Different Sorts of Mean Place

A particularly confusing aspect of published mean places is that they are sensitive to the precise way they were determined. A mean place is not directly observable, even with fundamental instruments such as transit circles, and to produce a mean place will involve relying on some existing star catalogue, for example the fundamental catalogues FK4 and FK5, and applying given mathematical models of precession, nutation, aberration and so on. Note in particular that no star catalogue, even a fundamental catalogue such as FK4 or FK5, defines a coordinate system, strictly speaking; it is merely a list of star positions and proper motions. However, once the stars from a given catalogue are used as position calibrators, e.g. for transit-circle observations or for plate reductions, then a broader sense of there being a coordinate grid naturally arises, and such phrases as ``in the system of the FK4'' can legitimately be employed. However, there is no formal link between the two concepts - no ``standard least squares fit'' between reality and the inevitably flawed catalogues. All such catalogues suffer at some level from systematic, zonal distortions of both the star positions and of the proper motions, and include measurement errors peculiar to individual stars.

Many of these complications are of little significance except to specialists. However, observational astronomers cannot escape exposure to at least the two main varieties of mean place, loosely called FK4 and FK5, and should be aware of certain pitfalls. For most practical purposes the more recent system, FK5, is free of surprises and tolerates naive use well. FK4, in contrast, contains two important traps:

• The FK4 system rotates at about

  $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ per century relative to distant galaxies. This is manifested as a systematic distortion in the proper motions of all FK4-derived catalogues, which will in turn pollute any astrometry done using those catalogues. For example, FK4-based astrometry of a QSO using plates taken decades apart will reveal a non-zero fictitious proper motion, and any FK4 star which happens to have zero proper motion is, in fact, slowly moving against the distant background. The FK4 frame rotates because it was established before the nature of the Milky Way, and hence the existence of systematic motions of nearby stars, had been recognized.

• Star positions in the FK4 system are part-corrected for annual aberration (see above) and embody the so-called E-terms of aberration.

The change from the old FK4-based system to FK5 occurred at the beginning of 1984 as part of a package of resolutions made by the IAU in 1976, along with the adoption of J2000 as the reference epoch. Star positions in the newer, FK5, system are free from the E-terms, and the system is a much better approximation to an inertial frame (about five times better).

It may occasionally be convenient to specify the FK4 fictitious proper motion directly. In FK4, the centennial proper motion of (for example) a QSO is:

$\mu_\alpha=-$$0^{\rm s}\hspace{-0.3em}.015869$+(($0^{\rm s}\hspace{-0.3em}.029032$$~\sin \alpha +$$0^{\rm s}\hspace{-0.3em}.000340$$~\cos \alpha ) \sin \delta -$$0^{\rm s}\hspace{-0.3em}.000105$$~\cos \alpha -$$0^{\rm s}\hspace{-0.3em}.000083$$~\sin \alpha ) \sec \delta$
$\mu_\delta\,=+$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.43549$ $~\cos \alpha -$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00510$ $~\sin \alpha + ($ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00158$ $~\sin \alpha -$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00125$ $~\cos \alpha ) \sin \delta -$ $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00066$ $~\cos \delta$