La stabilité des lunes de Saturne, Janus et Epiméthée: de l'observation astronomique à la théorie KAM

16 pages, 7 figures, article de vulgarisation scientifiqueImage des Mathshttps://images.math.cnrs.fr/Janus-et-Epimethee-un-ballet-perpetuel-autour-de-Saturne.htmlPopular 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