| 1 | #include "sofa.h"
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| 2 |
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| 3 | void iauNut80(double date1, double date2, double *dpsi, double *deps)
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| 4 | /*
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| 5 | ** - - - - - - - - -
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| 6 | ** i a u N u t 8 0
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| 7 | ** - - - - - - - - -
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| 8 | **
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| 9 | ** Nutation, IAU 1980 model.
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| 10 | **
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| 11 | ** This function is part of the International Astronomical Union's
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| 12 | ** SOFA (Standards Of Fundamental Astronomy) software collection.
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| 13 | **
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| 14 | ** Status: canonical model.
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| 15 | **
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| 16 | ** Given:
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| 17 | ** date1,date2 double TT as a 2-part Julian Date (Note 1)
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| 18 | **
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| 19 | ** Returned:
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| 20 | ** dpsi double nutation in longitude (radians)
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| 21 | ** deps double nutation in obliquity (radians)
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| 22 | **
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| 23 | ** Notes:
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| 24 | **
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| 25 | ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
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| 26 | ** convenient way between the two arguments. For example,
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| 27 | ** JD(TT)=2450123.7 could be expressed in any of these ways,
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| 28 | ** among others:
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| 29 | **
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| 30 | ** date1 date2
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| 31 | **
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| 32 | ** 2450123.7 0.0 (JD method)
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| 33 | ** 2451545.0 -1421.3 (J2000 method)
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| 34 | ** 2400000.5 50123.2 (MJD method)
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| 35 | ** 2450123.5 0.2 (date & time method)
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| 36 | **
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| 37 | ** The JD method is the most natural and convenient to use in
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| 38 | ** cases where the loss of several decimal digits of resolution
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| 39 | ** is acceptable. The J2000 method is best matched to the way
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| 40 | ** the argument is handled internally and will deliver the
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| 41 | ** optimum resolution. The MJD method and the date & time methods
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| 42 | ** are both good compromises between resolution and convenience.
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| 43 | **
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| 44 | ** 2) The nutation components are with respect to the ecliptic of
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| 45 | ** date.
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| 46 | **
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| 47 | ** Called:
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| 48 | ** iauAnpm normalize angle into range +/- pi
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| 49 | **
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| 50 | ** Reference:
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| 51 | **
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| 52 | ** Explanatory Supplement to the Astronomical Almanac,
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| 53 | ** P. Kenneth Seidelmann (ed), University Science Books (1992),
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| 54 | ** Section 3.222 (p111).
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| 55 | **
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| 56 | ** This revision: 2013 June 18
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| 57 | **
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| 58 | ** SOFA release 2015-02-09
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| 59 | **
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| 60 | ** Copyright (C) 2015 IAU SOFA Board. See notes at end.
