| 1 | #include "sofa.h"
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| 2 |
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| 3 | double iauS00(double date1, double date2, double x, double y)
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| 4 | /*
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| 5 | ** - - - - - - -
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| 6 | ** i a u S 0 0
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| 7 | ** - - - - - - -
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| 8 | **
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| 9 | ** The CIO locator s, positioning the Celestial Intermediate Origin on
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| 10 | ** the equator of the Celestial Intermediate Pole, given the CIP's X,Y
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| 11 | ** coordinates. Compatible with IAU 2000A precession-nutation.
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| 12 | **
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| 13 | ** This function is part of the International Astronomical Union's
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| 14 | ** SOFA (Standards Of Fundamental Astronomy) software collection.
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| 15 | **
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| 16 | ** Status: canonical model.
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| 17 | **
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| 18 | ** Given:
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| 19 | ** date1,date2 double TT as a 2-part Julian Date (Note 1)
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| 20 | ** x,y double CIP coordinates (Note 3)
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| 21 | **
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| 22 | ** Returned (function value):
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| 23 | ** double the CIO locator s in radians (Note 2)
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| 24 | **
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| 25 | ** Notes:
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| 26 | **
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| 27 | ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
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| 28 | ** convenient way between the two arguments. For example,
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| 29 | ** JD(TT)=2450123.7 could be expressed in any of these ways,
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| 30 | ** among others:
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| 31 | **
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| 32 | ** date1 date2
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| 33 | **
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| 34 | ** 2450123.7 0.0 (JD method)
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| 35 | ** 2451545.0 -1421.3 (J2000 method)
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| 36 | ** 2400000.5 50123.2 (MJD method)
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| 37 | ** 2450123.5 0.2 (date & time method)
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| 38 | **
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| 39 | ** The JD method is the most natural and convenient to use in
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| 40 | ** cases where the loss of several decimal digits of resolution
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| 41 | ** is acceptable. The J2000 method is best matched to the way
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| 42 | ** the argument is handled internally and will deliver the
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| 43 | ** optimum resolution. The MJD method and the date & time methods
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| 44 | ** are both good compromises between resolution and convenience.
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| 45 | **
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| 46 | ** 2) The CIO locator s is the difference between the right ascensions
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| 47 | ** of the same point in two systems: the two systems are the GCRS
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| 48 | ** and the CIP,CIO, and the point is the ascending node of the
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| 49 | ** CIP equator. The quantity s remains below 0.1 arcsecond
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| 50 | ** throughout 1900-2100.
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| 51 | **
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| 52 | ** 3) The series used to compute s is in fact for s+XY/2, where X and Y
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| 53 | ** are the x and y components of the CIP unit vector; this series
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| 54 | ** is more compact than a direct series for s would be. This
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| 55 | ** function requires X,Y to be supplied by the caller, who is
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| 56 | ** responsible for providing values that are consistent with the
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| 57 | ** supplied date.
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| 58 | **
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| 59 | ** 4) The model is consistent with the IAU 2000A precession-nutation.
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| 60 | **
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| 61 | ** Called:
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| 62 | ** iauFal03 mean anomaly of the Moon
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| 63 | ** iauFalp03 mean anomaly of the Sun
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| 64 | ** iauFaf03 mean argument of the latitude of the Moon
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| 65 | ** iauFad03 mean elongation of the Moon from the Sun
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| 66 | ** iauFaom03 mean longitude of the Moon's ascending node
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| 67 | ** iauFave03 mean longitude of Venus
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| 68 | ** iauFae03 mean longitude of Earth
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| 69 | ** iauFapa03 general accumulated precession in longitude
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| 70 | **
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| 71 | ** References:
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| 72 | **
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| 73 | ** Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
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| 74 | ** "Expressions for the Celestial Intermediate Pole and Celestial
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| 75 | ** Ephemeris Origin consistent with the IAU 2000A precession-
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| 76 | ** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
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| 77 | **
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| 78 | ** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
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| 79 | ** intermediate origin" (CIO) by IAU 2006 Resolution 2.
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| 80 | **
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| 81 | ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
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| 82 | ** IERS Technical Note No. 32, BKG (2004)
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| 83 | **
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| 84 | ** This revision: 2013 June 18
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| 85 | **
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| 86 | ** SOFA release 2015-02-09
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| 87 | **
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| 88 | ** Copyright (C) 2015 IAU SOFA Board. See notes at end.
