The initial parameters about resonant orbits in the Earth-Moon system were investigated in this study. Resonant orbits with different ratios are obtained in the two-body problem and planar circular restricted three-body problem (i.e., PCRTBP). It is found that the eccentricity and initial phase are two important initial parameters of resonant orbits that affect the closest distance between the spacecraft and the Moon. Potential resonant transition or resonant flyby may occur depending on the possibility of the spacecraft approaching the Moon. Based on an analysis of ballistic capture and flyby, the Kepler energy and the planet’s perturbed gravitational sphere are used as criteria to establish connections between the initial parameters and the possible “steady” resonant orbits. The initial parameter intervals that can cause instability of the resonant orbits in the CRTBP are obtained. Examples of resonant orbits in 1:2 and 2:1 resonances are provided to verify the proposed criteria.

中文翻译：

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月球系统共振轨道的初始参数分析

本研究研究了月球系统中共振轨道的初始参数。在二体问题和平面圆约束三体问题（即PCRTBP）中获得了具有不同比率的共振轨道。已经发现，偏心率和初始相位是谐振轨道的两个重要的初始参数，它们影响航天器与月球之间的最接近距离。根据航天器接近月球的可能性，可能会发生潜在的共振过渡或共振飞越。基于对弹道捕获和飞越的分析，开普勒能量和行星的扰动引力球被用作在初始参数和可能的“稳定”共振轨道之间建立联系的标准。获得了可能导致CRTBP中谐振轨道不稳定的初始参数间隔。提供了以1：2和2：1共振的共振轨道的示例，以验证建议的标准。