A simple approximate analysis of the linear stability of ring systems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We give a simple linear stability analysis of a system of n equal mass bodies in circular orbit about a single more massive body. A full analysis requires the possibility of perturbing all bodies. If the massive body is sufficiently dominant, then one can ignore perturbations to it. In this paper, we give a linear stability analysis based on perturbations to just one of the small ring bodies. Such an analysis could be justified by assuming that this one body has mass zero. But, we do not make this assumption. Therefore, it is surprising that the result we obtain agrees to within a factor of 2 with the result one obtains by considering perturbations to all ring bodies. We also give a simple back-of-the-envelope computation that shows that our stability mass threshold is consistent with the observed optical density of Saturn's rings.

Original languageEnglish (US)
Title of host publicationNEW TRENDS IN ASTRODYNAMICS AND APPLICATIONS III
Pages169-174
Number of pages6
DOIs
StatePublished - Mar 26 2007
EventNEW TRENDS IN ASTRODYNAMICS AND APPLICATIONS III - Princeton, NJ, United States
Duration: Aug 16 2006Aug 18 2006

Publication series

NameAIP Conference Proceedings
Volume886
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherNEW TRENDS IN ASTRODYNAMICS AND APPLICATIONS III
CountryUnited States
CityPrinceton, NJ
Period8/16/068/18/06

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Keywords

  • Celestial mechanics
  • Linear stability
  • Saturn's rings

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