Long-term dynamics of Methone, Anthe and Pallene

We numerically investigate the long-term dynamics of the Saturnʹs 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 (Q) and longitudes of pericentric distances (w) of Mimas (subscript 1) and Pallene (subscript 2), which critical argument is w2 — w1 — Q1 +Q2. 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) long-term numerical simulations involving both small satellites are strongly affected by small changes in the initial conditions.