On Libration Points in the Asteroid–Research Probe System

Abstract

This paper is dedicated to a study of relative motion in the field of homogeneous spheroid bodies. It is assumed that an asteroid’s satellite does not affect its translational and rotational motion by inertia. The latter motion has the form of rotation in the mode of regular precession. The case in which the asteroid is an ellipsoid of revolution is considered. A system of conditions that the libration points must satisfy is constructed; it is shown that its solution is two types of libration points, which differ in their location with respect to the constant vector of the angular momentum and the axis of symmetry of the ellipsoid. Thereafter, the stability of libration points is investigated numerically and analytically in the first approximation.