La stabilit\'e des lunes de Saturne, Janus et \'Epim\'eth\'ee: de l'observation astronomique \`a la th\'eorie KAM

TL;DR

This paper explores the unique orbital dynamics of Saturn's moons Janus and Epimetheus, demonstrating their stable co-orbital trajectories through a connection between astronomical observations and KAM theory.

Contribution

It establishes the existence of perpetually stable co-orbital trajectories for Janus and Epimetheus by linking astronomical phenomena to KAM theory.

Findings

Existence of quasi-periodic horseshoe-shaped orbits

Stable co-orbital trajectories for Janus and Epimetheus

Application of KAM theory to celestial mechanics

Abstract

Popular science article associated with the work `On the co-orbital motion in the three-body problem: existence of quasi-periodic horseshoe-shaped orbits" (arXiv:1806.07262) from the same authors. Janus and Epimetheus are two moons of Saturn which exhibit a really peculiar dynamics. As they orbit on circular trajectories whose radii are only 50 km apart (less than their respective diameters), every four (terrestrial) 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. In this article, we describe how, from this specific astronomical problem to the KAM theory, we came to prove the existence of perpetually stable trajectories associated with the Janus and Epimetheus orbits.