Surfaces of minimal energy and their singular points in the problem of stellar approaches toward the solar system

Abstract

Planetary motion during stellar approaches toward the Solar System is examined in the framework of the three-dimensional restricted three-body problem. The exact expression of the force function without a series expansion is used. Regions of possible motion of a planet are determined. Surfaces of minimal energy, which are generalizations of surfaces of zero velocity, are plotted. Singular (exceptional) points of these surfaces are determined, and their type and Lyapunov stability are ascertained. The results thus obtained are shown in the form of figures and tables. Refs 5. Figs 2. Table 1.