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arXiv · 1508.00875

Families of periodic orbits in the planar Hill four-body problem

Jaime Burgos-Garcia
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Abstract

In this work we perform a numerical exploration of the families of planar periodic orbits in the Hill's approximation in the restricted four body problem, that is, after a symplectic scaling, two massive bodies are sent to infinity, by mean of expanding the potential as a power series in m3^1/3, (the mass of the third small primary) and taking the limit case when m3 tends to zero. The limiting Hamiltonian depends on a parameter mu (the mass of the second primary) and possesses some dynamical features from both the classical restricted three- body problem and the restricted four-body problem. We explore the families of periodic orbits of the infinitesimal particle for some values of the mass pa- rameter, these explorations show interesting properties regarding the periodic orbits for this problem, in particular for the Sun-Jupiter-asteroid case. We also offer details on the horizontal and vertical stability of each family.

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Jaime Burgos-Garcia. 2015-08-04. Families of periodic orbits in the planar Hill four-body problem. https://doi.org/10.1007/s10509-016-2943-5

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