Escape and Capture in the RTBP

Abstract

We study the escape and capture in the Planar and Circular Restricted Three Body Problem(RTBP) when the mass m of the secondary body is small enough. The RTBP has essentially different characteristics when m is zero or not. The non-integrability of the problem for m ≠ 0 causes homoclinic phenomena that do not exist for m = 0: we show here some of the phenomena related to the escape and capture orbits when the Jacobi constant C is big enough. Otherwise, the diffusion of parabolic orbits near the collision with the secondary is much richer for m ≠ 0: the changes of sidereal energy in paths near collision are proved to be more important in some cases than in pure collision, which is the sole possibility of change for m = 0. The last analysis is done using a simple model of that orbits in the RTBP made by matching arcs of Keplerian orbits on a suitable circle centered at that small body.