Approximate solution to the Two-Body problem perturbed by periodic acceleration

Abstract

In this paper, author proposes an approach to approximate orbital dynamics in the model of a perturbed Two--Body problem, which leads to a system of equations with a closed-form solution. The approach is based on representing the components of the disturbing acceleration by Fourier series in eccentric longitude with constant coefficients, writing out the equations of the perturbed two-body problem in terms of modified equinoctial elements, and averaging the right-hand sides of the equations of motion over the mean longitude on one orbit. It is discovered that the influence of disturbing acceleration on the resulting averaged equations can be parameterized by a finite set of scalar parameters, which are the coefficients of the Fourier series. Solutions of the averaged equations are found in a closed form in case of orbits with low eccentricity.