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On the Symmetric Central Configurations of Three Coorbital Satellites

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Abstract

We study the symmetric central configurations of the (1+3)-body problem, where three bodies (called satellites) are infinitesimal and the remaining one body is dominant. For this problem, in 2011, Corbera et al. (Celest Mech Dyn Astron 109:27–43, 2011) obtained the bifurcation value of mass parameter at which the number of central configurations changes by variables substitution and resultant theory. In this work, by qualitative analysis, we prove the sufficient and necessary conditions for producing the bifurcation value of mass parameter and figure out this value. Furthermore, we prove in detail why and how the number of central configurations changes when the mass parameter changes.

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Acknowledgements

The authors sincerely express their gratitude to Professor Shiqing Zhang for his help and guidance. This paper is supported by Sichuan Science and Technology Program (No.2023NSFSC0079).

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Sichuan Science and Technology Program (No.2023NSFSC0079).

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Authors and Affiliations

  1. School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang, 621010, Sichuan, China

    Jian Chen, Peng Bi, Liping Zeng & Nan Yao

  2. School of Information Engineering, Southwest University of Science and Technology, Mianyang, 621010, Sichuan, China

    Mingfang Yang

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  1. Jian Chen
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Correspondence to Jian Chen.

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Chen, J., Yang, M., Bi, P. et al. On the Symmetric Central Configurations of Three Coorbital Satellites. Qual. Theory Dyn. Syst. 22, 149 (2023). https://doi.org/10.1007/s12346-023-00851-7

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