#include "erfa.h"
double eraS06(double date1, double date2, double x, double y)
/*
** - - - - - - -
** e r a S 0 6
** - - - - - - -
**
** The CIO locator s, positioning the Celestial Intermediate Origin on
** the equator of the Celestial Intermediate Pole, given the CIP's X,Y
** coordinates. Compatible with IAU 2006/2000A precession-nutation.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
** x,y double CIP coordinates (Note 3)
**
** Returned (function value):
** double the CIO locator s in radians (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 CIO locator s is the difference between the right ascensions
** of the same point in two systems: the two systems are the GCRS
** and the CIP,CIO, and the point is the ascending node of the
** CIP equator. The quantity s remains below 0.1 arcsecond
** throughout 1900-2100.
**
** 3) The series used to compute s is in fact for s+XY/2, where X and Y
** are the x and y components of the CIP unit vector; this series
** is more compact than a direct series for s would be. This
** function requires X,Y to be supplied by the caller, who is
** responsible for providing values that are consistent with the
** supplied date.
**
** 4) The model is consistent with the "P03" precession (Capitaine et
** al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the
** IAU 2000A nutation (with P03 adjustments).
**
** 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., Wallace, P.T. & Chapront, J., 2003, Astron.
** Astrophys. 432, 355
**
** McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003),
** IERS Technical Note No. 32, BKG
**
** 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, w0, w1, w2, w3, w4, w5;
/* Fundamental arguments */
double fa[8];
/* Returned value */
double s;
/* --------------------- */
/* The series for s+XY/2 */
/* --------------------- */
typedef struct {
int nfa[8]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
double s, c; /* sine and cosine coefficients */
} TERM;
/* Polynomial coefficients */
static const double sp[] = {
/* 1-6 */
94.00e-6,
3808.65e-6,
-122.68e-6,
-72574.11e-6,
27.98e-6,
15.62e-6
};
/* Terms of order t^0 */
static const TERM s0[] = {
/* 1-10 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 },
{{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-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}, 4.57e-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 },
{{ 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 },
{{ 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 s1[] = {
/* 1 - 3 */
{{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 },
{{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.73e-6, -0.03e-6 },
{{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 }
};
/* Terms of order t^2 */
static const TERM s2[] = {
/* 1-10 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.52e-6, -0.17e-6 },
{{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 },
{{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 },
{{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 },
{{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 },
{{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 },
{{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 },
{{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 },
/* 11-20 */
{{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 },
{{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 },
{{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 },
{{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 },
{{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 },
{{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 },
{{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 },
{{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 },
{{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 },
{{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 },
/* 21-25 */
{{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 },
{{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 },
{{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 },
{{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 },
{{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 }
};
/* Terms of order t^3 */
static const TERM s3[] = {
/* 1-4 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.42e-6 },
{{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.46e-6 },
{{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.25e-6 },
{{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.23e-6 }
};
/* Terms of order t^4 */
static const TERM s4[] = {
/* 1-1 */
{{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 }
};
/* Number of terms in the series */
static const int NS0 = (int) (sizeof s0 / sizeof (TERM));
static const int NS1 = (int) (sizeof s1 / sizeof (TERM));
static const int NS2 = (int) (sizeof s2 / sizeof (TERM));
static const int NS3 = (int) (sizeof s3 / sizeof (TERM));
static const int NS4 = (int) (sizeof s4 / 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 s. */
w0 = sp[0];
w1 = sp[1];
w2 = sp[2];
w3 = sp[3];
w4 = sp[4];
w5 = sp[5];
for (i = NS0-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)s0[i].nfa[j] * fa[j];
}
w0 += s0[i].s * sin(a) + s0[i].c * cos(a);
}
for (i = NS1-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)s1[i].nfa[j] * fa[j];
}
w1 += s1[i].s * sin(a) + s1[i].c * cos(a);
}
for (i = NS2-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)s2[i].nfa[j] * fa[j];
}
w2 += s2[i].s * sin(a) + s2[i].c * cos(a);
}
for (i = NS3-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)s3[i].nfa[j] * fa[j];
}
w3 += s3[i].s * sin(a) + s3[i].c * cos(a);
}
for (i = NS4-1; i >= 0; i--) {
a = 0.0;
for (j = 0; j < 8; j++) {
a += (double)s4[i].nfa[j] * fa[j];
}
w4 += s4[i].s * sin(a) + s4[i].c * cos(a);
}
s = (w0 +
(w1 +
(w2 +
(w3 +
(w4 +
w5 * t) * t) * t) * t) * t) * ERFA_DAS2R - x*y/2.0;
return s;
}
/*----------------------------------------------------------------------
**
**
** 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.
**
*/