Photometric Modeling of the Epsilon Ring of Uranus and Its Spacing of Particles

The ring model of Irvine (1966, J. Geophys. Res.71, 2931-2937) is used to explain the longitudinal brightness variation of the ɛ ring of Uranus observed by Voyager 2 and with the Hubble Space Telescope, while basic ring properties are based on occultation data. The observations span a factor of 600 in the range of phase angles (0.03-20°) which allows the rejection of previous simpler ring models. Particles of the ɛ ring are more densely packed than estimated previously. The average volume filling factor is at least 0.06, corresponding to mean particle separations of about twice their diameters or less. Plots are presented which allow the prediction of photometric properties of all uranian rings for various earth-based geometries.