Resonance orbits and the rings of Uranus

Abstract

SOON after the discovery of the rings of Uranus^1–3 it was suggested⁴ that the ring system might be determined by the perturbations of the satellite pairs Ariel–Titania and Ariel–Oberon. Aksnes⁵, and Goldreich and Nicholson⁶ have questioned this hypothesis; the latter showing that the strongest perturbations on the ring system can be expected to arise from the satellite pair Miranda-Ariel and the 4 : 1 resonance of Miranda. Goldreich and Nicholson also pointed out that the differences in the ring radii α–β, γ–δ and ε₁–ε₂ are known to a high degree of accuracy (typically ∼±15 km) which is considerably better than the absolute ring radii. My calculations of the separations of these ring pairs reported here suggest that the radii of the α and γ rings, and perhaps the ε₁ and ε₂ components as reported by Elliott et al.¹, are governed by the resonances of Miranda and Ariel, with consistent further application of resonance theory to the location of the β and δ rings requiring the presence of an additional hypothetical satellite moving around Uranus. Without this hypothesis the observed ring system seems to be outside the scope of resonance theory alone.