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A note on the full two-body problem and related restricted full three-body problem

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A Correction to this article was published on 11 February 2022

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Abstract

Truncating at the second order of the mutual potential between two rigid bodies, time-explicit first order solutions to the rotations and the orbital motion of the two bodies in the planar full two-body problem (F2BP) are constructed. Based on this analytical solution, equations of motion (EOMs) for the related restricted full three-body problem are given. In the case of the synchronous or double synchronous states for the full two-body problem, EOMs for the related restricted full three-body problem (RF3BP) are also given. At last, one example—the “collinear libration point” in the binary asteroid system—is given.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11322330 and 11673072) and National Basic Research Program of China (Grant No. 2013CB834100).

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Authors and Affiliations

  1. School of Astronomy and Space Science, Nanjing University, Nanjing, 210023, China

    Xiyun Hou & Xiaosheng Xin

  2. Institute of Astrodynamics and Space Environment, Nanjing University, Nanjing, 210093, China

    Xiyun Hou & Xiaosheng Xin

Authors
  1. Xiyun Hou
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  2. Xiaosheng Xin
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Correspondence to Xiyun Hou.

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Xiyun Hou received his Ph.D. degree in astronomy from Nanjing University, China, in 2008. Now he is a professor at the School of Astronomy and Space Science of Nanjing University. His research interest focuses on the intersection of celestial mechanics and astrodynamics. Currently, he is doing research related to asteroids, including the dynamical evolution of these natural bodies, and the orbital dynamics of the probe or particles around them.

Xiaosheng Xin received his Ph.D. degree in astronomy from Nanjing University, China, in 2017. His research interest focuses on astrodynamics, especially the orbital dynamics of spacecraft or natural bodies around asteroids.

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Hou, X., Xin, X. A note on the full two-body problem and related restricted full three-body problem. Astrodyn 2, 39–52 (2018). https://doi.org/10.1007/s42064-017-0010-9

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  • DOI: https://doi.org/10.1007/s42064-017-0010-9

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