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# p06e

erfa.p06e(date1, date2)

  Precession angles, IAU 2006, equinox based.

  Parameters
    date1 double array
    date2 double array
  Returns
    eps0 double array
    psia double array
    oma double array
    bpa double array
    bqa double array
    pia double array
    bpia double array
    epsa double array
    chia double array
    za double array
    zetaa double array
    thetaa double array
    pa double array
    gam double array
    phi double array
    psi double array

  Notes

  Wraps ERFA function `eraP06e`. The ERFA documentation is:

      - - - - - - - -
       e r a P 0 6 e
      - - - - - - - -

      Precession angles, IAU 2006, equinox based.

      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 (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

      This revision:  2021 May 11

      Copyright (C) 2013-2021, NumFOCUS Foundation.
      Derived, with permission, from the SOFA library.  See notes at end of file.