Abstract
The Sun-Earth-Moon system is modeled by the restricted problem of three bodies, and the curves of zero velocity are used to define the limits of stability of the Moon's orbit about the Earth. By holding the relative distances fixed, and maintaining the circular velocities of the Earth and Moon while their masses are varied by a common factor (λ=m′ E/m E=m′ M/m M), it is found that the possibility of the Moon leaving Earth orbit and orbiting the Sun exists for the range of values 0.005<λ<0.4.
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References
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Williams, B.G. A note on the limits of stability for the restricted problem of three bodies as applied to the Sun-Earth-Moon system. Celestial Mechanics 19, 357–358 (1979). https://doi.org/10.1007/BF01231014
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DOI: https://doi.org/10.1007/BF01231014