A Semianalytical Method for Constructing Nearly Equatorial Orbits of Hypothetical Satellites of Asteroids with an Almost Spheroidal Shape

Abstract

The problem of the motion of a particle with a negligible mass (satellite) near the equatorial plane of a spheroidal body, in particular, an asteroid, is considered. To a first approximation, the motions can be separated into equatorial and latitudinal components for low inclinations of the satellite orbit. The equatorial central motion, when the force function depends only on the satellite’s distance to the coordinate origin (the asteroid’s center of mass), is constructed by the previously proposed semianalytical method. The construction of the latitudinal motion envisages the solution of a linearized system of second-order differential equations with periodic coefficients by numerically determining the monodromy matrix on the period of the equatorial motion and its temporal analytic continuation. The model problems of the perturbed motion of nearly equatorial hypothetical satellites of Ceres and Vesta are considered. The methodical accuracy has been estimated by a comparison with the numerical solution.