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

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Abstract

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.

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Acknowledgements

The authors would like to acknowledge the support from the National Natural Science Foundation of China (Grants No. 11272004 and 11422001) and the National Basic Research Program of China (973 Program, 2012CB720000).

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  1. School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China

    Shengping Gong & Junfeng Li

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  1. Shengping Gong
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  2. Junfeng Li
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Correspondence to Shengping Gong.

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Gong, S., Li, J. Analytical criteria of Hill stability in the elliptic restricted three body problem. Astrophys Space Sci 358, 37 (2015). https://doi.org/10.1007/s10509-015-2436-y

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