2021/09/28 by Johannes Reiff, Jonas C. J. Zatsch, Jörg Main +1
Physics and Astronomy · Mathematics · #astro-ph.EP #cond-mat.stat-mech #math.DS #physics.chem-ph
paper · pdf · doi:10.1016/j.cnsns.2021.106053
published as Commun. Nonlinear Sci. Numer. Simulat. 104, 106053 (2022) · Main article has 15 pages, 6 figures. For convenience to the reader there is a some text overlap between parts of Appendix B of this manuscript and Section C of the Supplemental Material in arXiv:2011.04029
arxiv created 2021/09/28 · arxiv updated 2021/10/15
The five libration points of a sun-planet system are stable or unstable fixed positions at which satellites or asteroids can remain fixed relative to the two orbiting bodies. A moon orbiting around the planet causes a time-dependent perturbation on the system. Here, we address the sense in which invariant structure remains. We employ a transition state theory developed previously for periodically driven systems with a rank-1 saddle in the context of chemical reactions. We find that a satellite can be parked on a so-called time-periodic transition state trajectory -- which is an orbit restricted to the vicinity of the libration point L2 for infinitely long time -- and investigate the stability properties of that orbit.