Celestial Coordinates for the APF

The celestial coordinate model that EOST implemented in the code of the TelescopeServer process does not correspond to any celestial reference system that the IAU has ever recommended. Discounting the complexities documented below, for many practical purposes the APF can be assumed to use the same celestial reference system as the FK5 catalog. Described below is, however, a caution about the interpretation of the catalog epoch that can be used with the APF.

Most of the transformations in the TelescopeServer code correspond to the IAU 1980 Theory of Nutation http://adsabs.harvard.edu/abs/1982CeMec..27...79S which employs the precession model of Lieske et al. based on the IAU 1976 System of Astronomical Constants http://adsabs.harvard.edu/abs/1977A%26A....58....1L

Unfortunately, the APF telescope uses the expression for Universal Time originally published by Simon Newcomb in Volume VI of Astronomical Papers prepared for the use of the American Ephemeris and Nautical Almanac (i.e, the Tables of the Sun) in 1898. http://books.google.com/books?id=j8MRAAAAYAAJ&pg=PT6 The celestial reference system of the FK5 catalog uses the 1982 expression for Universal Time from Aoki et al. http://adsabs.harvard.edu/abs/1982A%26A...105..359A

Therefore the celestial reference system of the APF telescope is slowly rotating with respect to the celestial reference system of the FK5 catalog. Nevertheless, for the lifetime of the APF telescope this discrepancy should be inconsequential so long as the pointing model for the APF is updated regularly.

The interpretation of epoch

The celestial reference frame in the FK5 catalog has the mean equator and equinox of J2000, and this is commonly referred to as the equinox of a celestial coordinate. As with most catalogs, the positions of stars in FK5 catalog are given for an epoch which is computed from the mean of the observations of that object which contributed to its position in the catalog.

Again unfortunately, the APF TelescopeServer does not implement a clear distinction between the equinox of the celestial reference frame and the epoch of the celestial coordinates in that reference frame. The APF TelescopeServer assumes that all coordinates are input with epoch J2000. This is inconsequential for galaxies and stars distant enough to have effectively zero proper motion, but it constrains the way that coordinates can be input for nearer objects with significant motions.

Therefore there are two ways that correct coordinates can be provided to the APF telescope.

  1. Supply the coordinates that the object would have in the celestial reference frame of the FK5 catalog with equinox J2000 at epoch J2000 (i.e., the coordinates where it was then), and also supply the proper motion of the object.
  2. Supply the coordinates that the object would have in the celestial reference frame of the FK5 catalog with equinox J2000 at epoch of date (i.e., pre-apply proper motion and give the coordinates where it would be today), and supply values of zero for the proper motion of the object.

Most use of APF has employed the first strategy. The second strategy has not been verified.

The units of proper motion

The native units for proper motion in the APF TelescopeServer are radian/second, but these are not used by star catalogs. The KTL service eostele provides two ways of expressing the proper motion which more nearly match traditional use in catalogs.

  1. arc velocity across the sky, with both declination and right ascension expressed in milliarcsecond/year
  2. change rate of catalog coordinates, with declination expressed in arcsecond/century and right ascension expressed in second/century

Arc velocity is the proper motion at that location on the sky projected onto unit vectors pointing toward N and E of the celestial reference frame. Arc velocity is independent of declination. To be more precise, the units of arc proper motion used here are arcsecond/(365.25 UT days) whereas, e.g., the Hipparcos catalog is expressed in arcsecond/(Julian year of Terrestrial Time).

Change rate of catalog coordinates is exactly that. Thus the value of the proper motion in right ascension includes a factor of the cosine of the declination. To be more precise, the units of catalog proper motion in right ascension used here are (sidereal second)/(Julian century of UT days) whereas many catalogs are expressed in (sidereal second)/(Besselian century of Terrestrial Time).

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