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#include "sofa.h"
void iauLtpequ(double epj, double veq[3])
/*
** - - - - - - - - - -
** i a u L t p e q u
** - - - - - - - - - -
**
** Long-term precession of the equator.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** epj double Julian epoch (TT)
**
** Returned:
** veq double[3] equator pole unit vector
**
** Notes:
**
** 1) The returned vector is with respect to the J2000.0 mean equator
** and equinox.
**
** 2) The Vondrak et al. (2011, 2012) 400 millennia precession model
** agrees with the IAU 2006 precession at J2000.0 and stays within
** 100 microarcseconds during the 20th and 21st centuries. It is
** accurate to a few arcseconds throughout the historical period,
** worsening to a few tenths of a degree at the end of the
** +/- 200,000 year time span.
**
** References:
**
** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
** expressions, valid for long time intervals, Astron.Astrophys. 534,
** A22
**
** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
** expressions, valid for long time intervals (Corrigendum),
** Astron.Astrophys. 541, C1
**
** This revision: 2016 February 9
**
** SOFA release 2020-07-21
**
** Copyright (C) 2020 IAU SOFA Board. See notes at end.
*/
{
/* Polynomial coefficients */
enum { NPOL = 4 };
static const double xypol[2][NPOL] = {
{ 5453.282155,
0.4252841,
-0.00037173,
-0.000000152},
{-73750.930350,
-0.7675452,
-0.00018725,
0.000000231}
};
/* Periodic coefficients */
static const double xyper[][5] = {
{ 256.75, -819.940624,75004.344875,81491.287984, 1558.515853},
{ 708.15,-8444.676815, 624.033993, 787.163481, 7774.939698},
{ 274.20, 2600.009459, 1251.136893, 1251.296102,-2219.534038},
{ 241.45, 2755.175630,-1102.212834,-1257.950837,-2523.969396},
{2309.00, -167.659835,-2660.664980,-2966.799730, 247.850422},
{ 492.20, 871.855056, 699.291817, 639.744522, -846.485643},
{ 396.10, 44.769698, 153.167220, 131.600209,-1393.124055},
{ 288.90, -512.313065, -950.865637, -445.040117, 368.526116},
{ 231.10, -819.415595, 499.754645, 584.522874, 749.045012},
{1610.00, -538.071099, -145.188210, -89.756563, 444.704518},
{ 620.00, -189.793622, 558.116553, 524.429630, 235.934465},
{ 157.87, -402.922932, -23.923029, -13.549067, 374.049623},
{ 220.30, 179.516345, -165.405086, -210.157124, -171.330180},
{1200.00, -9.814756, 9.344131, -44.919798, -22.899655}
};
static const int NPER = (int) ( sizeof xyper / 5 / sizeof (double) );
/* Miscellaneous */
int i;
double t, x, y, w, a, s, c;
/* Centuries since J2000. */
t = ( epj - 2000.0 ) / 100.0;
/* Initialize X and Y accumulators. */
x = 0.0;
y = 0.0;
/* Periodic terms. */
w = D2PI * t;
for ( i = 0; i < NPER; i++ ) {
a = w / xyper[i][0];
s = sin(a);
c = cos(a);
x += c*xyper[i][1] + s*xyper[i][3];
y += c*xyper[i][2] + s*xyper[i][4];
}
/* Polynomial terms. */
w = 1.0;
for ( i = 0; i < NPOL; i++ ) {
x += xypol[0][i]*w;
y += xypol[1][i]*w;
w *= t;
}
/* X and Y (direction cosines). */
x *= DAS2R;
y *= DAS2R;
/* Form the equator pole vector. */
veq[0] = x;
veq[1] = y;
w = 1.0 - x*x - y*y;
veq[2] = w < 0.0 ? 0.0 : sqrt(w);
/*----------------------------------------------------------------------
**
** Copyright (C) 2020
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
** CONDITIONS WHICH APPLY TO ITS USE.
**
** 1. The Software is owned by the IAU SOFA Board ("SOFA").
**
** 2. Permission is granted to anyone to use the SOFA software for any
** purpose, including commercial applications, free of charge and
** without payment of royalties, subject to the conditions and
** restrictions listed below.
**
** 3. You (the user) may copy and distribute SOFA source code to others,
** and use and adapt its code and algorithms in your own software,
** on a world-wide, royalty-free basis. That portion of your
** distribution that does not consist of intact and unchanged copies
** of SOFA source code files is a "derived work" that must comply
** with the following requirements:
**
** a) Your work shall be marked or carry a statement that it
** (i) uses routines and computations derived by you from
** software provided by SOFA under license to you; and
** (ii) does not itself constitute software provided by and/or
** endorsed by SOFA.
**
** b) The source code of your derived work must contain descriptions
** of how the derived work is based upon, contains and/or differs
** from the original SOFA software.
**
** c) The names of all routines in your derived work shall not
** include the prefix "iau" or "sofa" or trivial modifications
** thereof such as changes of case.
**
** d) The origin of the SOFA components of your derived work must
** not be misrepresented; you must not claim that you wrote the
** original software, nor file a patent application for SOFA
** software or algorithms embedded in the SOFA software.
**
** e) These requirements must be reproduced intact in any source
** distribution and shall apply to anyone to whom you have
** granted a further right to modify the source code of your
** derived work.
**
** Note that, as originally distributed, the SOFA software is
** intended to be a definitive implementation of the IAU standards,
** and consequently third-party modifications are discouraged. All
** variations, no matter how minor, must be explicitly marked as
** such, as explained above.
**
** 4. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 5. The SOFA software is provided "as is" and SOFA makes no warranty
** as to its use or performance. SOFA does not and cannot warrant
** the performance or results which the user may obtain by using the
** SOFA software. SOFA makes no warranties, express or implied, as
** to non-infringement of third party rights, merchantability, or
** fitness for any particular purpose. In no event will SOFA be
** liable to the user for any consequential, incidental, or special
** damages, including any lost profits or lost savings, even if a
** SOFA representative has been advised of such damages, or for any
** claim by any third party.
**
** 6. The provision of any version of the SOFA software under the terms
** and conditions specified herein does not imply that future
** versions will also be made available under the same terms and
** conditions.
*
** In any published work or commercial product which uses the SOFA
** software directly, acknowledgement (see www.iausofa.org) is
** appreciated.
**
** Correspondence concerning SOFA software should be addressed as
** follows:
**
** By email: sofa@ukho.gov.uk
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}