| 1 | #include "erfa.h"
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| 2 |
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| 3 | double eraS06(double date1, double date2, double x, double y)
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| 4 | /*
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| 5 | ** - - - - - - -
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| 6 | ** e r a S 0 6
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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 2006/2000A precession-nutation.
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| 12 | **
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| 13 | ** Given:
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| 14 | ** date1,date2 double TT as a 2-part Julian Date (Note 1)
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| 15 | ** x,y double CIP coordinates (Note 3)
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| 16 | **
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| 17 | ** Returned (function value):
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| 18 | ** double the CIO locator s in radians (Note 2)
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| 19 | **
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| 20 | ** Notes:
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| 21 | **
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| 22 | ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
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| 23 | ** convenient way between the two arguments. For example,
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| 24 | ** JD(TT)=2450123.7 could be expressed in any of these ways,
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| 25 | ** among others:
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| 26 | **
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| 27 | ** date1 date2
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| 28 | **
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| 29 | ** 2450123.7 0.0 (JD method)
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| 30 | ** 2451545.0 -1421.3 (J2000 method)
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| 31 | ** 2400000.5 50123.2 (MJD method)
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| 32 | ** 2450123.5 0.2 (date & time method)
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| 33 | **
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| 34 | ** The JD method is the most natural and convenient to use in
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| 35 | ** cases where the loss of several decimal digits of resolution
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| 36 | ** is acceptable. The J2000 method is best matched to the way
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| 37 | ** the argument is handled internally and will deliver the
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| 38 | ** optimum resolution. The MJD method and the date & time methods
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| 39 | ** are both good compromises between resolution and convenience.
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| 40 | **
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| 41 | ** 2) The CIO locator s is the difference between the right ascensions
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| 42 | ** of the same point in two systems: the two systems are the GCRS
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| 43 | ** and the CIP,CIO, and the point is the ascending node of the
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| 44 | ** CIP equator. The quantity s remains below 0.1 arcsecond
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| 45 | ** throughout 1900-2100.
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| 46 | **
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| 47 | ** 3) The series used to compute s is in fact for s+XY/2, where X and Y
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| 48 | ** are the x and y components of the CIP unit vector; this series
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| 49 | ** is more compact than a direct series for s would be. This
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| 50 | ** function requires X,Y to be supplied by the caller, who is
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| 51 | ** responsible for providing values that are consistent with the
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| 52 | ** supplied date.
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| 53 | **
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| 54 | ** 4) The model is consistent with the "P03" precession (Capitaine et
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| 55 | ** al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the
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| 56 | ** IAU 2000A nutation (with P03 adjustments).
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| 57 | **
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| 58 | ** Called:
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| 59 | ** eraFal03 mean anomaly of the Moon
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| 60 | ** eraFalp03 mean anomaly of the Sun
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| 61 | ** eraFaf03 mean argument of the latitude of the Moon
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| 62 | ** eraFad03 mean elongation of the Moon from the Sun
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| 63 | ** eraFaom03 mean longitude of the Moon's ascending node
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| 64 | ** eraFave03 mean longitude of Venus
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| 65 | ** eraFae03 mean longitude of Earth
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| 66 | ** eraFapa03 general accumulated precession in longitude
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| 67 | **
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| 68 | ** References:
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| 69 | **
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| 70 | ** Capitaine, N., Wallace, P.T. & Chapront, J., 2003, Astron.
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| 71 | ** Astrophys. 432, 355
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| 72 | **
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| 73 | ** McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003),
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| 74 | ** IERS Technical Note No. 32, BKG
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| 75 | **
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| 76 | ** Copyright (C) 2013-2017, NumFOCUS Foundation.
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| 77 | ** Derived, with permission, from the SOFA library. See notes at end of file.
