Stability regions in the n-body problem: The distant retrograde orbits family case

The stability of the three body family of Distant Retrograde Orbits (DROs) is investigated under the mission scenarios of the NASA Asteroid Redirect Robotic Mission (ARRM). The full coupled orbital-attitude stability of small asteroids initialized on DROs over long time is analysed; effects of the Moon eccentricity, the Sun and major planets in the solar system attraction and the nonconservative SRP and Yarkovsky action on small size low mass and irregular shape bodies such asteroids and boulders are considered. The stability study is performed using the chaotic indicator MEGNO as tool to distinguish regular from chaotic regions. The analyses on the CR3BP case are compared with the results of two major tools adopted in the study of the three body problem, namely the Monodromy Matrix and the Poincaré maps to search for confirmation, on the long term, of the stability properties of the family when the quasi-periodic orbits around the elliptic point tend to vanish. Then, the results related to the increased complexity in the model obtained by inserting the Moon eccentricity and the asteroid ellipsoidal model are discussed. MEGNO chaotic indicator confirms the stability of DROs family also when the quasi-periodic region around the elliptic point vanishes in correspondence of the intersection with the triple periodic orbit of the same family. The model enhancements show a progressive reduction of the global stability of the family, a strong component due to the rotational state of the rigid body.