slaAop -


void slaAop(rap, dap, date, dut, elongm, phim, hm, xp, yp, tdk, pmb, rh, wl, tlr, aob, zob, hob, dob, rob)


double rap
double dap
double date
double dut
double elongm
double phim
double hm
double xp
double yp
double tdk
double pmb
double rh
double wl
double tlr
double *aob
double *zob
double *hob
double *dob
double *rob


  Apparent to observed place, for optical sources distant from
  the solar system.


     rap     double  geocentric apparent right ascension
     dap     double  geocentric apparent declination
     date    double  UTC date/time (Modified Julian Date, JD-2400000.5)
     dut     double  delta UT:  UT1-UTC (UTC seconds)
     elongm  double  mean longitude of the observer (radians, east +ve)
     phim    double  mean geodetic latitude of the observer (radians)
     hm      double  observer's height above sea level (metres)
     xp      double  polar motion x-coordinate (radians)
     yp      double  polar motion y-coordinate (radians)
     tdk     double  local ambient temperature (DegK; std=273.155)
     pmb     double  local atmospheric pressure (mB; std=1013.25)
     rh      double  local relative humidity (in the range 0.0-1.0)
     wl      double  effective wavelength (micron, e.g. 0.55)
     tlr     double  tropospheric lapse rate (DegK/metre, e.g. 0.0065)


     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 (radians)


   1)  This routine returns zenith distance rather than elevation
       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.  Providing the meteorological parameters are
       known accurately and there are no gross local effects, the
       predicted apparent RA,Dec should be within about 0.1 arcsec
       for a zenith distance of less than 70 degrees.  Even at a
       topocentric zenith distance of 90 degrees, the accuracy in
       elevation should be better than 1 arcmin;  useful results
       are available for a further 3 degrees, beyond which the
       slaRefro routine returns a fixed value of the refraction.
       The complementary routines slaAop (or slaAopqk) and slaOap
       (or slaOapqk) are self-consistent to better than 1 micro-
       arcsecond all over the celestial sphere.

   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)  "Apparent" place means the geocentric apparent right ascension
       and declination, which is obtained from a catalogue mean place
       by allowing for space motion, parallax, precession, nutation,
       annual aberration, and the Sun's gravitational lens effect.  For
       star positions in the FK5 system (i.e. J2000), these effects can
       be applied by means of the slaMap etc routines.  Starting from
       other mean place systems, additional transformations will be
       needed;  for example, FK4 (i.e. B1950) mean places would first
       have to be converted to FK5, which can be done with the
       slaFk425 etc routines.

   5)  "Observed" Az,El means the position that would be seen by a
       perfect theodolite located at the observer.  This is obtained
       from the geocentric apparent 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, using the geodetic latitude corrected for polar
       motion, and is the position that would be seen by a perfect
       equatorial located at the observer and with its polar axis
       aligned to the Earth's axis of rotation (n.b. not to the
       refracted pole).  Finally, the RA is obtained by subtracting
       the HA from the local apparent ST.

   6)  To predict the required setting of a real telescope, the
       observed place produced by this routine would have to be
       adjusted for the tilt of the azimuth or polar axis of the
       mounting (with appropriate corrections for mount flexures),
       for non-perpendicularity between the mounting axes, for the
       position of the rotator axis and the pointing axis relative
       to it, for tube flexure, for gear and encoder errors, and
       finally for encoder zero points.  Some telescopes would, of
       course, exhibit other properties which would need to be
       accounted for at the appropriate point in the sequence.

   7)  This routine takes time to execute, due mainly to the
       rigorous integration used to evaluate the refraction.
       For processing multiple stars for one location and time,
       call slaAoppa once followed by one call per star to slaAopqk.
       Where a range of times within a limited period of a few hours
       is involved, and the highest precision is not required, call
       slaAoppa once, followed by a call to slaAoppat each time the
       time changes, followed by one call per star to slaAopqk.

   8)  The date argument is UTC expressed as an MJD.  This is,
       strictly speaking, wrong, because of leap seconds.  However,
       as long as the delta UT and the UTC are consistent there
       are no difficulties, except during a leap second.  In this
       case, the start of the 61st second of the final minute should
       begin a new MJD day and the old pre-leap delta UT should
       continue to be used.  As the 61st second completes, the MJD
       should revert to the start of the day as, simultaneously,
       the delta UTC changes by one second to its post-leap new value.

   9)  The delta UT (UT1-UTC) is tabulated in IERS circulars and
       elsewhere.  It increases by exactly one second at the end of
       each UTC leap second, introduced in order to keep delta UT
       within +/- 0.9 seconds.

       The longitude required by the present routine is east-positive,
       in accordance with geographical convention (and right-handed).
       In particular, note that the longitudes returned by the
       slaObs routine are west-positive, following astronomical
       usage, and must be reversed in sign before use in the present

  11)  The polar coordinates xp,yp can be obtained from IERS
       circulars and equivalent publications.  The maximum amplitude
       is about 0.3 arcseconds.  If xp,yp values are unavailable,
       use xp=yp=0.0.  See page B60 of the 1988 Astronomical Almanac
       for a definition of the two angles.

  12)  The height above sea level of the observing station, hm,
       can be obtained from the Astronomical Almanac (Section J
       in the 1988 edition), or via the routine slaObs.  If p,
       the pressure in millibars, is available, an adequate
       estimate of hm can be obtained from the expression

             hm = -8149.9415 * log(p/1013.25);

       (See Astrophysical Quantities, C.W.Allen, 3rd edition,
       section 52.)  Similarly, if the pressure p is not known,
       it can be estimated from the height of the observing
station, hm as follows

             p = 1013.25 * exp(-hm/8149.9415);

       Note, however, that the refraction is proportional to the
       pressure and that an accurate p value is important for
       precise work.


 slaAoppa, slaAopqk

  P.T.Wallace   Starlink   31 October 1993