Resonances, chaos, and short-term interactions among the inner uranian satellites

The Portia group of Uranian satellites, representing 9 of the planet's 13 tiny innermost moons, form a densely packed dynamical system. Hubble Space Telescope observations indicate that their orbits have changed significantly over two decades, and long-term numerical integrations show that their orbits are unstable over millions of years. To investigate the dynamical interactions of the Portia group satellites on the decade timescale over which orbital changes have been observed, we have performed a suite of 100-1000 yr N-body numerical integrations for a range of assumed satellite masses, which are at present not tightly constrained by observations. As first noted by Dawson et al. and recently investigated independently by Quillen & (Robert) French, the moons are configured in chains of interlinked first- and second-order eccentric resonances that contribute to chaotic behavior. We explore in detail several of the strongest of these interlinked resonances. The first such chain is a quintet of orbital resonances: Bianca is near a resonance with Cressida, which is itself near a resonance with Desdemona. Desdemona, in turn, is near a resonance with Portia, which is itself near a resonance with Juliet. The five participating resonances are: Cressida and Bianca (16:15), Desdemona and Cressida (47:46), Portia and Desdemona (13:12), and Portia and Juliet (51:49). A second such chain is a set of two interlinked resonances: Cupid and Belinda (58:57) and Belinda and Perdita (44:43). We also report the new identification of a companion set of second-order inclination-type resonances (Cressida and Bianca (32:30), Desdemona and Cressida (94:92), Portia and Desdemona (26:24), Portia and Juliet (51:49), Cupid and Belinda (116:114), and Belinda and Perdita (88:86)), some of which result in quite strongly coupled variations in the inclinations of the interacting satellites. Using a robust formulation of orbital elements that accounts for the oblateness of Uranus, we probe the dynamical interactions among the moons in the time and frequency domains, and also in phase space, using numerical integrations of subsets of the inner moons, for a range of assumed masses. Several of the satellites are near mean-motion resonance with more than one neighbor, and undergo orbital variations at two nearly equal resonant frequencies. Such configurations of two interlinked resonances can result in chaotic behavior, associated with the transition of one resonant argument from circulation to libration. We demonstrate that, even on the short timescales investigated here, the dynamical interactions, onset of chaos, and associated Lyapunov times are highly sensitive to the masses of the interacting satellites.