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| 89 | */
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| 90 | {
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| 91 | /* Time since J2000.0, in Julian centuries */
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| 92 | double t;
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| 93 |
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| 94 | /* Miscellaneous */
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| 95 | int i, j;
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| 96 | double a, w0, w1, w2, w3, w4, w5;
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| 97 |
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| 98 | /* Fundamental arguments */
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| 99 | double fa[8];
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| 100 |
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| 101 | /* Returned value */
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| 102 | double s;
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| 103 |
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| 104 | /* --------------------- */
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| 105 | /* The series for s+XY/2 */
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| 106 | /* --------------------- */
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| 107 |
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| 108 | typedef struct {
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| 109 | int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
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| 110 | double s, c; /* sine and cosine coefficients */
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| 111 | } TERM;
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| 112 |
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| 113 | /* Polynomial coefficients */
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| 114 | static const double sp[] = {
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| 115 |
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| 116 | /* 1-6 */
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| 117 | 94.00e-6,
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| 118 | 3808.35e-6,
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| 119 | -119.94e-6,
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| 120 | -72574.09e-6,
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| 121 | 27.70e-6,
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| 122 | 15.61e-6
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| 123 | };
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| 124 |
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| 125 | /* Terms of order t^0 */
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| 126 | static const TERM s0[] = {
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| 127 |
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| 128 | /* 1-10 */
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| 129 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 },
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| 130 | {{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6 },
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| 131 | {{ 0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6 },
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| 132 | {{ 0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6 },
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| 133 | {{ 0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6 },
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| 134 | {{ 0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6 },
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| 135 | {{ 0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6 },
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| 136 | {{ 0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6 },
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| 137 | {{ 0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6 },
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| 138 | {{ 0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6 },
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| 139 |
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| 140 | /* 11-20 */
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| 141 | {{ 1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6 },
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| 142 | {{ 1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6 },
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| 143 | {{ 0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6 },
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| 144 | {{ 0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6 },
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| 145 | {{ 0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6 },
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| 146 | {{ 0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6 },
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| 147 | {{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6 },
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| 148 | {{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6 },
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| 149 | {{ 1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6 },
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| 150 | {{ 1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6 },
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| 151 |
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| 152 | /* 21-30 */
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| 153 | {{ 0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6 },
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| 154 | {{ 0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6 },
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| 155 | {{ 0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6 },
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| 156 | {{ 0, 0, 0, 0, 0, 8,-13, -1}, 0.10e-6, -0.05e-6 },
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| 157 | {{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6 },
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| 158 | {{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
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| 159 | {{ 0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6 },
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| 160 | {{ 1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
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| 161 | {{ 1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
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| 162 | {{ 0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6 },
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| 163 |
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| 164 | /* 31-33 */
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| 165 | {{ 0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6 },
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| 166 | {{ 1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6 },
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| 167 | {{ 1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6 }
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| 168 | };
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| 169 |
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| 170 | /* Terms of order t^1 */
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| 171 | static const TERM s1[] ={
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| 172 |
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| 173 | /* 1-3 */
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| 174 | {{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 },
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| 175 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.71e-6, -0.03e-6 },
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| 176 | {{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 }
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| 177 | };
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| 178 |
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| 179 | /* Terms of order t^2 */
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| 180 | static const TERM s2[] ={
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| 181 |
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| 182 | /* 1-10 */
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| 183 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.53e-6, -0.17e-6 },
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| 184 | {{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 },
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| 185 | {{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 },
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| 186 | {{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 },
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| 187 | {{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 },
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| 188 | {{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 },
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| 189 | {{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 },
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| 190 | {{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 },
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| 191 | {{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 },
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| 192 | {{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 },
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| 193 |
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| 194 | /* 11-20 */
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| 195 | {{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 },
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| 196 | {{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 },
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| 197 | {{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 },
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| 198 | {{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 },
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| 199 | {{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 },
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| 200 | {{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 },
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| 201 | {{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 },
