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#include "erfa.h" |
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double eraS06(double date1, double date2, double x, double y) |
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/* |
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** - - - - - - - |
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** e r a S 0 6 |
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** - - - - - - - |
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** |
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** The CIO locator s, positioning the Celestial Intermediate Origin on |
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** the equator of the Celestial Intermediate Pole, given the CIP's X,Y |
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** coordinates. Compatible with IAU 2006/2000A precession-nutation. |
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** |
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** Given: |
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** date1,date2 double TT as a 2-part Julian Date (Note 1) |
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** x,y double CIP coordinates (Note 3) |
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** |
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** Returned (function value): |
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** double the CIO locator s in radians (Note 2) |
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** |
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** Notes: |
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** |
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** 1) The TT date date1+date2 is a Julian Date, apportioned in any |
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** convenient way between the two arguments. For example, |
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** JD(TT)=2450123.7 could be expressed in any of these ways, |
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** among others: |
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** |
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** date1 date2 |
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** |
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** 2450123.7 0.0 (JD method) |
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** 2451545.0 -1421.3 (J2000 method) |
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** 2400000.5 50123.2 (MJD method) |
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** 2450123.5 0.2 (date & time method) |
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** |
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** The JD method is the most natural and convenient to use in |
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** cases where the loss of several decimal digits of resolution |
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** is acceptable. The J2000 method is best matched to the way |
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** the argument is handled internally and will deliver the |
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** optimum resolution. The MJD method and the date & time methods |
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** are both good compromises between resolution and convenience. |
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** |
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** 2) The CIO locator s is the difference between the right ascensions |
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** of the same point in two systems: the two systems are the GCRS |
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** and the CIP,CIO, and the point is the ascending node of the |
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** CIP equator. The quantity s remains below 0.1 arcsecond |
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** throughout 1900-2100. |
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** |
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** 3) The series used to compute s is in fact for s+XY/2, where X and Y |
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** are the x and y components of the CIP unit vector; this series |
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** is more compact than a direct series for s would be. This |
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** function requires X,Y to be supplied by the caller, who is |
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** responsible for providing values that are consistent with the |
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** supplied date. |
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** |
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** 4) The model is consistent with the "P03" precession (Capitaine et |
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** al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the |
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** IAU 2000A nutation (with P03 adjustments). |
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** |
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** Called: |
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** eraFal03 mean anomaly of the Moon |
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** eraFalp03 mean anomaly of the Sun |
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** eraFaf03 mean argument of the latitude of the Moon |
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** eraFad03 mean elongation of the Moon from the Sun |
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** eraFaom03 mean longitude of the Moon's ascending node |
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** eraFave03 mean longitude of Venus |
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** eraFae03 mean longitude of Earth |
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** eraFapa03 general accumulated precession in longitude |
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** |
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** References: |
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** |
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** Capitaine, N., Wallace, P.T. & Chapront, J., 2003, Astron. |
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** Astrophys. 432, 355 |
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** |
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** McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003), |
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** IERS Technical Note No. 32, BKG |
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** |
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** Copyright (C) 2013-2019, NumFOCUS Foundation. |
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** Derived, with permission, from the SOFA library. See notes at end of file. |
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*/ |
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{ |
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/* Time since J2000.0, in Julian centuries */ |
