Additions to Hill's Theory of Saturn

Abstract

A comparison between Hill's Tables of Saturn and the orbit recently obtained by numerical integration indicated errors in the Tables that seemed to be connected with the secular perturbations and with the great inequality. It is of course possible that the errors are the consequence of some numerical mistake, either in Hill's theory or in the Tables. L. E. Cunningham has indeed discovered a mistake at the very beginning of the theory, which affects the whole of it, but which probably is not large enough to account for the errors in the Tables. There may be other mistakes, as yet undiscovered; and a complete numerical verification of Hill's theory is much to be desired. But it also seems worth-while to inquire whether Hill's theory may be incomplete by reason of his overlooking portions of the disturbing forces that might produce important perturbations; this is the subject of the present article.

Published in The Astronomical Journal, Vol. 57, No. 2, p33-35, May 1952.