau_C2I00B ( DATE1, DATE2, RC2I ) CALL iau_C2I06A ( DATE1, DATE2, RC2I ) CALL iau_C2IBPN ( DATE1, DATE2, RBPN, RC2I ) CALL iau_C2IXY ( DATE1, DATE2, X, Y, RC2I ) CALL iau_C2IXYS ( X, Y, S, RC2I ) CALL iau_C2T00A ( TTA, TTB, UTA, UTB, XP, YP, RC2T ) CALL iau_C2T00B ( TTA, TTB, UTA, UTB, XP, YP, RC2T ) CALL iau_C2T06A ( TTA, TTB, UTA, UTB, XP, YP, RC2T ) CALL iau_C2TCEO ( RC2I, ERA, RPOM, RC2T ) CALL iau_C2TCIO ( RC2I, ERA, RPOM, RC2T ) CALL iau_C2TEQX ( RBPN, GST, RPOM, RC2T ) CALL iau_C2TPE ( TTA, TTB, UTA, UTB, DPSI, DEPS, XP, YP, RC2T ) CALL iau_C2TXY ( TTA, TTB, UTA, UTB, X, Y, XP, YP, RC2T ) CALL iau_CAL2JD ( IY, IM, ID, DJM0, DJM, J ) CALL iau_D2DTF ( SCALE, NDP, D1, D2, IY, IM, ID, IHMSF, J ) CALL iau_DAT ( IY, IM, ID, FD, DELTAT, J ) D = iau_DTDB ( DATE1, DATE2, UT, ELONG, U, V ) CALL iau_DTF2D ( SCALE, IY, IM, ID, IHR, IMN, SEC, D1, D2, J ) CALL iau_ECEQ06 ( DATE1, DATE2, DL, DB, DR, DD ) CALL iau_ECM06 ( DATE1, DATE2, RM ); D = iau_EE00 ( DATE1, DATE2, EPSA, DPSI ) D = iau_EE00A ( DATE1, DATE2 ) D = iau_EE00B ( DATE1, DATE2 ) D = iau_EE06A ( DATE1, DATE2 ) D = iau_EECT00 ( DATE1, DATE2 ) CALL iau_EFORM ( N, A, F, J ) D = iau_EO06A ( DATE1, DATE2 ) D = iau_EORS ( RNPB, S ) D = iau_EPB ( DJ1, DJ2 ) CALL iau_EPB2JD ( EPB, DJM0, DJM ) D = iau_EPJ ( DJ1, DJ2 ) CALL iau_EPJ2JD ( EPJ, DJM0, DJM ) CALL iau_EPV00 ( DJ1, DJ2, PVH, PVB, J ) CALL iau_EQEC06 ( DATE1, DATE2, DR, DD, DL, DB ) D = iau_EQEQ94 ( DATE1, DATE2 ) D = iau_ERA00 ( DJ1, DJ2 ) D = iau_FAD03 ( T ) D = iau_FAE03 ( T ) D = iau_FAF03 ( T ) D = iau_FAJU03 ( T ) D = iau_FAL03 ( T ) D = iau_FALP03 ( T ) D = iau_FAMA03 ( T ) D = iau_FAME03 ( T ) D = iau_FANE03 ( T ) D = iau_FAOM03 ( T ) D = iau_FAPA03 ( T ) D = iau_FASA03 ( T ) D = iau_FAUR03 ( T ) D = iau_FAVE03 ( T ) CALL iau_FK52H ( R5, D5, DR5, DD5, PX5, RV5, : RH, DH, DRH, DDH, PXH, RVH ) CALL iau_FK5HIP ( R5H, S5H ) CALL iau_FK5HZ ( R5, D5, DATE1, DATE2, RH, DH ) CALL iau_FW2M ( GAMB, PHIB, PSI, EPS, R ) CALL iau_FW2XY ( GAMB, PHIB, PSI, EPS, X, Y ) CALL iau_G2ICRS ( DL, DB, DR, DD ) CALL iau_GC2GD ( N, XYZ, ELONG, PHI, HEIGHT, J ) CALL iau_GC2GDE ( A, F, XYZ, ELONG, PHI, HEIGHT, J ) CALL iau_GD2GC ( N, ELONG, PHI, HEIGHT, XYZ, J ) CALL iau_GD2GCE ( A, F, ELONG, PHI, HEIGHT, XYZ, J ) D = iau_GMST00 ( UTA, UTB, TTA, TTB ) D = iau_GMST06 ( UTA, UTB, TTA, TTB ) D = iau_GMST82 ( UTA, UTB ) D = iau_GST00A ( UTA, UTB, TTA, TTB ) D = iau_GST00B ( UTA, UTB ) D = iau_GST06 ( UTA, UTB, TTA, TTB, RNPB ) D = iau_GST06A ( UTA, UTB, TTA, TTB ) D = iau_GST94 ( UTA, UTB ) CALL iau_H2FK5 ( RH, DH, DRH, DDH, PXH, RVH, : R5, D5, DR5, DD5, PX5, RV5 ) CALL iau_HFK5Z ( RH, DH, DATE1, DATE2, R5, D5, DR5, DD5 ) CALL iau_ICRS2G ( DR, DD, DL, DB ) CALL iau_JD2CAL ( DJ1, DJ2, IY, IM, ID, FD, J ) CALL iau_JDCALF ( NDP, DJ1, DJ2, IYMDF, J ) CALL iau_LD ( BM, P, Q, E, EM, DLIM, P1 ) CALL iau_LDN ( N, B, OB, SC, SN ) CALL iau_LDSUN ( P, E, EM, P1 ) CALL iau_LTECEQ ( EPJ, DL, DB, DR, DD ) CALL iau_LTECM ( EPJ, RM] ) CALL iau_LTEQEC ( EPJ, DR, DD, DL, DB ) CALL iau_LTP ( EPJ, RP ) CALL iau_LTPB ( EPJ, RPB ) CALL iau_LTPECL ( EPJ, VEC ) CALL iau_LTPEQU ( EPJ, VEQ ) CALL iau_NUM00A ( DATE1, DATE2, RMATN ) CALL iau_NUM00B ( DATE1, DATE2, RMATN ) CALL iau_NUM06A ( DATE1, DATE2, RMATN ) CALL iau_NUMAT ( EPSA, DPSI, DEPS, RMATN ) CALL iau_NUT00A ( DATE1, DATE2, DPSI, DEPS ) CALL iau_NUT00B ( DATE1, DATE2, DPSI, DEPS ) CALL iau_NUT06A ( DATE1, DATE2, DPSI, DEPS ) CALL iau_NUT80 ( DATE1, DATE2, DPSI, DEPS ) CALL iau_NUTM80 ( DATE1, DATE2, RMATN ) D = iau_OBL06 ( DATE1, DATE2 ) D = iau_OBL80 ( DATE1, DATE2 ) CALL iau_PB06 ( DATE1, DATE2, BZETA, BZ, BTHETA ) CALL iau_PFW06 ( DATE1, DATE2, GAMB, PHIB, PSIB, EPSA ) CALL iau_PLAN94 ( DATE1, DATE2, NP, PV, J ) CALL iau_PMAT00 ( DATE1, DATE2, RBP ) CALL iau_PMAT06 ( DATE1, DATE2, RBP ) CALL iau_PMAT76 ( DATE1, DATE2, RMATP ) CALL iau_PMPX ( RC, DC, PR, PD, PX, RV, PMT, POB, PCO ) CALL iau_PMSAFE ( RA1, DEC1, PMR1, PMD1, PX1, RV1, : EP1A, EP1B, EP2A, EP2B, : RA2, DEC2, PMR2, PMD2, PX2, RV2, J ) CALL iau_PN00 ( DATE1, DATE2, DPSI, DEPS, : EPSA, RB, RP, RBP, RN, RBPN ) CALL iau_PN00A ( DATE1, DATE2, : DPSI, DEPS, EPSA, RB, RP, RBP, RN, RBPN ) CALL iau_PN00B ( DATE1, DATE2, : DPSI, DEPS, EPSA, RB, RP, RBP, RN, RBPN ) CALL iau_PN06 ( DATE1, DATE2, DPSI, DEPS, : EPSA, RB, RP, RBP, RN, RBPN ) CALL iau_PN06A ( DATE1, DATE2, : DPSI, DEPS, RB, RP, RBP, RN, RBPN ) CALL iau_PNM00A ( DATE1, DATE2, RBPN ) CALL iau_PNM00B ( DATE1, DATE2, RBPN ) CALL iau_PNM06A ( DATE1, DATE2, RNPB ) CALL iau_PNM80 ( DATE1, DATE2, RMATPN ) CALL iau_P06E ( DATE1, DATE2, : EPS0, PSIA, OMA, BPA, BQA, PIA, BPIA, : EPSA, CHIA, ZA, ZETAA, THETAA, PA, GAM, PHI, PSI ) CALL iau_POM00 ( XP, YP, SP, RPOM ) CALL iau_PR00 ( DATE1, DATE2, DPSIPR, DEPSPR ) CALL iau_PREC76 ( DATE01, DATE02, DATE11, DATE12, ZETA, Z, THETA ) CALL iau_PVSTAR ( PV, RA, DEC, PMR, PMD, PX, RV, J ) CALL iau_PVTOB ( ELONG, PHI, HM, XP, YP, SP, THETA, PV ) CALL iau_REFCO ( PHPA, TC, RH, WL, REFA, REFB ) D = iau_S00 ( DATE1, DATE2, X, Y ) D = iau_S00A ( DATE1, DATE2 ) D = iau_S00B ( DATE1, DATE2 ) D = iau_S06 ( DATE1, DATE2, X, Y ) D = iau_S06A ( DATE1, DATE2 ) D = iau_SP00 ( DATE1, DATE2 ) CALL iau_STARPM ( RA1, DEC1, PMR1, PMD1, PX1, RV1, : EP1A, EP1B, EP2A, EP2B, : RA2, DEC2, PMR2, PMD2, PX2, RV2, J ) CALL iau_STARPV ( RA, DEC, PMR, PMD, PX, RV, PV, J ) CALL iau_TAITT ( TAI1, TAI2, TT1, TT2, J ) CALL iau_TAIUT1 ( TAI1, TAI2, DTA, UT11, UT12, J ) CALL iau_TAIUTC ( TAI1, TAI2, UTC1, UTC2, J ) CALL iau_TCBTDB ( TCB1, TCB2, TDB1, TDB2, J ) CALL