Revealing the properties of the out-of-plane points of equilibrium of the restricted 3-body problem with non-spherical radiating bodies

Abstract

Our target is to understand and also reveal the dynamics of the out-of-plane points of equilibrium of the restricted version of the 3-body problem with equally massed radiating bodies that have either prolate or oblate shapes. We use standard root-finding numerical methods of high accuracy for determining the coordinates of the locations of the out-of-plane equilibria and also for computing their linear stability. For obtaining a global view of how the two system’s parameters, that is the prolateness/oblateness coefficient and the radiation pressure factor, affect the equilibria dynamics we perform a systematic and thorough scan of the parameters space. Our analysis suggests that the out-of-plane equilibria are highly affected by these two parameters and play a key role in the overall dynamics of the system.