Abstract
A small particle moves in the vicinity of two masses, forming a close binary, in orbit about a distant mass. Unique, uniformly valid solutions of this four-body problem are found for motion near both equilateral triangle points of the binary system in terms of a small parameter ε, where the primaries move in accordance with a uniformly-valid three-body solution. Accuracy is maintained within a constant errorO(ε8), and the solutions are uniformly valid as ε tends to zero for time intervalsO(ε−3). Orbital position errors nearL 4 andL 5 of the Earth-Moon system are found to be less than 5% when numerically-generated periodic solutions are used as a standard of comparison.
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Barkham, P.G.D., Modi, V.J. & Soudack, A.C. Asymptotic solutions in the many-body problem. Celestial Mechanics 15, 5–20 (1977). https://doi.org/10.1007/BF01229044
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DOI: https://doi.org/10.1007/BF01229044