SUBROUTINE iau_PFW06 ( DATE1, DATE2, GAMB, PHIB, PSIB, EPSA ) *+ * - - - - - - - - - - * i a u _ P F W 0 6 * - - - - - - - - - - * * Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation). * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: canonical model. * * Given: * DATE1,DATE2 d TT as a 2-part Julian Date (Note 1) * * Returned: * GAMB d F-W angle gamma_bar (radians) * PHIB d F-W angle phi_bar (radians) * PSIB d F-W angle psi_bar (radians) * EPSA d 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 * * 2450123.7D0 0D0 (JD method) * 2451545D0 -1421.3D0 (J2000 method) * 2400000.5D0 50123.2D0 (MJD method) * 2450123.5D0 0.2D0 (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 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: * iau_OBL06 mean obliquity, IAU 2006 * * This revision: 2007 June 8 * * Copyright (C) 2007 IAU SOFA Review Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2, GAMB, PHIB, PSIB, EPSA * Arcseconds to radians DOUBLE PRECISION DAS2R PARAMETER ( DAS2R = 4.848136811095359935899141D-6 ) * Reference epoch (J2000), JD DOUBLE PRECISION DJ0 PARAMETER ( DJ0 = 2451545D0 ) * Days per Julian century DOUBLE PRECISION DJC PARAMETER ( DJC = 36525D0 ) DOUBLE PRECISION T DOUBLE PRECISION iau_OBL06 * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Interval between fundamental date J2000.0 and given date (JC). T = ( ( DATE1-DJ0 ) + DATE2 ) / DJC * P03 bias+precession angles. GAMB = ( -0.052928D0 + : ( 10.556378D0 + : ( 0.4932044D0 + : ( -0.00031238D0 + : ( -0.000002788D0 + : ( 0.0000000260D0 ) : * T ) * T ) * T ) * T ) * T ) * DAS2R PHIB = ( 84381.412819D0 + : ( -46.811016D0 + : ( 0.0511268D0 + : ( 0.00053289D0 + : ( -0.000000440D0 + : ( -0.0000000176D0 ) : * T ) * T ) * T ) * T ) * T ) * DAS2R PSIB = ( -0.041775D0 + : ( 5038.481484D0 + : ( 1.5584175D0 + : ( -0.00018522D0 + : ( -0.000026452D0 + : ( -0.0000000148D0 ) : * T ) * T ) * T ) * T ) * T ) * DAS2R EPSA = iau_OBL06 ( DATE1, DATE2 ) * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2007 * Standards Of Fundamental Astronomy Review Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS * WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Review Board ("the Board"). * * 2. The Software is made available free of charge for use by: * * a) private individuals for non-profit research; and * * b) non-profit educational, academic and research institutions. * * 3. Commercial use of the Software is specifically excluded from the * terms and conditions of this license. Commercial use of the * Software is subject to the prior written agreement of the Board on * terms to be agreed. * * 4. The provision of any version of the 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. * * 5. The user may modify the Software for his/her own purposes. The * user may distribute the modified software provided that the Board * is informed and that a copy of the modified software is made * available to the Board on request. All modifications made by the * user shall be clearly identified to show how the modified software * differs from the original Software, and the name(s) of the * affected routine(s) shall be changed. The original SOFA Software * License text must be present. * * 6. In any published work produced by the user and which includes * results achieved by using the Software, the user shall acknowledge * that the Software was used in producing the information contained * in such publication. * * 7. The user may incorporate or embed the Software into other software * products which he/she may then give away free of charge but not * sell provided the user makes due acknowledgement of the use which * he/she has made of the Software in creating such software * products. Any redistribution of the Software in this way shall be * made under the same terms and conditions under which the user * received it from the SOFA Center. * * 8. The user shall not cause the Software to be brought into * disrepute, either by misuse, or use for inappropriate tasks, or by * inappropriate modification. * * 9. The Software is provided to the user "as is" and the Board makes * no warranty as to its use or performance. The Board does not and * cannot warrant the performance or results which the user may * obtain by using the Software. The Board 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 the Board be liable to the user for any consequential, * incidental, or special damages, including any lost profits or lost * savings, even if a Board representative has been advised of such * damages, or for any claim by any third party. * * Correspondence concerning SOFA software should be addressed as * follows: * * Internet email: sofa@rl.ac.uk * Postal address: IAU SOFA Center * Rutherford Appleton Laboratory * Chilton, Didcot, Oxon OX11 0QX * United Kingdom * * *----------------------------------------------------------------------- END