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 Poincare surface of sections mapping technique. Here we compute such maps for various Jacobian energies. While the computation of classic Poincare 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 Poincare 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. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

In this study, the planar circular restricted three-body problem was numerically investigated and applied to the Sun-Jupiter-particle problem. By combining qualitative mapping techniques with quantitative techniques, the study successfully traced a given trajectory in phase space and classified orbits in detail based on their dynamical character.