A numerical study of the orbits of second species of the planar circular RTBP

Details A numerical study of the orbits of second species of the planar circular RTBP A numerical study of the orbits of second species of the planar circular RTBP

Feb 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cemda.103..143f&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 103, Issue 2, pp.143-162

Astronomy and Astrophysics

Astronomy

1

Restricted Three Body Problem, Second Species, Periodic Orbits, Chaotic Motion, Quasi-Collision Orbits

Scientific paper

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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