Data Mining-Based Cislunar Escape-Family Analysis in The Multi-Body Models

TL;DR

The study tackles the problem of characterizing escape trajectories from a 167 km Earth orbit in the Earth-Moon system, exploring both the planar PCR3BP and the Sun-Earth/Moon planar PBCR4BP to quantify solar perturbation effects. It constructs global maps of escape trajectories via grid search over departure states parameterized by $\alpha_i$ and $\beta_i$, applies a refined escape criterion with $r>R_d$ and $E>0$ (and $E_2>0$ for PBCR4BP), and employs DBSCAN on $[\sin\alpha_i,\cos\alpha_i,\hat{\beta}_i]$ to identify escape families after pre-filtering by a single lunar gravity assist. The results reveal 19 escape families in the Earth-Moon PCR3BP, 24 in the PBCR4BP with $\theta_{S i}=0^\circ$, and 32 in the PBCR4BP with $\theta_{S i}=90^\circ$, with PBCR4BP introducing new families and sometimes removing others. Solar gravity perturbation generally increases the number of escape trajectories and alters the generalized energy $E$ after the lunar gravity assist, but it has a limited effect on reducing the Earth injection $\Delta v_i$, suggesting that the Earth-Moon PCR3BP can be a practical first-stage model for trajectory design, pending verification in higher-fidelity PBCR4BP models. The work provides a data-driven methodology for escape-family identification and offers actionable insights into model selection and initial-state design for interplanetary transfer planning.

Abstract

Escape trajectories from the Earth-Moon system play an important role in interplanetary transfer. This paper focuses on the escape trajectories from a 167 km circular Earth orbit in the Earth-Moon planar circular three-body problem and the Sun-Earth/Moon planar bicircular four-body problem and is denoted to providing a comprehensive analysis on these escape trajectories. To achieve these purposes, the global maps of escape trajectories are constructed, and escape trajectories with one lunar gravity assist are pre-filtered. Then, an effective method to identification escape families is proposed based on dynamical analysis and data mining techniques. Once the escape families are identified, the corresponding characteristics are analyzed to provide insights into the construction of escape trajectories. Based on these escape families, the effects of the solar gravity perturbation on the number of escape trajectories, the emergence and disappearance of escape families, variation in generalized energy, and transfer characteristics are further summarized, providing insights into the model selection in the escape trajectory construction. This paper establishes an analysis methodology of escape trajectories from a perspective of escape families, deepening the understanding of escape dynamics.

Figures (25)

• Figure 1: The $\left(\alpha_i,\text{ }\beta_i\right)$ map of identified escape trajectories in the Earth-Moon PCR3BP.
• Figure 2: The $\left(\alpha_i,\text{ }\beta_i\right)$ map of identified escape trajectories in the Sun-Earth/Moon PBCR4BP. (a) $\theta_{\text{S}i}=0\text{ }\deg$; (b) $\theta_{\text{S}i}=90\text{ }\deg$; (c) $\theta_{\text{S}i}=180\text{ }\deg$; (d) $\theta_{\text{S}i}=270\text{ }\deg$.
• Figure 3: The schematic of LGA.
• Figure 4: The $\left(\alpha_i,\text{ }\beta_i\right)$ map of identified escape trajectories with LGAs in the Earth-Moon PCR3BP.
• Figure 5: The $\left(\alpha_i,\text{ }\beta_i\right)$ map of identified escape trajectories with LGAs in the Sun-Earth/Moon PBCR4BP. (a) $\theta_{\text{S}i}=0\text{ }\deg$; (b) $\theta_{\text{S}i}=90\text{ }\deg$.