Astro-PAL

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erfasrc/src/p06e.c  view on Meta::CPAN

**     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 (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 ERFA functions:
**
**     . eraXy06  contains the polynomial parts of the X and Y series.
**
**     . eraS06  contains the polynomial part of the s+XY/2 series.
**
**     . eraPfw06  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 ERFA is the version of the Fukushima-
**     Williams angles that refers directly to the GCRS pole.  These
**     angles may be calculated by calling the function eraPfw06.  ERFA
**     also supports the direct computation of the CIP GCRS X,Y by
**     series, available by calling eraXy06.
**
**  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.
**
**  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:
**     eraObl06     mean obliquity, IAU 2006
**
**  Copyright (C) 2013-2020, 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;

/* Obliquity at J2000.0. */

   *eps0 = 84381.406 * ERFA_DAS2R;

/* Luni-solar precession. */

   *psia = ( 5038.481507     +
           (   -1.0790069    +
           (   -0.00114045   +
           (    0.000132851  +
           (   -0.0000000951 )
           * t) * t) * t) * t) * t * ERFA_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 * ERFA_DAS2R;

/* Ecliptic pole x, J2000.0 ecliptic triad. */

   *bpa = (  4.199094     +
          (  0.1939873    +
          ( -0.00022466   +
          ( -0.000000912  +
          (  0.0000000120 )
          * t) * t) * t) * t) * t * ERFA_DAS2R;

/* Ecliptic pole -y, J2000.0 ecliptic triad. */



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