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| 202 | {{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 },
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| 203 | {{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 },
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| 204 | {{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 },
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| 205 |
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| 206 | /* 21-25 */
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| 207 | {{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 },
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| 208 | {{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 },
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| 209 | {{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 },
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| 210 | {{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 },
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| 211 | {{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 }
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| 212 | };
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| 213 |
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| 214 | /* Terms of order t^3 */
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| 215 | static const TERM s3[] ={
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| 216 |
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| 217 | /* 1-4 */
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| 218 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.51e-6 },
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| 219 | {{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.39e-6 },
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| 220 | {{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.24e-6 },
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| 221 | {{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.22e-6 }
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| 222 | };
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| 223 |
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| 224 | /* Terms of order t^4 */
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| 225 | static const TERM s4[] ={
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| 226 |
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| 227 | /* 1-1 */
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| 228 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 }
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| 229 | };
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| 230 |
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| 231 | /* Number of terms in the series */
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| 232 | const int NS0 = (int) (sizeof s0 / sizeof (TERM));
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| 233 | const int NS1 = (int) (sizeof s1 / sizeof (TERM));
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| 234 | const int NS2 = (int) (sizeof s2 / sizeof (TERM));
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| 235 | const int NS3 = (int) (sizeof s3 / sizeof (TERM));
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| 236 | const int NS4 = (int) (sizeof s4 / sizeof (TERM));
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| 237 |
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| 238 | /*--------------------------------------------------------------------*/
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| 239 |
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| 240 | /* Interval between fundamental epoch J2000.0 and current date (JC). */
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| 241 | t = ((date1 - DJ00) + date2) / DJC;
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| 242 |
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| 243 | /* Fundamental Arguments (from IERS Conventions 2003) */
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| 244 |
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| 245 | /* Mean anomaly of the Moon. */
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| 246 | fa[0] = iauFal03(t);
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| 247 |
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| 248 | /* Mean anomaly of the Sun. */
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| 249 | fa[1] = iauFalp03(t);
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| 250 |
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| 251 | /* Mean longitude of the Moon minus that of the ascending node. */
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| 252 | fa[2] = iauFaf03(t);
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| 253 |
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| 254 | /* Mean elongation of the Moon from the Sun. */
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| 255 | fa[3] = iauFad03(t);
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| 256 |
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| 257 | /* Mean longitude of the ascending node of the Moon. */
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| 258 | fa[4] = iauFaom03(t);
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| 259 |
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| 260 | /* Mean longitude of Venus. */
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| 261 | fa[5] = iauFave03(t);
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| 262 |
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| 263 | /* Mean longitude of Earth. */
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| 264 | fa[6] = iauFae03(t);
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| 265 |
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| 266 | /* General precession in longitude. */
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| 267 | fa[7] = iauFapa03(t);
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| 268 |
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| 269 | /* Evaluate s. */
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| 270 | w0 = sp[0];
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| 271 | w1 = sp[1];
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| 272 | w2 = sp[2];
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| 273 | w3 = sp[3];
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| 274 | w4 = sp[4];
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| 275 | w5 = sp[5];
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| 276 |
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| 277 | for (i = NS0-1; i >= 0; i--) {
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| 278 | a = 0.0;
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| 279 | for (j = 0; j < 8; j++) {
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| 280 | a += (double)s0[i].nfa[j] * fa[j];
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| 281 | }
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| 282 | w0 += s0[i].s * sin(a) + s0[i].c * cos(a);
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| 283 | }
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| 284 |
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| 285 | for (i = NS1-1; i >= 0; i--) {
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| 286 | a = 0.0;
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| 287 | for (j = 0; j < 8; j++) {
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| 288 | a += (double)s1[i].nfa[j] * fa[j];
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| 289 | }
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| 290 | w1 += s1[i].s * sin(a) + s1[i].c * cos(a);
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| 291 | }
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| 292 |
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| 293 | for (i = NS2-1; i >= 0; i--) {
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| 294 | a = 0.0;
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| 295 | for (j = 0; j < 8; j++) {
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| 296 | a += (double)s2[i].nfa[j] * fa[j];
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| 297 | }
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| 298 | w2 += s2[i].s * sin(a) + s2[i].c * cos(a);
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| 299 | }
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| 300 |
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| 301 | for (i = NS3-1; i >= 0; i--) {
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| 302 | a = 0.0;
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| 303 | for (j = 0; j < 8; j++) {
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| 304 | a += (double)s3[i].nfa[j] * fa[j];
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| 305 | }
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| 306 | w3 += s3[i].s * sin(a) + s3[i].c * cos(a);
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| 307 | }
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| 308 |
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| 309 | for (i = NS4-1; i >= 0; i--) {
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| 310 | a = 0.0;
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| 311 | for (j = 0; j < 8; j++) {
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| 312 | a += (double)s4[i].nfa[j] * fa[j];
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| 313 | }
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| 314 | w4 += s4[i].s * sin(a) + s4[i].c * cos(a);
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| 315 | }
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| 316 |
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| 317 | s = (w0 +
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| 318 | (w1 +
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| 319 | (w2 +
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| 320 | (w3 +
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| 321 | (w4 +
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| 322 | w5 * t) * t) * t) * t) * t) * DAS2R - x*y/2.0;
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| 323 |
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| 324 | return s;
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| 325 |
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| 326 | /*----------------------------------------------------------------------
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| 327 | **
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| 328 | ** Copyright (C) 2015
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| 329 | ** Standards Of Fundamental Astronomy Board
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| 330 | ** of the International Astronomical Union.
