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C. A. McGhee, R. G. French (Wellesley Coll.)
The Uranian rings were discovered nearly a quarter century ago, and since that time, a rich set of Earthbased and Voyager occultation observations have made it possible to determine the orbits of the rings to remarkable precision. During the 1980's, Uranus' orbit traversed the rich star field of the Milky Way, as seen from the Earth, providing many opportunities for high-SNR stellar occultations by the rings. The most recent published orbit solution [French et al., ``Uranus," U.~of Ariz.~Press (Bergstralh et al., Eds.) 1991, Tucson Az.; from French et al., Icarus 73, 349--378 (1988)] was based on 11 digitally recorded stellar occultations observed from 1977 to 1986, and the 1986 Voyager RSS, PPS and UVS occultations. We have successfully observed an additional 11 groundbased stellar occultations between 1987 and 1996. We are also digitizing several early high-SNR occultation data sets that were recorded on stripcharts. These results are being incorporated into a new global solution for the orbits of the rings, and the pole direction and gravitational harmonic coefficients of Uranus. The twenty-year time baseline of the full data set has substantially reduced the uncertainties in the fitted parameters from the previous solution. For example, the formal errors in the orbital elements for ring 6 are (new solution, previous solution): \sigma(a)=(0.12, 0.26) km, \sigma(e)=(2.3, 4.0)\times{10-6}, \sigma(\varpi)=(0.19, 0.34)\circ, \sigma(i)=(0.0004, 0.0010)\circ, and \sigma(\Omega)=(0.19, 0.62)\circ. Individual apsidal precession and nodal regression rates are also much more accurately known: \sigma(\dot\varpi)=(0.31, 0.83)\times{10-4}\circ/{\rm day}, \sigma(\dot\Omega)=(0.53, 1.45)\times{10-4}\circ/{\rm day}. The pole direction is now determined to an accuracy of \sigma(\alphaP)=1.7'' and \sigma(\deltaP)=1.4'', and the fractional errors in J2 and J4 are \sigma(J2)/J2=(3.3, 9.6)\times{10-5}, \sigma(J4)/J4=(0.5, 1.6)\times{10-2}. The accuracy of the new solution will make it possible to set limits on weak dynamical effects, such as shepherd-satellite-induced precession of individual rings. As part of this investigation, we are also exploring ring radial structure, such as variations in ring width and optical depth with ring longitude. This work was supported in part by NASA Planetary Geology and Geophysics Program grant NAG5-4046.