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

Astronomy and Astrophysics – Astrophysics

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Scientific paper

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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