#include "sofa.h" void iauP06e(double date1, double date2, double *eps0, double *psia, double *oma, double *bpa, double *bqa, double *pia, double *bpia, double *epsa, double *chia, double *za, double *zetaa, double *thetaa, double *pa, double *gam, double *phi, double *psi) /* ** - - - - - - - - ** i a u P 0 6 e ** - - - - - - - - ** ** Precession angles, IAU 2006, equinox based. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical models. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned (see Note 2): ** eps0 double epsilon_0 ** psia double psi_A ** oma double omega_A ** bpa double P_A ** bqa double Q_A ** pia double pi_A ** bpia double Pi_A ** epsa double obliquity epsilon_A ** chia double chi_A ** za double z_A ** zetaa double zeta_A ** thetaa double theta_A ** pa double p_A ** gam double F-W angle gamma_J2000 ** phi double F-W angle phi_J2000 ** psi double 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 ** ** 2450123.7 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) This function 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 ** 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. ** ** 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 functions: ** ** . iauXy06 contains the polynomial parts of the X and Y series. ** ** . iauS06 contains the polynomial part of the s+XY/2 series. ** ** . iauPfw06 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 function. ** ** 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 function iauPfw06. SOFA ** also supports the direct computation of the CIP GCRS X,Y by ** series, available by calling iauXy06. ** ** 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. ** ** 8) It is permissible to re-use the same variable in the returned ** arguments. The quantities are stored in the stated order. ** ** Reference: ** ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 ** ** Called: ** iauObl06 mean obliquity, IAU 2006 ** ** This revision: 2013 June 18 ** ** SOFA release 2018-01-30 ** ** Copyright (C) 2018 IAU SOFA Board. See notes at end. */ { double t; /* Interval between fundamental date J2000.0 and given date (JC). */ t = ((date1 - DJ00) + date2) / DJC; /* Obliquity at J2000.0. */ *eps0 = 84381.406 * DAS2R; /* Luni-solar precession. */ *psia = ( 5038.481507 + ( -1.0790069 + ( -0.00114045 + ( 0.000132851 + ( -0.0000000951 ) * t) * t) * t) * t) * t * DAS2R; /* Inclination of mean equator with respect to the J2000.0 ecliptic. */ *oma = *eps0 + ( -0.025754 + ( 0.0512623 + ( -0.00772503 + ( -0.000000467 + ( 0.0000003337 ) * t) * t) * t) * t) * t * DAS2R; /* Ecliptic pole x, J2000.0 ecliptic triad. */ *bpa = ( 4.199094 + ( 0.1939873 + ( -0.00022466 + ( -0.000000912 + ( 0.0000000120 ) * t) * t) * t) * t) * t * DAS2R; /* Ecliptic pole -y, J2000.0 ecliptic triad. */ *bqa = ( -46.811015 + ( 0.0510283 + ( 0.00052413 + ( -0.000000646 + ( -0.0000000172 ) * t) * t) * t) * t) * t * DAS2R; /* Angle between moving and J2000.0 ecliptics. */ *pia = ( 46.998973 + ( -0.0334926 + ( -0.00012559 + ( 0.000000113 + ( -0.0000000022 ) * t) * t) * t) * t) * t * DAS2R; /* Longitude of ascending node of the moving ecliptic. */ *bpia = ( 629546.7936 + ( -867.95758 + ( 0.157992 + ( -0.0005371 + ( -0.00004797 + ( 0.000000072 ) * t) * t) * t) * t) * t) * DAS2R; /* Mean obliquity of the ecliptic. */ *epsa = iauObl06(date1, date2); /* Planetary precession. */ *chia = ( 10.556403 + ( -2.3814292 + ( -0.00121197 + ( 0.000170663 + ( -0.0000000560 ) * t) * t) * t) * t) * t * DAS2R; /* Equatorial precession: minus the third of the 323 Euler angles. */ *za = ( -2.650545 + ( 2306.077181 + ( 1.0927348 + ( 0.01826837 + ( -0.000028596 + ( -0.0000002904 ) * t) * t) * t) * t) * t) * DAS2R; /* Equatorial precession: minus the first of the 323 Euler angles. */ *zetaa = ( 2.650545 + ( 2306.083227 + ( 0.2988499 + ( 0.01801828 + ( -0.000005971 + ( -0.0000003173 ) * t) * t) * t) * t) * t) * DAS2R; /* Equatorial precession: second of the 323 Euler angles. */ *thetaa = ( 2004.191903 + ( -0.4294934 + ( -0.04182264 + ( -0.000007089 + ( -0.0000001274 ) * t) * t) * t) * t) * t * DAS2R; /* General precession. */ *pa = ( 5028.796195 + ( 1.1054348 + ( 0.00007964 + ( -0.000023857 + ( 0.0000000383 ) * t) * t) * t) * t) * t * DAS2R; /* Fukushima-Williams angles for precession. */ *gam = ( 10.556403 + ( 0.4932044 + ( -0.00031238 + ( -0.000002788 + ( 0.0000000260 ) * t) * t) * t) * t) * t * DAS2R; *phi = *eps0 + ( -46.811015 + ( 0.0511269 + ( 0.00053289 + ( -0.000000440 + ( -0.0000000176 ) * t) * t) * t) * t) * t * DAS2R; *psi = ( 5038.481507 + ( 1.5584176 + ( -0.00018522 + ( -0.000026452 + ( -0.0000000148 ) * t) * t) * t) * t) * t * DAS2R; return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2018 ** 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 ** **--------------------------------------------------------------------*/ }