Determination of optimal trajectories in the dynamics of the restricted three or four-body problems considering elliptical arrival orbit

Abstract

This research project aims to study optimal impulsive transfers in the dynamics of the restricted three or four-body problems with application to lunar and interplanetary missions, including the ones with swing-by maneuvers. The basic problem consists in transferring a space vehicle from a circular low earth orbit to an elliptical orbit around the moon or around a planet (Mars) by means of an application of two impulses (instantaneous changes of velocity) in the way that the total fuel consumption of the mission is minimized. The dynamics of the restricted three or four-body problem will also consider the eccentricities of the orbits of the earth, the moon or the destiny planet. As an extension of the lunar mission considering the tridimensional models, the earth-to-earth mission with a close approach with the moon will be introduced. Due to the considerable saving of the fuel consumption provided by such maneuver; this one can be utilized in several applications as, for instance, to insert a satellite in an orbit with large inclination and large eccentricity as the Molniya orbit. Gradient techniques - gradient method and gradient with restoration method - will be employed to determine the optimal solutions. (AU)