Qualitative study of ballistic capture at Mars via Lagrangian descriptors

TL;DR

This study explores how Lagrangian descriptors can identify ballistic capture orbits near Mars by revealing phase space structures, offering a new approach that bypasses traditional variational equation methods.

Contribution

It introduces a novel technique using Lagrangian descriptors and Roberts' operator to detect ballistic capture orbits in the Mars vicinity within the planar elliptic restricted three-body problem.

Findings

Lagrangian descriptors effectively distinguish different dynamical behaviors.

Separatrices correlate well with weak stability boundaries.

The method offers a dynamics insight without propagating variational equations.

Abstract

Lagrangian descriptors reveal the dynamical skeleton governing transport mechanisms of a generic flow. In doing so, they unveil geometrical structures in the phase space that separate regions with different qualitative behavior. This work investigates to what extent Lagrangian descriptors provide information about non-Keplerian motion in Mars proximity, which is modeled under the planar elliptic restricted three-body problem. We propose a novel technique to reveal ballistic capture orbits extracting separatrices of the phase space highlighted by Lagrangian descriptor scalar fields. The Roberts' operator to approximate the gradient is used to detect the edges in the fields. Results demonstrate the chaos indicator ability to distinguish sets of initial conditions exhibiting different dynamics, including ballistic capture ones. Separatrices are validated against reference weak stability boundary derived on similar integration intervals. Compared to other techniques, Lagrangian descriptors provide dynamics insight bypassing the propagation of the variational equations.