Abstract
For the 1+5-body problem, we study the relationship between the masses of 5 satellites and given symmetric configurations, where the symmetry axis contains one satellite. Under certain assumptions, we find analytically some central configurations for suitable positive masses. Also, we prove that for certain symmetric configuration of these satellites, there exists a one-parameter family of mass vectors for which such configuration is a central configuration. Furthermore, we present some numerical results for configurations and derive the positive masses for these satellites, such that these configurations are central configurations.
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Acknowledgements
The authors sincerely thank the referees and the editor for their many valuable comments which helped us to improve the paper both in the content and also in the form. The authors sincerely thank Natural Science Foundation of China (No. 11703006) and the Scientific Research Foundation of Huaiyin Institute of Technology (17HGZ004). Also the second author would like to thank Jiangsu Overseas Visiting Scholar Program for University Prominent Young and Middle-aged Teachers and Presidents.
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Su, X., Deng, C. On the symmetric central configurations for the planar 1+5-body problem with small arbitrary masses. Celest Mech Dyn Astron 134, 28 (2022). https://doi.org/10.1007/s10569-022-10080-w
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DOI: https://doi.org/10.1007/s10569-022-10080-w