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| 61 | */
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| 62 | {
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| 63 | double t, el, elp, f, d, om, dp, de, arg, s, c;
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| 64 | int j;
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| 65 |
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| 66 | /* Units of 0.1 milliarcsecond to radians */
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| 67 | const double U2R = DAS2R / 1e4;
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| 68 |
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| 69 | /* ------------------------------------------------ */
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| 70 | /* Table of multiples of arguments and coefficients */
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| 71 | /* ------------------------------------------------ */
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| 72 |
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| 73 | /* The units for the sine and cosine coefficients are 0.1 mas and */
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| 74 | /* the same per Julian century */
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| 75 |
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| 76 | static const struct {
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| 77 | int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
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| 78 | double sp,spt; /* longitude sine, 1 and t coefficients */
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| 79 | double ce,cet; /* obliquity cosine, 1 and t coefficients */
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| 80 | } x[] = {
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| 81 |
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| 82 | /* 1-10 */
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| 83 | { 0, 0, 0, 0, 1, -171996.0, -174.2, 92025.0, 8.9 },
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| 84 | { 0, 0, 0, 0, 2, 2062.0, 0.2, -895.0, 0.5 },
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| 85 | { -2, 0, 2, 0, 1, 46.0, 0.0, -24.0, 0.0 },
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| 86 | { 2, 0, -2, 0, 0, 11.0, 0.0, 0.0, 0.0 },
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| 87 | { -2, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 },
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| 88 | { 1, -1, 0, -1, 0, -3.0, 0.0, 0.0, 0.0 },
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| 89 | { 0, -2, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 },
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| 90 | { 2, 0, -2, 0, 1, 1.0, 0.0, 0.0, 0.0 },
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| 91 | { 0, 0, 2, -2, 2, -13187.0, -1.6, 5736.0, -3.1 },
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| 92 | { 0, 1, 0, 0, 0, 1426.0, -3.4, 54.0, -0.1 },
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| 93 |
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| 94 | /* 11-20 */
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| 95 | { 0, 1, 2, -2, 2, -517.0, 1.2, 224.0, -0.6 },
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| 96 | { 0, -1, 2, -2, 2, 217.0, -0.5, -95.0, 0.3 },
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| 97 | { 0, 0, 2, -2, 1, 129.0, 0.1, -70.0, 0.0 },
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| 98 | { 2, 0, 0, -2, 0, 48.0, 0.0, 1.0, 0.0 },
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| 99 | { 0, 0, 2, -2, 0, -22.0, 0.0, 0.0, 0.0 },
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| 100 | { 0, 2, 0, 0, 0, 17.0, -0.1, 0.0, 0.0 },
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| 101 | { 0, 1, 0, 0, 1, -15.0, 0.0, 9.0, 0.0 },
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| 102 | { 0, 2, 2, -2, 2, -16.0, 0.1, 7.0, 0.0 },
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| 103 | { 0, -1, 0, 0, 1, -12.0, 0.0, 6.0, 0.0 },
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| 104 | { -2, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 },
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| 105 |
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| 106 | /* 21-30 */
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| 107 | { 0, -1, 2, -2, 1, -5.0, 0.0, 3.0, 0.0 },
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| 108 | { 2, 0, 0, -2, 1, 4.0, 0.0, -2.0, 0.0 },
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| 109 | { 0, 1, 2, -2, 1, 4.0, 0.0, -2.0, 0.0 },
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| 110 | { 1, 0, 0, -1, 0, -4.0, 0.0, 0.0, 0.0 },
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| 111 | { 2, 1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 },
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| 112 | { 0, 0, -2, 2, 1, 1.0, 0.0, 0.0, 0.0 },
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| 113 | { 0, 1, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 },
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| 114 | { 0, 1, 0, 0, 2, 1.0, 0.0, 0.0, 0.0 },
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| 115 | { -1, 0, 0, 1, 1, 1.0, 0.0, 0.0, 0.0 },
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| 116 | { 0, 1, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 },
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| 117 |
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| 118 | /* 31-40 */
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| 119 | { 0, 0, 2, 0, 2, -2274.0, -0.2, 977.0, -0.5 },
