Approximate Integrable Model of the Asteroid–Satellite System

Abstract

The paper builds an integrable model of the relative motion of the asteroid–satellite system with parameters typical of the Main Asteroid Belt. It roughly describes the main effects of the evolution of the relative orbit and rotation of bodies, in particular, the dependence of the evolution of the orbit on the rotation of the asteroid. The model does not depend on resonances. Only the ratio of the sizes of bodies to the distance between the and the ratio of this distance to the distance to the Sun are considered sufficiently small.