The radius and ellipticity of Uranus from its occultation of SAO 158687

From occultation timings obtained from the Kuiper Airborne Observatory and from Cape Town for Mar. 10, 1977 occultation of SAO 158687 by Uranus, the equatorial radius, Re, of the planet has been determined to be 26,228 + or - 30 km and its ellipticity epsilon = 1 - Rp/Re = 0.033 + or - 0.007. These values refer to the 1.0 x 10 to the 14th/cu cm number-density level, under the assumption that the upper atmosphere is composed of H2 and He with a mean molecular weight mu = 2.20. The dominant source of uncertainty is the position of the center of the ring system, which was used to define the center of Uranus in our analysis. A rotation rate of 12.8 + or - 1.7 hours for the planet is implied by our value for the ellipticity, under the assumption that Uranus is in hydrostatic equilibrium below the 1.0 x 10 to the 14th/cu cm number density level.