#include "erfa.h" void eraPfw06(double date1, double date2, double *gamb, double *phib, double *psib, double *epsa) /* ** - - - - - - - - - ** e r a P f w 0 6 ** - - - - - - - - - ** ** Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation). ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** gamb double F-W angle gamma_bar (radians) ** phib double F-W angle phi_bar (radians) ** psib double F-W angle psi_bar (radians) ** epsa double F-W angle epsilon_A (radians) ** ** 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) Naming the following points: ** ** e = J2000.0 ecliptic pole, ** p = GCRS pole, ** E = mean ecliptic pole of date, ** and P = mean pole of date, ** ** the four Fukushima-Williams angles are as follows: ** ** gamb = gamma_bar = epE ** phib = phi_bar = pE ** psib = psi_bar = pEP ** epsa = epsilon_A = EP ** ** 3) The matrix representing the combined effects of frame bias and ** precession is: ** ** PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb) ** ** 4) The matrix representing the combined effects of frame bias, ** precession and nutation is simply: ** ** NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb) ** ** where dP and dE are the nutation components with respect to the ** ecliptic of date. ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** ** Called: ** eraObl06 mean obliquity, IAU 2006 ** ** Copyright (C) 2013-2017, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { double t; /* Interval between fundamental date J2000.0 and given date (JC). */ t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC; /* P03 bias+precession angles. */ *gamb = ( -0.052928 + ( 10.556378 + ( 0.4932044 + ( -0.00031238 + ( -0.000002788 + ( 0.0000000260 ) * t) * t) * t) * t) * t) * ERFA_DAS2R; *phib = ( 84381.412819 + ( -46.811016 + ( 0.0511268 + ( 0.00053289 + ( -0.000000440 + ( -0.0000000176 ) * t) * t) * t) * t) * t) * ERFA_DAS2R; *psib = ( -0.041775 + ( 5038.481484 + ( 1.5584175 + ( -0.00018522 + ( -0.000026452 + ( -0.0000000148 ) * t) * t) * t) * t) * t) * ERFA_DAS2R; *epsa = eraObl06(date1, date2); return; } /*---------------------------------------------------------------------- ** ** ** Copyright (C) 2013-2017, 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. ** */