| [1457] | 1 | /* nutation (in IAU (1980) expression) and abberation; stern
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| 2 | * on an HP PA processor, this reproduces the Almanac nutation values
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| 3 | * (given to 0.001") EXACTLY over 750 days (1995 and 1996)
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| 4 | */
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| [2551] | 5 | #include <stdio.h>
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| [1457] | 6 | #include <math.h>
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| 7 |
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| 8 | #include "astro.h"
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| 9 |
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| 10 | #define NUT_SCALE 1e4
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| 11 | #define NUT_SERIES 106
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| 12 | #define NUT_MAXMUL 4
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| 13 | #define SECPERCIRC (3600.*360.)
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| 14 |
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| 15 | /* Delaunay arguments, in arc seconds; they differ slightly from ELP82B */
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| 16 | static double delaunay[5][4] = {
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| 17 | {485866.733, 1717915922.633, 31.310, 0.064}, /* M', moon mean anom */
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| 18 | {1287099.804, 129596581.224, -0.577, -0.012}, /* M, sun mean anom */
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| 19 | {335778.877, 1739527263.137, -13.257, 0.011}, /* F, moon arg lat */
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| 20 | {1072261.307, 1602961601.328, -6.891, 0.019}, /* D, elong moon sun */
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| 21 | {450160.280, -6962890.539, 7.455, 0.008}, /* Om, moon l asc node */
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| 22 | };
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| 23 |
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| 24 | /* multipliers for Delaunay arguments */
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| 25 | static short multarg[NUT_SERIES][5] = {
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| 26 | /* bounds: -2..3, -2..2, -2/0/2/4, -4..4, 0..2 */
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| 27 | {0, 0, 0, 0, 1},
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| 28 | {0, 0, 0, 0, 2},
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| 29 | {-2, 0, 2, 0, 1},
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| 30 | {2, 0, -2, 0, 0},
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| 31 | {-2, 0, 2, 0, 2},
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| 32 | {1, -1, 0, -1, 0},
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| 33 | {0, -2, 2, -2, 1},
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| 34 | {2, 0, -2, 0, 1},
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| 35 | {0, 0, 2, -2, 2},
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| 36 | {0, 1, 0, 0, 0},
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| 37 | {0, 1, 2, -2, 2},
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| 38 | {0, -1, 2, -2, 2},
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| 39 | {0, 0, 2, -2, 1},
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| 40 | {2, 0, 0, -2, 0},
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| 41 | {0, 0, 2, -2, 0},
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| 42 | {0, 2, 0, 0, 0},
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| 43 | {0, 1, 0, 0, 1},
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| 44 | {0, 2, 2, -2, 2},
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| 45 | {0, -1, 0, 0, 1},
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| 46 | {-2, 0, 0, 2, 1},
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| 47 | {0, -1, 2, -2, 1},
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| 48 | {2, 0, 0, -2, 1},
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| 49 | {0, 1, 2, -2, 1},
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| 50 | {1, 0, 0, -1, 0},
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| 51 | {2, 1, 0, -2, 0},
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| 52 | {0, 0, -2, 2, 1},
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| 53 | {0, 1, -2, 2, 0},
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| 54 | {0, 1, 0, 0, 2},
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| 55 | {-1, 0, 0, 1, 1},
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| 56 | {0, 1, 2, -2, 0},
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| 57 | {0, 0, 2, 0, 2},
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| 58 | {1, 0, 0, 0, 0},
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| 59 | {0, 0, 2, 0, 1},
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| 60 | {1, 0, 2, 0, 2},
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| 61 | {1, 0, 0, -2, 0},
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| 62 | {-1, 0, 2, 0, 2},
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| 63 | {0, 0, 0, 2, 0},
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| 64 | {1, 0, 0, 0, 1},
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| 65 | {-1, 0, 0, 0, 1},
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| 66 | {-1, 0, 2, 2, 2},
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| 67 | {1, 0, 2, 0, 1},
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| 68 | {0, 0, 2, 2, 2},
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| 69 | {2, 0, 0, 0, 0},
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| 70 | {1, 0, 2, -2, 2},
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| 71 | {2, 0, 2, 0, 2},
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| 72 | {0, 0, 2, 0, 0},
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| 73 | {-1, 0, 2, 0, 1},
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| 74 | {-1, 0, 0, 2, 1},
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| 75 | {1, 0, 0, -2, 1},
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| 76 | {-1, 0, 2, 2, 1},
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| 77 | {1, 1, 0, -2, 0},
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| 78 | {0, 1, 2, 0, 2},
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| 79 | {0, -1, 2, 0, 2},
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| 80 | {1, 0, 2, 2, 2},
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| 81 | {1, 0, 0, 2, 0},
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| 82 | {2, 0, 2, -2, 2},
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| 83 | {0, 0, 0, 2, 1},
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| 84 | {0, 0, 2, 2, 1},
