Journal Article

Motion around a monopole + ring system – I. Stability of equatorial circular orbits versus regularity of three-dimensional motion

Javier Ramos-Caro, Juan F. Pedraza and Patricio S. Letelier

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 414, issue 4, pages 3105-3116
Published in print July 2011 | ISSN: 0035-8711
Published online July 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.18618.x
Motion around a monopole + ring system – I. Stability of equatorial circular orbits versus regularity of three-dimensional motion

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We study the motion of test particles around a centre of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan and Morgan discs. We deal with two kinds of bounded orbits: (i) equatorial circular orbits and (ii) general three-dimensional orbits. The first case provides a method to perform a linear stability analysis of these structures by studying the behaviour of vertical and epicyclic frequencies as functions of the mass ratio, the size of the ring and/or the quadrupolar deformation. In the second case, we study the influence of these parameters in the regularity or chaoticity of motion. We find that there is a close connection between linear stability (or instability) of equatorial circular orbits and regularity (or chaoticity) of the three-dimensional motion.

Keywords: chaos; celestial mechanics; planets and satellites: rings

Journal Article.  7959 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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