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# fk45z

erfa.fk45z(r1950, d1950, bepoch)

  Convert a B1950.0 FK4 star position to J2000.0 FK5, assuming zero proper motion in the FK5 system.

  Parameters:
    r1950 double array
    d1950 double array
    bepoch double array
  Returns:
    r2000 double array
    d2000 double array

  Notes

  Wraps ERFA function `eraFk45z`. The ERFA documentation is:

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

      Convert a B1950.0 FK4 star position to J2000.0 FK5, assuming zero
      proper motion in the FK5 system.

      This function converts a star's catalog data from the old FK4
      (Bessel-Newcomb) system to the later IAU 1976 FK5 (Fricke) system,
      in such a way that the FK5 proper motion is zero.  Because such a
      star has, in general, a non-zero proper motion in the FK4 system,
      the function requires the epoch at which the position in the FK4
      system was determined.

      Given:
         r1950,d1950    double   B1950.0 FK4 RA,Dec at epoch (rad)
         bepoch         double   Besselian epoch (e.g. 1979.3)

      Returned:
         r2000,d2000    double   J2000.0 FK5 RA,Dec (rad)

      Notes:

      1) The epoch bepoch is strictly speaking Besselian, but if a
         Julian epoch is supplied the result will be affected only to a
         negligible extent.

      2) The method is from Appendix 2 of Aoki et al. (1983), but using
         the constants of Seidelmann (1992).  See the function eraFk425
         for a general introduction to the FK4 to FK5 conversion.

      3) Conversion from equinox B1950.0 FK4 to equinox J2000.0 FK5 only
         is provided for.  Conversions for different starting and/or
         ending epochs 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.

      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.

      Called:
         eraAnp       normalize angle into range 0 to 2pi
         eraC2s       p-vector to spherical
         eraEpb2jd    Besselian epoch to Julian date
         eraEpj       Julian date to Julian epoch
         eraPdp       scalar product of two p-vectors
         eraPmp       p-vector minus p-vector
         eraPpsp      p-vector plus scaled p-vector
         eraPvu       update a pv-vector
         eraS2c       spherical to p-vector

      This revision:   2023 March 4

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