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Stability of two groups of multi-revolution elliptic halo orbits in the elliptic restricted three-body problem

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Abstract

The multi-revolution elliptic halo (ME-Halo) orbit is a kind of strictly periodic orbit existing in the elliptic restricted three-body problem (ERTBP) model. Its remarkable features include that it survives the eccentricity perturbation of the primaries, it has a long period commeasurable with the primary period and that its stability property varies greatly as the eccentricity. The authors utilized continuation methods together with the multi-segment optimization method to generate two groups of ME-Halo orbits, and then systematically investigated their stability evolution with respect to the eccentricity and the mass ratio of the primaries. These parameters show complicate impacts on the stability. Some ME-Halo orbits can possess more than one pairs of real eigenvalue, some have negative real eigenvalues or complex eigenvalues out of the unit circle. For certain parameters, continuation failures are observed to be accompanied by a series of eigenvalue collision and bifurcations. The results in this paper can help to understand the nonautonomous dynamic of the ERTBP and can further aid in understanding the dynamical environment for real-world applications and, thus, contribute to the trajectory development process.

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Acknowledgments

The research presented in this paper was supported by the State Key Program of National Natural Science of China (Grant No. 11432001). The authors would like to thank all editors and the anonymous reviewers for all their hard work. The reviewers not only gave critical comments on the paper which greatly improves the quality of this paper, but also generously shared their knowledge, insights and suggestions with us, which are very helpful for our future research.

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  1. Beihang University, Beijing, China

    Hao Peng & Shijie Xu

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  1. Hao Peng
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  2. Shijie Xu
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Correspondence to Hao Peng.

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Peng, H., Xu, S. Stability of two groups of multi-revolution elliptic halo orbits in the elliptic restricted three-body problem. Celest Mech Dyn Astr 123, 279–303 (2015). https://doi.org/10.1007/s10569-015-9635-2

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