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Study of lunar gravity assist orbits in the restricted four-body problem

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Abstract

In this paper, the lunar gravity assist (LGA) orbits starting from the Earth are investigated in the Sun–Earth–Moon–spacecraft restricted four-body problem (RFBP). First of all, the sphere of influence of the Earth–Moon system (SOIEM) is derived. Numerical calculation displays that inside the SOIEM, the effect of the Sun on the LGA orbits is quite small, but outside the SOIEM, the Sun perturbation can remarkably influence the trend of the LGA orbit. To analyze the effect of the Sun, the RFBP outside the SOIEM is approximately replaced by a planar circular restricted three-body problem, where, in the latter case, the Sun and the Earth–Moon barycenter act as primaries. The stable manifolds associated with the libration point orbit and their Poincaré sections on the SOIEM are applied to investigating the LGA orbit. According to our research, the patched LGA orbits on the Poincaré sections can efficiently distinguish the transit LGA orbits from the non-transit LGA orbits under the RFBP. The former orbits can pass through the region around libration point away from the SOIEM, but the latter orbits will bounce back to the SOIEM. Besides, the stable transit probability is defined and analyzed. According to the variant requirement of the space mission, the results obtained can help us select the LGA orbit and the launch window.

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Acknowledgments

This work was supported by the State Key Program of National Natural Science Foundation of China under Grant 11432001 and the National Natural Science Foundation of China under Grant 11402021. The authors also thank the Innovation Foundation of BUAA for PhD Graduates and the China Scholarship Council (CSC) for fellowship support.

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  1. School of Astronautics, Beihang University, Beijing, 100191, China

    Yi Qi & Shijie Xu

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  1. Yi Qi
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  2. Shijie Xu
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Correspondence to Yi Qi.

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Qi, Y., Xu, S. Study of lunar gravity assist orbits in the restricted four-body problem. Celest Mech Dyn Astr 125, 333–361 (2016). https://doi.org/10.1007/s10569-016-9686-z

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  • DOI: https://doi.org/10.1007/s10569-016-9686-z

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