On approximate construction of near equatorial orbits of the satellites of spheroidal celestial bodies
The problem about a motion of material point (satellite) with negligible small mass nearby the equatorial plane of spheroidal body, in particular asteroid, is considered. For the small inclinations of satellite orbit in the first approximation dividing of motions is possible into equatorial and latitudinal components. Equatorial central motion, when a power function depends only on distance of satellite to origin of coordinates (centre of mass of asteroid), is constructed by offered early a semi-analytical method. The construction of latitudinal motion foresees the solution of linearized system of second order differential equations with periodic coefficients by numeral determination of monodromy matrix on the period of equatorial motion and its analytical continuation at time. Model problems are considered about perturbed motion of hypothetical almost equatorial satellites of Ceres and Vesta. The estimation of methodical accuracy is obtained by comparing to the numerical solution.
potential of spheroid, near equatorial orbits, hypothetical satellites of Ceres and of Vesta