#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) 2013-2015, 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) 2013-2015, 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. ** */