iau_TCGTT ( TCG1, TCG2, TT1, TT2, J ) CALL iau_TDBTCB ( TDB1, TDB2, TCB1, TCB2, J ) CALL iau_TDBTT ( TDB1, TDB2, DTR, TT1, TT2, J ) CALL iau_TTTAI ( TT1, TT2, TAI1, TAI2, J ) CALL iau_TTTCG ( TT1, TT2, TCG1, TCG2, J ) CALL iau_TTTDB ( TT1, TT2, DTR, TDB1, TDB2, J ) CALL iau_TTUT1 ( TT1, TT2, DT, UT11, UT12, J ) CALL iau_UT1TAI ( UT11, UT12, TAI1, TAI2, J ) CALL iau_UT1TT ( UT11, UT12, DT, TT1, TT2, J ) CALL iau_UT1UTC ( UT11, UT12, DUT, UTC1, UTC2, J ) CALL iau_UTCTAI ( UTC1, UTC2, DTA, TAI1, TAI2, J ) CALL iau_UTCUT1 ( UTC1, UTC2, DUT, UT11, UT12, J ) CALL iau_XY06 ( DATE1, DATE2, X, Y ) CALL iau_XYS00A ( DATE1, DATE2, X, Y, S ) CALL iau_XYS00B ( DATE1, DATE2, X, Y, S ) CALL iau_XYS06A ( DATE1, DATE2, X, Y, S ) CALLS: C VERSION iauAb ( pnat, v, s, bm1, ppr ); iauApcg ( date1, date2, eb, eh, &astrom ); iauApcg13 ( date1, date2, &astrom ); iauApci ( date1, date2, eb, eh, x, y, s, &astrom ); iauApci13 ( date1, date2, &astrom, &eo ); iauApco ( date1, date2, eb, eh, x, y, s, theta, elong, phi, hm, xp, yp, sp, refa, refb, &astrom ); i = iauApco13 ( utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom, &eo ); iauApcs ( date1, date2, pv, eb, eh, &astrom ); iauApcs13 ( date1, date2, pv, &astrom ); iauAper ( theta, &astrom ); iauAper13 ( ut11, ut12, &astrom ); iauApio ( sp, theta, elong, phi, hm, xp, yp, refa, refb, &astrom ); i = iauApio13 ( utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &astrom ); iauAtci13 ( rc, dc, pr, pd, px, rv, date1, date2, &ri, &di, &eo ); iauAtciq ( rc, dc, pr, pd, px, rv, &astrom, &ri, &di ); iauAtciqn ( rc, dc, pr, pd, px, rv, astrom, n, b, &ri, &di ); iauAtciqz ( rc, dc, &astrom, &ri, &di ); i = iauAtco13 ( rc, dc, pr, pd, px, rv, utc1, utc2, dut1, elong phi, hm, xp, yp, phpa, tc, rh, wl, aob, zob, hob, dob, rob, eo ); iauAtic13 ( ri, di, date1, date2, &rc, &dc, &eo ); iauAticq ( ri, di, &astrom, &rc, &dc ); iauAtciqn ( ri, di, astrom, n, b, &rc, &dc ); i = iauAtio13 ( ri, di, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, aob, zob, hob, dob, rob ); iauAtioq ( ri, di, &astrom, &aob, &zob, &hob, &dob, &rob ); i = iauAtoc13 ( type, ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &rc, &dc ); i = iauAtoi13 ( type, ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl, &ri, &di ); iauAtoiq ( type, ob1, ob2, &astrom, &ri, &di ); iauBi00 ( &dpsibi, &depsbi, &dra ); iauBp00 ( date1, date2, rb, rp, rbp ); iauBp06 ( date1, date2, rb, rp, rbp ); iauBpn2xy ( rbpn, &x, &y ); iauC2i00a ( date1, date2, rc2i ); iauC2i00b ( date1, date2, rc2i ); iauC2i06a ( date1, date2, rc2i ); iauC2ibpn ( date1, date2, rbpn, rc2i ); iauC2ixy ( date1, date2, x, y, rc2i ); iauC2ixys ( x, y, s, rc2i ); iauC2t00a ( tta, ttb, uta, utb, xp, yp, rc2t ); iauC2t00b ( tta, ttb, uta, utb, xp, yp, rc2t ); iauC2t06a ( tta, ttb, uta, utb, xp, yp, rc2t ); iauC2tcio ( rc2i, era, rpom, rc2t ); iauC2teqx ( rbpn, gst, rpom, rc2t ); iauC2tpe ( tta, ttb, uta, utb, dpsi, deps, xp, yp, rc2t ); iauC2txy ( tta, ttb, uta, utb, x, y, xp, yp, rc2t ); i = iauCal2jd ( iy, im, id, &djm0, &djm ); i = iauD2dtf ( scale, ndp, d1, d2, &iy, &im, &id, ihmsf ); i = iauDat ( iy, im, id, fd, &deltat ); d = iauDtdb ( date1, date2, ut, elong, u, v ); i = iauDtf2d ( scale, iy, im, id, ihr, imn, sec, &d1, &d2 ); iauEceq06 ( date1, date2, dl, db, &dr, &dd ); iauEcm06 ( date1, date2, rm ); d = iauEe00 ( date1, date2, epsa, dpsi ); d = iauEe00a ( date1, date2 ); d = iauEe00b ( date1, date2 ); d = iauEe06 ( date1, date2 ); d = iauEect00 ( date1, date2 ); i = iauEform ( n, &a, &f ); d = iauEo06 ( date1, date2 ); d = iauEors ( rnpb, s ); d = iauEpb ( dj1, dj2 ); iauEpb2jd ( epb, &djm0, &djm ); d = iauEpj ( dj1, dj2 ); iauEpj2jd ( epj, &djm0, &djm ); i = iauEpv00 ( dj1, dj2, pvh, pvb ); iauEqec06 ( date1, date2, dr, dd, &dl, &db ); d = iauEqeq94 ( date1, date2 ); d = iauEra00 ( dj1, dj2 ); d = iauFad03 ( t ); d = iauFae03 ( t ); d = iauFaf03 ( t ); d = iauFaju03 ( t ); d = iauFal03 ( t ); d = iauFalp03 ( t ); d = iauFama03 ( t ); d = iauFame03 ( t ); d = iauFane03 ( t ); d = iauFaom03 ( t ); d = iauFapa03 ( t ); d = iauFasa03 ( t ); d = iauFaur03 ( t ); d = iauFave03 ( t ); iauFk52h ( r5, d5, dr5, dd5, px5, rv5, &rh, &dh, &drh, &ddh, &pxh, &rvh ); iauFk5hip ( r5h, s5h ); iauFk5hz ( r5, d5, date1, date2, &rh, &dh ); iauFw2m ( gamb, phib, psi, eps, r ); iauFw2xy ( gamb, phib, psi, eps, &x, &y ); iauG2icrs ( dl, db, &dr, &dd ); i = iauGc2gd ( n, xyz, &elong, &phi, &height ); i = iauGc2gde ( a, f, xyz, &elong, &phi, &height ); i = iauGd2gc ( n, elong, phi, height, xyz ); i = iauGd2gce ( a, f, elong, phi, height, xyz ); d = iauGmst00 ( uta, utb, tta, ttb ); d = iauGmst06 ( uta, utb, tta, ttb ); d = iauGmst82 ( uta, utb ); d = iauGst00a ( uta, utb, tta, ttb ); d = iauGst00b ( uta, utb ); d = iauGst06 ( uta, utb, tta, ttb, rnpb ); d = iauGst06a ( uta, utb, tta, ttb ); d = iauGst94 ( uta, utb ); iauH2fk5 ( rh, dh, drh, ddh, pxh, rvh, &r5, &d5, &dr5, &dd5, &px5, &rv5 ); iauHfk5z ( rh, dh, date1, date2, &r5, &d5, &dr5, &dd5 ); iauIcrs2g ( dr, dd, &dl, &db ); i = iauJd2cal ( dj1, dj2, &iy, &im, &id, &fd ); i = iauJdcalf ( ndp, dj1, dj2, iymdf ); iauLd ( bm, p, q, e, em, dlim, p1 ); iauLdn ( n, b, ob, sc, sn ); iauLdsun ( p, e, em, p1 ); iauLteceq ( epj, dl, db, &dr, &dd ); iauLtecm ( epj, rm ); iauLteqec ( epj, dr, dd, &dl, &db ); iauLtp ( epj, rp ); iauLtpb ( epj, rpb ); iauLtpecl ( epj, vec ); iauLtpequ ( epj, veq ); iauNum00a ( date1, date2, rmatn ); iauNum00b ( date1, date2, rmatn ); iauNum06a ( date1, date2, rmatn ); iauNumat ( epsa, dpsi, deps, rmatn ); iauNut00a ( date1, date2, &dpsi, &deps ); iauNut00b ( date1, date2, &dpsi, &deps ); iauNut06a ( date1, date2, &dpsi, &deps ); iauNut80 ( date1, date2, &dpsi, &deps ); iauNutm80 ( date1, date2, rmatn ); d = iauObl06 ( date1, date2 ); d = iauObl80 ( date1, date2 ); iauPb06 ( date1, date2, &bzeta, &bz, &btheta ); iauPfw06 ( date1, date2, &gamb, &phib, &psib, &epsa ); i = iauPlan94 ( date1, date2, np, pv ); iauPmat00 ( date1, date2, rbp ); iauPmat06 ( date1, date2, rbp ); iauPmat76 ( date1, date2, rmatp ); iauPmpx ( rc, dc, pr, pd, px, rv, pmt, pob, pco ); i = iauPmsafe ( ra1, dec1, pmr1, pmd1, px1, rv1, ep1a, ep1b, ep2a, ep2b, &ra2, &dec2, &pmr2, &pmd2, &px2, &rv2); iauPn00 ( date1, date2, dpsi, deps, &epsa, rb, rp, rbp, rn, rbpn ); iauPn00a ( date1, date2, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn ); iauPn00b ( date1, date2, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn ); iauPn06 ( date1, date2, dpsi, deps, &epsa, rb, rp, rbp, rn, rbpn ); iauPn06a ( date1, date2, &dpsi, &deps, &epsa, rb, rp, rbp, rn, rbpn ); iauPnm00a ( date1, date2, rbpn ); iauPnm00b ( date1, date2, rbpn ); iauPnm06a ( date1, date2, rnpb ); iauPnm80 ( date1, date2, rmatpn ); iauP06e ( date1, date2, &eps0, &psia, &oma, &bpa, &bqa, &pia, &bpia, &epsa, &chia, &za, &zetaa, &thetaa, &pa, &gam, &phi, &psi ); iauPom00 ( xp, yp, sp, rpom ); iauPr00 ( date1, date2, &dpsipr, &depspr ); iauPrec76 ( date01, date02, date11, date12, &zeta, &z, &theta ); i = iauPvstar ( pv, &ra, &dec, &pmr, &pmd, &px, &rv ); iauPvtob ( elong, phi, hm, xp, yp, sp, theta, pv ); iauRefco ( phpa, tc, rh, wl, refa, refb ); d = iauS00 ( date1, date2, x, y ); d = iauS00a ( date1, date2 ); d = iauS00b ( date1, date2 ); d = iauS06 ( date1, date2, x, y ); d = iauS06a ( date1, date2 ); d = iauSp00 ( date1, date2 ); i = iauStarpm ( ra1, dec1, pmr1, pmd1, px1, rv1, ep1a, ep1b, ep2a, ep2b, &ra2, &dec2, &pmr2, &pmd2, &px2, &rv2 ); i = iauStarpv ( ra, dec, pmr, pmd, px, rv, pv ); i = iauTaitt ( tai1, tai2, &tt1, &tt2 ); i = iauTaiut1 ( tai1, tai2, dta, &ut11, &ut12 ); i = iauTaiutc ( tai1, tai2, &utc1, &utc2 ); i = iauTcbtdb ( tcb1, tcb2, &tdb1, &tdb2 ); i = iauTcgtt ( tcg1, tcg2, &tt1, &tt2 ); i = iauTdbtcb ( tdb1, tdb2, &tcb1, &tcb2 ); i = iauTdbtt ( tdb1, tdb2, dtr, &tt1, &tt2 ); i = iauTttai ( tt1, tt2, &tai1, &tai2 ); i = iauTttcg ( tt1, tt2, &tcg1, &tcg2 ); i = iauTttdb ( tt1, tt2, dtr, &tdb1, &tdb2 ); i = iauTtut1 ( tt1, tt2, dt, &ut11, &ut12 ); i = iauUt1tai ( ut11, ut12, &tai1, &tai2 ); i = iauUt1tt ( ut11, ut12, dt, &tt1, &tt2 ); i = iauUt1utc ( ut11, ut12, dut, &utc1, &utc2 ); i = iauUtctai ( utc1, utc2, dta, &tai1, &tai2 ); i = iauUtcut1 ( utc1, utc2, dut, &ut11, &ut12 ); iauXy06 ( date1, date2, &x, &y ); iauXys00a ( date1, date2, &x, &y, &s ); iauXys00b ( date1, date2, &x, &y, &s ); iauXys06a ( date1, date2, &x, &y, &s ); sofa/20160503_c/c/doc/sofa_vml.lis0000644000113000011300000002444213027221063015464 0ustar bellsbellssofa_vml.lis 2013 October 8 -------------------------- SOFA Vector/Matrix Library -------------------------- PREFACE The routines described here comprise the SOFA vector/matrix library. Their general appearance and coding style conforms to conventions agreed by the SOFA Board, and their functions, names and algorithms have been ratified by the Board. Procedures for soliciting and agreeing additions to the library are still evolving. PROGRAMMING LANGUAGES The SOFA routines are available in two programming languages at present: Fortran 77 and ANSI C. There is a one-to-one relationship between the two language versions. The naming convention is such that a SOFA routine referred to generically as "EXAMPL" exists as a Fortran subprogram iau_EXAMPL and a C function iauExampl. The calls for the two versions are very similar, with the same arguments in the same order. In a few cases, the C equivalent of a Fortran SUBROUTINE subprogram uses a return value rather than an argument. GENERAL PRINCIPLES The library consists mostly of routines which operate on ordinary Cartesian vectors (x,y,z) and 3x3 rotation matrices. However, there is also support for vectors which represent velocity as well as position and vectors which represent rotation instead of position. The vectors which represent both position and velocity may be considered still to have dimensions (3), but to comprise elements each of which is two numbers, representing the value itself and the time derivative. Thus: * "Position" or "p" vectors (or just plain 3-vectors) have dimension (3) in Fortran and [3] in C. * "Position/velocity" or "pv" vectors have dimensions (3,2) in Fortran and [2][3] in C. * "Rotation" or "r" matrices have dimensions (3,3) in Fortran and [3][3] in C. When used for rotation, they are "orthogonal"; the inverse of such a matrix is equal to the transpose. Most of the routines in this library do not assume that r-matrices are necessarily orthogonal and in fact work on any 3x3 matrix. * "Rotation" or "r" vectors have dimensions (3) in Fortran and [3] in C. Such vectors are a combination of the Euler axis and angle and are convertible to and from r-matrices. The direction is the axis of rotation and the magnitude is the angle of rotation, in radians. Because the amount of rotation can be scaled up and down simply by multiplying the vector by a scalar, r-vectors are useful for representing spins about an axis which is fixed. * The above rules mean that in terms of memory address, the three velocity components of a pv-vector follow the