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| 85 | {1, 0, 2, -2, 1},
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| 86 | {0, 0, 0, -2, 1},
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| 87 | {1, -1, 0, 0, 0},
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| 88 | {2, 0, 2, 0, 1},
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| 89 | {0, 1, 0, -2, 0},
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| 90 | {1, 0, -2, 0, 0},
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| 91 | {0, 0, 0, 1, 0},
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| 92 | {1, 1, 0, 0, 0},
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| 93 | {1, 0, 2, 0, 0},
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| 94 | {1, -1, 2, 0, 2},
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| 95 | {-1, -1, 2, 2, 2},
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| 96 | {-2, 0, 0, 0, 1},
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| 97 | {3, 0, 2, 0, 2},
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| 98 | {0, -1, 2, 2, 2},
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| 99 | {1, 1, 2, 0, 2},
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| 100 | {-1, 0, 2, -2, 1},
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| 101 | {2, 0, 0, 0, 1},
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| 102 | {1, 0, 0, 0, 2},
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| 103 | {3, 0, 0, 0, 0},
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| 104 | {0, 0, 2, 1, 2},
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| 105 | {-1, 0, 0, 0, 2},
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| 106 | {1, 0, 0, -4, 0},
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| 107 | {-2, 0, 2, 2, 2},
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| 108 | {-1, 0, 2, 4, 2},
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| 109 | {2, 0, 0, -4, 0},
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| 110 | {1, 1, 2, -2, 2},
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| 111 | {1, 0, 2, 2, 1},
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| 112 | {-2, 0, 2, 4, 2},
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| 113 | {-1, 0, 4, 0, 2},
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| 114 | {1, -1, 0, -2, 0},
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| 115 | {2, 0, 2, -2, 1},
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| 116 | {2, 0, 2, 2, 2},
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| 117 | {1, 0, 0, 2, 1},
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| 118 | {0, 0, 4, -2, 2},
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| 119 | {3, 0, 2, -2, 2},
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| 120 | {1, 0, 2, -2, 0},
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| 121 | {0, 1, 2, 0, 1},
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| 122 | {-1, -1, 0, 2, 1},
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| 123 | {0, 0, -2, 0, 1},
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| 124 | {0, 0, 2, -1, 2},
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| 125 | {0, 1, 0, 2, 0},
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| 126 | {1, 0, -2, -2, 0},
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| 127 | {0, -1, 2, 0, 1},
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| 128 | {1, 1, 0, -2, 1},
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| 129 | {1, 0, -2, 2, 0},
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| 130 | {2, 0, 0, 2, 0},
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| 131 | {0, 0, 2, 4, 2},
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| 132 | {0, 1, 0, 1, 0}
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| 133 | };
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| 134 |
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| 135 | /* amplitudes which have secular terms; in 1/NUT_SCALE arc seconds
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| 136 | * {index, constant dPSI, T/10 in dPSI, constant in dEPS, T/10 in dEPS}
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| 137 | */
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| 138 | static long ampsecul[][5] = {
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| 139 | {0 ,-171996 ,-1742 ,92025 ,89},
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| 140 | {1 ,2062 ,2 ,-895 ,5},
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| 141 | {8 ,-13187 ,-16 ,5736 ,-31},
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| 142 | {9 ,1426 ,-34 ,54 ,-1},
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| 143 | {10 ,-517 ,12 ,224 ,-6},
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| 144 | {11 ,217 ,-5 ,-95 ,3},
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| 145 | {12 ,129 ,1 ,-70 ,0},
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| 146 | {15 ,17 ,-1 ,0 ,0},
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| 147 | {17 ,-16 ,1 ,7 ,0},
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| 148 | {30 ,-2274 ,-2 ,977 ,-5},
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| 149 | {31 ,712 ,1 ,-7 ,0},
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| 150 | {32 ,-386 ,-4 ,200 ,0},
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| 151 | {33 ,-301 ,0 ,129 ,-1},
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| 152 | {37 ,63 ,1 ,-33 ,0},
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| 153 | {38 ,-58 ,-1 ,32 ,0},
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| 154 | /* termination */ { -1, }
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| 155 | };
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| 156 |
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| 157 | /* amplitudes which only have constant terms; same unit as above
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| 158 | * {dPSI, dEPS}
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| 159 | * indexes which are already in ampsecul[][] are zeroed
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| 160 | */
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| 161 | static short ampconst[NUT_SERIES][2] = {
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| 162 | {0,0},
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| 163 | {0,0},
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| 164 | {46,-24},
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| 165 | {11,0},
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| 166 | {-3,1},
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| 167 | {-3,0},
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| 168 | {-2,1},
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| 169 | {1,0},
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| 170 | {0,0},
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| 171 | {0,0},
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| 172 | {0,0},
