Abstract
In this work, we revisit the planar restricted four-body problem to study the dynamics of an infinitesimal mass under the gravitational force produced by three heavy bodies with unequal masses, forming an equilateral triangle configuration. We unify known results about the existence and linear stability of the equilibrium points of this problem which have been obtained earlier, either as relative equilibria or a central configuration of the planar restricted \((3 + 1)\)-body problem. It is the first attempt in this direction. A systematic numerical investigation is performed to obtain the resonance curves in the mass space. We use these curves to answer the question about the existing boundary between the domains of linear stability and instability. The characterization of the total number of stable points found inside the stability domain is discussed.
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Acknowledgements
The first author was supported by a UAM fellowship of doctoral studies. The second author was partially supported by Special Program to Support Teaching and Research Projects 2021 from CBI UAM-Iztapalapa (México).
The authors would like to thank the anonymous reviewers for their comments and fruitful suggestions to improve the quality of the paper.
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This study was funded by the Universidad Autónoma Metropolitana (Metropolitan Autonomous University) Mexico.
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José Alejandro Zepeda Ramírez and Martha Alvarez-Ramírez contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript.
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Zepeda Ramírez, J.A., Alvarez–Ramírez, M. Equilibrium points and their linear stability in the planar equilateral restricted four-body problem: a review and new results. Astrophys Space Sci 367, 77 (2022). https://doi.org/10.1007/s10509-022-04108-8
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DOI: https://doi.org/10.1007/s10509-022-04108-8