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double t; |
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/* Miscellaneous */ |
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int i, j; |
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double a, w0, w1, w2, w3, w4, w5; |
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/* Fundamental arguments */ |
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double fa[8]; |
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/* Returned value */ |
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double s; |
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/* --------------------- */ |
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/* The series for s+XY/2 */ |
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/* --------------------- */ |
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typedef struct { |
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int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */ |
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double s, c; /* sine and cosine coefficients */ |
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} TERM; |
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/* Polynomial coefficients */ |
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static const double sp[] = { |
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/* 1-6 */ |
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94.00e-6, |
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3808.65e-6, |
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-122.68e-6, |
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-72574.11e-6, |
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27.98e-6, |
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15.62e-6 |
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}; |
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/* Terms of order t^0 */ |
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static const TERM s0[] = { |
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/* 1-10 */ |
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{{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 }, |
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{{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6 }, |
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{{ 0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6 }, |
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{{ 0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6 }, |
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{{ 0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6 }, |
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{{ 0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6 }, |
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{{ 0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6 }, |
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{{ 0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6 }, |
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{{ 0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6 }, |
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{{ 0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6 }, |
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/* 11-20 */ |
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{{ 1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6 }, |
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{{ 1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6 }, |
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{{ 0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6 }, |
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{{ 0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6 }, |
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{{ 0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6 }, |
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{{ 0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6 }, |
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{{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6 }, |
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{{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6 }, |
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{{ 1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6 }, |
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{{ 1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6 }, |
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/* 21-30 */ |
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{{ 0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6 }, |
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{{ 0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6 }, |
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{{ 0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6 }, |
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{{ 0, 0, 0, 0, 0, 8,-13, -1}, 0.10e-6, -0.05e-6 }, |
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{{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6 }, |
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{{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 }, |
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{{ 0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6 }, |
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{{ 1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6 }, |
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{{ 1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 }, |
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{{ 0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6 }, |
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/* 31-33 */ |
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{{ 0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6 }, |
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{{ 1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6 }, |
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{{ 1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6 } |
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}; |
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/* Terms of order t^1 */ |
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static const TERM s1[] = { |
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/* 1 - 3 */ |
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{{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 }, |
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{{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.73e-6, -0.03e-6 }, |
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{{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 } |
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}; |
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/* Terms of order t^2 */ |
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static const TERM s2[] = { |
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/* 1-10 */ |
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{{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.52e-6, -0.17e-6 }, |
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{{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 }, |