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| 78 | */
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| 79 | {
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| 80 | /* Time since J2000.0, in Julian centuries */
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| 81 | double t;
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| 82 |
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| 83 | /* Miscellaneous */
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| 84 | int i, j;
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| 85 | double a, w0, w1, w2, w3, w4, w5;
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| 86 |
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| 87 | /* Fundamental arguments */
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| 88 | double fa[8];
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| 89 |
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| 90 | /* Returned value */
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| 91 | double s;
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| 92 |
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| 93 | /* --------------------- */
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| 94 | /* The series for s+XY/2 */
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| 95 | /* --------------------- */
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| 96 |
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| 97 | typedef struct {
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| 98 | int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
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| 99 | double s, c; /* sine and cosine coefficients */
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| 100 | } TERM;
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| 101 |
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| 102 | /* Polynomial coefficients */
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| 103 | static const double sp[] = {
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| 104 |
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| 105 | /* 1-6 */
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| 106 | 94.00e-6,
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| 107 | 3808.65e-6,
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| 108 | -122.68e-6,
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| 109 | -72574.11e-6,
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| 110 | 27.98e-6,
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| 111 | 15.62e-6
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| 112 | };
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| 113 |
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| 114 | /* Terms of order t^0 */
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| 115 | static const TERM s0[] = {
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| 116 |
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| 117 | /* 1-10 */
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| 118 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 },
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| 119 | {{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6 },
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| 120 | {{ 0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6 },
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| 121 | {{ 0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6 },
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| 122 | {{ 0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6 },
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| 123 | {{ 0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6 },
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| 124 | {{ 0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6 },
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| 125 | {{ 0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6 },
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| 126 | {{ 0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6 },
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| 127 | {{ 0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6 },
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| 128 |
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| 129 | /* 11-20 */
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| 130 | {{ 1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6 },
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| 131 | {{ 1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6 },
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| 132 | {{ 0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6 },
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| 133 | {{ 0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6 },
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| 134 | {{ 0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6 },
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| 135 | {{ 0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6 },
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| 136 | {{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6 },
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| 137 | {{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6 },
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| 138 | {{ 1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6 },
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| 139 | {{ 1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6 },
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| 140 |
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| 141 | /* 21-30 */
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| 142 | {{ 0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6 },
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| 143 | {{ 0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6 },
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| 144 | {{ 0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6 },
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| 145 | {{ 0, 0, 0, 0, 0, 8,-13, -1}, 0.10e-6, -0.05e-6 },
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| 146 | {{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6 },
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| 147 | {{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
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| 148 | {{ 0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6 },
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| 149 | {{ 1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
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| 150 | {{ 1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
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| 151 | {{ 0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6 },
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| 152 |
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| 153 | /* 31-33 */
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| 154 | {{ 0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6 },
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| 155 | {{ 1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6 },
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| 156 | {{ 1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6 }
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| 157 | };
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| 158 |
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| 159 | /* Terms of order t^1 */
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| 160 | static const TERM s1[] = {
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| 161 |
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| 162 | /* 1 - 3 */
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| 163 | {{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 },
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| 164 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.73e-6, -0.03e-6 },
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| 165 | {{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 }
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| 166 | };
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| 167 |
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| 168 | /* Terms of order t^2 */
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| 169 | static const TERM s2[] = {
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| 170 |
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| 171 | /* 1-10 */
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| 172 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.52e-6, -0.17e-6 },
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| 173 | {{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 },
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| 174 | {{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 },
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| 175 | {{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 },
