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- atioq

# atioq

erfa.atioq(ri, di, astrom)

  Quick CIRS to observed place transformation.

  Parameters:
    ri double array
    di double array
    astrom eraASTROM array
  Returns:
    aob double array
    zob double array
    hob double array
    dob double array
    rob double array

  Notes

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

      - - - - - - - - -
       e r a A t i o q
      - - - - - - - - -

      Quick CIRS to observed place transformation.

      Use of this function is appropriate when efficiency is important and
      where many star positions are all to be transformed for one date.
      The star-independent astrometry parameters can be obtained by
      calling eraApio[13] or eraApco[13].

      Given:
         ri     double     CIRS right ascension
         di     double     CIRS declination
         astrom eraASTROM* star-independent astrometry parameters:
          pmt    double       PM time interval (SSB, Julian years)
          eb     double[3]    SSB to observer (vector, au)
          eh     double[3]    Sun to observer (unit vector)
          em     double       distance from Sun to observer (au)
          v      double[3]    barycentric observer velocity (vector, c)
          bm1    double       sqrt(1-|v|^2): reciprocal of Lorenz factor
          bpn    double[3][3] bias-precession-nutation matrix
          along  double       longitude + s' (radians)
          xpl    double       polar motion xp wrt local meridian (radians)
          ypl    double       polar motion yp wrt local meridian (radians)
          sphi   double       sine of geodetic latitude
          cphi   double       cosine of geodetic latitude
          diurab double       magnitude of diurnal aberration vector
          eral   double       "local" Earth rotation angle (radians)
          refa   double       refraction constant A (radians)
          refb   double       refraction constant B (radians)

      Returned:
         aob    double          observed azimuth (radians: N=0,E=90)
         zob    double          observed zenith distance (radians)
         hob    double          observed hour angle (radians)
         dob    double          observed declination (radians)
         rob    double          observed right ascension (CIO-based, radians)

      Notes:

      1) This function returns zenith distance rather than altitude in
         order to reflect the fact that no allowance is made for
         depression of the horizon.

      2) The accuracy of the result is limited by the corrections for
         refraction, which use a simple A*tan(z) + B*tan^3(z) model.
         Providing the meteorological parameters are known accurately and
         there are no gross local effects, the predicted observed
         coordinates should be within 0.05 arcsec (optical) or 1 arcsec
         (radio) for a zenith distance of less than 70 degrees, better
         than 30 arcsec (optical or radio) at 85 degrees and better
         than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.

         Without refraction, the complementary functions eraAtioq and
         eraAtoiq are self-consistent to better than 1 microarcsecond all
         over the celestial sphere.  With refraction included, consistency
         falls off at high zenith distances, but is still better than
         0.05 arcsec at 85 degrees.

      3) It is advisable to take great care with units, as even unlikely
         values of the input parameters are accepted and processed in
         accordance with the models used.

      4) The CIRS RA,Dec is obtained from a star catalog mean place by
         allowing for space motion, parallax, the Sun's gravitational lens
         effect, annual aberration and precession-nutation.  For star
         positions in the ICRS, these effects can be applied by means of
         the eraAtci13 (etc.) functions.  Starting from classical "mean
         place" systems, additional transformations will be needed first.

      5) "Observed" Az,El means the position that would be seen by a
         perfect geodetically aligned theodolite.  This is obtained from
         the CIRS RA,Dec by allowing for Earth orientation and diurnal
         aberration, rotating from equator to horizon coordinates, and
         then adjusting for refraction.  The HA,Dec is obtained by
         rotating back into equatorial coordinates, and is the position
         that would be seen by a perfect equatorial with its polar axis
         aligned to the Earth's axis of rotation.  Finally, the
         (CIO-based) RA is obtained by subtracting the HA from the local
         ERA.

      6) The star-independent CIRS-to-observed-place parameters in ASTROM
         may be computed with eraApio[13] or eraApco[13].  If nothing has
         changed significantly except the time, eraAper[13] may be used to
         perform the requisite adjustment to the astrom structure.

      Called:
         eraS2c       spherical coordinates to unit vector
         eraC2s       p-vector to spherical
         eraAnp       normalize angle into range 0 to 2pi

      This revision:   2022 August 30

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