The determination of space trajectories around an equilibrium points is a very challenging task, because, in addition to the natural instability of these points, in particular the collinear ones, there are still disturbances due to other celestial bodies and non-gravitational forces that affect the trajectory of a spacecraft from the nominal one. It is proposed, in this study, the search for Halos and/or Lissajous orbits around the L1 and/or L2 equilibrium point in the Earth-Moon system, taking into account several perturbations, among them the solar radiation pressure and the gravitational effects of some bodies of the Solar System. Since Halo orbits are generally unstable, it will be necessary to make use of orbital maneuvers to maintain the orbit within a region around the reference path (nominal orbit). The idea is to find the locations and at times when it is necessary to perform the maneuvers, as well as the magnitude and direction of the thrusts to be applied, to keep the spacecraft in a certain region. In this case, the times to perform the maneuver is a strategic parameter to define the control to be applied to the spacecraft, besides the parameters related to thethrust, the magnitude and direction of the propulsive system. It is also intended to make use of the integrals of the accelerations of the bodies that disturb the movement of the spacecraft to measure the effects of each disturbing body, to have a better understanding of the system.This project will give significant contributions to the LUMIO mission, which will be carried out by ESA, It has a good potential to be used in Brazilian space missions, like ASTER, a Brazilian deep space mission that aims to explore an asteroid triple system (2001SN263).
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