Astrophysics, abstract
astro-ph/0606510

From: R.J. Vanderbei [view email]

Date: Wed, 21 Jun 2006 07:43:55 GMT (6kb)

Linear Stability of Ring Systems

Authors: Robert J. Vanderbei

Comments: 8 pages, associated website is this http URL

Consider the planar (n+1)-body problem consisting of a large central body of mass M surrounded by a large number, n, of smaller bodies each having a common mass $m$ distributed uniformly in a circle of radius r and in circular orbit about the central body. By analyzing the situation where one of the smaller bodies is perturbed from this ideal configuration, a linear stability analysis shows that the system is linearly stable if m <= 0.982 M/n^3 . Numerical simulation indicates that this stability threshold is correct to within a factor of about 2.

http://arxiv.org/abs/astro-ph/0606510