Escape of a Subsystem in a N-Body Problem. Application to the Three Body Problem

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We have obtained sufficient conditions for escape of a subsystem formed by p particles (1 < p < n-1) in a n-body problem. This result generalize a previous result given by Patnaik (1975) in which p=1. We have obtained it by means a generalization of α-approach concept. This is applied to the subsystems obtained by a hierarchical decomposition of the n-bodies.

Using a relation between the largest and the smallest mutual distances in the three body problem given by Marchai and Bozis (1982), we can relate the hierarchical arrangement of the particles with the non-existence of α-approach. From this result we obtain a new set of sufficient initial conditions for escape in this problem.