Orbital maneuvers between the Earth and the Lagrangian points in the Earth-Moon and the Sun-Earth systems

Abstract

The goal of the present project is to follow the studies of models and methods that are used to obtain optimal space trajectories, from the point of view of minimum fuel consumption, to transfer a spacecraft between the Earth and the Lagrangean points in the Earth-Moon and Sun-Earth. Those are equilibrium points of the equations of motion of the restricted three-body problem and, if a spacecraft is located in one of these points with initial zero velocity it will stay in that point forever. This fact makes those points very good candidates for astronautical applications, because they can accommodate space stations that require low fuel consumption for stationkeeping. Those points are determined using the restricted three-body problem, but the trajectories will be studied with several options for the dynamics, like the three-dimensional problem, the elliptic three-body problem and the bicircular four-body problem. It is a continuation of the research that is under development by the proponent. After that, the matrix of sensibility will also be studied, with the goal of studying the stability of those orbits.