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{{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 }, |
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{{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 }, |
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{{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 }, |
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{{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 }, |
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{{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 }, |
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{{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 }, |
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{{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 }, |
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{{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 }, |
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/* 11-20 */ |
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{{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 }, |
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{{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 }, |
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{{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 }, |
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{{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 }, |
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{{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 }, |
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{{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 }, |
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{{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 }, |
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{{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 }, |
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{{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 }, |
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{{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 }, |
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/* 21-25 */ |
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{{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 }, |
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{{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 }, |
198
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{{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 }, |
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{{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 }, |
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{{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 } |
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}; |
202
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203
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/* Terms of order t^3 */ |
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static const TERM s3[] = { |
205
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/* 1-4 */ |
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{{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.42e-6 }, |
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{{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.46e-6 }, |
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{{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.25e-6 }, |
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{{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.23e-6 } |
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}; |
212
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213
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/* Terms of order t^4 */ |
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static const TERM s4[] = { |
215
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216
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/* 1-1 */ |
217
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{{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 } |
218
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}; |
219
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220
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/* Number of terms in the series */ |
221
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static const int NS0 = (int) (sizeof s0 / sizeof (TERM)); |
222
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static const int NS1 = (int) (sizeof s1 / sizeof (TERM)); |
223
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static const int NS2 = (int) (sizeof s2 / sizeof (TERM)); |
224
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static const int NS3 = (int) (sizeof s3 / sizeof (TERM)); |
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static const int NS4 = (int) (sizeof s4 / sizeof (TERM)); |
226
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227
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/*--------------------------------------------------------------------*/ |
228
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229
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/* Interval between fundamental epoch J2000.0 and current date (JC). */ |
230
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3
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t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC; |
231
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232
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/* Fundamental Arguments (from IERS Conventions 2003) */ |
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234
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/* Mean anomaly of the Moon. */ |
235
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3
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fa[0] = eraFal03(t); |
236
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237
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/* Mean anomaly of the Sun. */ |
238
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3
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fa[1] = eraFalp03(t); |
239
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240
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/* Mean longitude of the Moon minus that of the ascending node. */ |
241
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3
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fa[2] = eraFaf03(t); |
242
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243
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/* Mean elongation of the Moon from the Sun. */ |
244
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3
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fa[3] = eraFad03(t); |
245
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246
|
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/* Mean longitude of the ascending node of the Moon. */ |
247
|
3
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fa[4] = eraFaom03(t); |
248
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249
|
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/* Mean longitude of Venus. */ |
