Abstract
We study the dynamics of the circular restricted 4-body problem with three primaries with equal masses at the collinear configuration of the 3-body problem with an infinitesimal mass. We calculate the equilibrium points and study their linear stability. By applying the Lyapunov theorem, we prove the existence of periodic orbits bifurcating from the equilibrium points and, further, prove that they continue in the full 4-body problem. Moreover, we prove analytically the existence of Hill and of comet-like periodic orbits.
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Acknowledgements
We thank to the reviewers their comments and suggestions which help us to improve the presentation of our results. The first author is supported by the Agencia Estatal de Investigación grant PID2019-104658GB-I00 (FEDER), the Agència de Gestió d’Ajuts Universitaris i de Recerca grant 2017SGR1617 and the H2020 European Research Council grant MSCA-RISE-2017-777911. The third author is partially supported by FCT/Portugal through UID/MAT/04459/2019.
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The second author dedicates this paper to Professor George Dincă on the occasion of his 80th birthday, with deep esteem and respect.
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Llibre, J., Paşca, D. & Valls, C. The circular restricted 4-body problem with three equal primaries in the collinear central configuration of the 3-body problem. Celest Mech Dyn Astr 133, 53 (2021). https://doi.org/10.1007/s10569-021-10052-6
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DOI: https://doi.org/10.1007/s10569-021-10052-6