Abstract
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.
Highlights
Mean motion resonance is a common phenomenon that exists when there is a simple integer relationship between frequencies or periods [1, 2]
Many resonant orbits can be found with a resonant ratio that is equal to the ratio of the orbital periods corresponding to the bodies in resonance, such as the 3:1 mean motion resonance found in the 55 Cancri planetary system [4, 5] and the 2:1 motion resonance in the extrasolar planetary systems HD 82943 [6] and Gliese 876 [7, 8]
This study focuses purely on resonant orbits losing steady ratios and attempts to locate the parameter intervals that can cause those orbits to lose their steady ratios as the secondary primary is approached, where the Earth-Moon system is taken as an example
Summary
Mean motion resonance is a common phenomenon that exists when there is a simple integer relationship between frequencies or periods [1, 2]. Flyby is one of those interesting phenomena related to mean motion resonance in the CRTBP that involves a gravity assist maneuver, followed by escape after approaching the secondary primary [18]. They explored their characteristics using a monodromy matrix and found that multiple flybys dramatically alter the resonant ratio [19]. Based on the definition of ballistic capture [24, 25] and flyby range [19, 21], the Kepler energy and perturbing planet’s sphere of influence are used as indices to establish connections between the initial parameters of resonant orbits and their possibilities of maintaining “steady” resonant ratios.
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