The current orbit of Methone (S/2004 S 1)

Abstract

The Cassini spacecraft discovered many close-in small satellites in Saturnian system, and several of them exhibit exotic orbital states due to interactions with Mimas and the oblateness of the planet. This work is devoted to Methone, which is currently involved in a 15:14 Mean-Motion Resonance with Mimas. We give an in deep study the current orbit of Methone by analyzing and identifying the short, resonant and long-term gravitational perturbations on its orbit. In addition, we perform numerical integrations of full equations of motion of ensembles of close-in small bodies orbiting the non-central field of Saturn. Spectral analyses of the orbits and interpretation of them in dynamical maps allow us to describe the orbit and the dynamics of Methone in view of resonant and long-term dynamics. We show that the current geometric orbit of Methone is aligned with Mimas' due to a forced resonant component in eccentricity, leading to simultaneous oscillations of several critical angles of the expanded disturbing function. Thus, we explain the simultaneous oscillations of four critical arguments associated to the resonance. The mapping of the Mimas-Methone resonance shows that the domains of the 15:14 Mimas-Methone resonance are dominated by regular motions associated to the Corotation resonance located at eccentricities lower than $\sim 0.015$ and osculating semi-major axis in the interval 194,660-194,730 km. Methone is currently located deeply within this site.