The hill stability of planetary motion under stellar approaches

Abstract

A planetary motion under the influence of a star passing near the Solar system is examined in the framework of the three-dimensional restricted three-body problem. The exact expression of the force function without expansion it in series is used. An integral invariant relation —quasi-integral —is found, and regions of possible motion of a passively gravitating body are determined. Surfaces of minimal energy which are generalizations of surfaces of zero velocity are plotted. The Hill stability of planetary motion is investigated when a star with a mass between one and five solar masses approaches the Solar system at a minimum distance of 50 AU up to 100 AU. The results obtained are shown in the form of tables. Refs 10. Tables 2.