Natural formations at the Earth Moon triangular point in perturbed restricted problems

Abstract

Previous studies for small formation flying dynamics about triangular libration points have determined the existence of regions of zero and minimum relative radial acceleration with respect to the nominal trajectory, that prevent from the expansion or contraction of the constellation. However, these studies only considered the gravitational force of the Earth and the Moon using the Circular Restricted Three Body Problem (CRTBP) scenario. Although the CRTBP model is a good approximation for the dynamics of spacecraft in the Earth-Moon system, the nominal trajectories around equilateral libration points are strongly affected when the primary orbit eccentricity and solar gravitational force are considered. In this manner, the goal of this work is the analysis of the best regions to place a formation that is flying close a bounded solution around $L_{4}$, taking into account the Moon's eccentricity and Sun's gravity. This model is not only more realistic for practical engineering applications but permits to determine more accurately the fuel consumption to maintain the geometry of the formation.