Apparent to observed place palAop
’ s height above sea level (metres) This routine returns zenith distance 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.
" 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 palMap 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 palFk425 etc
routines.
" 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.
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.
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 palAopqk. 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 palAopqk.
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=0.0. 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 produced by the present routine are with respect to the celestial pole. Corrections to the terrestrial pole can be computed using palPolmo.