The Set of Planar Orbits of Second Species in the RTBP

We present a brief summary of the conclusions of our work on 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. In this study, the value of the Jacobi constant is fixed, and we consider 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 find periodic orbits that combine S-type and T-type quasi-homoclinic arcs and we determine the symbolic dynamics of the full set of orbits of second12pc]First author considered as corresponding author. Please check. species.