Optimal transfers from Moon to $L_2$ halo orbit of the Earth-Moon system

TL;DR

This paper develops an optimization method to design low-cost lunar-to-Earth-Moon halo orbit transfers using invariant manifolds, demonstrating feasible trajectories for CubeSats with minimal velocity change.

Contribution

It introduces a nonlinear programming approach to optimize lunar to halo orbit transfers by exploiting stable invariant manifolds within the circular restricted three-body problem.

Findings

Low ΔV transfer solutions identified

Feasible CubeSat transfer trajectories demonstrated

Optimization framework effectively minimizes maneuver costs

Abstract

In this paper, we seek optimal solutions for a transfer from a parking orbit around the Moon to a halo orbit around $L_2$ of the Earth-Moon system, by applying a single maneuver and exploiting the stable invariant manifold of the hyperbolic parking solution at arrival. For that, we propose an optimization problem considering as variables both the orbital characteristics of a parking solution around the Moon, (namely, its Keplerian elements) and the characteristics of a transfer trajectory guided by the stable manifold of the arrival Halo orbit. The problem is solved by a nonlinear programming method (NLP), aiming to minimize the cost of $\Delta V$ to perform a single maneuver transfer, within the framework of the Earth-Moon system of the circular restricted three-body problem. Results with low $\Delta V$ and suitable time of flight show the feasibility of this kind of transfer for a Cubesat.