SUBROUTINE iau_P06E ( DATE1, DATE2, : EPS0, PSIA, OMA, BPA, BQA, PIA, BPIA, : EPSA, CHIA, ZA, ZETAA, THETAA, PA, : GAM, PHI, PSI ) *+ * - - - - - - - - - * i a u _ P 0 6 E * - - - - - - - - - * * Precession angles, IAU 2006, equinox based. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: canonical models. * * Given: * DATE1,DATE2 d TT as a 2-part Julian Date (Note 1) * * Returned (see Note 2): * EPS0 d epsilon_0 * PSIA d psi_A * OMA d omega_A * BPA d P_A * BQA d Q_A * PIA d pi_A * BPIA d Pi_A * EPSA d obliquity epsilon_A * CHIA d chi_A * ZA d z_A * ZETAA d zeta_A * THETAA d theta_A * PA d p_A * GAM d F-W angle gamma_J2000 * PHI d F-W angle phi_J2000 * PSI d F-W angle psi_J2000 * * 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) This routine returns the set of equinox based angles for the * Capitaine et al. "P03" precession theory, adopted by the IAU in * 2006. The angles are set out in Table 1 of Hilton et al. (2006): * * EPS0 epsilon_0 obliquity at J2000.0 * PSIA psi_A luni-solar precession * OMA omega_A inclination of equator wrt J2000.0 ecliptic * BPA P_A ecliptic pole x, J2000.0 ecliptic triad * BQA Q_A ecliptic pole -y, J2000.0 ecliptic triad * PIA pi_A angle between moving and J2000.0 ecliptics * BPIA Pi_A longitude of ascending node of the ecliptic * EPSA epsilon_A obliquity of the ecliptic * CHIA chi_A planetary precession * ZA z_A equatorial precession: -3rd 323 Euler angle * ZETAA zeta_A equatorial precession: -1st 323 Euler angle * THETAA theta_A equatorial precession: 2nd 323 Euler angle * PA p_A general precession (n.b. see below) * GAM gamma_J2000 J2000.0 RA difference of ecliptic poles * PHI phi_J2000 J2000.0 codeclination of ecliptic pole * PSI psi_J2000 longitude difference of equator poles, J2000.0 * * The returned values are all radians. * * Note that the t^5 coefficient in the series for p_A from Capitaine * et al. (2003) is incorrectly signed in Hilton et al. (2006). * * 3) Hilton et al. (2006) Table 1 also contains angles that depend on * models distinct from the P03 precession theory itself, namely the * IAU 2000A frame bias and nutation. The quoted polynomials are * used in other SOFA routines: * * . iau_XY06 contains the polynomial parts of the X and Y series. * * . iau_S06 contains the polynomial part of the s+XY/2 series. * * . iau_PFW06 implements the series for the Fukushima-Williams * angles that are with respect to the GCRS pole (i.e. the variants * that include frame bias). * * 4) The IAU resolution stipulated that the choice of parameterization * was left to the user, and so an IAU compliant precession * implementation can be constructed using various combinations of * the angles returned by the present routine. * * 5) The parameterization used by SOFA is the version of the Fukushima- * Williams angles that refers directly to the GCRS pole. These * angles may be calculated by calling the routine iau_PFW06. SOFA * also supports the direct computation of the CIP GCRS X,Y by * series, available by calling iau_XY06. * * 6) The agreement between the different parameterizations is at the * 1 microarcsecond level in the present era. * * 7) When constructing a precession formulation that refers to the GCRS * pole rather than the dynamical pole, it may (depending on the * choice of angles) be necessary to introduce the frame bias * explicitly. * * References: * * Capitaine, N., Wallace, P.T. & Chapront, J., 2003, * Astron.Astrophys., 412, 567 * * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 * * Called: * iau_OBL06 mean