Motion around a Monopole + Ring system: I. Stability of Equatorial Circular Orbits vs Regularity of Three-dimensional Motion

Understand

We study the motion of test particles around a center of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan & 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 behavior 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.