A Caltech Library Service

The dynamics of elliptical rings

Borderies, Nicole and Goldreich, Peter and Tremaine, Scott (1983) The dynamics of elliptical rings. Astronomical Journal, 88 (10). pp. 1560-1568. ISSN 0004-6256. doi:10.1086/113446.

PDF - Published Version
See Usage Policy.

PDF - Erratum
See Usage Policy.


Use this Persistent URL to link to this item:


We investigate the evolution of eccentric rings under the influence of (1) differential precession due to the planetary quadrupole moment; (2) self-gravity; (3) viscous forces due to interparticle collisions; and (4) eccentricity excitation by shepherd satellites. The principal conclusions are that: (a) Uniform precession can be enforced by self-gravity (Goldreich and Tremaine 1979b); the resulting configuration is both dynamically and secularly stable. (b) Due to viscous forces the line of apsides at the inner ring edge is not exactly aligned with the line of apsides at the outer edge; the apse shift may be detectable in the ɑ and β rings of Uranus. (c) The mean eccentricity is determined by a balance between viscous damping and excitation by shepherds. (d) We expect the dimensionless eccentricity gradient ɑΔe/Δɑ to be positive and of order unity in most eccentric rings, as observed.

Item Type:Article
Related URLs:
Additional Information:© 1983 American Astronomical Society. Received 24 May 1983. We thank J. Elliot, P. Nicholson, C. Porco, and C. Yoder for discussions. N. B. acknowledges a NSF U.S.-France exchange postdoctoral fellowship and a grant from ATP Planétologie 1982. P. G. acknowledges support from NSF Grant AST80-20005 and NASA Grant NGL-05-002-003. S. T. acknowledges support from NSF Grant AST-8210463 and NASA Grants NSG-7643 and NGL-22009-638.
Group:UNSPECIFIED, UNSPECIFIED, Division of Geological and Planetary Sciences
Funding AgencyGrant Number
ATP Planétologie 1982UNSPECIFIED
NSF U.S.-France exchange postdoctoral fellowshipUNSPECIFIED
Issue or Number:10
Record Number:CaltechAUTHORS:20130308-084452674
Persistent URL:
Official Citation:The dynamics of elliptical rings Borderies, N.; Goldreich, P.; Tremaine, S. Astronomical Journal (ISSN 0004-6256), vol. 88, Oct. 1983, p. 1560-1568.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37405
Deposited By: Ruth Sustaita
Deposited On:11 Mar 2013 20:19
Last Modified:09 Nov 2021 23:28

Repository Staff Only: item control page