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 (Ω) and longitudes of
pericentric distances (ϖ) of Mimas (subscript 1) and Pallene (subscript
2), which critical argument is ϖ2−ϖ1−Ω1+Ω2. 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.Comment: 9 pages; 4 figures. Submitted to Proceedings IAU Symposium No. S263,
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