Quantitative orbit classification of the planar restricted three-body problem with application to the motion of a satellite around Jupiter

In this work we numerically investigate the planar circular restricted three-body problem and apply this model to the Sun-Jupiter-particle problem where the particle is orbiting Jupiter. Our aim is to complement the qualitative mapping technique with quantitative techniques to trace a given trajectory in phase space. Qualitatively, this problem can be investigated using the Poincaré surface of sections mapping technique. Here we compute such maps for various Jacobian energies. While the computation of classic Poincaré surface of sections are useful to qualitatively classify phase-space regions with periodic, quasi-periodic, or chaotic motion, the method is inadequate to describe escape and/or collision orbits. To mitigate this shortcoming we complement such maps with the calculations of quantitative dynamical maps based on the Smaller-Alignment Index (SALI) technique. This allows for a complete assessment of the global dynamics of the problem resulting in a detailed classification of orbits of differing dynamical character. We revealed the network of simple periodic orbits around Jupiter, along with their linear stability. As a highlight, we identified a region of flipping orbits that are not detected with Poincaré surface of sections. We outline and discuss various assumptions. After a short review of the underlying model and applied numerical techniques, we present and discuss results from this work.