Studying the behaviour of averaged models in the third body perturbation problem

Abstract

The main goal of the present paper is to perform a study of the behaviour of the single and double averaged methods used to study the third-body perturbation problem in celestial mechanics. Both models are compared with the full elliptic restricted three-body problem. The study shows the differences between the values of the eccentricity and inclination of the satellite predicted by those models, showing the differences at every instant of time, as well as the integral over the time of the differences between the models. This integral is a new way to look at those differences and can give us a more complete view of the quality of the approximations, instead of just instantaneous views.