Uranian ring orbits from earth-based and Voyager occultation observations

A new kinematical model for the Uranian rings has been determined from a combination of previously analyzed Earth-based stellar occultation data, three new stellar occultation datasets obtained in 1985 and 1987, and Voyager 2 occultation results. The new Earth-based occultations were of stars U23, U25, and U28 from the prediction list Mink and Klemola (D.J. Mink and A. Klemola, 1985, Astron. J. 90, 1894-1899). The 4 May 1985 U23 occultation was observed from Cerro Tololo Interamerican Observatory (CTIO), McDonald Observatory, and Teide Observatory on Tenerife, and the 24 May 1985 U25 event wasobservedfrom CTIO, McDonald Observatory, and the IRTF on Mauna Kea. The 26 April 1987 U28 occultation was observed from the IRTF. Square-well models were fitted to the observedring profiles to determined ring midtimes, widths, and optical depths. Voyager photopolarimeter and ultraviolet spectrometer observations of them σ Sgr and β Per stellar occultations provided strong constraints on the direction of the planetary pole University of Hawaii, Honolulu, HI 96822. because of the oblique viewing geometry. Voyager radio science X-band occultation ring profiles observed with the Deep Space Station at Tidbinbilla were fitted with diffracted square-well models and strongly constrained the absolute radius scale of the ring system. The estimated accuracy of the new orbit solution is ±1 km in the semimajor axes of the rings, and ±0.01° in the direction of Uranus' pole. Rings 6, 5, 4, α, β, η, and ε{lunate} were fitted to elliptical, inclined orbits precessing under the influence of the gravitational harmonics, J₂ and J₄, with typical RMS ring plane residuals of a few hundred meters. The newly-discovered ring 1986U1R was fitted by a circular, equatorial model. The α and γ rings are shown to have excited normal modes which cause them to deviate significantly (several kilometers in orbital radius) from simple ellipses. The γ ring exhibits an m = 2 distortion with a best-fitting pattern speed of 23.43832 ± 0.00004 deg hr^-1. The radius corresponding to an m = 2 normal mode with this pattern speed falls within 1 km of the newly fitted semimajor axis of the ring, confirming the suggestionof Porco and Goldreich (C.C. Proco and P. Goldreich, 1987, Astron. J. 93, 724-729) that the σ-ring shape distortion is due to an excitation of its m = 2 normal mode. THe bizarre pattern of γ-ring observations is shown to be due to the combination of of an m = 1 and an m = 0 mode; the entire precessing elliptical ring undergoes radial oscillations with a frequency of 47.73198 ± 0.00019 deg hr^-1. The amplitude of the oscillations is 5.15 ± 0.33 km, remarkably closeto the amplitude ae = 5.19 ± 0.33 km of the m = 1 mode which is also present in the γ ring. The resonance radius for the m = 0 mode is within 1 km of the fitted semimajor axis of the ring. A comparison of satellite resonance locationsand fitted ring radii supports the suggestion of Porco and Goldreich (C.C. Proco and P. Goldreich, 1987, Astron. J. 93, 724-729) that 1986U7 is shepherding the outer edge of the σ ring and 1986U8 is shepherding the inner edge of the γring. The new orbit solution confirms their identification of the 24:25 outer eccentric resonance of 1986U7 with the inner edge of the ε{lunate} ring, the 14:13 inner eccentric resonance of 1986U8 with the outer edge, and the likehood that 1986U7 also shepherds 1986U1R.