In recent years, the study of asteroids has becoming very popular, which goes beyond the important study of the origin of the solar system. Topics like planetary defense and asteroid mining are increasingly at the center of the debate related to asteroids. Currently, the risk of collision of an asteroid with the Earth is considered small, but it is not negligible, and the current estimates are based on already known asteroids, but there are many others hidden from the present observations. Asteroid mining is increasing commercial interest in the exploration of the space, where success can open in a new era in space exploration. Within this new context, asteroids have become one of the preferred targets for deep-space space missions. However, asteroids are usually small bodies, where the gravitational force rivals other perturbing forces, such as solar radiation pressure and third-body perturbation. It is now known that many of these asteroids are multi-body systems. This makes the orbits around these bodies to be most often unstable, making necessary a constant station-keeping. It is also well known in the literature that, in terms of practical applications, the best way to save fuel with station-keeping is to place the spacecraft in a periodic or quasi-periodic orbit. With this in mind, this project aims to analyze the periodic and quasi-periodic orbits, and their stabilities, for the asteroid 65803 Didymos (double system), target of the AIDA mission, and the asteroid 2001SN263 (triple systems), possible target of the Brazilian mission ASTER. The analysis of these systems will be done using the circular restricted three body problem in three dimensions and their variants, which consider some disturbing forces (eg, solar radiation pressure). At the end of the project, it is expected to find enough information to determine the best regions for maintaining the spacecraft's orbit considering the mission objectives. Other systems of asteroids may be considered, depending on the interest of the moment based in new discoveries.
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