A numerical study of the orbits of second species of the planar circular RTBP |
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| Authors: | Joaquim Font Ana Nunes Carles Simó |
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| Institution: | (1) Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain;(2) CFTC/DFFCUL, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal |
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| Abstract: | We present a numerical study of the set of orbits of the planar circular restricted three body problem which undergo consecutive
close encounters with the small primary, or orbits of second species. The value of the Jacobi constant is fixed, and we restrict
the study to consecutive close encounters which occur within a maximal time interval. With these restrictions, the full set
of orbits of second species is found numerically from the intersections of the stable and unstable manifolds of the collision
singularity on the surface of section that corresponds to passage through the pericentre. A ‘skeleton’ of this set of curves
can be computed from the solutions of the two-body problem. The set of intersection points found in this limit corresponds
to the S-arcs and T-arcs of Hénon’s classification which verify the energy and time constraints, and can be used to construct
an alphabet to describe the orbits of second species. We give numerical evidence for the existence of a shift on this alphabet
that describes all the orbits with infinitely many close encounters with the small primary, and sketch a proof of the symbolic
dynamics. In particular, we find periodic orbits that combine S-type and T-type quasi-homoclinic arcs. |
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| Keywords: | Restricted three body problem Second species Periodic orbits Chaotic motion Quasi-collision orbits |
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