obliquity, IAU 2006 * * This revision: 2020 June 2 * * SOFA release 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION DATE1, DATE2, : EPS0, PSIA, OMA, BPA, BQA, PIA, BPIA, : EPSA, CHIA, ZA, ZETAA, THETAA, PA, : GAM, PHI, PSI * Arcseconds to radians DOUBLE PRECISION DAS2R PARAMETER ( DAS2R = 4.848136811095359935899141D-6 ) * Reference epoch (J2000.0), JD DOUBLE PRECISION DJ00 PARAMETER ( DJ00 = 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-DJ00 ) + DATE2 ) / DJC * Obliquity at J2000.0. EPS0 = 84381.406D0 * DAS2R * Luni-solar precession. PSIA = ( 5038.481507D0 + : ( -1.0790069D0 + : ( -0.00114045D0 + : ( 0.000132851D0 + : ( -0.0000000951D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R * Inclination of mean equator with respect to the J2000.0 ecliptic. OMA = EPS0 + ( -0.025754D0 + : ( 0.0512623D0 + : ( -0.00772503D0 + : ( -0.000000467D0 + : ( 0.0000003337D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R * Ecliptic pole x, J2000.0 ecliptic triad. BPA = ( 4.199094D0 + : ( 0.1939873D0 + : ( -0.00022466D0 + : ( -0.000000912D0 + : ( 0.0000000120D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R * Ecliptic pole -y, J2000.0 ecliptic triad. BQA = ( -46.811015D0 + : ( 0.0510283D0 + : ( 0.00052413D0 + : ( -0.000000646D0 + : ( -0.0000000172D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R * Angle between moving and J2000.0 ecliptics. PIA = ( 46.998973D0 + : ( -0.0334926D0 + : ( -0.00012559D0 + : ( 0.000000113D0 + : ( -0.0000000022D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R * Longitude of ascending node of the moving ecliptic. BPIA = ( 629546.7936D0 + : ( -867.95758D0 + : ( 0.157992D0 + : ( -0.0005371D0 + : ( -0.00004797D0 + : ( 0.000000072D0 ) : * T ) * T ) * T ) * T ) * T ) * DAS2R * Mean obliquity of the ecliptic. EPSA = iau_OBL06 ( DATE1, DATE2 ) * Planetary precession. CHIA = ( 10.556403D0 + : ( -2.3814292D0 + : ( -0.00121197D0 + : ( 0.000170663D0 + : ( -0.0000000560D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R * Equatorial precession: minus the third of the 323 Euler angles. ZA = ( -2.650545D0 + : ( 2306.077181D0 + : ( 1.0927348D0 + : ( 0.01826837D0 + : ( -0.000028596D0 + : ( -0.0000002904D0 ) : * T ) * T ) * T ) * T ) * T ) * DAS2R * Equatorial precession: minus the first of the 323 Euler angles. ZETAA = ( 2.650545D0 + : ( 2306.083227D0 + : ( 0.2988499D0 + : ( 0.01801828D0 + : ( -0.000005971D0 + : ( -0.0000003173D0 ) : * T ) * T ) * T ) * T ) * T ) * DAS2R * Equatorial precession: second of the 323 Euler angles. THETAA = ( 2004.191903D0 + : ( -0.4294934D0 + : ( -0.04182264D0 + : ( -0.000007089D0 + : ( -0.0000001274D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R * General precession. PA = ( 5028.796195D0 + : ( 1.1054348D0 + : ( 0.00007964D0 + : ( -0.000023857D0 + : ( -0.0000000383D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R * Fukushima-Williams angles for precession. GAM = ( 10.556403D0 + : ( 0.4932044D0 + : ( -0.00031238D0 + : ( -0.000002788D0 + : ( 0.0000000260D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R PHI = EPS0 + ( -46.811015D0 + : ( 0.0511269D0 + : ( 0.00053289D0 + : ( -0.000000440D0 + : ( -0.0000000176D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R PSI = ( 5038.481507D0 + : ( 1.5584176D0 + : ( -0.00018522D0 + : ( -0.000026452D0 + : ( -0.0000000148D0 ) : * T ) * T ) * T ) * T ) * T * DAS2R * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2023 * 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 * *----------------------------------------------------------------------- END