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# fk425

erfa.fk425(r1950, d1950, dr1950, dd1950, p1950, v1950)

  Convert B1950.0 FK4 star catalog data to J2000.0 FK5.

  Parameters:
    r1950 double array
    d1950 double array
    dr1950 double array
    dd1950 double array
    p1950 double array
    v1950 double array
  Returns:
    r2000 double array
    d2000 double array
    dr2000 double array
    dd2000 double array
    p2000 double array
    v2000 double array

  Notes

  Wraps ERFA function `eraFk425`. The ERFA documentation is:

      - - - - - - - - -
       e r a F k 4 2 5
      - - - - - - - - -

      Convert B1950.0 FK4 star catalog data to J2000.0 FK5.

      This function converts a star's catalog data from the old FK4
      (Bessel-Newcomb) system to the later IAU 1976 FK5 (Fricke) system.

      Given: (all B1950.0, FK4)
         r1950,d1950    double   B1950.0 RA,Dec (rad)
         dr1950,dd1950  double   B1950.0 proper motions (rad/trop.yr)
         p1950          double   parallax (arcsec)
         v1950          double   radial velocity (km/s, +ve = moving away)

      Returned: (all J2000.0, FK5)
         r2000,d2000    double   J2000.0 RA,Dec (rad)
         dr2000,dd2000  double   J2000.0 proper motions (rad/Jul.yr)
         p2000          double   parallax (arcsec)
         v2000          double   radial velocity (km/s, +ve = moving away)

      Notes:

      1) The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt,
         and are per year rather than per century.

      2) The conversion is somewhat complicated, for several reasons:

         . Change of standard epoch from B1950.0 to J2000.0.

         . An intermediate transition date of 1984 January 1.0 TT.

         . A change of precession model.

         . Change of time unit for proper motion (tropical to Julian).

         . FK4 positions include the E-terms of aberration, to simplify
           the hand computation of annual aberration.  FK5 positions
           assume a rigorous aberration computation based on the Earth's
           barycentric velocity.

         . The E-terms also affect proper motions, and in particular cause
           objects at large distances to exhibit fictitious proper
           motions.

         The algorithm is based on Smith et al. (1989) and Yallop et al.
         (1989), which presented a matrix method due to Standish (1982) as
         developed by Aoki et al. (1983), using Kinoshita's development of
         Andoyer's post-Newcomb precession.  The numerical constants from
         Seidelmann (1992) are used canonically.

      3) Conversion from B1950.0 FK4 to J2000.0 FK5 only is provided for.
         Conversions for different epochs and equinoxes would require
         additional treatment for precession, proper motion and E-terms.

      4) In the FK4 catalog the proper motions of stars within 10 degrees
         of the poles do not embody differential E-terms effects and
         should, strictly speaking, be handled in a different manner from
         stars outside these regions.  However, given the general lack of
         homogeneity of the star data available for routine astrometry,
         the difficulties of handling positions that may have been
         determined from astrometric fields spanning the polar and non-
         polar regions, the likelihood that the differential E-terms
         effect was not taken into account when allowing for proper motion
         in past astrometry, and the undesirability of a discontinuity in
         the algorithm, the decision has been made in this ERFA algorithm
         to include the effects of differential E-terms on the proper
         motions for all stars, whether polar or not.  At epoch J2000.0,
         and measuring "on the sky" rather than in terms of RA change, the
         errors resulting from this simplification are less than
         1 milliarcsecond in position and 1 milliarcsecond per century in
         proper motion.

      Called:
         eraAnp       normalize angle into range 0 to 2pi
         eraPv2s      pv-vector to spherical coordinates
         eraPdp       scalar product of two p-vectors
         eraPvmpv     pv-vector minus pv_vector
         eraPvppv     pv-vector plus pv_vector
         eraS2pv      spherical coordinates to pv-vector
         eraSxp       multiply p-vector by scalar

      References:

         Aoki, S. et al., 1983, "Conversion matrix of epoch B1950.0
         FK4-based positions of stars to epoch J2000.0 positions in
         accordance with the new IAU resolutions".  Astron.Astrophys.
         128, 263-267.

         Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the
         Astronomical Almanac", ISBN 0-935702-68-7.

         Smith, C.A. et al., 1989, "The transformation of astrometric
         catalog systems to the equinox J2000.0".  Astron.J. 97, 265.

         Standish, E.M., 1982, "Conversion of positions and proper motions
         from B1950.0 to the IAU system at J2000.0".  Astron.Astrophys.,
         115, 1, 20-22.

         Yallop, B.D. et al., 1989, "Transformation of mean star places
         from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
         Astron.J. 97, 274.

      This revision:   2023 March 20

      Copyright (C) 2013-2023, NumFOCUS Foundation.
      Derived, with permission, from the SOFA library.  See notes at end of file.