Abstract
We present some families of horseshoe periodic orbits in the general planar three-body problem for the case of two equal masses. The considered system is a symmetric version of the one formed by Saturn, Janus and Epimetheus. We use a mass ratio equal to 35×10−5, corresponding to 105 times the Saturn-Janus mass parameter of the restricted case; for this mass ratio the satellites have a significantly bigger influence on the planet than in the classical Saturn, Janus and Epimetheus system. To obtain periodic orbits, we search those horseshoe orbits passing through two reversible configurations. A particular kind of periodic orbits where the minor bodies follow the same path is discussed.
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Bengochea, A., Falconi, M. & Pérez-Chavela, E. Symmetric horseshoe periodic orbits in the general planar three-body problem. Astrophys Space Sci 333, 399–408 (2011). https://doi.org/10.1007/s10509-011-0641-x
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DOI: https://doi.org/10.1007/s10509-011-0641-x