Determination of Planetary Masses from the Motions of Comets

Abstract

A brief survey is given of past determinations of the masses of the principal planets from analyses of the motions of comets. Some numerical experiments using comets which have close approaches to Jupiter are made. As a result of these experiments, it is concluded that the conventional least squares solution for the correction to the mass of Jupiter is inadequate for comets which have a close approach to Jupiter. It is further concluded that perhaps, in some cases, the apparent presence of nongravitational forces is merely a manifestation of the failure of the conventional orbit correction process to adjust correctly the orbits of objects which undergo very large perturbations, and it also may be a consequence of errors in the adopted planetary masses. It is suggested that the use of partial derivatives obtained through the numerical integration of the variational equations may overcome the difficulties.