Zero velocity surfaces are deduced in the restricted three-body problem by using the Jacobi integral. These surfaces are the boundaries of the Hill-regions: regions where the motion of the third, massless particle around the two primaries is not possible. V. Szebehely generalized this result for the planar elliptic restricted three-body problem. In a recent paper – Makó and Szenkovits (2004) presented a generalization of this result for the spatial elliptic restricted three-body problem, where the existence of an invariant relation was proved – analogous to the Jacobi integral in the restricted problem. For small eccentricities, this invariant relation can be approximated with zero velocity surfaces, given by implicit equations, delimiting the pulsating Hill-regions. In this paper we present the polynomial representation of these zero velocity surfaces.
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