Orbital dynamics in the planar Saturn-Titan system

TL;DR

This study investigates the complex orbital dynamics in the Saturn-Titan system using numerical methods, revealing fractal basin boundaries and dependencies on orbital energy, with implications for space mission planning.

Contribution

It provides a detailed numerical analysis of orbital behaviors and basin structures in the Saturn-Titan system within the planar circular restricted three-body problem.

Findings

High complexity of orbital regions around Titan.

Fractal basin boundaries observed across energy regimes.

Strong dependence of basin properties on orbital energy.

Abstract

We use the planar circular restricted three-body problem in order to numerically investigate the orbital dynamics of orbits of a spacecraft, or a comet, or an asteroid in the Saturn-Titan system in a scattering region around the Titan. The orbits can escape through the necks around the Lagrangian points $L_1$ and $L_2$ or collide with the surface of the Titan. We explore all the four possible Hill's regions depending on the value of the Jacobi constant. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of orbits and distinguishing between three types of motion: (i) bounded, (ii) escaping and (iii) collisional. In particular, we locate the different basins and we relate them with the corresponding spatial distributions of the escape and crash times. Our results reveal the high complexity of this planetary system. Furthermore, the numerical analysis shows a strong dependence of the properties of the considered basins with the total orbital energy, with a remarkable presence of fractal basin boundaries along all the regimes. We hope our contribution to be useful in both space mission design and study of planetary systems.