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| 176 | {{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 },
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| 177 | {{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 },
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| 178 | {{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 },
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| 179 | {{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 },
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| 180 | {{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 },
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| 181 | {{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 },
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| 182 |
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| 183 | /* 11-20 */
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| 184 | {{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 },
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| 185 | {{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 },
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| 186 | {{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 },
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| 187 | {{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 },
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| 188 | {{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 },
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| 189 | {{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 },
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| 190 | {{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 },
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| 191 | {{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 },
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| 192 | {{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 },
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| 193 | {{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 },
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| 194 |
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| 195 | /* 21-25 */
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| 196 | {{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 },
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| 197 | {{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 },
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| 198 | {{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 },
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| 199 | {{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 },
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| 200 | {{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 }
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| 201 | };
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| 202 |
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| 203 | /* Terms of order t^3 */
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| 204 | static const TERM s3[] = {
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| 205 |
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| 206 | /* 1-4 */
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| 207 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.42e-6 },
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| 208 | {{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.46e-6 },
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| 209 | {{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.25e-6 },
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| 210 | {{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.23e-6 }
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| 211 | };
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| 212 |
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| 213 | /* Terms of order t^4 */
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| 214 | static const TERM s4[] = {
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| 215 |
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| 216 | /* 1-1 */
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| 217 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 }
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| 218 | };
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| 219 |
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| 220 | /* Number of terms in the series */
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| 221 | static const int NS0 = (int) (sizeof s0 / sizeof (TERM));
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| 222 | static const int NS1 = (int) (sizeof s1 / sizeof (TERM));
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| 223 | static const int NS2 = (int) (sizeof s2 / sizeof (TERM));
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| 224 | static const int NS3 = (int) (sizeof s3 / sizeof (TERM));
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| 225 | static const int NS4 = (int) (sizeof s4 / sizeof (TERM));
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| 226 |
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| 227 | /*--------------------------------------------------------------------*/
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| 228 |
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| 229 | /* Interval between fundamental epoch J2000.0 and current date (JC). */
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| 230 | t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
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| 231 |
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| 232 | /* Fundamental Arguments (from IERS Conventions 2003) */
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| 233 |
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| 234 | /* Mean anomaly of the Moon. */
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| 235 | fa[0] = eraFal03(t);
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| 236 |
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| 237 | /* Mean anomaly of the Sun. */
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| 238 | fa[1] = eraFalp03(t);
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| 239 |
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| 240 | /* Mean longitude of the Moon minus that of the ascending node. */
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| 241 | fa[2] = eraFaf03(t);
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| 242 |
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| 243 | /* Mean elongation of the Moon from the Sun. */
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| 244 | fa[3] = eraFad03(t);
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| 245 |
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| 246 | /* Mean longitude of the ascending node of the Moon. */
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| 247 | fa[4] = eraFaom03(t);
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| 248 |
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| 249 | /* Mean longitude of Venus. */
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| 250 | fa[5] = eraFave03(t);
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| 251 |
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| 252 | /* Mean longitude of Earth. */
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| 253 | fa[6] = eraFae03(t);
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| 254 |
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| 255 | /* General precession in longitude. */
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| 256 | fa[7] = eraFapa03(t);
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| 257 |
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| 258 | /* Evaluate s. */
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| 259 | w0 = sp[0];
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| 260 | w1 = sp[1];
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| 261 | w2 = sp[2];
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| 262 | w3 = sp[3];
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| 263 | w4 = sp[4];
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| 264 | w5 = sp[5];
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| 265 |
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| 266 | for (i = NS0-1; i >= 0; i--) {
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| 267 | a = 0.0;
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| 268 | for (j = 0; j < 8; j++) {
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| 269 | a += (double)s0[i].nfa[j] * fa[j];
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| 270 | }
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| 271 | w0 += s0[i].s * sin(a) + s0[i].c * cos(a);
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| 272 | }
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| 273 |
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| 274 | for (i = NS1-1; i >= 0; i--) {
