Abstract
We consider the bifurcation of 3D periodic orbits from the plane of motion of the primaries in the restricted three-body problem with oblateness. The simplest 3D periodic orbits branch-off at the plane periodic orbits of indifferent vertical stability. We describe briefly suitable numerical techniques and apply them to produce the first few such vertical-critical orbits of the basic families of periodic orbits of the problem, for varying mass parameter μ and fixed oblateness coefficent A1 = 0.005, as well as for varying A1 and fixed μ = 1/2. The horizontal stability of these orbits is also determined leading to predictions about the stability of the branching 3D orbits.
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Perdios, E., Kanavos, S. & Markellos, V. Bifurcations of Plane to 3d Periodic Orbits in the Restricted Three-Body Problem with Oblateness. Astrophysics and Space Science 262, 75–87 (1998). https://doi.org/10.1023/A:1001831319656
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DOI: https://doi.org/10.1023/A:1001831319656