Discontinuous Behavior of Time-of-Flight Distribution for Bi-impulsive Earth-Moon Transfers in the Three-Body Model

TL;DR

This paper investigates the solution space of bi-impulsive Earth-Moon transfers in the three-body problem, revealing a discontinuous behavior in the time-of-flight distribution related to departure phase angles, which enhances transfer planning insights.

Contribution

It reports a novel discontinuous behavior in the time-of-flight distribution for bi-impulsive transfers, expanding understanding of the solution space in the three-body model.

Findings

Discontinuous time-of-flight distribution observed for different departure phases.

Analysis of transfer parameters reveals complex solution space behavior.

Provides insights for more effective transfer trajectory construction.

Abstract

As interest in the Earth-Moon transfers renewed around the world, understanding the solution space of transfer trajectories facilitates the construction of transfers. This paper is devoted to reporting a novel or less-reported phenomenon about the solution space of bi-impulsive Earth-Moon transfers in the Earth-Moon planar circular restricted three-body problem. Differing from the previous works focusing on the transfer characteristics of the solution space, we focus on the distribution of the construction parameters, i.e., departure phase angle at the Earth parking orbit, initial-to-circular velocity ratio, and time of flight. Firstly, the construction method of bi-impulsive transfers is described, and the solutions satisfying the given constraints are obtained from the grid search method and trajectory correction. Then, the distribution of the obtained solutions is analyzed, and an interesting phenomenon about the discontinuous behavior of the time-of-flight distribution for each departure phase angle is observed and briefly reported. This phenomenon can further provide useful insight into the construction of bi-impulsive transfers, deepening the understanding of the corresponding solution space.