Third order solution of orbital perturbations of artificial earth satellites.

A third order solution of the orbital perturbation of artificial earth satellites is presented, which is closed for eccentricity, making use of the intermediate orbit and the elliptic orbit perturbation theory, in addition to various methods for the computation of fast and slow variables. Vinti's (1961) method is generalized, and the corresponding accurate solution of the intermediate orbit is given. The method may be applied to the motion of natural satellites in the solar system for cases when the primary body is an oblate planet with revolutionary symmetry.