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| 331 | **
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| 332 | ** =====================
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| 333 | ** SOFA Software License
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| 334 | ** =====================
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| 335 | **
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| 336 | ** NOTICE TO USER:
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| 337 | **
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| 338 | ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
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| 339 | ** CONDITIONS WHICH APPLY TO ITS USE.
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| 340 | **
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| 341 | ** 1. The Software is owned by the IAU SOFA Board ("SOFA").
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| 342 | **
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| 343 | ** 2. Permission is granted to anyone to use the SOFA software for any
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| 344 | ** purpose, including commercial applications, free of charge and
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| 345 | ** without payment of royalties, subject to the conditions and
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| 346 | ** restrictions listed below.
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| 347 | **
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| 348 | ** 3. You (the user) may copy and distribute SOFA source code to others,
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| 349 | ** and use and adapt its code and algorithms in your own software,
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| 350 | ** on a world-wide, royalty-free basis. That portion of your
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| 351 | ** distribution that does not consist of intact and unchanged copies
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| 352 | ** of SOFA source code files is a "derived work" that must comply
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| 353 | ** with the following requirements:
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| 354 | **
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| 355 | ** a) Your work shall be marked or carry a statement that it
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| 356 | ** (i) uses routines and computations derived by you from
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| 357 | ** software provided by SOFA under license to you; and
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| 358 | ** (ii) does not itself constitute software provided by and/or
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| 359 | ** endorsed by SOFA.
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| 360 | **
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| 361 | ** b) The source code of your derived work must contain descriptions
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| 362 | ** of how the derived work is based upon, contains and/or differs
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| 363 | ** from the original SOFA software.
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| 364 | **
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| 365 | ** c) The names of all routines in your derived work shall not
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| 366 | ** include the prefix "iau" or "sofa" or trivial modifications
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| 367 | ** thereof such as changes of case.
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| 368 | **
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| 369 | ** d) The origin of the SOFA components of your derived work must
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| 370 | ** not be misrepresented; you must not claim that you wrote the
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| 371 | ** original software, nor file a patent application for SOFA
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| 372 | ** software or algorithms embedded in the SOFA software.
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| 373 | **
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| 374 | ** e) These requirements must be reproduced intact in any source
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| 375 | ** distribution and shall apply to anyone to whom you have
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| 376 | ** granted a further right to modify the source code of your
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| 377 | ** derived work.
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| 378 | **
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| 379 | ** Note that, as originally distributed, the SOFA software is
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| 380 | ** intended to be a definitive implementation of the IAU standards,
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| 381 | ** and consequently third-party modifications are discouraged. All
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| 382 | ** variations, no matter how minor, must be explicitly marked as
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| 383 | ** such, as explained above.
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| 384 | **
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| 385 | ** 4. You shall not cause the SOFA software to be brought into
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| 386 | ** disrepute, either by misuse, or use for inappropriate tasks, or
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| 387 | ** by inappropriate modification.
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| 388 | **
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| 389 | ** 5. The SOFA software is provided "as is" and SOFA makes no warranty
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| 390 | ** as to its use or performance. SOFA does not and cannot warrant
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| 391 | ** the performance or results which the user may obtain by using the
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| 392 | ** SOFA software. SOFA makes no warranties, express or implied, as
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| 393 | ** to non-infringement of third party rights, merchantability, or
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| 394 | ** fitness for any particular purpose. In no event will SOFA be
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| 395 | ** liable to the user for any consequential, incidental, or special
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| 396 | ** damages, including any lost profits or lost savings, even if a
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| 397 | ** SOFA representative has been advised of such damages, or for any
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| 398 | ** claim by any third party.
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| 399 | **
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| 400 | ** 6. The provision of any version of the SOFA software under the terms
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| 401 | ** and conditions specified herein does not imply that future
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| 402 | ** versions will also be made available under the same terms and
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| 403 | ** conditions.
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| 404 | *
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| 405 | ** In any published work or commercial product which uses the SOFA
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| 406 | ** software directly, acknowledgement (see www.iausofa.org) is
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| 407 | ** appreciated.
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| 408 | **
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| 409 | ** Correspondence concerning SOFA software should be addressed as
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| 410 | ** follows:
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| 411 | **
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| 412 | ** By email: sofa@ukho.gov.uk
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| 413 | ** By post: IAU SOFA Center
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| 414 | ** HM Nautical Almanac Office
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| 415 | ** UK Hydrographic Office
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| 416 | ** Admiralty Way, Taunton
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| 417 | ** Somerset, TA1 2DN
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| 418 | ** United Kingdom
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| 419 | **
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| 420 | **--------------------------------------------------------------------*/
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| 421 | }
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