| 1 | #include "erfa.h"
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| 2 |
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| 3 | double eraEect00(double date1, double date2)
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| 4 | /*
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| 5 | ** - - - - - - - - - -
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| 6 | ** e r a E e c t 0 0
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| 7 | ** - - - - - - - - - -
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| 8 | **
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| 9 | ** Equation of the equinoxes complementary terms, consistent with
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| 10 | ** IAU 2000 resolutions.
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| 11 | **
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| 12 | ** Given:
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| 13 | ** date1,date2 double TT as a 2-part Julian Date (Note 1)
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| 14 | **
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| 15 | ** Returned (function value):
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| 16 | ** double complementary terms (Note 2)
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| 17 | **
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| 18 | ** Notes:
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| 19 | **
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| 20 | ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
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| 21 | ** convenient way between the two arguments. For example,
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| 22 | ** JD(TT)=2450123.7 could be expressed in any of these ways,
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| 23 | ** among others:
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| 24 | **
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| 25 | ** date1 date2
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| 26 | **
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| 27 | ** 2450123.7 0.0 (JD method)
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| 28 | ** 2451545.0 -1421.3 (J2000 method)
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| 29 | ** 2400000.5 50123.2 (MJD method)
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| 30 | ** 2450123.5 0.2 (date & time method)
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| 31 | **
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| 32 | ** The JD method is the most natural and convenient to use in
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| 33 | ** cases where the loss of several decimal digits of resolution
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| 34 | ** is acceptable. The J2000 method is best matched to the way
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| 35 | ** the argument is handled internally and will deliver the
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| 36 | ** optimum resolution. The MJD method and the date & time methods
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| 37 | ** are both good compromises between resolution and convenience.
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| 38 | **
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| 39 | ** 2) The "complementary terms" are part of the equation of the
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| 40 | ** equinoxes (EE), classically the difference between apparent and
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| 41 | ** mean Sidereal Time:
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| 42 | **
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| 43 | ** GAST = GMST + EE
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| 44 | **
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| 45 | ** with:
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| 46 | **
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| 47 | ** EE = dpsi * cos(eps)
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| 48 | **
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| 49 | ** where dpsi is the nutation in longitude and eps is the obliquity
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| 50 | ** of date. However, if the rotation of the Earth were constant in
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| 51 | ** an inertial frame the classical formulation would lead to
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| 52 | ** apparent irregularities in the UT1 timescale traceable to side-
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| 53 | ** effects of precession-nutation. In order to eliminate these
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| 54 | ** effects from UT1, "complementary terms" were introduced in 1994
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| 55 | ** (IAU, 1994) and took effect from 1997 (Capitaine and Gontier,
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| 56 | ** 1993):
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| 57 | **
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| 58 | ** GAST = GMST + CT + EE
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| 59 | **
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| 60 | ** By convention, the complementary terms are included as part of
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| 61 | ** the equation of the equinoxes rather than as part of the mean
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| 62 | ** Sidereal Time. This slightly compromises the "geometrical"
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| 63 | ** interpretation of mean sidereal time but is otherwise
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| 64 | ** inconsequential.
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| 65 | **
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| 66 | ** The present function computes CT in the above expression,
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| 67 | ** compatible with IAU 2000 resolutions (Capitaine et al., 2002, and
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| 68 | ** IERS Conventions 2003).
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| 69 | **
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| 70 | ** Called:
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| 71 | ** eraFal03 mean anomaly of the Moon
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| 72 | ** eraFalp03 mean anomaly of the Sun
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| 73 | ** eraFaf03 mean argument of the latitude of the Moon
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| 74 | ** eraFad03 mean elongation of the Moon from the Sun
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| 75 | ** eraFaom03 mean longitude of the Moon's ascending node
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| 76 | ** eraFave03 mean longitude of Venus
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| 77 | ** eraFae03 mean longitude of Earth
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| 78 | ** eraFapa03 general accumulated precession in longitude
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| 79 | **
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| 80 | ** References:
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| 81 | **
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| 82 | ** Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275,
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| 83 | ** 645-650 (1993)
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| 84 | **
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| 85 | ** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
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| 86 | ** implement the IAU 2000 definition of UT1", Astronomy &
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| 87 | ** Astrophysics, 406, 1135-1149 (2003)
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| 88 | **
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| 89 | ** IAU Resolution C7, Recommendation 3 (1994)
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| 90 | **
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| 91 | ** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
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| 92 | ** IERS Technical Note No. 32, BKG (2004)
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| 93 | **
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| 94 | ** Copyright (C) 2013-2017, NumFOCUS Foundation.
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| 95 | ** Derived, with permission, from the SOFA library. See notes at end of file.