three position components. Application code is permitted to exploit this and all other knowledge of the internal layouts: that x, y and z appear in that order and are in a right-handed Cartesian coordinate system etc. For example, the cp function (copy a p-vector) can be used to copy the velocity component of a pv-vector (indeed, this is how the CPV routine is coded). * The routines provided do not completely fill the range of operations that link all the various vector and matrix options, but are confined to functions that are required by other parts of the SOFA software or which are likely to prove useful. In addition to the vector/matrix routines, the library contains some routines related to spherical angles, including conversions to and from sexagesimal format. Using the library requires knowledge of vector/matrix methods, spherical trigonometry, and methods of attitude representation. These topics are covered in many textbooks, including "Spacecraft Attitude Determination and Control", James R. Wertz (ed.), Astrophysics and Space Science Library, Vol. 73, D. Reidel Publishing Company, 1986. OPERATIONS INVOLVING P-VECTORS AND R-MATRICES Initialize ZP zero p-vector ZR initialize r-matrix to null IR initialize r-matrix to identity Copy/extend/extract CP copy p-vector CR copy r-matrix Build rotations RX rotate r-matrix about x RY rotate r-matrix about y RZ rotate r-matrix about z Spherical/Cartesian conversions S2C spherical to unit vector C2S unit vector to spherical S2P spherical to p-vector P2S p-vector to spherical Operations on vectors PPP p-vector plus p-vector PMP p-vector minus p-vector PPSP p-vector plus scaled p-vector PDP inner (=scalar=dot) product of two p-vectors PXP outer (=vector=cross) product of two p-vectors PM modulus of p-vector PN normalize p-vector returning modulus SXP multiply p-vector by scalar Operations on matrices RXR r-matrix multiply TR transpose r-matrix Matrix-vector products RXP product of r-matrix and p-vector TRXP product of transpose of r-matrix and p-vector Separation and position-angle SEPP angular separation from p-vectors SEPS angular separation from spherical coordinates PAP position-angle from p-vectors PAS position-angle from spherical coordinates Rotation vectors RV2M r-vector to r-matrix RM2V r-matrix to r-vector OPERATIONS INVOLVING PV-VECTORS Initialize ZPV zero pv-vector Copy/extend/extract CPV copy pv-vector P2PV append zero velocity to p-vector PV2P discard velocity component of pv-vector Spherical/Cartesian conversions S2PV spherical to pv-vector PV2S pv-vector to spherical Operations on vectors PVPPV pv-vector plus pv-vector PVMPV pv-vector minus pv-vector PVDPV inner (=scalar=dot) product of two pv-vectors PVXPV outer (=vector=cross) product of two pv-vectors PVM modulus of pv-vector SXPV multiply pv-vector by scalar S2XPV multiply pv-vector by two scalars PVU update pv-vector PVUP update pv-vector discarding velocity Matrix-vector products RXPV product of r-matrix and pv-vector TRXPV product of transpose of r-matrix and pv-vector OPERATIONS ON ANGLES ANP normalize radians to range 0 to 2pi ANPM normalize radians to range -pi to +pi A2TF decompose radians into hours, minutes, seconds A2AF decompose radians into degrees, arcminutes, arcseconds AF2A degrees, arcminutes, arcseconds to radians D2TF decompose days into hours, minutes, seconds TF2A hours, minutes, seconds to radians TF2D hours, minutes, seconds to days CALLS: FORTRAN VERSION CALL iau_A2AF ( NDP, ANGLE, SIGN, IDMSF ) CALL iau_A2TF ( NDP, ANGLE, SIGN, IHMSF ) CALL iau_AF2A ( S, IDEG, IAMIN, ASEC, RAD, J ) D = iau_ANP ( A ) D = iau_ANPM ( A ) CALL iau_C2S ( P, THETA, PHI ) CALL iau_CP ( P, C ) CALL iau_CPV ( PV, C ) CALL iau_CR ( R, C ) CALL iau_D2TF ( NDP, DAYS, SIGN, IHMSF ) CALL iau_IR ( R ) CALL iau_P2PV ( P, PV ) CALL iau_P2S ( P, THETA, PHI, R ) CALL iau_PAP ( A, B, THETA ) CALL iau_PAS ( AL, AP, BL, BP, THETA ) CALL iau_PDP ( A, B, ADB ) CALL iau_PM ( P, R ) CALL iau_PMP ( A, B, AMB ) CALL iau_PN ( P, R, U ) CALL iau_PPP ( A, B, APB ) CALL iau_PPSP ( A, S, B, APSB ) CALL iau_PV2P ( PV, P ) CALL iau_PV2S ( PV, THETA, PHI, R, TD, PD, RD ) CALL iau_PVDPV ( A, B, ADB ) CALL iau_PVM ( PV, R, S ) CALL iau_PVMPV ( A, B, AMB ) CALL iau_PVPPV ( A, B, APB ) CALL iau_PVU ( DT, PV, UPV ) CALL iau_PVUP ( DT, PV, P ) CALL iau_PVXPV ( A, B, AXB ) CALL iau_PXP ( A, B, AXB ) CALL iau_RM2V ( R, P ) CALL iau_RV2M ( P, R ) CALL iau_RX ( PHI, R ) CALL iau_RXP ( R, P, RP ) CALL iau_RXPV ( R, PV, RPV ) CALL iau_RXR ( A, B, ATB ) CALL iau_RY ( THETA, R ) CALL iau_RZ ( PSI, R ) CALL iau_S2C ( THETA, PHI, C ) CALL iau_S2P ( THETA, PHI, R, P ) CALL iau_S2PV ( THETA, PHI, R, TD, PD, RD, PV ) CALL iau_S2XPV ( S1, S2, PV ) CALL iau_SEPP ( A, B, S ) CALL iau_SEPS ( AL, AP, BL, BP, S ) CALL iau_SXP ( S, P, SP ) CALL iau_SXPV ( S, PV, SPV ) CALL iau_TF2A ( S, IHOUR, IMIN, SEC, RAD, J ) CALL iau_TF2D ( S, IHOUR, IMIN, SEC, DAYS, J ) CALL iau_TR ( R, RT ) CALL iau_TRXP ( R, P, TRP ) CALL iau_TRXPV ( R, PV, TRPV ) CALL iau_ZP ( P ) CALL iau_ZPV ( PV ) CALL iau_ZR ( R ) CALLS: C VERSION iauA2af ( ndp, angle, &sign, idmsf ); iauA2tf ( ndp, angle, &sign, ihmsf ); i = iauAf2a ( s, ideg, iamin, asec, &rad ); d = iauAnp ( a ); d = iauAnpm ( a ); iauC2s ( p, &theta, &phi ); iauCp ( p, c ); iauCpv ( pv, c ); iauCr ( r, c ); iauD2tf ( ndp, days, &sign, ihmsf ); iauIr ( r ); iauP2pv ( p, pv ); iauP2s ( p, &theta, &phi, &r ); d = iauPap ( a, b ); d = iauPas ( al, ap, bl, bp ); d = iauPdp ( a, b ); d = iauPm ( p ); iauPmp ( a, b, amb ); iauPn ( p, &r, u ); iauPpp ( a, b, apb ); iauPpsp ( a, s, b, apsb ); iauPv2p ( pv, p ); iauPv2s ( pv, &theta, &phi, &r, &td, &pd, &rd ); iauPvdpv ( a, b, adb ); iauPvm ( pv, &r, &s ); iauPvmpv ( a, b, amb ); iauPvppv ( a, b, apb ); iauPvu ( dt, pv, upv ); iauPvup ( dt, pv, p ); iauPvxpv ( a, b, axb ); iauPxp ( a, b, axb ); iauRm2v ( r, p ); iauRv2m ( p, r ); iauRx ( phi, r ); iauRxp ( r, p, rp ); iauRxpv ( r, pv, rpv ); iauRxr ( a, b, atb ); iauRy ( theta, r ); iauRz ( psi, r ); iauS2c ( theta, phi, c ); iauS2p ( theta, phi, r, p ); iauS2pv ( theta, phi, r, td, pd, rd, pV ); iauS2xpv ( s1, s2, pv ); 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0 obj <> /Contents 1249 0 R >> endobj 1253 0 obj <> /Contents 1254 0 R >> endobj 1258 0 obj <> /Contents 1259 0 R >> endobj 1263 0 obj <> /Contents 1264 0 R >> endobj 1268 0 obj <> /Contents 1269 0 R >> endobj 1273 0 obj <> /Contents 1274 0 R >> endobj 1278 0 obj <> /Contents 1279 0 R >> endobj 1283 0 obj <> /Contents 1284 0 R >> endobj 1288 0 obj <> /Contents 1289 0 R >> endobj 1293 0 obj <> /Contents 1294 0 R >> endobj 1298 0 obj <> /Contents 1299 0 R >> endobj 1303 0 obj <> /Contents 1304 0 R >> endobj 1308 0 obj <> /Contents 1309 0 R >> endobj 1313 0 obj <> /Contents 1314 0 R >> endobj 1318 0 obj <> /Contents 1319 0 R >> endobj 1323 0 obj <> /Contents 1324 0 R >> endobj 1328 0 obj <> /Contents 1329 0 R >> endobj 1333 0 obj <> /Contents 1334 0 R >> endobj 1338 0 obj <> /Contents 1339 0 R >> endobj 1343 0 obj <> /Contents 1344 0 R >> endobj 1348 0 obj <> /Contents 1349 0 R >> endobj 1353 0 obj <> /Contents 1354 0 R >> endobj 1358 0 obj <> /Contents 1359 0 R >> endobj 1363 0 obj <> /Contents 1364 0 R >> endobj 1368 0 obj <> /Contents 1369 0 R >> endobj 1373 0 obj <> /Contents 1374 0 R >> endobj 1378 0 obj <> /Contents 1379 0 R >> endobj 1383 0 obj <> /Contents 1384 0 R >> endobj 1388 0 obj <> /Contents 1389 0 R >> endobj 1393 0 obj <> /Contents 1394 0 R >> endobj 1398 0 obj <> /Contents 1399 0 R >> endobj 1403 0 obj <> /Contents 1404 0 R >> endobj 1408 0 obj <> /Contents 1409 0 R >> endobj 1413 0 obj <> /Contents 1414 0 R >> endobj 1418 0 obj <> /Contents 1419 0 R >> endobj 1423 0 obj <> /Contents 1424 0 R >> endobj 1428 0 obj <> /Contents 1429 0 R >> endobj 1433 0 obj <> /Contents 1434 0 R >> endobj 1438 0 obj <> /Contents 1439 0 R >> endobj 1443 0 obj <> /Contents 1444 0 R >> endobj 1448 0 obj <> /Contents 1449 0 R >> endobj 1453 0 obj <> /Contents 1454 0 R >> endobj 1458 0 obj <> /Contents 1459 0 R >> endobj 1463 0 obj <> /Contents 1464 0 R >> endobj 1468 0 obj <> /Contents 1469 0 R >> endobj 1473 0 obj <> /Contents 1474 0 R >> endobj 1478 0 obj <> /Contents 1479 0 R >> endobj 1483 0 obj <> /Contents 1484 0 R >> endobj 1488 0 obj <> /Contents 1489 0 R >> endobj 1493 0 obj <> /Contents 1494 0 R >> endobj 1498 0 obj <> /Contents 1499 0 R >> endobj 1503 0 obj <> /Contents 1504 0 R >> endobj 1508 0 obj <> /Contents 1509 0 R >> endobj 1513 0 obj <> /Contents 1514 0 R >> endobj 1518 0 obj <> /Contents 1519 0 R >> endobj 1523 0 obj <> /Contents 1524 0 R >> endobj 1528 0 obj <> /Contents 1529 0 R >> endobj 1533 0 obj <> /Contents 1534 0 R >> endobj 1538 0 obj <> /Contents 1539 0 R >> endobj 1543 0 obj <> /Contents 1544 0 R >> endobj 1548 0 obj <> /Contents 1549 0 R >> endobj 1553 0 obj <> /Contents 1554 0 R >> endobj 1558 0 obj <> /Contents 1559 0 R >> endobj 1563 0 obj <> /Contents 1564 0 R >> endobj 1568 0 obj <> /Contents 1569 0 R >> endobj 1573 0 obj <> /Contents 1574 0 R >> endobj 1578 0 obj <> /Contents 1579 0 R >> endobj 1583 0 obj <> /Contents 1584 0 R >> endobj 1588 0 obj <> /Contents 1589 0 R >> endobj 1593 0 obj <> /Contents 1594 0 R >> endobj 1598 0 obj <> /Contents 1599 0 R >> endobj 1603 0 obj <> /Contents 1604 0 R >> endobj 1608 0 obj <> /Contents 1609 0 R >> endobj 1613 0 obj <> /Contents 1614 0 R >> endobj 1618 0 obj <> /Contents 1619 0 R >> endobj 1623 0 obj <> /Contents 1624 0 R >> endobj 1628 0 obj <> /Contents 1629 0 R >> endobj 1633 0 obj <> /Contents 1634 0 R >> endobj 1638 0 obj <> /Contents 1639 0 R >> endobj 1643 0 obj <> /Contents 1644 0 R >> endobj 1648 0 obj <> /Contents 1649 0 R >> endobj 1653 0 obj <> /Contents 1654 0 R >> endobj 1658 0 obj <> /Contents 1659 0 R >> endobj 1663 0 obj <> /Contents 1664 0 R >> endobj 1668 0 obj <> /Contents 1669 0 R >> endobj 1673 0 obj <> /Contents 1674 0 R >> endobj 1678 0 obj <> /Contents 1679 0 R >> endobj 1683 0 obj <> /Contents 1684 0 R >> endobj 1688 0 obj <> /Contents 1689 0 R >> endobj 1693 0 obj <> /Contents 1694 0 R >> endobj 1698 0 obj <> /Contents 1699 0 R >> endobj 1703 0 obj <> /Contents 1704 0 R >> endobj 1708 0 obj <> /Contents 1709 0 R >> endobj 1713 0 obj <> /Contents 1714 0 R >> endobj 1718 0 obj <> /Contents 1719 0 R >> endobj 1723 0 obj <> /Contents 1724 0 R >> endobj 1728 0 obj <> /Contents 1729 0 R >> endobj 1733 0 obj <> /Contents 1734 0 R >> endobj 1738 0 obj <> /Contents 1739 0 R >> endobj 1743 0 obj <> /Contents 1744 0 R >> endobj 3 0 obj << /Type /Pages /Kids [ 5 0 R 13 0 R 18 0 R 23 0 R 28 0 R 33 0 R 38 0 R 43 0 R 48 0 R 53 0 R 58 0 R 63 0 R 68 0 R 73 0 R 78 0 R 83 0 R 88 0 R 93 0 R 98 0 R 103 0 R 108 0 R 113 0 R 118 0 R 123 0 R 128 0 R 133 0 R 138 0 R 143 0 R 148 0 R 153 0 R 158 0 R 163 0 R 168 0 R 173 0 R 178 0 R 183 0 R 188 0 R 193 0 R 198 0 R 203 0 R 208 0 R 213 0 R 218 0 R 223 0 R 228 0 R 233 0 R 238 0 R 243 0 R 248 0 R 253 0 R 258 0 R 263 0 R 268 0 R 273 0 R 278 0 R 283 0 R 288 0 R 293 0 R 298 0 R 303 0 R 308 0 R 313 0 R 318 0 R 323 0 