Long-term dynamics of Methone, Anthe and Pallene

TL;DR

This study uses numerical simulations to analyze the long-term orbital stability of Saturn's small satellites Methone, Anthe, and Pallene, revealing resonance effects and potential chaos in their orbital evolution.

Contribution

It provides new insights into the long-term dynamics and stability of these satellites, highlighting the role of resonances and chaos in their orbital behavior.

Findings

Pallene's evolution is influenced by a quasi secular resonance with Mimas.

Methone and Anthe exhibit chaotic orbits with crossing trajectories.

Small initial condition changes significantly affect their long-term orbital paths.

Abstract

We numerically investigate the long-term dynamics of the Saturn's small satellites Methone (S/2004 S1), Anthe (S/2007 S4) and Pallene (S/2004 S2). In our numerical integrations, these satellites are disturbed by non-spherical shape of Saturn and the six nearest regular satellites. The stability of the small bodies is studied here by analyzing long-term evolution of their orbital elements. We show that long-term evolution of Pallene is dictated by a quasi secular resonance involving the ascending nodes ($\Omega$) and longitudes of pericentric distances ($\varpi$) of Mimas (subscript 1) and Pallene (subscript 2), which critical argument is $\varpi_2-\varpi_1-\Omega_1+\Omega_2$. Long-term orbital evolution of Methone and Anthe are probably chaotic since: i) their orbits randomly cross the orbit of Mimas in time scales of thousands years); ii) numerical simulations involving both small satellites are strongly affected by small changes in the initial conditions.