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| 96 | */
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| 97 | {
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| 98 | /* Time since J2000.0, in Julian centuries */
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| 99 | double t;
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| 100 |
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| 101 | /* Miscellaneous */
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| 102 | int i, j;
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| 103 | double a, s0, s1;
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| 104 |
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| 105 | /* Fundamental arguments */
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| 106 | double fa[14];
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| 107 |
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| 108 | /* Returned value. */
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| 109 | double eect;
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| 110 |
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| 111 | /* ----------------------------------------- */
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| 112 | /* The series for the EE complementary terms */
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| 113 | /* ----------------------------------------- */
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| 114 |
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| 115 | typedef struct {
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| 116 | int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
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| 117 | double s, c; /* sine and cosine coefficients */
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| 118 | } TERM;
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| 119 |
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| 120 | /* Terms of order t^0 */
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| 121 | static const TERM e0[] = {
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| 122 |
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| 123 | /* 1-10 */
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| 124 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, 2640.96e-6, -0.39e-6 },
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| 125 | {{ 0, 0, 0, 0, 2, 0, 0, 0}, 63.52e-6, -0.02e-6 },
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| 126 | {{ 0, 0, 2, -2, 3, 0, 0, 0}, 11.75e-6, 0.01e-6 },
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| 127 | {{ 0, 0, 2, -2, 1, 0, 0, 0}, 11.21e-6, 0.01e-6 },
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| 128 | {{ 0, 0, 2, -2, 2, 0, 0, 0}, -4.55e-6, 0.00e-6 },
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| 129 | {{ 0, 0, 2, 0, 3, 0, 0, 0}, 2.02e-6, 0.00e-6 },
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| 130 | {{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.98e-6, 0.00e-6 },
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| 131 | {{ 0, 0, 0, 0, 3, 0, 0, 0}, -1.72e-6, 0.00e-6 },
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| 132 | {{ 0, 1, 0, 0, 1, 0, 0, 0}, -1.41e-6, -0.01e-6 },
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| 133 | {{ 0, 1, 0, 0, -1, 0, 0, 0}, -1.26e-6, -0.01e-6 },
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| 134 |
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| 135 | /* 11-20 */
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| 136 | {{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.63e-6, 0.00e-6 },
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| 137 | {{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.63e-6, 0.00e-6 },
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| 138 | {{ 0, 1, 2, -2, 3, 0, 0, 0}, 0.46e-6, 0.00e-6 },
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| 139 | {{ 0, 1, 2, -2, 1, 0, 0, 0}, 0.45e-6, 0.00e-6 },
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| 140 | {{ 0, 0, 4, -4, 4, 0, 0, 0}, 0.36e-6, 0.00e-6 },
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| 141 | {{ 0, 0, 1, -1, 1, -8, 12, 0}, -0.24e-6, -0.12e-6 },
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| 142 | {{ 0, 0, 2, 0, 0, 0, 0, 0}, 0.32e-6, 0.00e-6 },
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| 143 | {{ 0, 0, 2, 0, 2, 0, 0, 0}, 0.28e-6, 0.00e-6 },
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| 144 | {{ 1, 0, 2, 0, 3, 0, 0, 0}, 0.27e-6, 0.00e-6 },
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| 145 | {{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.26e-6, 0.00e-6 },
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| 146 |
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| 147 | /* 21-30 */
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| 148 | {{ 0, 0, 2, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 },
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| 149 | {{ 0, 1, -2, 2, -3, 0, 0, 0}, 0.19e-6, 0.00e-6 },
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| 150 | {{ 0, 1, -2, 2, -1, 0, 0, 0}, 0.18e-6, 0.00e-6 },
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| 151 | {{ 0, 0, 0, 0, 0, 8,-13, -1}, -0.10e-6, 0.05e-6 },
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| 152 | {{ 0, 0, 0, 2, 0, 0, 0, 0}, 0.15e-6, 0.00e-6 },
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| 153 | {{ 2, 0, -2, 0, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
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| 154 | {{ 1, 0, 0, -2, 1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
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| 155 | {{ 0, 1, 2, -2, 2, 0, 0, 0}, -0.14e-6, 0.00e-6 },
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| 156 | {{ 1, 0, 0, -2, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
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| 157 | {{ 0, 0, 4, -2, 4, 0, 0, 0}, 0.13e-6, 0.00e-6 },
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| 158 |
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| 159 | /* 31-33 */
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| 160 | {{ 0, 0, 2, -2, 4, 0, 0, 0}, -0.11e-6, 0.00e-6 },
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| 161 | {{ 1, 0, -2, 0, -3, 0, 0, 0}, 0.11e-6, 0.00e-6 },
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| 162 | {{ 1, 0, -2, 0, -1, 0, 0, 0}, 0.11e-6, 0.00e-6 }
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| 163 | };
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| 164 |
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| 165 | /* Terms of order t^1 */
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| 166 | static const TERM e1[] = {
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| 167 | {{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.87e-6, 0.00e-6 }
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| 168 | };
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| 169 |
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| 170 | /* Number of terms in the series */
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| 171 | const int NE0 = (int) (sizeof e0 / sizeof (TERM));
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| 172 | const int NE1 = (int) (sizeof e1 / sizeof (TERM));
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| 173 |
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| 174 | /*--------------------------------------------------------------------*/
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| 175 |
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| 176 | /* Interval between fundamental epoch J2000.0 and current date (JC). */
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| 177 | t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
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| 178 |
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| 179 | /* Fundamental Arguments (from IERS Conventions 2003) */
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| 180 |
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| 181 | /* Mean anomaly of the Moon. */
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| 182 | fa[0] = eraFal03(t);
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| 183 |
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| 184 | /* Mean anomaly of the Sun. */
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| 185 | fa[1] = eraFalp03(t);
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| 186 |
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| 187 | /* Mean longitude of the Moon minus that of the ascending node. */
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| 188 | fa[2] = eraFaf03(t);
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| 189 |
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| 190 | /* Mean elongation of the Moon from the Sun. */
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| 191 | fa[3] = eraFad03(t);
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| 192 |
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| 193 | /* Mean longitude of the ascending node of the Moon. */
