Stable orbits exist around both the Earth and the Moon simultaneously
Stable orbital configurations, such as libration point orbits, Distant Retrograde Orbits, and Halo orbits, exist within the combined gravitational field of the Earth-Moon system.
The retrieved literature extensively discusses stable orbits (like DROs, Halo orbits, and libration point orbits) in the Earth-Moon system where a spacecraft is influenced simultaneously by the gravitational fields of both bodies. Therefore, the claim that stable orbits exist in this combined multi-body system is well-supported by orbital mechanics and cislunar trajectory research.
L. Capdevila. A transfer network linking Earth, Moon, and the triangular libration point regions in the Earth-Moon system. 2018. https://doi.org/10.1016/J.ASR.2018.06.045
Paper [0] discusses practical stability and transfer networks in the Earth-Moon system involving libration points, Distant Retrograde Orbits, and Near-Rectilinear Halo Orbits influenced by both bodies.
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Smith TR, Bosanac N. Motion Primitive Approach to Spacecraft Trajectory Design in a Multi-body System.. 2023. https://doi.org/10.1007/s40295-023-00395-7
Paper [8] explores trajectory design and stable periodic orbits within the multi-body gravitational environment of the Earth-Moon system.
Wang K, Li K, Lv S, Jiao Y, Shen Y, Yue Z, Xu K. Multi-orbit lunar GNSS constellation design with distant retrograde orbit and Halo orbit combination.. 2023. https://doi.org/10.1038/s41598-023-37348-x
Paper [9] analyzes Halo orbits and Distant Retrograde Orbits in the Earth-Moon system for satellite constellations, demonstrating stable motion in the combined gravitational environment.
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