Rings and small satellites
Neptune's ring arcs
Around Neptune, four arcs are confined in a 40 degrees azimuthal range. These incomplete rings have been stable since their discovery in 1984 (Hubbard et al. 1986), while they should be destroyed in a few months through differential Keplerian motion. Nevertheless, images obtained since 2002 with the Keck, VLT, HST telescopes (de Pater et al. 2005, Renner et al. 2014, Showalter et al. 2013, 2017) show some significant changes in the brightness and longitudes of the arcs.
A satellite on an eccentric/inclined orbit creates corotation resonance sites where arcs can be azimuthally confined (Goldreich et al. 1986). Such a resonance has been identified (Porco 1991), the 42:43 corotation inclination resonance forced by the nearby satellite Galatea. However, the arcs finally revealed to lie close to but not within this resonance (Dumas et al. 1999, Sicardy et al. 1999). Therefore the mass of the arcs must be taken into account in the corotation model to explain the stability of these structures (Namouni and Porco 2002). Alternatively, relative equilibrium positions between few co-orbital bodies generalizing the Lagrange L4/L5 configurations can be considered (Renner and Sicardy 2004, Renner et al. 2014).
Saturn's small satellites
Thanks to the Cassini ISS observations, the orbits and masses of Saturn's inner satellites (Atlas, Prometheus, Pandora, Janus, Epimetheus) are derived with a high precision (Cooper et al. 2015). Small changes in the semi-major axis of Atlas, the closest object to the main rings, occur on very short timescales. In fact, the orbit of this satellite is chaotic with a Lyapunov time of order 10 years, as a direct consequence of the coupled 54:53 resonant interaction (corotation/Lindblad) with Prometheus (Renner et al. 2016). This makes Atlas another example in the Solar System where chaotic motions can be observed "live", following the already known case of Prometheus-Pandora (Cooper et al. 2004, Goldreich and Rappaport 2003, Renner et al. 2005).
Poincaré surface of section for Atlas (in red). The angle is the 54:53 corotation eccentricity resonance argument with the satellite Prometheus, and χ measures the Atlas’ distance from the exact resonance. The coupling with the nearby 54:53 Lindblad resonance (in blue) leads to a chaotic motion (Renner et al. 2016).
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Last update Wednesday 15 November 2017