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| 194 | fa[4] = eraFaom03(t);
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| 195 |
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| 196 | /* Mean longitude of Venus. */
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| 197 | fa[5] = eraFave03(t);
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| 198 |
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| 199 | /* Mean longitude of Earth. */
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| 200 | fa[6] = eraFae03(t);
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| 201 |
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| 202 | /* General precession in longitude. */
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| 203 | fa[7] = eraFapa03(t);
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| 204 |
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| 205 | /* Evaluate the EE complementary terms. */
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| 206 | s0 = 0.0;
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| 207 | s1 = 0.0;
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| 208 |
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| 209 | for (i = NE0-1; i >= 0; i--) {
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| 210 | a = 0.0;
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| 211 | for (j = 0; j < 8; j++) {
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| 212 | a += (double)(e0[i].nfa[j]) * fa[j];
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| 213 | }
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| 214 | s0 += e0[i].s * sin(a) + e0[i].c * cos(a);
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| 215 | }
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| 216 |
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| 217 | for (i = NE1-1; i >= 0; i--) {
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| 218 | a = 0.0;
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| 219 | for (j = 0; j < 8; j++) {
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| 220 | a += (double)(e1[i].nfa[j]) * fa[j];
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| 221 | }
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| 222 | s1 += e1[i].s * sin(a) + e1[i].c * cos(a);
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| 223 | }
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| 224 |
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| 225 | eect = (s0 + s1 * t ) * ERFA_DAS2R;
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| 226 |
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| 227 | return eect;
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| 228 |
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| 229 | }
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| 230 | /*----------------------------------------------------------------------
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| 231 | **
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| 232 | **
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| 233 | ** Copyright (C) 2013-2017, NumFOCUS Foundation.
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| 234 | ** All rights reserved.
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| 235 | **
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| 236 | ** This library is derived, with permission, from the International
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| 237 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
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| 238 | ** available from http://www.iausofa.org.
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| 239 | **
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| 240 | ** The ERFA version is intended to retain identical functionality to
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| 241 | ** the SOFA library, but made distinct through different function and
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| 242 | ** file names, as set out in the SOFA license conditions. The SOFA
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| 243 | ** original has a role as a reference standard for the IAU and IERS,
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| 244 | ** and consequently redistribution is permitted only in its unaltered
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| 245 | ** state. The ERFA version is not subject to this restriction and
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| 246 | ** therefore can be included in distributions which do not support the
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| 247 | ** concept of "read only" software.
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| 248 | **
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| 249 | ** Although the intent is to replicate the SOFA API (other than
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| 250 | ** replacement of prefix names) and results (with the exception of
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| 251 | ** bugs; any that are discovered will be fixed), SOFA is not
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| 252 | ** responsible for any errors found in this version of the library.
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| 253 | **
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| 254 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
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| 255 | ** that you are using a library derived from SOFA, rather than SOFA
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| 256 | ** itself.
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| 257 | **
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| 258 | **
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| 259 | ** TERMS AND CONDITIONS
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| 260 | **
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| 261 | ** Redistribution and use in source and binary forms, with or without
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| 262 | ** modification, are permitted provided that the following conditions
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| 263 | ** are met:
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| 264 | **
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| 265 | ** 1 Redistributions of source code must retain the above copyright
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| 266 | ** notice, this list of conditions and the following disclaimer.
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| 267 | **
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| 268 | ** 2 Redistributions in binary form must reproduce the above copyright
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| 269 | ** notice, this list of conditions and the following disclaimer in
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| 270 | ** the documentation and/or other materials provided with the
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| 271 | ** distribution.
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| 272 | **
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| 273 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
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| 274 | ** the International Astronomical Union nor the names of its
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| 275 | ** contributors may be used to endorse or promote products derived
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| 276 | ** from this software without specific prior written permission.
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| 277 | **
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| 278 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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| 279 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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| 280 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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| 281 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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| 282 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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| 283 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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| 284 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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| 285 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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| 286 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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| 287 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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| 288 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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| 289 | ** POSSIBILITY OF SUCH DAMAGE.
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| 290 | **
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| 291 | */
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