Secular perturbations of the translational-rotational motion in the problem of the two non-stationary bodies: sphere - axisymmetric body

Abstract

In this article we consider mutually gravitating non-stationary two bodies: first body is "central it is a sphere with a spherical density distribution, the second body is "satellite which has an axisymmetric dynamic structure and form. Newtonian force interaction is characterized by an approximate expression of the force function, which takes into account the second harmonic. Masses of bodies change isotropic in the different rates. Equations of the perturbed translational-rotational motion of satellite are deduced in the new osculating elements. Full secular perturbations of translational-rotational motion of non-stationary axisymmetric body for arbitrary laws of variation of masses and sizes are obtained. As a result, it is possible to study the translational-rotational motion of the axisymmetric body in two cases of nonstationary: the first case - the variation of the size of the axisymmetric body with variable mass is homothetic and shape remains unchanged, the second case is non-stationary axisymmetric body characterized by variable size, variable masses and variable oblate.