THE ANALYSIS OF STAR CATALOGS .1. AN INTERCOMPARISON AMONG THE FK3, THE FK4, AND THE FK5

Progress in the construction of the fundamental catalogs allows one to ask the following questions: ''Now that we have the FK5 with which to measure by, how good was the FK4? The FK3? How realistic were the err or estimates they gave for their equatorial coordinates and their prop er motions? Have their residual systematic differences continued to de crease in amplitude?'' and so forth. Similar questions could be asked of the GC and the N30, and a companion paper will similarly analyze th em. Finally, the identical series of questions could be asked of the A GK2, AGK3, AGK3U sequence. In this paper we develop a general method t o objectively investigate, post facto, the true quality of star catalo g error estimates. We present a complete mathematical formulation of t he questions above and delineate the calculations needed to address th em. Our initial numerical applications are restricted to a straightfor ward examination of the mean errors of the coordinates and proper moti ons in the FK3 (using the FK4 and the FK5 for comparison) and in the F K4 (using the FK5 for comparison). However, we can simply and consiste ntly interpret the results of these computations-for the FK catalogs f ail to follow the predictions of mathematical statistics-only if the F K3 and the FK4 contain high angular frequency systematic errors. These errors, at the mean epochs of place of the older catalogs, are larger than the random errors in the FK5 system. We expect that our new abil ity to discern these features means that we can also prevent them duri ng compilation. Finally, note that the concepts behind our procedures are completely general and can be applied to any set of compiled data- astrometric, photometric, geodetic, and so forth.