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| 173 | {0,0},
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| 174 | {0,0},
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| 175 | {48,1},
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| 176 | {-22,0},
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| 177 | {0,0},
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| 178 | {-15,9},
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| 179 | {0,0},
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| 180 | {-12,6},
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| 181 | {-6,3},
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| 182 | {-5,3},
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| 183 | {4,-2},
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| 184 | {4,-2},
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| 185 | {-4,0},
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| 186 | {1,0},
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| 187 | {1,0},
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| 188 | {-1,0},
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| 189 | {1,0},
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| 190 | {1,0},
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| 191 | {-1,0},
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| 192 | {0,0},
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| 193 | {0,0},
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| 194 | {0,0},
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| 195 | {0,0},
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| 196 | {-158,-1},
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| 197 | {123,-53},
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| 198 | {63,-2},
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| 199 | {0,0},
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| 200 | {0,0},
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| 201 | {-59,26},
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| 202 | {-51,27},
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| 203 | {-38,16},
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| 204 | {29,-1},
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| 205 | {29,-12},
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| 206 | {-31,13},
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| 207 | {26,-1},
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| 208 | {21,-10},
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| 209 | {16,-8},
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| 210 | {-13,7},
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| 211 | {-10,5},
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| 212 | {-7,0},
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| 213 | {7,-3},
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| 214 | {-7,3},
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| 215 | {-8,3},
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| 216 | {6,0},
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| 217 | {6,-3},
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| 218 | {-6,3},
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| 219 | {-7,3},
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| 220 | {6,-3},
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| 221 | {-5,3},
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| 222 | {5,0},
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| 223 | {-5,3},
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| 224 | {-4,0},
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| 225 | {4,0},
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| 226 | {-4,0},
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| 227 | {-3,0},
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| 228 | {3,0},
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| 229 | {-3,1},
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| 230 | {-3,1},
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| 231 | {-2,1},
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| 232 | {-3,1},
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| 233 | {-3,1},
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| 234 | {2,-1},
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| 235 | {-2,1},
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| 236 | {2,-1},
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| 237 | {-2,1},
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| 238 | {2,0},
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| 239 | {2,-1},
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| 240 | {1,-1},
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| 241 | {-1,0},
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| 242 | {1,-1},
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| 243 | {-2,1},
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| 244 | {-1,0},
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| 245 | {1,-1},
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| 246 | {-1,1},
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| 247 | {-1,1},
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| 248 | {1,0},
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| 249 | {1,0},
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| 250 | {1,-1},
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| 251 | {-1,0},
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| 252 | {-1,0},
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| 253 | {1,0},
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| 254 | {1,0},
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| 255 | {-1,0},
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| 256 | {1,0},
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| 257 | {1,0},
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| 258 | {-1,0},
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| 259 | {-1,0},
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| 260 | {-1,0},
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| 261 | {-1,0},
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| 262 | {-1,0},
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| 263 | {-1,0},
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| 264 | {-1,0},
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| 265 | {1,0},
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| 266 | {-1,0},
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| 267 | {1,0}
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| 268 | };
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| 269 |
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| [2551] | 270 | /* given the modified JD, mj, find the nutation in obliquity, *deps, and
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| [1457] | 271 | * the nutation in longitude, *dpsi, each in radians.
