#include "sofam.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: 2010 January 18 ** ** SOFA release 2012-03-01 ** ** Copyright (C) 2012 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) 2012 ** 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 ** **--------------------------------------------------------------------*/ }