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| 120 | { 1, 0, 0, 0, 0, 712.0, 0.1, -7.0, 0.0 },
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| 121 | { 0, 0, 2, 0, 1, -386.0, -0.4, 200.0, 0.0 },
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| 122 | { 1, 0, 2, 0, 2, -301.0, 0.0, 129.0, -0.1 },
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| 123 | { 1, 0, 0, -2, 0, -158.0, 0.0, -1.0, 0.0 },
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| 124 | { -1, 0, 2, 0, 2, 123.0, 0.0, -53.0, 0.0 },
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| 125 | { 0, 0, 0, 2, 0, 63.0, 0.0, -2.0, 0.0 },
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| 126 | { 1, 0, 0, 0, 1, 63.0, 0.1, -33.0, 0.0 },
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| 127 | { -1, 0, 0, 0, 1, -58.0, -0.1, 32.0, 0.0 },
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| 128 | { -1, 0, 2, 2, 2, -59.0, 0.0, 26.0, 0.0 },
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| 129 |
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| 130 | /* 41-50 */
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| 131 | { 1, 0, 2, 0, 1, -51.0, 0.0, 27.0, 0.0 },
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| 132 | { 0, 0, 2, 2, 2, -38.0, 0.0, 16.0, 0.0 },
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| 133 | { 2, 0, 0, 0, 0, 29.0, 0.0, -1.0, 0.0 },
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| 134 | { 1, 0, 2, -2, 2, 29.0, 0.0, -12.0, 0.0 },
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| 135 | { 2, 0, 2, 0, 2, -31.0, 0.0, 13.0, 0.0 },
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| 136 | { 0, 0, 2, 0, 0, 26.0, 0.0, -1.0, 0.0 },
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| 137 | { -1, 0, 2, 0, 1, 21.0, 0.0, -10.0, 0.0 },
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| 138 | { -1, 0, 0, 2, 1, 16.0, 0.0, -8.0, 0.0 },
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| 139 | { 1, 0, 0, -2, 1, -13.0, 0.0, 7.0, 0.0 },
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| 140 | { -1, 0, 2, 2, 1, -10.0, 0.0, 5.0, 0.0 },
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| 141 |
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| 142 | /* 51-60 */
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| 143 | { 1, 1, 0, -2, 0, -7.0, 0.0, 0.0, 0.0 },
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| 144 | { 0, 1, 2, 0, 2, 7.0, 0.0, -3.0, 0.0 },
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| 145 | { 0, -1, 2, 0, 2, -7.0, 0.0, 3.0, 0.0 },
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| 146 | { 1, 0, 2, 2, 2, -8.0, 0.0, 3.0, 0.0 },
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| 147 | { 1, 0, 0, 2, 0, 6.0, 0.0, 0.0, 0.0 },
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| 148 | { 2, 0, 2, -2, 2, 6.0, 0.0, -3.0, 0.0 },
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| 149 | { 0, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 },
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| 150 | { 0, 0, 2, 2, 1, -7.0, 0.0, 3.0, 0.0 },
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| 151 | { 1, 0, 2, -2, 1, 6.0, 0.0, -3.0, 0.0 },
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| 152 | { 0, 0, 0, -2, 1, -5.0, 0.0, 3.0, 0.0 },
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| 153 |
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| 154 | /* 61-70 */
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| 155 | { 1, -1, 0, 0, 0, 5.0, 0.0, 0.0, 0.0 },
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| 156 | { 2, 0, 2, 0, 1, -5.0, 0.0, 3.0, 0.0 },
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| 157 | { 0, 1, 0, -2, 0, -4.0, 0.0, 0.0, 0.0 },
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| 158 | { 1, 0, -2, 0, 0, 4.0, 0.0, 0.0, 0.0 },
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| 159 | { 0, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0 },
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| 160 | { 1, 1, 0, 0, 0, -3.0, 0.0, 0.0, 0.0 },
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| 161 | { 1, 0, 2, 0, 0, 3.0, 0.0, 0.0, 0.0 },
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| 162 | { 1, -1, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 },
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| 163 | { -1, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 },
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| 164 | { -2, 0, 0, 0, 1, -2.0, 0.0, 1.0, 0.0 },
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| 165 |
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| 166 | /* 71-80 */
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| 167 | { 3, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 },
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| 168 | { 0, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 },
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| 169 | { 1, 1, 2, 0, 2, 2.0, 0.0, -1.0, 0.0 },
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| 170 | { -1, 0, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 },
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| 171 | { 2, 0, 0, 0, 1, 2.0, 0.0, -1.0, 0.0 },
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| 172 | { 1, 0, 0, 0, 2, -2.0, 0.0, 1.0, 0.0 },
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| 173 | { 3, 0, 0, 0, 0, 2.0, 0.0, 0.0, 0.0 },
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| 174 | { 0, 0, 2, 1, 2, 2.0, 0.0, -1.0, 0.0 },
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| 175 | { -1, 0, 0, 0, 2, 1.0, 0.0, -1.0, 0.0 },
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| 176 | { 1, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 },
