Himalia and Phoebe: Little moons that punch above their weight

Small bodies in the solar system are usually treated as massless particles. While a sufficient approximation for many purposes, the small but finite mass of some of these (mass ratio μ=10^{-10}-10^{-8} of primary) can have observable consequences on the local population. Numerical experiments have shown this to be true for the orbital neighbourhood of Himalia, a prograde irregular moon of Jupiter (Christou 2005). In a recent demonstration of the same mechanism in a different context, Novaković et al. (2015) showed that the dwarf planet Ceres activates its own secular resonances, causing the long-term diffusion of asteroids in the middle part of the Main Belt.Seeking to better understand the dynamics caused by “internecine” interactions, we have constructed a semi-analytical model of a test particle’s secular evolution in the Sun-Planet-massive moon-particle restricted 4-body problem. By combining the Kozai-Lidov formalism with a model of coorbital motion valid for non-planar & non-circular orbits (Namouni 1999) we have overcome the difficulty in treating the interaction between potentially-crossing neighbouring orbits.We have applied this model to the cases of (a) J6 Himalia, a jovian irregular satellite (μ≃ 2× 10^{-9}) and the largest in a family of five moons, and (b) S9 Phoebe, a retrograde irregular moon of Saturn with μ=1.5× 10^{-8} which, curiously, is not associated with a family (Ćuk et al. 2003). We observe numerous instances of capture into secular resonances where the critical angle is a linear combination of the relative nodes and apses of the particle and the perturber. In particular we are able to reproduce the libration of the differential node found by Christou (2005). We generate fictitious families of test particles around Himalia and Phoebe and find that, while ~8% of local phase space is occupied by these resonances for Himalia, this figure is ~16% for Phoebe. We confirm these results using N-body integrations of the full equations of motion. During the meeting, we will show examples of orbital evolution in the resonances, describe the principal features of the dynamics and discuss the implications for the long-term evolution of families of small bodies.