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| 272 | */
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| 273 | void
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| [2551] | 274 | nutation (
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| 275 | double mj,
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| 276 | double *deps, /* on input: precision parameter in arc seconds */
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| 277 | double *dpsi)
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| [1457] | 278 | {
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| [2551] | 279 | static double lastmj = -10000, lastdeps, lastdpsi;
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| [1457] | 280 | double T, T2, T3, T10; /* jul cent since J2000 */
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| 281 | double prec; /* series precis in arc sec */
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| 282 | int i, isecul; /* index in term table */
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| 283 | static double delcache[5][2*NUT_MAXMUL+1];
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| 284 | /* cache for multiples of delaunay args
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| 285 | * [M',M,F,D,Om][-min*x, .. , 0, .., max*x]
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| 286 | * make static to have unfilled fields cleared on init
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| 287 | */
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| 288 |
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| [2551] | 289 | if (mj == lastmj) {
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| [1457] | 290 | *deps = lastdeps;
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| 291 | *dpsi = lastdpsi;
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| 292 | return;
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| 293 | }
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| 294 |
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| 295 | prec = 0.0;
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| 296 |
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| 297 | #if 0 /* this is if deps should contain a precision value */
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| 298 | prec =* deps;
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| 299 | if (prec < 0.0 || prec > 1.0) /* accept only sane value */
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| 300 | prec = 1.0;
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| 301 | #endif
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| 302 |
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| 303 | /* augment for abundance of small terms */
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| 304 | prec *= NUT_SCALE/10;
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| 305 |
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| [2551] | 306 | T = (mj - J2000)/36525.;
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| [1457] | 307 | T2 = T * T;
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| 308 | T3 = T2 * T;
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| 309 | T10 = T/10.;
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| 310 |
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| 311 | /* calculate delaunay args and place in cache */
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| 312 | for (i = 0; i < 5; ++i) {
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| 313 | double x;
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| 314 | short j;
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| 315 |
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| 316 | x = delaunay[i][0] +
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| 317 | delaunay[i][1] * T +
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| 318 | delaunay[i][2] * T2 +
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| 319 | delaunay[i][3] * T3;
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| 320 |
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| 321 | /* convert to radians */
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| 322 | x /= SECPERCIRC;
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| 323 | x -= floor(x);
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| 324 | x *= 2.*PI;
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| 325 |
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| 326 | /* fill cache table */
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| 327 | for (j = 0; j <= 2*NUT_MAXMUL; ++j)
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| 328 | delcache[i][j] = (j - NUT_MAXMUL) * x;
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| 329 | }
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| 330 |
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| 331 | /* find dpsi and deps */
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| 332 | lastdpsi = lastdeps = 0.;
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| 333 | for (i = isecul = 0; i < NUT_SERIES ; ++i) {
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| 334 | double arg = 0., ampsin, ampcos;
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| 335 | short j;
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| 336 |
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| 337 | if (ampconst[i][0] || ampconst[i][1]) {
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| 338 | /* take non-secular terms from simple array */
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| 339 | ampsin = ampconst[i][0];
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| 340 | ampcos = ampconst[i][1];
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| 341 | } else {
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| 342 | /* secular terms from different array */
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| 343 | ampsin = ampsecul[isecul][1] + ampsecul[isecul][2] * T10;
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| 344 | ampcos = ampsecul[isecul][3] + ampsecul[isecul][4] * T10;
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| 345 | ++isecul;
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| 346 | }
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| 347 |
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| 348 | for (j = 0; j < 5; ++j)
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| 349 | arg += delcache[j][NUT_MAXMUL + multarg[i][j]];
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| 350 |
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| 351 | if (fabs(ampsin) >= prec)
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| 352 | lastdpsi += ampsin * sin(arg);
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| 353 |
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| 354 | if (fabs(ampcos) >= prec)
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| 355 | lastdeps += ampcos * cos(arg);
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| 356 |
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| 357 | }
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| 358 |
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| 359 | /* convert to radians.
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| 360 | */
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| 361 | lastdpsi = degrad(lastdpsi/3600./NUT_SCALE);
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| 362 | lastdeps = degrad(lastdeps/3600./NUT_SCALE);
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| 363 |
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| [2551] | 364 | lastmj = mj;
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| [1457] | 365 | *deps = lastdeps;
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| 366 | *dpsi = lastdpsi;
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| 367 | }
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| 368 |
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| [2551] | 369 | /* given the modified JD, mj, correct, IN PLACE, the right ascension *ra
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| [1457] | 370 | * and declination *dec (both in radians) for nutation.