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| 177 |
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| 178 | /* 81-90 */
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| 179 | { -2, 0, 2, 2, 2, 1.0, 0.0, -1.0, 0.0 },
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| 180 | { -1, 0, 2, 4, 2, -2.0, 0.0, 1.0, 0.0 },
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| 181 | { 2, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 },
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| 182 | { 1, 1, 2, -2, 2, 1.0, 0.0, -1.0, 0.0 },
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| 183 | { 1, 0, 2, 2, 1, -1.0, 0.0, 1.0, 0.0 },
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| 184 | { -2, 0, 2, 4, 2, -1.0, 0.0, 1.0, 0.0 },
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| 185 | { -1, 0, 4, 0, 2, 1.0, 0.0, 0.0, 0.0 },
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| 186 | { 1, -1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 },
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| 187 | { 2, 0, 2, -2, 1, 1.0, 0.0, -1.0, 0.0 },
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| 188 | { 2, 0, 2, 2, 2, -1.0, 0.0, 0.0, 0.0 },
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| 189 |
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| 190 | /* 91-100 */
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| 191 | { 1, 0, 0, 2, 1, -1.0, 0.0, 0.0, 0.0 },
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| 192 | { 0, 0, 4, -2, 2, 1.0, 0.0, 0.0, 0.0 },
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| 193 | { 3, 0, 2, -2, 2, 1.0, 0.0, 0.0, 0.0 },
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| 194 | { 1, 0, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 },
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| 195 | { 0, 1, 2, 0, 1, 1.0, 0.0, 0.0, 0.0 },
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| 196 | { -1, -1, 0, 2, 1, 1.0, 0.0, 0.0, 0.0 },
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| 197 | { 0, 0, -2, 0, 1, -1.0, 0.0, 0.0, 0.0 },
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| 198 | { 0, 0, 2, -1, 2, -1.0, 0.0, 0.0, 0.0 },
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| 199 | { 0, 1, 0, 2, 0, -1.0, 0.0, 0.0, 0.0 },
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| 200 | { 1, 0, -2, -2, 0, -1.0, 0.0, 0.0, 0.0 },
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| 201 |
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| 202 | /* 101-106 */
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| 203 | { 0, -1, 2, 0, 1, -1.0, 0.0, 0.0, 0.0 },
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| 204 | { 1, 1, 0, -2, 1, -1.0, 0.0, 0.0, 0.0 },
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| 205 | { 1, 0, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 },
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| 206 | { 2, 0, 0, 2, 0, 1.0, 0.0, 0.0, 0.0 },
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| 207 | { 0, 0, 2, 4, 2, -1.0, 0.0, 0.0, 0.0 },
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| 208 | { 0, 1, 0, 1, 0, 1.0, 0.0, 0.0, 0.0 }
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| 209 | };
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| 210 |
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| 211 | /* Number of terms in the series */
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| 212 | const int NT = (int) (sizeof x / sizeof x[0]);
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| 213 |
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| 214 | /*--------------------------------------------------------------------*/
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| 215 |
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| 216 | /* Interval between fundamental epoch J2000.0 and given date (JC). */
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| 217 | t = ((date1 - DJ00) + date2) / DJC;
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| 218 |
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| 219 | /* --------------------- */
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| 220 | /* Fundamental arguments */
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| 221 | /* --------------------- */
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| 222 |
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| 223 | /* Mean longitude of Moon minus mean longitude of Moon's perigee. */
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| 224 | el = iauAnpm(
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| 225 | (485866.733 + (715922.633 + (31.310 + 0.064 * t) * t) * t)
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| 226 | * DAS2R + fmod(1325.0 * t, 1.0) * D2PI);
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| 227 |
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| 228 | /* Mean longitude of Sun minus mean longitude of Sun's perigee. */
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| 229 | elp = iauAnpm(
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| 230 | (1287099.804 + (1292581.224 + (-0.577 - 0.012 * t) * t) * t)
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| 231 | * DAS2R + fmod(99.0 * t, 1.0) * D2PI);
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| 232 |
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| 233 | /* Mean longitude of Moon minus mean longitude of Moon's node. */
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| 234 | f = iauAnpm(
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| 235 | (335778.877 + (295263.137 + (-13.257 + 0.011 * t) * t) * t)
