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Apse Alignment of Narrow Eccentric Planetary Rings

Chiang, E. I. and Goldreich, P. (2000) Apse Alignment of Narrow Eccentric Planetary Rings. Astrophysical Journal, 540 (2). pp. 1084-1090. ISSN 0004-637X. doi:10.1086/309372.

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The boundaries of the Uranian ∈, α, and β rings can be fitted by Keplerian ellipses. The pair of ellipses that outline a given ring share a common line of apsides. Apse alignment is surprising because the quadrupole moment of Uranus induces differential precession. We propose that rigid precession is maintained by a balance of forces due to ring self-gravity, planetary oblateness, and interparticle collisions. Collisional impulses play an especially dramatic role near ring edges. Pressure-induced accelerations are maximal near edges because there (1) velocity dispersions are enhanced by resonant satellite perturbations and (2) the surface density declines steeply. Remarkably, collisional forces felt by material in the last ~100 m of a ~10 km wide ring can increase equilibrium masses up to a factor of ~100. New ring surface densities are derived that accord with Voyager radio measurements. In contrast to previous models, collisionally modified self-gravity appears to allow for both negative and positive eccentricity gradients; why all narrow planetary rings exhibit positive eccentricity gradients remains an open question.

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Additional Information:© 2000 The American Astronomical Society. Received 2000 January 10; accepted 2000 April 10. Financial support for this research was provided by NSF grant 94-14232 and by a Caltech Kingsley Foundation Fellowship held by E. C. We thank an anonymous referee for useful comments.
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Caltech Kingsley Foundation FellowshipUNSPECIFIED
Subject Keywords:celestial mechanics, stellar dynamics - planets and satellites: individual (Uranus) - solar system: general
Issue or Number:2
Record Number:CaltechAUTHORS:20130225-095427902
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Official Citation:Apse Alignment of Narrow Eccentric Planetary Rings E. I. Chiang and P. Goldreich 2000 ApJ 540 1084
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37108
Deposited By: Tony Diaz
Deposited On:25 Feb 2013 21:16
Last Modified:09 Nov 2021 23:26

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