Precession of the є ring of Uranus

The boundaries of the є ring can be fit by aligned Keplerian ellipses. Differential precession due to the quadrupole moment of Uranus tends to destroy the apse alignment. We propose that apse alignment is maintained by the self-gravity of the ring. The required ring mass ~5 x 10^(18) g which corresponds to a surface density at quadrature ~25 g cm^(-2).