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| 236 | * DAS2R + fmod(1342.0 * t, 1.0) * D2PI);
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| 237 |
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| 238 | /* Mean elongation of Moon from Sun. */
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| 239 | d = iauAnpm(
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| 240 | (1072261.307 + (1105601.328 + (-6.891 + 0.019 * t) * t) * t)
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| 241 | * DAS2R + fmod(1236.0 * t, 1.0) * D2PI);
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| 242 |
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| 243 | /* Longitude of the mean ascending node of the lunar orbit on the */
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| 244 | /* ecliptic, measured from the mean equinox of date. */
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| 245 | om = iauAnpm(
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| 246 | (450160.280 + (-482890.539 + (7.455 + 0.008 * t) * t) * t)
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| 247 | * DAS2R + fmod(-5.0 * t, 1.0) * D2PI);
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| 248 |
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| 249 | /* --------------- */
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| 250 | /* Nutation series */
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| 251 | /* --------------- */
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| 252 |
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| 253 | /* Initialize nutation components. */
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| 254 | dp = 0.0;
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| 255 | de = 0.0;
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| 256 |
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| 257 | /* Sum the nutation terms, ending with the biggest. */
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| 258 | for (j = NT-1; j >= 0; j--) {
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| 259 |
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| 260 | /* Form argument for current term. */
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| 261 | arg = (double)x[j].nl * el
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| 262 | + (double)x[j].nlp * elp
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| 263 | + (double)x[j].nf * f
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| 264 | + (double)x[j].nd * d
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| 265 | + (double)x[j].nom * om;
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| 266 |
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| 267 | /* Accumulate current nutation term. */
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| 268 | s = x[j].sp + x[j].spt * t;
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| 269 | c = x[j].ce + x[j].cet * t;
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| 270 | if (s != 0.0) dp += s * sin(arg);
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| 271 | if (c != 0.0) de += c * cos(arg);
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| 272 | }
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| 273 |
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| 274 | /* Convert results from 0.1 mas units to radians. */
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| 275 | *dpsi = dp * U2R;
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| 276 | *deps = de * U2R;
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| 277 |
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| 278 | return;
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| 279 |
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| 280 | /*----------------------------------------------------------------------
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| 281 | **
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| 282 | ** Copyright (C) 2015
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| 283 | ** Standards Of Fundamental Astronomy Board
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| 284 | ** of the International Astronomical Union.
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| 285 | **
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| 286 | ** =====================
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| 287 | ** SOFA Software License
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| 288 | ** =====================
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| 289 | **
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| 290 | ** NOTICE TO USER:
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| 291 | **
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| 292 | ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
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| 293 | ** CONDITIONS WHICH APPLY TO ITS USE.
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| 294 | **
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| 295 | ** 1. The Software is owned by the IAU SOFA Board ("SOFA").
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| 296 | **
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| 297 | ** 2. Permission is granted to anyone to use the SOFA software for any
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| 298 | ** purpose, including commercial applications, free of charge and
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| 299 | ** without payment of royalties, subject to the conditions and
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| 300 | ** restrictions listed below.
