### SLA_OAP

Observed to Apparent

ACTION:
Observed to apparent place.
CALL:
CALL sla_OAP (TYPE, OB1, OB2, DATE, DUT, ELONGM, PHIM, HM, XP, YP, TDK, PMB, RH, WL, TLR, RAP, DAP)
##### GIVEN:
 TYPE C*(*) type of coordinates – ‘R’, ‘H’ or ‘A’ (see below) OB1 D observed Az, HA or RA (radians; Az is N=0, E=$9{0}^{\circ }$) OB2 D observed zenith distance or $\delta$ (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:
 RAP,DAP D geocentric apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$

NOTES:
(1)
Only the first character of the TYPE argument is significant. ‘R’ or ‘r’ indicates that OBS1 and OBS2 are the observed right ascension and declination; ‘H’ or ‘h’ indicates that they are hour angle (west +ve) and declination; anything else (‘A’ or ‘a’ is recommended) indicates that OBS1 and OBS2 are azimuth (north zero, east $9{0}^{\circ }$) and zenith distance. (Zenith distance is used 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)
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 related to the observed $\left[\phantom{\rule{0.3em}{0ex}}h,\delta \phantom{\rule{0.3em}{0ex}}\right]$ via the standard rotation, using the geodetic latitude (corrected for polar motion), while the observed HA and RA are related simply through the local apparent ST. Observed $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ or $\left[\phantom{\rule{0.3em}{0ex}}h,\delta \phantom{\rule{0.3em}{0ex}}\right]$ thus means 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). By removing from the observed place the effects of atmospheric refraction and diurnal aberration, the geocentric apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ is obtained.
(5)
Frequently, mean rather than apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ will be required, in which case further transformations will be necessary. The sla_AMP etc. routines will convert the apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ produced by the present routine into an FK5 J2000 mean place, by allowing for the Sun’s gravitational lens effect, annual aberration, nutation and precession. Should FK4 B1950 coordinates be required, the routines sla_FK524 etc. will also have to be applied.
(6)
To convert to apparent $\left[\phantom{\rule{0.3em}{0ex}}\alpha ,\delta \phantom{\rule{0.3em}{0ex}}\right]$ the coordinates read from a real telescope, corrections would have to be applied for encoder zero points, gear and encoder errors, tube flexure, the position of the rotator axis and the pointing axis relative to it, non-perpendicularity between the mounting axes, and finally for the tilt of the azimuth or polar axis of the mounting (with appropriate corrections for mount flexures). 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_OAPQK. 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_OAPQK.
(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 mb, 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 from the terrestrial pole can be computed using sla_POLMO.