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#include "erfa.h"
double eraEect00(double date1, double date2)
/*
** - - - - - - - - - -
** e r a E e c t 0 0
** - - - - - - - - - -
**
** Equation of the equinoxes complementary terms, consistent with
** IAU 2000 resolutions.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned (function value):
** double complementary terms (Note 2)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The "complementary terms" are part of the equation of the
** equinoxes (EE), classically the difference between apparent and
** mean Sidereal Time:
**
** GAST = GMST + EE
**
** with:
**
** EE = dpsi * cos(eps)
**
** where dpsi is the nutation in longitude and eps is the obliquity
** of date. However, if the rotation of the Earth were constant in
** an inertial frame the classical formulation would lead to
** apparent irregularities in the UT1 timescale traceable to side-
** effects of precession-nutation. In order to eliminate these
** effects from UT1, "complementary terms" were introduced in 1994
** (IAU, 1994) and took effect from 1997 (Capitaine and Gontier,
** 1993):
**
** GAST = GMST + CT + EE
**
** By convention, the complementary terms are included as part of
** the equation of the equinoxes rather than as part of the mean
** Sidereal Time. This slightly compromises the "geometrical"
** interpretation of mean sidereal time but is otherwise
** inconsequential.
**
** The present function computes CT in the above expression,
** compatible with IAU 2000 resolutions (Capitaine et al., 2002, and
** IERS Conventions 2003).
**
** Called:
** eraFal03 mean anomaly of the Moon
** eraFalp03 mean anomaly of the Sun
** eraFaf03 mean argument of the latitude of the Moon
** eraFad03 mean elongation of the Moon from the Sun
** eraFaom03 mean longitude of the Moon's ascending node
** eraFave03 mean longitude of Venus
** eraFae03 mean longitude of Earth
** eraFapa03 general accumulated precession in longitude
**
** References:
**
** Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275,
** 645-650 (1993)
**
** Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
** implement the IAU 2000 definition of UT1", Astronomy &
** Astrophysics, 406, 1135-1149 (2003)
**
** IAU Resolution C7, Recommendation 3 (1994)
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* Time since J2000.0, in Julian centuries */
double t;
/* Miscellaneous */
int i, j;
double a, s0, s1;
/* Fundamental arguments */
double fa[14];
/* Returned value. */
double eect;
/* ----------------------------------------- */
/* The series for the EE complementary terms */
/* ----------------------------------------- */
typedef struct {
int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
double s, c; /* sine and cosine coefficients */
} TERM;
/* Terms of order t^0 */
static const TERM e0[] = {
/* 1-10 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, 2640.96e-6, -0.39e-6 },
{{ 0, 0, 0, 0, 2, 0, 0, 0}, 63.52e-6, -0.02e-6 },
{{ 0, 0, 2, -2, 3, 0, 0, 0}, 11.75e-6, 0.01e-6 },
{{ 0, 0, 2, -2, 1, 0, 0, 0}, 11.21e-6, 0.01e-6 },
{{ 0, 0, 2, -2, 2, 0, 0, 0}, -4.55e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 3, 0, 0, 0}, 2.02e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.98e-6, 0.00e-6 },
{{ 0, 0, 0, 0, 3, 0, 0, 0}, -1.72e-6, 0.00e-6 },
{{ 0, 1, 0, 0, 1, 0, 0, 0}, -1.41e-6, -0.01e-6 },
{{ 0, 1, 0, 0, -1, 0, 0, 0}, -1.26e-6, -0.01e-6 },
/* 11-20 */
{{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.63e-6, 0.00e-6 },
{{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.63e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 3, 0, 0, 0}, 0.46e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 1, 0, 0, 0}, 0.45e-6, 0.00e-6 },
{{ 0, 0, 4, -4, 4, 0, 0, 0}, 0.36e-6, 0.00e-6 },
{{ 0, 0, 1, -1, 1, -8, 12, 0}, -0.24e-6, -0.12e-6 },
{{ 0, 0, 2, 0, 0, 0, 0, 0}, 0.32e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 2, 0, 0, 0}, 0.28e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 3, 0, 0, 0}, 0.27e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.26e-6, 0.00e-6 },
