Using invariant manifolds to capture an asteroid near the L3 point of the Earth-Moon Bicircular model

Abstract

This paper focuses on the capture of Near-Earth Asteroids (NEAs) in a neighbourhood of the L3 point of the Earth-Moon system. The dynamical model for the motion of the asteroid is the planar Earth-Moon-Sun Bicircular problem (BCP). It is known that the L3 point of the Restricted Three-Body Problem is replaced, in the BCP, by a periodic orbit of centre×saddle type, with a family of mildly hyperbolic tori that is born from the elliptic direction of this periodic orbit. It is remarkable that some pieces of the stable manifolds of these tori escape (backward in time) the Earth-Moon system and become nearly circular orbits around the Sun. In this work we compute this family of invariant tori and also high order approximations to their stable/unstable manifolds. We show how to use these manifolds to compute an impulsive transfer of a NEA to an invariant tori near L3. As an example, we study the capture of the asteroid 2006 RH120 in its approach of 2006. We show that there are several opportunities for this capture, with different costs. It is remarkable that one of them requires a Δv as low as 20 m/s.