#include "erfa.h" double eraS06(double date1, double date2, double x, double y) /* ** - - - - - - - ** e r a 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. ** ** 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: ** eraFal03 mean anomaly of the Moon ** eraFalp03 mean anomaly of the Sun ** eraFaf03 mean argument of the latitude of the Moon ** eraFad03 mean elongation of the Moon from the Sun ** eraFaom03 mean longitude of the Moon's ascending node ** eraFave03 mean longitude of Venus ** eraFae03 mean longitude of Earth ** eraFapa03 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 ** ** Copyright (C) 2013-2017, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { /* 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 - ERFA_DJ00) + date2) / ERFA_DJC; /* Fundamental Arguments (from IERS Conventions 2003) */ /* Mean anomaly of the Moon. */ fa[0] = eraFal03(t); /* Mean anomaly of the Sun. */ fa[1] = eraFalp03(t); /* Mean longitude of the Moon minus that of the ascending node. */ fa[2] = eraFaf03(t); /* Mean elongation of the Moon from the Sun. */ fa[3] = eraFad03(t); /* Mean longitude of the ascending node of the Moon. */ fa[4] = eraFaom03(t); /* Mean longitude of Venus. */ fa[5] = eraFave03(t); /* Mean longitude of Earth. */ fa[6] = eraFae03(t); /* General precession in longitude. */ fa[7] = eraFapa03(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) * ERFA_DAS2R - x*y/2.0; return s; } /*---------------------------------------------------------------------- ** ** ** Copyright (C) 2013-2017, NumFOCUS Foundation. ** All rights reserved. ** ** This library is derived, with permission, from the International ** Astronomical Union's "Standards of Fundamental Astronomy" library, ** available from http://www.iausofa.org. ** ** The ERFA version is intended to retain identical functionality to ** the SOFA library, but made distinct through different function and ** file names, as set out in the SOFA license conditions. The SOFA ** original has a role as a reference standard for the IAU and IERS, ** and consequently redistribution is permitted only in its unaltered ** state. The ERFA version is not subject to this restriction and ** therefore can be included in distributions which do not support the ** concept of "read only" software. ** ** Although the intent is to replicate the SOFA API (other than ** replacement of prefix names) and results (with the exception of ** bugs; any that are discovered will be fixed), SOFA is not ** responsible for any errors found in this version of the library. ** ** If you wish to acknowledge the SOFA heritage, please acknowledge ** that you are using a library derived from SOFA, rather than SOFA ** itself. ** ** ** TERMS AND CONDITIONS ** ** Redistribution and use in source and binary forms, with or without ** modification, are permitted provided that the following conditions ** are met: ** ** 1 Redistributions of source code must retain the above copyright ** notice, this list of conditions and the following disclaimer. ** ** 2 Redistributions in binary form must reproduce the above copyright ** notice, this list of conditions and the following disclaimer in ** the documentation and/or other materials provided with the ** distribution. ** ** 3 Neither the name of the Standards Of Fundamental Astronomy Board, ** the International Astronomical Union nor the names of its ** contributors may be used to endorse or promote products derived ** from this software without specific prior written permission. ** ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ** POSSIBILITY OF SUCH DAMAGE. ** */