A study of double and single second order averaged models to evaluate third body perturbation considering elliptic orbits for the perturbing body

Abstract

In this paper the equations for the variations of the keplerian elements of the orbit of a spacecraft perturbed by a third-body is developed using a single averaged approach over the motion of the spacecraft, considering an elliptic orbit for the disturbing body. Then, a comparison is made of the results obtained by this approach and the more used double averaged technique, as well as with the full elliptic restricted three body problem. The assumptions used in both models are the same ones of the restricted three body problem. The disturbing function is expanded in Legendre polynomials up to the second-order in both cases. After that, the equations of motion are obtained from the planetary equations and several numerical simulations are made to obtain the evolution of the orbit of the spacecraft under both models. In particular, some characteristics known from the circular perturbing body are studied under the elliptical model: circular, elliptic equatorial orbits and frozen orbits. Different initial eccentricities for the perturbed body are considered, since the effect of this variable is one of the goals of the present study. The results obtained show the impact of this parameter as well as the differences between both models compared to the full elliptic restricted three body problem. Regions below, near and above the well known critical angle of the third body perturbation are considered, as well as different altitudes for the orbit of the spacecraft. (AU)