By J. B. Tatum
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Additional info for Celestial Mechanics Vol.2
Nevertheless some comparison with the old and the new may be of interest. When CCDs first came into use in astrometry, it was early evident that useful images could be obtained on a CCD far faster than on a photographic emulsion, that far fainter stars could be reached, and higher precision was obtainable. Initial misgivings were that the devices were small and covered only a small area of sky, so that only a few comparison stars were available. Available star catalogues contained positions of only a few hundred thousand stars.
However, the stars with the “worst” proper motions are generally also those with the smallest proper motions; it can probably be assumed that the stars with significant proper motions also have proper motions that are well determined. The situation changed in the 1990s with the widespread introduction of CCDs and the publication of the Guide Star Catalog containing positions of about half a billion stars down to about magnitude 21. With modern instrumentation one would never normally consider using comparison stars anything like as bright as magnitude 9 (the faint limit of the SAO Catalog).
It remains now to find expressions for tan ε sin γ and tan ε cos γ in terms of the right ascensions and declinations of Q and of C. 4, the spherical triangle PCQ. 2 from which one can (eventually) calculate the standard coordinates (ξ , η) of the star. It is also possible to calculate explicit expressions for tan ε sin γ and for tanε cos γ. Thus, by further applications of the spherical triangle formulas, we have tan ε = cos D . 3 by sin γ gives tan ε sin γ except that tan γ appears on the right hand side.
Celestial Mechanics Vol.2 by J. B. Tatum