Isolating Neighborhood Trajectory Computations in Non-Autonomous Systems Including the Elliptic Restricted Three-Body Problem

TL;DR

This paper extends isolating neighborhood methods to non-autonomous celestial mechanics models, including the elliptic restricted three-body problem, enabling more accurate trajectory computations near libration points.

Contribution

It introduces a novel application of isolating neighborhood techniques to non-autonomous systems like the ERTBP, improving trajectory analysis accuracy.

Findings

Computed simplified isolating neighborhood boundaries around libration points.

Successfully used boundaries with bisection method to find forward asymptotic trajectories.

Tracked orbits around libration points in non-autonomous models.

Abstract

Isolating block and isolating neighborhood methods have previously been implemented to find transit trajectories and orbits around libration points in the autonomous circular restricted three-body problem. For some applications, the direct computation of these types of trajectories in non-autonomous models more closely approximating real-world ephemerides is beneficial. Here, we apply isolating neighborhood methods to non-autonomous systems, including the elliptic restricted three-body problem (ERTBP). Specifically, simplified isolating neighborhood boundaries are computed around libration points in the ERTBP. These boundaries are used in combination with a bisection method to compute the forward asymptotic trajectories of the isolated invariant set and track orbits around a libration point.