An Analytical Approach to the Determination of Stellar Fields of View

Book excerpt: This paper describes a scheme to determine the size of the circular field of view that is both necessary and sufficient to include at least some specified number, n, of stars from a given set, independent of the orientation of the field within the celestial sphere. A geometrical proof of the scheme is presented, and all equations needed to effect the scheme are derived. The scheme is thus shown to be entirely analytical and to involve no assumptions concerning the distribution of the stars. Numerical results are presented in which the 1064 stars brighter than, or equal in brightness to, an apparent visual magnitude of +4.7 are considered. The size and location of the necessary fields of view are tabulated as a function of limiting star brightness for n=1, n=2, and n=3. Finally, the meaning and importance of the data are discussed and related to star sensor technology.