Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system

TL;DR

This study investigates the complex escape dynamics and fractal basin boundaries in the three-dimensional Earth-Moon system, revealing how initial conditions and energy levels influence orbit types and system stability.

Contribution

It provides a detailed numerical analysis of 3D orbital behaviors, including escape, collision, and bounded motion, highlighting the fractal nature of basin boundaries in the Earth-Moon system.

Findings

High complexity of basin structures in 3D system

Strong dependence of basin properties on energy and initial z-coordinate

Presence of fractal basin boundaries across regimes

Abstract

The orbital dynamics of a spacecraft, or a comet, or an asteroid in the Earth-Moon system in a scattering region around the Moon using the three dimensional version of the circular restricted three-body problem is numerically investigated. The test particle can move in bounded orbits around the Moon or escape through the openings around the Lagrange points $L_1$ and $L_2$ or even collide with the surface of the Moon. We explore in detail the first four of the five possible Hill's regions configurations depending on the value of the Jacobi constant which is of course related with the total orbital energy. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of orbits in several two-dimensional types of planes and distinguishing between four types of motion: (i) ordered bounded, (ii) trapped chaotic, (iii) escaping and (iv) collisional. In particular, we locate the different basins and we relate them with the corresponding spatial distributions of the escape and collision times. Our outcomes reveal the high complexity of this planetary system. Furthermore, the numerical analysis suggests a strong dependence of the properties of the considered basins with both the total orbital energy and the initial value of the $z$ coordinate, with a remarkable presence of fractal basin boundaries along all the regimes. Our results are compared with earlier ones regarding the planar version of the Earth-Moon system.