Observed to apparent place palOap
’ R’ , ’ H’ or ’ A’ (see below) ’ s height above sea level (metres) 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 90 deg) 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.)
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 palRefro routine returns a fixed value of the refraction. The complementary routines palAop (or palAopqk) and palOap (or palOapqk) are self-consistent to better than 1 micro- arcsecond all over the celestial sphere.
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.
" Observed" Az,El means the position that would be seen by a perfect theodolite located at the
observer. This is related to the observed HA,Dec 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" RA,Dec or HA,Dec 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 RA,Dec is
obtained.
Frequently, mean rather than apparent RA,Dec will be required, in which case further transformations
will be necessary. The palAmp etc routines will convert the apparent RA,Dec 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" (1950) coordinates be needed, the routines
palFk524 etc will also need to be applied.
To convert to apparent RA,Dec 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.
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 palAoppa once followed by one call per star to palOapqk. Where a range of times within a limited period of a few hours is involved, and the highest precision is not required, call palAoppa once, followed by a call to palAoppat each time the time changes, followed by one call per star to palOapqk.
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.
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.
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 palOBS routine are west-positive, following astronomical usage, and must be reversed in sign before use in the present routine.
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=0D0. See page B60 of the 1988 Astronomical Almanac for a definition of the two angles.
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 palOBS. If P, the pressure in millibars, is available, an adequate estimate of HM can be obtained from the expression
HM -29.3TSLLOG(P/1013.25).
where TSL is the approximate sea-level air temperature in K (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 1013.25EXP(-HM/(29.3TSL)).
Note, however, that the refraction is nearly proportional to the pressure and that an accurate P value is important for precise work.
The azimuths etc. used by the present routine are with respect to the celestial pole. Corrections from the terrestrial pole can be computed using palPolmo.