### SLA_AOP

Apparent to Observed

ACTION:
Apparent to observed place, for sources distant from the solar system.
CALL:
CALL sla_AOP (RAP, DAP, DATE, DUT, ELONGM, PHIM, HM, XP, YP, TDK, PMB, RH, WL, TLR, 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) DATE D UTC date/time (Modified Julian Date, JD$-$2400000.5) DUT D $\Delta$UT: UT1$-$UTC (UTC seconds) ELONGM D observer’s mean longitude (radians, east +ve) PHIM D observer’s mean geodetic latitude (radians) HM D observer’s height above sea level (metres) XP,YP D polar motion $\left[\phantom{\rule{0.3em}{0ex}}x,y\phantom{\rule{0.3em}{0ex}}\right]$ coordinates (radians) TDK D local ambient temperature (K; std=273.15D0) PMB D local atmospheric pressure (mb; std=1013.25D0) RH D local relative humidity (in the range 0D0 – 1D0) WL D effective wavelength ($\mu m$, e.g. 0.55D0) TLR D tropospheric lapse rate (K per metre, e.g. 0.0065D0)

##### 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 $\delta$ (radians) ROB D observed $\alpha$ (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)
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 sla_AOPPA once followed by one call per star to sla_AOPQK. Where a range of times within a limited period of a few hours is involved, and the highest precision is not required, call sla_AOPPA once, followed by a call to sla_AOPPAT each time the time changes, followed by one call per star to sla_AOPQK.
(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 $\Delta$UT 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 $±$$0$$s$$\phantom{\rule{-3.28502pt}{0ex}}.9$.
(10)
IMPORTANT – TAKE CARE WITH THE LONGITUDE SIGN CONVENTION. 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 sla_OBS routine are west-positive (as in the Astronomical Almanac before 1984) and must be reversed in sign before use in the present routine.
(11)
The polar coordinates XP,YP can be obtained from IERS circulars and equivalent publications. The maximum amplitude is about ′′03. If XP,YP values are unavailable, use XP=YP=0D0. 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 sla_OBS. If P, the pressure in millibars, is available, an adequate estimate of HM can be obtained from the following expression:

HM=-29.3D0*TSL*LOG(P/1013.25D0)

where TSL is the approximate sea-level air temperature in K (see Astrophysical Quantities, C.W.Allen, 3rd edition, §52). Similarly, if the pressure P is not known, it can be estimated from the height of the observing station, HM as follows:

P=1013.25D0*EXP(-HM/(29.3D0*TSL))

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

(13)
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.