/* 21-30 */
{{ 0, 0, 2, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 },
{{ 0, 1, -2, 2, -3, 0, 0, 0}, 0.19e-6, 0.00e-6 },
{{ 0, 1, -2, 2, -1, 0, 0, 0}, 0.18e-6, 0.00e-6 },
{{ 0, 0, 0, 0, 0, 8,-13, -1}, -0.10e-6, 0.05e-6 },
{{ 0, 0, 0, 2, 0, 0, 0, 0}, 0.15e-6, 0.00e-6 },
{{ 2, 0, -2, 0, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 },
{{ 1, 0, 0, -2, 1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 2, 0, 0, 0}, -0.14e-6, 0.00e-6 },
{{ 1, 0, 0, -2, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 },
{{ 0, 0, 4, -2, 4, 0, 0, 0}, 0.13e-6, 0.00e-6 },
/* 31-33 */
{{ 0, 0, 2, -2, 4, 0, 0, 0}, -0.11e-6, 0.00e-6 },
{{ 1, 0, -2, 0, -3, 0, 0, 0}, 0.11e-6, 0.00e-6 },
{{ 1, 0, -2, 0, -1, 0, 0, 0}, 0.11e-6, 0.00e-6 }
};
/* Terms of order t^1 */
static const TERM e1[] = {
{{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.87e-6, 0.00e-6 }
};
/* Number of terms in the series */
const int NE0 = (int) (sizeof e0 / sizeof (TERM));
const int NE1 = (int) (sizeof e1 / sizeof (TERM));
/*--------------------------------------------------------------------*/
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
/* Fundamental Arguments (from IERS Conventions 2003) */
/* Mean anomaly of the Moon. */
fa[0] = eraFal03(t);
/* Mean anomaly of the Sun. */
fa[1] = eraFalp03(t);
/* Mean longitude of the Moon minus that of the ascending node. */
fa[2] = eraFaf03(t);
/* Mean elongation of the Moon from the Sun. */
fa[3] = eraFad03(t);
/* Mean longitude of the ascending node of the Moon. */
fa[4] = eraFaom03(t);
/* Mean longitude of Venus. */
fa[5] = eraFave03(t);
/* Mean longitude of Earth. */
fa[6] = eraFae03(t);
/* General precession in longitude. */
fa[7] = eraFapa03(t);
/* Evaluate the EE complementary terms. */
s0 = 0.0;
s1 = 0.0;
for (i = NE0-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)(e0[i].nfa[j]) * fa[j];
}
s0 += e0[i].s * sin(a) + e0[i].c * cos(a);
}
for (i = NE1-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)(e1[i].nfa[j]) * fa[j];
}
s1 += e1[i].s * sin(a) + e1[i].c * cos(a);
}
eect = (s0 + s1 * t ) * ERFA_DAS2R;
return eect;
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** All rights reserved.
**
** This library is derived, with permission, from the International
** Astronomical Union's "Standards of Fundamental Astronomy" library,
** available from http://www.iausofa.org.
**
** The ERFA version is intended to retain identical functionality to
** the SOFA library, but made distinct through different function and
** file names, as set out in the SOFA license conditions. The SOFA
** original has a role as a reference standard for the IAU and IERS,
** and consequently redistribution is permitted only in its unaltered
** state. The ERFA version is not subject to this restriction and
** therefore can be included in distributions which do not support the
** concept of "read only" software.
**
** Although the intent is to replicate the SOFA API (other than
** replacement of prefix names) and results (with the exception of
** bugs; any that are discovered will be fixed), SOFA is not
** responsible for any errors found in this version of the library.
**
** If you wish to acknowledge the SOFA heritage, please acknowledge
** that you are using a library derived from SOFA, rather than SOFA
** itself.
**
**
** TERMS AND CONDITIONS
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
** 1 Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
**
** 2 Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in
** the documentation and/or other materials provided with the
** distribution.
**
** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
** the International Astronomical Union nor the names of its
** contributors may be used to endorse or promote products derived
** from this software without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
*/
|
