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 2017-04-20 ** ** Copyright (C) 2017 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) 2017 ** 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: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
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: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
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 2015-02-09 ** ** Copyright (C) 2015 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) 2015 ** 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: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }