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It is well accepted that knowing the composition and the orbital evolution ofasteroids may help us to understand the process of formation of the SolarSystem. It is also known that asteroids can represent a threat to our planet.Such important role made space missions to asteroids a very popular topic inthe current astrodynamics and astronomy studies. By taking into account theincreasingly interest in space missions to asteroids, especially to multiplesystems, we present a study aimed to characterize the stable and unstableregions around the triple system of asteroids (45) Eugenia. The goal is tocharacterize unstable and stable regions of this system and compare with thesystem 2001 SN263 - the target of the ASTER mission. Besides, Prado (2014) useda new concept for mapping orbits considering the disturbance received by thespacecraft from all the perturbing forces individually. This method was alsoapplied to (45) Eugenia. We present the stable and unstable regions forparticles with relative inclination between 0 and 180 degrees. We found that(45) Eugenia presents larger stable regions for both, prograde and retrogradecases. This is mainly because the satellites of this system are small whencompared to the primary body, and because they are not so close to each other.We also present a comparison between those two triple systems, and a discussionon how these results may guide us in the planning of future missions.

Mapping stable direct and retrograde orbits around the triple system of asteroids (45) Eugenia