Resumen de On the stability of the planar n + 1 ring body problem with quasi-homogeneous potentials

Mercedes Arribas Jiménez , Antonio Elipe Sánchez , Manuel Pedro Palacios Latasa

• In a previous work we analyzed the linear stability of the planar n+1 ring body problem where the potential of the central body is a Manev’s type potential. By introducing a perturbation parameter (ǫ0) to the Newtonian potential associated with the central primary, we showed that unstable cases for the unperturbed problem, as n ≤ 6, may become stable for some values of the perturbation.

  The purpose of this paper is to study the possibility of increasing the range of values of the mass parameter (μ = m/m0) and the parameter ǫ0 that let stable the configuration. For that, we introduce a second perturbation term (with parameter ǫ1) to the Newtonian potential of the bodies in the ring. We show some results for different values of the parameters.