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| 371 | */
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| 372 | void
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| [2551] | 373 | nut_eq (double mj, double *ra, double *dec)
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| [1457] | 374 | {
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| [2551] | 375 | static double lastmj = -10000;
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| [1457] | 376 | static double a[3][3]; /* rotation matrix */
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| 377 | double xold, yold, zold, x, y, z;
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| 378 |
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| [2551] | 379 | if (mj != lastmj) {
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| [1457] | 380 | double epsilon, dpsi, deps;
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| 381 | double se, ce, sp, cp, sede, cede;
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| 382 |
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| [2551] | 383 | obliquity(mj, &epsilon);
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| 384 | nutation(mj, &deps, &dpsi);
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| [1457] | 385 |
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| 386 | /* the rotation matrix a applies the nutation correction to
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| 387 | * a vector of equatoreal coordinates Xeq to Xeq' by 3 subsequent
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| 388 | * rotations: R1 - from equatoreal to ecliptic system by
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| 389 | * rotation of angle epsilon about x, R2 - rotate ecliptic
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| 390 | * system by -dpsi about its z, R3 - from ecliptic to equatoreal
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| 391 | * by rotation of angle -(epsilon + deps)
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| 392 | *
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| 393 | * Xeq' = A * Xeq = R3 * R2 * R1 * Xeq
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| 394 | *
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| 395 | * [ 1 0 0 ]
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| 396 | * R1 = [ 0 cos(eps) sin(eps) ]
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| 397 | * [ 0 - sin(eps) cos(eps) ]
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| 398 | *
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| 399 | * [ cos(dpsi) - sin(dpsi) 0 ]
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| 400 | * R2 = [ sin(dpsi) cos(dpsi) 0 ]
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| 401 | * [ 0 0 1 ]
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| 402 | *
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| 403 | * [ 1 0 0 ]
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| 404 | * R3 = [ 0 cos(eps + deps) - sin(eps + deps) ]
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| 405 | * [ 0 sin(eps + deps) cos(eps + deps) ]
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| 406 | *
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| 407 | * for efficiency, here is a explicitely:
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| 408 | */
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| 409 |
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| 410 | se = sin(epsilon);
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| 411 | ce = cos(epsilon);
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| 412 | sp = sin(dpsi);
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| 413 | cp = cos(dpsi);
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| 414 | sede = sin(epsilon + deps);
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| 415 | cede = cos(epsilon + deps);
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| 416 |
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| 417 | a[0][0] = cp;
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| 418 | a[0][1] = -sp*ce;
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| 419 | a[0][2] = -sp*se;
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| 420 |
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| 421 | a[1][0] = cede*sp;
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| 422 | a[1][1] = cede*cp*ce+sede*se;
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| 423 | a[1][2] = cede*cp*se-sede*ce;
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| 424 |
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| 425 | a[2][0] = sede*sp;
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| 426 | a[2][1] = sede*cp*ce-cede*se;
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| 427 | a[2][2] = sede*cp*se+cede*ce;
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| 428 |
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| [2551] | 429 | lastmj = mj;
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| [1457] | 430 | }
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| 431 |
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| 432 | sphcart(*ra, *dec, 1.0, &xold, &yold, &zold);
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| 433 | x = a[0][0] * xold + a[0][1] * yold + a[0][2] * zold;
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| 434 | y = a[1][0] * xold + a[1][1] * yold + a[1][2] * zold;
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| 435 | z = a[2][0] * xold + a[2][1] * yold + a[2][2] * zold;
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| 436 | cartsph(x, y, z, ra, dec, &zold); /* radius should be 1.0 */
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| 437 | if (*ra < 0.) *ra += 2.*PI; /* make positive for display */
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| 438 | }
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| 439 |
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| 440 | /* For RCS Only -- Do Not Edit */
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| [3111] | 441 | static char *rcsid[2] = {(char *)rcsid, "@(#) $RCSfile: nutation.c,v $ $Date: 2006-11-22 13:53:30 $ $Revision: 1.6 $ $Name: not supported by cvs2svn $"};
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