What Perturbs the 
Rings of Uranus?
R. G. FRENCH 1,
J. A. KANGAS 2, and
J. L. ELLIOT 3
1 Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge 02139.
2 Department of Physics, Massachusetts Institute of Technology, Cambridge 02139.
3 Department of Earth, Atmospheric, and Planetary Sciences and Department of Physics, Massachusetts Institute of Technology, Cambridge 02139.
The
and
rings have by far the largest radial perturbations of any of the nine known Uranian rings. These two rings deviate from Keplerian orbits, having typical root-mean-square residuals of about 3 kilometers (compared to a few hundred meters for the other seven known rings). Possible causes for the perturbations include nearby shepherd satellites and Lindblad resonances. If shepherd satellites are responsible, they could be as large as several tens of kilometers in diameter. The perturbation patterns of the
and
rings have been examined for evidence of Lindblad resonances of azimuthal wave number m = 0, 1, 2, 3, and 4. The
ring radial residuals are well matched by a 2:1 Lindblad resonance. If this represents a real physical phenomenon and is not an artifact of undersampling, then the most plausible interpretation is that there is an undiscovered satellite orbiting 76,522 ± 8 kilometers from Uranus, with an orbital period of 15.3595 ± 0.0001 hours and a radius of 75 to 100 kilometers. Such a satellite would be easily detected by the Voyager spacecraft when it encounters Uranus. The 2:1 resonance location is 41 ± 9 kilometers inside the
ring, which makes it unlikely that the resonance is due to a viscous instability within the ring. In contrast, no low-order Lindblad resonance matches the
ring perturbations, which are probably caused by one or more shepherd satellites large enough to be clearly visible in Voyager images.
Submitted on November 20, 1985
Accepted on December 26, 1985