The self-gravity of Uranian rings

We derive an approximate, analytic expression for the self-gravity of Uranian elliptical rings at any point in the N-streamline formalism ( N → ∞), and numerically evaluate by a Monte Carlo calculation, the correction factor γ that corrects for the approximations used in the derivation. We confirm that the 2-streamline ( N = 2) model overestimates the mass of the ring: for the ɛ, α, ßrings, the mass given by the N-streamline model ( N → ∞) is only 2/5 that by the 2-streamline model.