Asymptotic solutions in the many-body problem |
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| Authors: | P G D Barkham V J Modi A C Soudack |
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| Institution: | (1) The University of British Columbia, Vancouver, B.C., Canada |
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| 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  , where the primaries move in accordance with a uniformly-valid three-body solution. Accuracy is maintained within a constant errorO(8), and the solutions are uniformly valid as tends to zero for time intervalsO(–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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