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#include "erfa.h"
void eraPrec76(double date01, double date02, double date11, double date12,
double *zeta, double *z, double *theta)
/*
** - - - - - - - - - -
** e r a P r e c 7 6
** - - - - - - - - - -
**
** IAU 1976 precession model.
**
** This function forms the three Euler angles which implement general
** precession between two dates, using the IAU 1976 model (as for the
** FK5 catalog).
**
** Given:
** date01,date02 double TDB starting date (Note 1)
** date11,date12 double TDB ending date (Note 1)
**
** Returned:
** zeta double 1st rotation: radians cw around z
** z double 3rd rotation: radians cw around z
** theta double 2nd rotation: radians ccw around y
**
** Notes:
**
** 1) The dates date01+date02 and date11+date12 are Julian Dates,
** apportioned in any convenient way between the arguments daten1
** and daten2. For example, JD(TDB)=2450123.7 could be expressed in
** any of these ways, among others:
**
** daten1 daten2
**
** 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
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
** The two dates may be expressed using different methods, but at
** the risk of losing some resolution.
**
** 2) The accumulated precession angles zeta, z, theta are expressed
** through canonical polynomials which are valid only for a limited
** time span. In addition, the IAU 1976 precession rate is known to
** be imperfect. The absolute accuracy of the present formulation
** is better than 0.1 arcsec from 1960AD to 2040AD, better than
** 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for
** the whole of the period 500BC to 3000AD. The errors exceed
** 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec
** outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to
** 8200AD.
**
** 3) The three angles are returned in the conventional order, which
** is not the same as the order of the corresponding Euler
** rotations. The precession matrix is
** R_3(-z) x R_2(+theta) x R_3(-zeta).
**
** Reference:
**
** Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations
** (6) & (7), p283.
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double t0, t, tas2r, w;
/* Interval between fundamental epoch J2000.0 and start date (JC). */
t0 = ((date01 - ERFA_DJ00) + date02) / ERFA_DJC;
/* Interval over which precession required (JC). */
t = ((date11 - date01) + (date12 - date02)) / ERFA_DJC;
/* Euler angles. */
tas2r = t * ERFA_DAS2R;
w = 2306.2181 + (1.39656 - 0.000139 * t0) * t0;
*zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r;
*z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r;
*theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0)
+ ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r;
return;
}
/*----------------------------------------------------------------------
**
**
** 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.
**
*/
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