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| 275 | a = 0.0;
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| 276 | for (j = 0; j < 8; j++) {
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| 277 | a += (double)s1[i].nfa[j] * fa[j];
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| 278 | }
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| 279 | w1 += s1[i].s * sin(a) + s1[i].c * cos(a);
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| 280 | }
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| 281 |
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| 282 | for (i = NS2-1; i >= 0; i--) {
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| 283 | a = 0.0;
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| 284 | for (j = 0; j < 8; j++) {
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| 285 | a += (double)s2[i].nfa[j] * fa[j];
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| 286 | }
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| 287 | w2 += s2[i].s * sin(a) + s2[i].c * cos(a);
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| 288 | }
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| 289 |
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| 290 | for (i = NS3-1; i >= 0; i--) {
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| 291 | a = 0.0;
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| 292 | for (j = 0; j < 8; j++) {
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| 293 | a += (double)s3[i].nfa[j] * fa[j];
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| 294 | }
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| 295 | w3 += s3[i].s * sin(a) + s3[i].c * cos(a);
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| 296 | }
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| 297 |
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| 298 | for (i = NS4-1; i >= 0; i--) {
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| 299 | a = 0.0;
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| 300 | for (j = 0; j < 8; j++) {
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| 301 | a += (double)s4[i].nfa[j] * fa[j];
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| 302 | }
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| 303 | w4 += s4[i].s * sin(a) + s4[i].c * cos(a);
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| 304 | }
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| 305 |
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| 306 | s = (w0 +
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| 307 | (w1 +
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| 308 | (w2 +
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| 309 | (w3 +
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| 310 | (w4 +
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| 311 | w5 * t) * t) * t) * t) * t) * ERFA_DAS2R - x*y/2.0;
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| 312 |
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| 313 | return s;
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| 314 |
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| 315 | }
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| 316 | /*----------------------------------------------------------------------
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| 317 | **
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| 318 | **
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| 319 | ** Copyright (C) 2013-2017, NumFOCUS Foundation.
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| 320 | ** All rights reserved.
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| 321 | **
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| 322 | ** This library is derived, with permission, from the International
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| 323 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
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| 324 | ** available from http://www.iausofa.org.
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| 325 | **
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| 326 | ** The ERFA version is intended to retain identical functionality to
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| 327 | ** the SOFA library, but made distinct through different function and
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| 328 | ** file names, as set out in the SOFA license conditions. The SOFA
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| 329 | ** original has a role as a reference standard for the IAU and IERS,
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| 330 | ** and consequently redistribution is permitted only in its unaltered
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| 331 | ** state. The ERFA version is not subject to this restriction and
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| 332 | ** therefore can be included in distributions which do not support the
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| 333 | ** concept of "read only" software.
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| 334 | **
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| 335 | ** Although the intent is to replicate the SOFA API (other than
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| 336 | ** replacement of prefix names) and results (with the exception of
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| 337 | ** bugs; any that are discovered will be fixed), SOFA is not
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| 338 | ** responsible for any errors found in this version of the library.
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| 339 | **
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| 340 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
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| 341 | ** that you are using a library derived from SOFA, rather than SOFA
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| 342 | ** itself.
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| 343 | **
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| 344 | **
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| 345 | ** TERMS AND CONDITIONS
|
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| 346 | **
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| 347 | ** Redistribution and use in source and binary forms, with or without
|
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| 348 | ** modification, are permitted provided that the following conditions
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| 349 | ** are met:
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| 350 | **
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| 351 | ** 1 Redistributions of source code must retain the above copyright
|
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| 352 | ** notice, this list of conditions and the following disclaimer.
|
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| 353 | **
|
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| 354 | ** 2 Redistributions in binary form must reproduce the above copyright
|
|---|
| 355 | ** notice, this list of conditions and the following disclaimer in
|
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| 356 | ** the documentation and/or other materials provided with the
|
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| 357 | ** distribution.
|
|---|
| 358 | **
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| 359 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
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| 360 | ** the International Astronomical Union nor the names of its
|
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| 361 | ** contributors may be used to endorse or promote products derived
|
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| 362 | ** from this software without specific prior written permission.
|
|---|
| 363 | **
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| 364 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
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| 365 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
|---|
| 366 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
|---|
| 367 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
|---|
| 368 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|---|
| 369 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
|---|
| 370 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|---|
| 371 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
|---|
| 372 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|---|
| 373 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
|---|
| 374 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
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| 375 | ** POSSIBILITY OF SUCH DAMAGE.
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| 376 | **
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| 377 | */
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