Analytical criteria of Hill stability in the elliptic restricted three body problem

Due to the time-dependent Jacobi integral in the elliptic restricted three body problem, it is difficult to develop analytical criteria of Hill stability. In this paper, the Hill stability of the orbit around the one primary is concerned. Several analytical criteria are established based on the bifurcation of the extremum of the Jacobi integral. One criterion is used to judge the Hill stability of the orbit with orbit size known. One criterion is used to judge the Hill stability of the orbit with orbital element completely known. These criteria are applied to the judge the Hill stability of Jupiter’s moons and planets in three stellar binaries.