Pulsating zero velocity surfaces and capture in the elliptic restricted three-body problems

Szenkovits, F. and Makó, Z. (2005) Pulsating zero velocity surfaces and capture in the elliptic restricted three-body problems. In: British-Romanian-Hungarian N+N+N Workshop for Young Researchers On Plasma- and Astrophysics: from laboratory to outer space Edited by I. Ballai, E. Forgács-Dajka, A. Marcu and K. Petrovay. Publications of the Astronomy Department of the Eötvös University (15). ELTE Sokszorosítóüzeme, Budapest, pp. 221-229.

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Abstract

Zero velocity surfaces are deduced in the gravitational restricted three-body problem by using the Jacobi-integral. These surfaces are the boundaries of the Hill's regions: regions where the motion of the third, massless particle around the two primaries is possible. V. Szebehely generalized this result for the planar elliptic restricted three-body problem. In a recent paper the authors presented a generalization of this result for the spatial elliptic restricted three-body problem, where the existence of an invariant relation was proved. From this invariant relation the equation of the zero velocity surfaces can be deduced. In this paper we discuss the pulsation and the change of the type of these zero velocity surfaces and we present applications to the phenomenon of the gravitational capture. In the model of the spatial elliptic restricted three-body problem criteria of the capture are deduced by using the pulsating Hill's regions.

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