250
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3
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fa[5] = eraFave03(t); |
251
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252
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|
/* Mean longitude of Earth. */ |
253
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3
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fa[6] = eraFae03(t); |
254
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255
|
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|
/* General precession in longitude. */ |
256
|
3
|
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|
fa[7] = eraFapa03(t); |
257
|
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258
|
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|
/* Evaluate s. */ |
259
|
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|
w0 = sp[0]; |
260
|
|
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|
w1 = sp[1]; |
261
|
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|
w2 = sp[2]; |
262
|
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|
w3 = sp[3]; |
263
|
|
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|
w4 = sp[4]; |
264
|
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|
w5 = sp[5]; |
265
|
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266
|
102
|
100
|
|
|
|
|
for (i = NS0-1; i >= 0; i--) { |
267
|
|
|
|
|
|
|
a = 0.0; |
268
|
891
|
100
|
|
|
|
|
for (j = 0; j < 8; j++) { |
269
|
792
|
|
|
|
|
|
a += (double)s0[i].nfa[j] * fa[j]; |
270
|
|
|
|
|
|
|
} |
271
|
99
|
|
|
|
|
|
w0 += s0[i].s * sin(a) + s0[i].c * cos(a); |
272
|
|
|
|
|
|
|
} |
273
|
|
|
|
|
|
|
|
274
|
12
|
100
|
|
|
|
|
for (i = NS1-1; i >= 0; i--) { |
275
|
|
|
|
|
|
|
a = 0.0; |
276
|
81
|
100
|
|
|
|
|
for (j = 0; j < 8; j++) { |
277
|
72
|
|
|
|
|
|
a += (double)s1[i].nfa[j] * fa[j]; |
278
|
|
|
|
|
|
|
} |
279
|
9
|
|
|
|
|
|
w1 += s1[i].s * sin(a) + s1[i].c * cos(a); |
280
|
|
|
|
|
|
|
} |
281
|
|
|
|
|
|
|
|
282
|
78
|
100
|
|
|
|
|
for (i = NS2-1; i >= 0; i--) { |
283
|
|
|
|
|
|
|
a = 0.0; |
284
|
675
|
100
|
|
|
|
|
for (j = 0; j < 8; j++) { |
285
|
600
|
|
|
|
|
|
a += (double)s2[i].nfa[j] * fa[j]; |
286
|
|
|
|
|
|
|
} |
287
|
75
|
|
|
|
|
|
w2 += s2[i].s * sin(a) + s2[i].c * cos(a); |
288
|
|
|
|
|
|
|
} |
289
|
|
|
|
|
|
|
|
290
|
15
|
100
|
|
|
|
|
for (i = NS3-1; i >= 0; i--) { |
291
|
|
|
|
|
|
|
a = 0.0; |
292
|
108
|
100
|
|
|
|
|
for (j = 0; j < 8; j++) { |
293
|
96
|
|
|
|
|
|
a += (double)s3[i].nfa[j] * fa[j]; |
294
|
|
|
|
|
|
|
} |
295
|
12
|
|
|
|
|
|
w3 += s3[i].s * sin(a) + s3[i].c * cos(a); |
296
|
|
|
|
|
|
|
} |
297
|
|
|
|
|
|
|
|
298
|
6
|
100
|
|
|
|
|
for (i = NS4-1; i >= 0; i--) { |
299
|
|
|
|
|
|
|
a = 0.0; |
300
|
27
|
100
|
|
|
|
|
for (j = 0; j < 8; j++) { |
301
|
24
|
|
|
|
|
|
a += (double)s4[i].nfa[j] * fa[j]; |
302
|
|
|
|
|
|
|
} |
303
|
3
|
|
|
|
|
|
w4 += s4[i].s * sin(a) + s4[i].c * cos(a); |
304
|
|
|
|
|
|
|
} |
305
|
|
|
|
|
|
|
|
306
|
6
|
|
|
|
|
|
s = (w0 + |
307
|
3
|
|
|
|
|
|
(w1 + |
308
|
3
|
|
|
|
|
|
(w2 + |
309
|
3
|
|
|
|
|
|
(w3 + |
310
|
3
|
|
|
|
|
|
(w4 + |
311
|
18
|
|
|
|
|
|
w5 * t) * t) * t) * t) * t) * ERFA_DAS2R - x*y/2.0; |
312
|
|
|
|
|
|
|
|
313
|
3
|
|
|
|
|
|
return s; |
314
|
|
|
|
|
|
|
|
315
|
|
|
|
|
|
|
} |
316
|
|
|
|
|
|
|
/*---------------------------------------------------------------------- |
317
|
|
|
|
|
|
|
** |
318
|
|
|
|
|
|
|
** |
319
|
|
|
|
|
|
|
** Copyright (C) 2013-2019, NumFOCUS Foundation. |
320
|
|
|
|
|
|
|
** All rights reserved. |
321
|
|
|
|
|
|
|
** |
322
|
|
|
|
|
|
|
** This library is derived, with permission, from the International |
323
|
|
|
|
|
|
|
** Astronomical Union's "Standards of Fundamental Astronomy" library, |
324
|
|
|
|
|
|
|
** available from http://www.iausofa.org. |
325
|
|
|
|
|
|
|
** |
326
|
|
|
|
|
|
|
** The ERFA version is intended to retain identical functionality to |
327
|
|
|
|
|
|
|
** the SOFA library, but made distinct through different function and |
328
|
|
|
|
|
|
|
** file names, as set out in the SOFA license conditions. The SOFA |
329
|
|
|
|
|
|
|
** original has a role as a reference standard for the IAU and IERS, |
330
|
|
|
|
|
|
|
** and consequently redistribution is permitted only in its unaltered |
331
|
|
|
|
|
|
|
** state. The ERFA version is not subject to this restriction and |
332
|
|
|
|
|
|
|
** therefore can be included in distributions which do not support the |
333
|
|
|
|
|
|
|
** concept of "read only" software. |
334
|
|
|
|
|
|
|
** |
335
|
|
|
|
|
|
|
** Although the intent is to replicate the SOFA API (other than |
336
|
|
|
|
|
|
|
** replacement of prefix names) and results (with the exception of |
337
|
|
|
|
|
|
|
** bugs; any that are discovered will be fixed), SOFA is not |
338
|
|
|
|
|
|
|
** responsible for any errors found in this version of the library. |
339
|
|
|
|
|
|
|
** |
340
|
|
|
|
|
|
|
** If you wish to acknowledge the SOFA heritage, please acknowledge |
341
|
|
|
|
|
|
|
** that you are using a library derived from SOFA, rather than SOFA |
342
|
|
|
|
|
|
|
** itself. |
343
|
|
|
|
|
|
|
** |
344
|
|
|
|
|
|
|
** |
345
|
|
|
|
|
|
|
** TERMS AND CONDITIONS |
346
|
|
|
|
|
|
|
** |
347
|
|
|
|
|
|
|
** Redistribution and use in source and binary forms, with or without |
348
|
|
|
|
|
|
|
** modification, are permitted provided that the following conditions |
349
|
|
|
|
|
|
|
** are met: |
350
|
|
|
|
|
|
|
** |
351
|
|
|
|
|
|
|
** 1 Redistributions of source code must retain the above copyright |
352
|
|
|
|
|
|
|
** notice, this list of conditions and the following disclaimer. |
353
|
|
|
|
|
|
|
** |
354
|
|
|
|
|
|
|
** 2 Redistributions in binary form must reproduce the above copyright |
355
|
|
|
|
|
|
|
** notice, this list of conditions and the following disclaimer in |
356
|
|
|
|
|
|
|
** the documentation and/or other materials provided with the |
357
|
|
|
|
|
|
|
** distribution. |
358
|
|
|
|
|
|
|
** |
359
|
|
|
|
|
|
|
** 3 Neither the name of the Standards Of Fundamental Astronomy Board, |
360
|
|
|
|
|
|
|
** the International Astronomical Union nor the names of its |
361
|
|
|
|
|
|
|
** contributors may be used to endorse or promote products derived |
362
|
|
|
|
|
|
|
** from this software without specific prior written permission. |
363
|
|
|
|
|
|
|
** |
364
|
|
|
|
|
|
|
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
365
|
|
|
|
|
|
|
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
366
|
|
|
|
|
|
|
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS |
367
|
|
|
|
|
|
|
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE |
368
|
|
|
|
|
|
|
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, |
369
|
|
|
|
|
|
|
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, |
370
|
|
|
|
|
|
|
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
371
|
|
|
|
|
|
|
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER |
372
|
|
|
|
|
|
|
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
373
|
|
|
|
|
|
|
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN |
374
|
|
|
|
|
|
|
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
375
|
|
|
|
|
|
|
** POSSIBILITY OF SUCH DAMAGE. |
376
|
|
|
|
|
|
|
** |
377
|
|
|
|
|
|
|
*/ |