### SLA_AOPQK

Quick Appt-to-Observed

ACTION:
Quick apparent to observed place (but see Note 8, below).
CALL:
CALL sla_AOPQK (RAP, DAP, AOPRMS, AOB, ZOB, HOB, DOB, ROB)
##### GIVEN:
 RAP,DAP D geocentric apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ (radians) AOPRMS D(14) star-independent apparent-to-observed parameters: (1) geodetic latitude (radians) (2,3) sine and cosine of geodetic latitude (4) magnitude of diurnal aberration vector (5) height (metres) (6) ambient temperature (K) (7) pressure (mb) (8) relative humidity (0 – 1) (9) wavelength ($\mu m$) (10) lapse rate (K per metre) (11,12) refraction constants A and B (radians) (13) longitude + eqn of equinoxes + “sidereal $\Delta$UT” (radians) (14) local apparent sidereal time (radians)

##### RETURNED:
 AOB D observed azimuth (radians: N=0, E=$9{0}^{\circ }$) ZOB D observed zenith distance (radians) HOB D observed Hour Angle (radians) DOB D observed Declination (radians) ROB D observed Right Ascension (radians)

NOTES:
(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 azimuth and elevation should be within about ′′01 for $\zeta <7{0}^{\circ }$. Even at a topocentric zenith distance of $9{0}^{\circ }$, the accuracy in elevation should be better than 1 arcminute; useful results are available for a further ${3}^{\circ }$, beyond which the sla_REFRO routine returns a fixed value of the refraction. The complementary routines sla_AOP (or sla_AOPQK) and sla_OAP (or sla_OAPQK) are self-consistent to better than 1 microarcsecond 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 $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ means the geocentric apparent right ascension and declination, which is obtained from a catalogue mean place by allowing for space motion, parallax, the Sun’s gravitational lens effect, annual aberration and precession-nutation. For star positions in the FK5 system (i.e. J2000), these effects can be applied by means of the sla_MAP 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 sla_FK425 etc. routines.
(5)
Observed $\left[\phantom{\rule{0.3em}{0ex}}Az,El\phantom{\rule{1em}{0ex}}\right]$ means the position that would be seen by a perfect theodolite located at the observer. This is obtained from the geocentric apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ by allowing for Earth orientation and diurnal aberration, rotating from equator to horizon coordinates, and then adjusting for refraction. The $\left[\phantom{\rule{0.3em}{0ex}}h,\delta \phantom{\rule{0.3em}{0ex}}\right]$ 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 $\alpha$ is obtained by subtracting the h 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)
The star-independent apparent-to-observed-place parameters in AOPRMS may be computed by means of the sla_AOPPA routine. If nothing has changed significantly except the time, the sla_AOPPAT routine may be used to perform the requisite partial recomputation of AOPRMS.
(8)
At zenith distances beyond about $7{6}^{\circ }$, the need for special care with the corrections for refraction causes a marked increase in execution time. Moreover, the effect gets worse with increasing zenith distance. Adroit programming in the calling application may allow the problem to be reduced. Prepare an alternative AOPRMS array, computed for zero air-pressure; this will disable the refraction corrections and cause rapid execution. Using this AOPRMS array, a preliminary call to the present routine will, depending on the application, produce a rough position which may be enough to establish whether the full, slow calculation (using the real AOPRMS array) is worthwhile. For example, there would be no need for the full calculation if the preliminary call had already established that the source was well below the elevation limits for a particular telescope.
(9)
The azimuths etc. used by the present routine are with respect to the celestial pole. Corrections to the terrestrial pole can be computed using sla_POLMO.