R 328 0 R 333 0 R 338 0 R 343 0 R 348 0 R 353 0 R 358 0 R 363 0 R 368 0 R 373 0 R 378 0 R 383 0 R 388 0 R 393 0 R 398 0 R 403 0 R 408 0 R 413 0 R 418 0 R 423 0 R 428 0 R 433 0 R 438 0 R 443 0 R 448 0 R 453 0 R 458 0 R 463 0 R 468 0 R 473 0 R 478 0 R 483 0 R 488 0 R 493 0 R 498 0 R 503 0 R 508 0 R 513 0 R 518 0 R 523 0 R 528 0 R 533 0 R 538 0 R 543 0 R 548 0 R 553 0 R 558 0 R 563 0 R 568 0 R 573 0 R 578 0 R 583 0 R 588 0 R 593 0 R 598 0 R 603 0 R 608 0 R 613 0 R 618 0 R 623 0 R 628 0 R 633 0 R 638 0 R 643 0 R 648 0 R 653 0 R 658 0 R 663 0 R 668 0 R 673 0 R 678 0 R 683 0 R 688 0 R 693 0 R 698 0 R 703 0 R 708 0 R 713 0 R 718 0 R 723 0 R 728 0 R 733 0 R 738 0 R 743 0 R 748 0 R 753 0 R 758 0 R 763 0 R 768 0 R 773 0 R 778 0 R 783 0 R 788 0 R 793 0 R 798 0 R 803 0 R 808 0 R 813 0 R 818 0 R 823 0 R 828 0 R 833 0 R 838 0 R 843 0 R 848 0 R 853 0 R 858 0 R 863 0 R 868 0 R 873 0 R 878 0 R 883 0 R 888 0 R 893 0 R 898 0 R 903 0 R 908 0 R 913 0 R 918 0 R 923 0 R 928 0 R 933 0 R 938 0 R 943 0 R 948 0 R 953 0 R 958 0 R 963 0 R 968 0 R 973 0 R 978 0 R 983 0 R 988 0 R 993 0 R 998 0 R 1003 0 R 1008 0 R 1013 0 R 1018 0 R 1023 0 R 1028 0 R 1033 0 R 1038 0 R 1043 0 R 1048 0 R 1053 0 R 1058 0 R 1063 0 R 1068 0 R 1073 0 R 1078 0 R 1083 0 R 1088 0 R 1093 0 R 1098 0 R 1103 0 R 1108 0 R 1113 0 R 1118 0 R 1123 0 R 1128 0 R 1133 0 R 1138 0 R 1143 0 R 1148 0 R 1153 0 R 1158 0 R 1163 0 R 1168 0 R 1173 0 R 1178 0 R 1183 0 R 1188 0 R 1193 0 R 1198 0 R 1203 0 R 1208 0 R 1213 0 R 1218 0 R 1223 0 R 1228 0 R 1233 0 R 1238 0 R 1243 0 R 1248 0 R 1253 0 R 1258 0 R 1263 0 R 1268 0 R 1273 0 R 1278 0 R 1283 0 R 1288 0 R 1293 0 R 1298 0 R 1303 0 R 1308 0 R 1313 0 R 1318 0 R 1323 0 R 1328 0 R 1333 0 R 1338 0 R 1343 0 R 1348 0 R 1353 0 R 1358 0 R 1363 0 R 1368 0 R 1373 0 R 1378 0 R 1383 0 R 1388 0 R 1393 0 R 1398 0 R 1403 0 R 1408 0 R 1413 0 R 1418 0 R 1423 0 R 1428 0 R 1433 0 R 1438 0 R 1443 0 R 1448 0 R 1453 0 R 1458 0 R 1463 0 R 1468 0 R 1473 0 R 1478 0 R 1483 0 R 1488 0 R 1493 0 R 1498 0 R 1503 0 R 1508 0 R 1513 0 R 1518 0 R 1523 0 R 1528 0 R 1533 0 R 1538 0 R 1543 0 R 1548 0 R 1553 0 R 1558 0 R 1563 0 R 1568 0 R 1573 0 R 1578 0 R 1583 0 R 1588 0 R 1593 0 R 1598 0 R 1603 0 R 1608 0 R 1613 0 R 1618 0 R 1623 0 R 1628 0 R 1633 0 R 1638 0 R 1643 0 R 1648 0 R 1653 0 R 1658 0 R 1663 0 R 1668 0 R 1673 0 R 1678 0 R 1683 0 R 1688 0 R 1693 0 R 1698 0 R 1703 0 R 1708 0 R 1713 0 R 1718 0 R 1723 0 R 1728 0 R 1733 0 R 1738 0 R 1743 0 R ] /Count 348 >> endobj 1 0 obj <> endobj 4 0 obj <> endobj 10 0 obj <> endobj 11 0 obj <> endobj 16 0 obj <> endobj 21 0 obj <> endobj 26 0 obj <> endobj 31 0 obj <> endobj 36 0 obj <> endobj 41 0 obj <> endobj 46 0 obj <> endobj 51 0 obj <> endobj 56 0 obj <> endobj 61 0 obj <> endobj 66 0 obj <> endobj 71 0 obj <> endobj 76 0 obj <> endobj 81 0 obj <> endobj 86 0 obj <> endobj 91 0 obj <> endobj 96 0 obj <> endobj 101 0 obj <> endobj 106 0 obj <> endobj 111 0 obj <> endobj 116 0 obj <> endobj 121 0 obj <> endobj 126 0 obj <> endobj 131 0 obj <> endobj 136 0 obj <> endobj 141 0 obj <> endobj 146 0 obj <> endobj 151 0 obj <> endobj 156 0 obj <> endobj 161 0 obj <> endobj 166 0 obj <> endobj 171 0 obj <> endobj 176 0 obj <> endobj 181 0 obj <> endobj 186 0 obj <> endobj 191 0 obj <> endobj 196 0 obj <> endobj 201 0 obj <> endobj 206 0 obj <> endobj 211 0 obj <> endobj 216 0 obj <> endobj 221 0 obj <> endobj 226 0 obj <> endobj 231 0 obj <> endobj 236 0 obj <> endobj 241 0 obj <> endobj 246 0 obj <> endobj 251 0 obj <> endobj 256 0 obj <> endobj 261 0 obj <> endobj 266 0 obj <> endobj 271 0 obj <> endobj 276 0 obj <> endobj 281 0 obj <> endobj 286 0 obj <> endobj 291 0 obj <> endobj 296 0 obj <> endobj 301 0 obj <> endobj 306 0 obj <> endobj 311 0 obj <> endobj 316 0 obj <> endobj 321 0 obj <> endobj 326 0 obj <> endobj 331 0 obj <> endobj 336 0 obj <> endobj 341 0 obj <> endobj 346 0 obj <> endobj 351 0 obj <> endobj 356 0 obj <> endobj 361 0 obj <> endobj 366 0 obj <> endobj 371 0 obj <> endobj 376 0 obj <> endobj 381 0 obj <> endobj 386 0 obj <> endobj 391 0 obj <> endobj 396 0 obj <> endobj 401 0 obj <> endobj 406 0 obj <> endobj 411 0 obj <> endobj 416 0 obj <> endobj 421 0 obj <> endobj 426 0 obj <> endobj 431 0 obj <> endobj 436 0 obj <> endobj 441 0 obj <> endobj 446 0 obj <> endobj 451 0 obj <> endobj 456 0 obj <> endobj 461 0 obj <> endobj 466 0 obj <> endobj 471 0 obj <> endobj 476 0 obj <> endobj 481 0 obj <> endobj 486 0 obj <> endobj 491 0 obj <> endobj 496 0 obj <> endobj 501 0 obj <> endobj 506 0 obj <> endobj 511 0 obj <> endobj 516 0 obj <> endobj 521 0 obj <> endobj 526 0 obj <> endobj 531 0 obj <> endobj 536 0 obj <> endobj 541 0 obj <> endobj 546 0 obj <> endobj 551 0 obj <> endobj 556 0 obj <> endobj 561 0 obj <> endobj 566 0 obj <> endobj 571 0 obj <> endobj 576 0 obj <> endobj 581 0 obj <> endobj 586 0 obj <> endobj 591 0 obj <> endobj 596 0 obj <> endobj 601 0 obj <> endobj 606 0 obj <> endobj 611 0 obj <> endobj 616 0 obj <> endobj 621 0 obj <> endobj 626 0 obj <> endobj 631 0 obj <> endobj 636 0 obj <> endobj 641 0 obj <> endobj 646 0 obj <> endobj 651 0 obj <> endobj 656 0 obj <> endobj 661 0 obj <> endobj 666 0 obj <> endobj 671 0 obj <> endobj 676 0 obj <> endobj 681 0 obj <> endobj 686 0 obj <> endobj 691 0 obj <> endobj 696 0 obj <> endobj 701 0 obj <> endobj 706 0 obj <> endobj 711 0 obj <> endobj 716 0 obj <> endobj 721 0 obj <> endobj 726 0 obj <> endobj 731 0 obj <> endobj 736 0 obj <> endobj 741 0 obj <> endobj 746 0 obj <> endobj 751 0 obj <> endobj 756 0 obj <> endobj 761 0 obj <> endobj 766 0 obj <> endobj 771 0 obj <> endobj 776 0 obj <> endobj 781 0 obj <> endobj 786 0 obj <> endobj 791 0 obj <> endobj 796 0 obj <> endobj 801 0 obj <> endobj 806 0 obj <> endobj 811 0 obj <> endobj 816 0 obj <> endobj 821 0 obj <> endobj 826 0 obj <> endobj 831 0 obj <> endobj 836 0 obj <> endobj 841 0 obj <> endobj 846 0 obj <> endobj 851 0 obj <> endobj 856 0 obj <> endobj 861 0 obj <> endobj 866 0 obj <> endobj 871 0 obj <> endobj 876 0 obj <> endobj 881 0 obj <> endobj 886 0 obj <> endobj 891 0 obj <> endobj 896 0 obj <> endobj 901 0 obj <> endobj 906 0 obj <> endobj 911 0 obj <> endobj 916 0 obj <> endobj 921 0 obj <> endobj 926 0 obj <> endobj 931 0 obj <> endobj 936 0 obj <> endobj 941 0 obj <> endobj 946 0 obj <> endobj 951 0 obj <> endobj 956 0 obj <> endobj 961 0 obj <> endobj 966 0 obj <> endobj 971 0 obj <> endobj 976 0 obj <> endobj 981 0 obj <> endobj 986 0 obj <> endobj 991 0 obj <> endobj 996 0 obj <> endobj 1001 0 obj <> endobj 1006 0 obj <> endobj 1011 0 obj <> endobj 1016 0 obj <> endobj 1021 0 obj <> endobj 1026 0 obj <> endobj 1031 0 obj <> endobj 1036 0 obj <> endobj 1041 0 obj <> endobj 1046 0 obj <> endobj 1051 0 obj <> endobj 1056 0 obj <> endobj 1061 0 obj <> endobj 1066 0 obj <> endobj 1071 0 obj <> endobj 1076 0 obj <> endobj 1081 0 obj <> endobj 1086 0 obj <> endobj 1091 0 obj <> endobj 1096 0 obj <> endobj 1101 0 obj <> endobj 1106 0 obj <> endobj 1111 0 obj <> endobj 1116 0 obj <> endobj 1121 0 obj <> endobj 1126 0 obj <> endobj 1131 0 obj <> endobj 1136 0 obj <> endobj 1141 0 obj <> endobj 1146 0 obj <> endobj 1151 0 obj <> endobj 1156 0 obj <> endobj 1161 0 obj <> endobj 1166 0 obj <> endobj 1171 0 obj <> endobj 1176 0 obj <> endobj 1181 0 obj <> endobj 1186 0 obj <> endobj 1191 0 obj <> endobj 1196 0 obj <> endobj 1201 0 obj <> endobj 1206 0 obj <> endobj 1211 0 obj <> endobj 1216 0 obj <> endobj 1221 0 obj <> endobj 1226 0 obj <> endobj 1231 0 obj <> endobj 1236 0 obj <> endobj 1241 0 obj <> endobj 1246 0 obj <> endobj 1251 0 obj <> endobj 1256 0 obj <> endobj 1261 0 obj <> endobj 1266 0 obj <> endobj 1271 0 obj <> endobj 1276 0 obj <> endobj 1281 0 obj <> endobj 1286 0 obj <> endobj 1291 0 obj <> endobj 1296 0 obj <> endobj 1301 0 obj <> endobj 1306 0 obj <> endobj 1311 0 obj <> endobj 1316 0 obj <> endobj 1321 0 obj <> endobj 1326 0 obj <> endobj 1331 0 obj <> endobj 1336 0 obj <> endobj 1341 0 obj <> endobj 1346 0 obj <> endobj 1351 0 obj <> endobj 1356 0 obj <> endobj 1361 0 obj <> endobj 1366 0 obj <> endobj 1371 0 obj <> endobj 1376 0 obj <> endobj 1381 0 obj <> endobj 1386 0 obj <> endobj 1391 0 obj <> endobj 1396 0 obj <> endobj 1401 0 obj <> endobj 1406 0 obj <> endobj 1411 0 obj <> endobj 1416 0 obj <> endobj 1421 0 obj <> endobj 1426 0 obj <> endobj 1431 0 obj <> endobj 1436 0 obj <> endobj 1441 0 obj <> endobj 1446 0 obj <> endobj 1451 0 obj <> endobj 1456 0 obj <> endobj 1461 0 obj <> endobj 1466 0 obj <> endobj 1471 0 obj <> endobj 1476 0 obj <> endobj 1481 0 obj <> endobj 1486 0 obj <> endobj 1491 0 obj <> endobj 1496 0 obj <> endobj 1501 0 obj <> endobj 1506 0 obj <> endobj 1511 0 obj <> endobj 1516 0 obj <> endobj 1521 0 obj <> endobj 1526 0 obj <> endobj 1531 0 obj <> endobj 1536 0 obj <> endobj 1541 0 obj <> endobj 1546 0 obj <> endobj 1551 0 obj <> endobj 1556 0 obj <> endobj 1561 0 obj <> endobj 1566 0 obj <> endobj 1571 0 obj <> endobj 1576 0 obj <> endobj 1581 0 obj <> endobj 1586 0 obj <> endobj 1591 0 obj <> endobj 1596 0 obj <> endobj 1601 0 obj <> endobj 1606 0 obj <> endobj 1611 0 obj <> endobj 1616 0 obj <> endobj 1621 0 obj <> endobj 1626 0 obj <> endobj 1631 0 obj <> endobj 1636 0 obj <> endobj 1641 0 obj <> endobj 1646 0 obj <> endobj 1651 0 obj <> endobj 1656 0 obj <> endobj 1661 0 obj <> endobj 1666 0 obj <> endobj 1671 0 obj <> endobj 1676 0 obj <> endobj 1681 0 obj <> endobj 1686 0 obj <> endobj 1691 0 obj <> endobj 1696 0 obj <> endobj 1701 0 obj <> endobj 1706 0 obj <> endobj 1711 0 obj <> endobj 1716 0 obj <> endobj 1721 0 obj <> endobj 1726 0 obj <> endobj 1731 0 obj <> endobj 1736 0 obj <> endobj 1741 0 obj <> endobj 1746 0 obj <> endobj 8 0 obj <> endobj 1742 0 obj <> endobj 1747 0 obj <> endobj 1737 0 obj <> endobj 1748 0 obj <> endobj 1732 0 obj <> endobj 1749 0 obj <> endobj 1727 0 obj <> endobj 1750 0 obj <> endobj 1722 0 obj <> endobj 1751 0 obj <> endobj 1717 0 obj <> endobj 1752 0 obj <> endobj 1712 0 obj <> endobj 1753 0 obj <> endobj 1707 0 obj <> endobj 1702 0 obj <> endobj 1697 0 obj <> endobj 1692 0 obj <> endobj 1687 0 obj <> endobj 1682 0 obj <> endobj 1754 0 obj <> endobj 1677 0 obj <> endobj 1755 0 obj <> endobj 1672 0 obj <> endobj 1756 0 obj <> endobj 1667 0 obj <> endobj 1757 0 obj <> endobj 1662 0 obj <> endobj 1758 0 obj <> endobj 1657 0 obj <> endobj 1759 0 obj <> endobj 1652 0 obj <> endobj 1760 0 obj <> endobj 1647 0 obj <> endobj 1761 0 obj <> endobj 1642 0 obj <> endobj 1762 0 obj <> endobj 1637 0 obj <> endobj 1763 0 obj <> endobj 1632 0 obj <> endobj 1764 0 obj <> endobj 1627 0 obj <> endobj 1765 0 obj <> endobj 1622 0 obj <> endobj 1766 0 obj <> endobj 1617 0 obj <> endobj 1767 0 obj <> endobj 1612 0 obj <> endobj 1768 0 obj <> endobj 1607 0 obj <> endobj 1769 0 obj <> endobj 1602 0 obj <> endobj 1770 0 obj <> endobj 1597 0 obj <> endobj 1771 0 obj <> endobj 1592 0 obj <> endobj 1772 0 obj <> endobj 1587 0 obj <> endobj 1773 0 obj <> endobj 1582 0 obj <> endobj 1774 0 obj <> endobj 1577 0 obj <> endobj 1775 0 obj <> endobj 1572 0 obj <> endobj 1776 0 obj <> endobj 1567 0 obj <> endobj 1777 0 obj <> endobj 1562 0 obj <> endobj 1778 0 obj <> endobj 1557 0 obj <> endobj 1779 0 obj <> endobj 1552 0 obj <> endobj 1780 0 obj <> endobj 1547 0 obj <> endobj 1781 0 obj <> endobj 1542 0 obj <> endobj 1782 0 obj <> endobj 1537 0 obj <> endobj 1783 0 obj <> endobj 1532 0 obj <> endobj 1784 0 obj <> endobj 1527 0 obj <> endobj 1785 0 obj <> endobj 1522 0 obj <> endobj 1786 0 obj <> endobj 1517 0 obj <> endobj 1787 0 obj <> endobj 1512 0 obj <> endobj 1788 0 obj <> endobj 1507 0 obj <> endobj 1789 0 obj <> endobj 1502 0 obj <> endobj 1790 0 obj <> endobj 1497 0 obj <> endobj 1791 0 obj <> endobj 1492 0 obj <> endobj 1792 0 obj <> endobj 1487 0 obj <> endobj 1793 0 obj <> endobj 1482 0 obj <> endobj 1794 0 obj <> endobj 1477 0 obj <> endobj 1795 0 obj <> endobj 1472 0 obj <> endobj 1796 0 obj <> endobj 1467 0 obj <> endobj 1797 0 obj <> endobj 1462 0 obj <> endobj 1798 0 obj <> endobj 1457 0 obj <> endobj 1799 0 obj <> endobj 1452 0 obj <> endobj 1447 0 obj <> endobj 1800 0 obj <> endobj 1442 0 obj <> endobj 1437 0 obj <> endobj 1801 0 obj <> endobj 1432 0 obj <> endobj 1427 0 obj <> endobj 1802 0 obj <> endobj 1422 0 obj <> endobj 1417 0 obj <> endobj 1803 0 obj <> endobj 1412 0 obj <> endobj 1804 0 obj <> endobj 1407 0 obj <> endobj 1805 0 obj <> endobj 1402 0 obj <> endobj 1806 0 obj <> endobj 1397 0 obj <> endobj 1807 0 obj <> endobj 1392 0 obj <> endobj 1808 0 obj <> endobj 1387 0 obj <> endobj 1809 0 obj <> endobj 1382 0 obj <> endobj 1810 0 obj <> endobj 1377 0 obj <> endobj 1811 0 obj <> endobj 1372 0 obj <> endobj 1812 0 obj <> endobj 1367 0 obj <> endobj 1813 0 obj <> endobj 1362 0 obj <> endobj 1814 0 obj <> endobj 1357 0 obj <> endobj 1815 0 obj <> endobj 1352 0 obj <> endobj 1816 0 obj <> endobj 1347 0 obj <> endobj 1817 0 obj <> endobj 1342 0 obj <> endobj 1818 0 obj <> endobj 1337 0 obj <> endobj 1819 0 obj <> endobj 1332 0 obj <> endobj 1820 0 obj <> endobj 1327 0 obj <> endobj 1821 0 obj <> endobj 1322 0 obj <> endobj 1822 0 obj <> endobj 1317 0 obj <> endobj 1823 0 obj <> endobj 1312 0 obj <> endobj 1824 0 obj <> endobj 1307 0 obj <> endobj 1825 0 obj <> endobj 1302 0 obj <> endobj 1826 0 obj <> endobj 1297 0 obj <> endobj 1827 0 obj <> endobj 1292 0 obj <> endobj 1828 0 obj <> endobj 1287 0 obj <> endobj 1829 0 obj <> endobj 1282 0 obj <> endobj 1277 0 obj <> endobj 1830 0 obj <> endobj 1272 0 obj <> endobj 1267 0 obj <> endobj 1831 0 obj <> endobj 1262 0 obj <> endobj 1832 0 obj <> endobj 1257 0 obj <> endobj 1833 0 obj <> endobj 1252 0 obj <> endobj 1834 0 obj <> endobj 1247 0 obj <> endobj 1835 0 obj <> endobj 1242 0 obj <> endobj 1836 0 obj <> endobj 1237 0 obj <> endobj 1837 0 obj <> endobj 1232 0 obj <> endobj 1838 0 obj <> endobj 1227 0 obj <> endobj 1839 0 obj <> endobj 1222 0 obj <> endobj 1840 0 obj <> endobj 1217 0 obj <> endobj 1841 0 obj <> endobj 1212 0 obj <> endobj 1842 0 obj <> endobj 1207 0 obj <> endobj 1843 0 obj <> endobj 1202 0 obj <> endobj 1844 0 obj <> endobj 1197 0 obj <> endobj 1845 0 obj <> endobj 1192 0 obj <> endobj 1846 0 obj <> endobj 1187 0 obj <> endobj 1847 0 obj <> endobj 1182 0 obj <> endobj 1848 0 obj <> endobj 1177 0 obj <> endobj 1849 0 obj <> endobj 1172 0 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Ԕ 8D-E iA 钍x{Q7)jzG.tɔZVdÜqiA]9`^$ Խ&匃4h KDQC#%-l 9h rN%e !@Aؗ-⾁w- a,m +{3جN<"O ,"KjLJW~$GW>Ju<塂qB+E[K%$`)q >LWyQ<,^endstream endobj 6 0 obj 394 endobj 4 0 obj <> /Contents 5 0 R >> endobj 3 0 obj << /Type /Pages /Kids [ 4 0 R ] /Count 1 >> endobj 1 0 obj <> endobj 8 0 obj <> endobj 7 0 obj <> endobj 2 0 obj <>endobj xref 0 9 0000000000 65535 f 0000000698 00000 n 0000000837 00000 n 0000000639 00000 n 0000000498 00000 n 0000000015 00000 n 0000000479 00000 n 0000000775 00000 n 0000000746 00000 n trailer << /Size 9 /Root 1 0 R /Info 2 0 R /ID [<0D017316E40B7138A4AB7B58174CDF3C><0D017316E40B7138A4AB7B58174CDF3C>] >> startxref 1020 %%EOF sofa/20160503_c/c/00READ.ME0000644000113000011300000000317113027221063013472 0ustar bellsbells SOFA-Issue: 2016-05-03 This is the IAU Standards of Fundamental Astronomy (SOFA) Libraries product, issued on 2016-05-03. The tag `SOFA-Issue' above defines this release and differentiates it from previous or subsequent releases of the SOFA product. The 00READ.ME file must remain with this distribution set. Changes made since the previous release are noted in the file changes.lis. Notes: 1/ Unix users: The distribution set contains a simple makefile which can be used to create a single object library for the SOFA Libraries. To build the object library: a/ Examine the makefile to be sure definition of the C compiler is correct for your system. You need an ANSI standard compliant C compiler. Edit the CCOMPC macro in the makefile as necessary. b/ To create libsofa.a, execute make: % make (where % is the shell prompt). c/ To remove the object files: % make clean To link with the SOFA library, include the library in the compile/link command in the normal Unix fashion, eg: % gcc myprog.c -o myprog libsofa.a You should specify the appropriate C compiler name for `gcc' in the above command sequence. 2/ Windows/DOS/Mac users: There is no `build' procedure to create a linkable object library or DLL for the SOFA Libraries. This is due to the many different C compilers and development environments available on Windows/DOS and Mac machines. To use the SOFA routines with your program(s), you must use your preferred development environment to create the appropriate library or DLL. IAU SOFA Center 2016/05/02