Finding regions of bounded motion in binary asteroid environment using Lagrangian descriptors

TL;DR

This paper demonstrates that Lagrangian descriptors effectively identify regions of bounded motion around Dimorphos in a binary asteroid system, even under complex perturbations like solar radiation pressure, aiding trajectory design.

Contribution

The study introduces the use of Lagrangian descriptors in the perturbed planar bi-elliptic restricted four-body problem to locate bounded motion regions near a binary asteroid, accounting for solar radiation pressure effects.

Findings

Lagrangian descriptors reveal phase space structures in unperturbed systems.

Solar radiation pressure disrupts bounded motion regions, increasing instability.

Lagrangian descriptors are computationally efficient for astrodynamics applications.

Abstract

Trajectory design in highly-perturbed environments like binary asteroids is challenging. It typically requires using realistic, non-autonomous dynamical models in which periodic solutions derived in autonomous systems vanish. In this work, Lagrangian descriptors are employed in the perturbed planar bi-elliptic restricted four-body problem to find regions of bounded motion over a finite horizon about Dimorphos, the secondary body of the (65803) Didymos binary system. Results show that Lagrangian descriptors successfully reveal phase space organizing structures both in the unperturbed and perturbed planar bi-elliptic restricted four-body problem. With no solar radiation pressure, regions of bounded motion are visually identified, so granting access to a vast selection of bounded orbits about Dimorphos. Conversely, the presence of solar radiation pressure breaks down the majority of structures, leading to a large region of unstable motion with rare exceptions. Lagrangian descriptors are computationally inexpensive dynamical indicators that could be conveniently applied to astrodynamics.