Hill stability of natural planet satellites in the restricted elliptic three-body problem

Abstract

The existence of the Jacobi integral in a restricted circular problem of three bodies allows the construction of Hill surfaces of zero velocity by means of which the Hill stability of the motion is established. In a restricted noncircular three-body problem, the creation of zero-velocity surfaces is impossible as the Jacobi integral does not exist. However, by means of an invariant integral relation, a so-called Jacobi quasi-integral, containing one unknown function, Lukyanov (2005) constructed the regions of possible motion changing over time and surfaces of the minimum energy limiting them. At zero value of eccentricity these surfaces will be transformed to zero-velocity surfaces for a restricted circular three-body problem. In the framework of a restricted elliptic three-body problem, the Hill stability of the motion of all planetary satellites is investigated. The surfaces of minimum energy limiting regions of possible motion and defining the Hill stability of the motion in an elliptic restricted three-body problem are constructed.