http://arxiv.org/abs/1806.07262
Janus and Epimetheus are two co-orbital moons of Saturn (the co-orbital motion is associated with trajectories in 1:1 mean-motion resonance) which exhibit a peculiar dynamics associated with horseshoe-shaped trajectories. As they orbit Saturn on quasi-coplanar and quasi-circular trajectories whose radii are only 50 km apart (less than their respective diameters), every four years the bodies are getting closer and their mutual gravitational influence leads to a swapping of the orbits. The outer moon becoming the inner one and vice-versa, this behavior generates horseshoe-shaped trajectories depicted in an adequate rotating frame.
In spite of analytical theories developed to describe their long-term dynamics as well as the indications provided by some numerical investigations, so far no rigorous long time stability results have been obtained even in the restricted three-body problem.
Following the idea of Arnol’d (1963) (but in a much more tricky context as it is 1:1-resonant, while Arnol’d situation relies on non-resonant Kepler orbits), we provide a rigorous proof of the existence of 2 dimensional-elliptic invariant tori associated with the Janus and Epimetheus horseshoe motion in the planar three-body problem using KAM theory.
L. Niederman, A. Pousse and P. Robutel
Wed, 20 Jun 18
18/58
Comments: 40 pages, 5 figures