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| 301 | **
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| 302 | ** 3. You (the user) may copy and distribute SOFA source code to others,
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| 303 | ** and use and adapt its code and algorithms in your own software,
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| 304 | ** on a world-wide, royalty-free basis. That portion of your
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| 305 | ** distribution that does not consist of intact and unchanged copies
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| 306 | ** of SOFA source code files is a "derived work" that must comply
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| 307 | ** with the following requirements:
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| 308 | **
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| 309 | ** a) Your work shall be marked or carry a statement that it
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| 310 | ** (i) uses routines and computations derived by you from
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| 311 | ** software provided by SOFA under license to you; and
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| 312 | ** (ii) does not itself constitute software provided by and/or
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| 313 | ** endorsed by SOFA.
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| 314 | **
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| 315 | ** b) The source code of your derived work must contain descriptions
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| 316 | ** of how the derived work is based upon, contains and/or differs
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| 317 | ** from the original SOFA software.
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| 318 | **
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| 319 | ** c) The names of all routines in your derived work shall not
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| 320 | ** include the prefix "iau" or "sofa" or trivial modifications
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| 321 | ** thereof such as changes of case.
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| 322 | **
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| 323 | ** d) The origin of the SOFA components of your derived work must
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| 324 | ** not be misrepresented; you must not claim that you wrote the
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| 325 | ** original software, nor file a patent application for SOFA
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| 326 | ** software or algorithms embedded in the SOFA software.
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| 327 | **
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| 328 | ** e) These requirements must be reproduced intact in any source
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| 329 | ** distribution and shall apply to anyone to whom you have
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| 330 | ** granted a further right to modify the source code of your
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| 331 | ** derived work.
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| 332 | **
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| 333 | ** Note that, as originally distributed, the SOFA software is
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| 334 | ** intended to be a definitive implementation of the IAU standards,
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| 335 | ** and consequently third-party modifications are discouraged. All
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| 336 | ** variations, no matter how minor, must be explicitly marked as
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| 337 | ** such, as explained above.
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| 338 | **
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| 339 | ** 4. You shall not cause the SOFA software to be brought into
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| 340 | ** disrepute, either by misuse, or use for inappropriate tasks, or
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| 341 | ** by inappropriate modification.
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| 342 | **
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| 343 | ** 5. The SOFA software is provided "as is" and SOFA makes no warranty
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| 344 | ** as to its use or performance. SOFA does not and cannot warrant
|
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| 345 | ** the performance or results which the user may obtain by using the
|
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| 346 | ** SOFA software. SOFA makes no warranties, express or implied, as
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| 347 | ** to non-infringement of third party rights, merchantability, or
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| 348 | ** fitness for any particular purpose. In no event will SOFA be
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| 349 | ** liable to the user for any consequential, incidental, or special
|
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| 350 | ** damages, including any lost profits or lost savings, even if a
|
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| 351 | ** SOFA representative has been advised of such damages, or for any
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| 352 | ** claim by any third party.
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| 353 | **
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| 354 | ** 6. The provision of any version of the SOFA software under the terms
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| 355 | ** and conditions specified herein does not imply that future
|
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| 356 | ** versions will also be made available under the same terms and
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| 357 | ** conditions.
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| 358 | *
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| 359 | ** In any published work or commercial product which uses the SOFA
|
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| 360 | ** software directly, acknowledgement (see www.iausofa.org) is
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| 361 | ** appreciated.
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| 362 | **
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| 363 | ** Correspondence concerning SOFA software should be addressed as
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| 364 | ** follows:
|
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| 365 | **
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| 366 | ** By email: sofa@ukho.gov.uk
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| 367 | ** By post: IAU SOFA Center
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| 368 | ** HM Nautical Almanac Office
|
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| 369 | ** UK Hydrographic Office
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| 370 | ** Admiralty Way, Taunton
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| 371 | ** Somerset, TA1 2DN
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| 372 | ** United Kingdom
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| 373 | **
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| 374 | **--------------------------------------------------------------------*/
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| 375 | }
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