#include "sofa.h"

void iauFk54z(double r2000, double d2000, double bepoch,
              double *r1950, double *d1950,
              double *dr1950, double *dd1950)
/*
**  - - - - - - - - -
**   i a u F k 5 4 z
**  - - - - - - - - -
**
**  Convert a J2000.0 FK5 star position to B1950.0 FK4, assuming zero
**  proper motion in FK5 and parallax.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     r2000,d2000    double   J2000.0 FK5 RA,Dec (rad)
**     bepoch         double   Besselian epoch (e.g. 1950.0)
**
**  Returned:
**     r1950,d1950    double   B1950.0 FK4 RA,Dec (rad) at epoch BEPOCH
**     dr1950,dd1950  double   B1950.0 FK4 proper motions (rad/trop.yr)
**
**  Notes:
**
**  1) In contrast to the iauFk524 function, here the FK5 proper
**     motions, the parallax and the radial velocity are presumed zero.
**
**  2) This function converts a star position from the IAU 1976 FK5
**    (Fricke) system to the former FK4 (Bessel-Newcomb) system, for
**     cases such as distant radio sources where it is presumed there is
**     zero parallax and no proper motion.  Because of the E-terms of
**     aberration, such objects have (in general) non-zero proper motion
**     in FK4, and the present function returns those fictitious proper
**     motions.
**
**  3) Conversion from B1950.0 FK4 to J2000.0 FK5 only is provided for.
**     Conversions involving other equinoxes would require additional
**     treatment for precession.
**
**  4) The position returned by this function is in the B1950.0 FK4
**     reference system but at Besselian epoch BEPOCH.  For comparison
**     with catalogs the BEPOCH argument will frequently be 1950.0. (In
**     this context the distinction between Besselian and Julian epoch
**     is insignificant.)
**
**  5) The RA component of the returned (fictitious) proper motion is
**     dRA/dt rather than cos(Dec)*dRA/dt.
**
**  Called:
**     iauAnp       normalize angle into range 0 to 2pi
**     iauC2s       p-vector to spherical
**     iauFk524     FK4 to FK5
**     iauS2c       spherical to p-vector
**
**  This revision:   2020 November 19
**
**  SOFA release 2021-05-12
**
**  Copyright (C) 2021 IAU SOFA Board.  See notes at end.
*/
{
   double r, d, pr, pd, px, rv, p[3], w, v[3];
   int i;


/* FK5 equinox J2000.0 to FK4 equinox B1950.0. */
   iauFk524(r2000, d2000, 0.0, 0.0, 0.0, 0.0,
            &r, &d, &pr, &pd, &px, &rv);

/* Spherical to Cartesian. */
   iauS2c(r, d, p);

/* Fictitious proper motion (radians per year). */
   v[0] = - pr*p[1] - pd*cos(r)*sin(d);
   v[1] =   pr*p[0] - pd*sin(r)*sin(d);
   v[2] =             pd*cos(d);

/* Apply the motion. */
   w = bepoch - 1950.0;
   for ( i = 0; i < 3; i++ ) {
      p[i] += w*v[i];
   }

/* Cartesian to spherical. */
   iauC2s(p, &w, d1950);
   *r1950 = iauAnp(w);

/* Fictitious proper motion. */
   *dr1950 = pr;
   *dd1950 = pd;

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2021
**  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
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**        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.
**
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**
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**
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**
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**
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*
**  In any published work or commercial product which uses the SOFA
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**
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**
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**
**--------------------------------------------------------------------*/
}