Other
Scientific paper
Dec 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976cemec..14..465b&link_type=abstract
Celestial Mechanics, vol. 14, Dec. 1976, p. 465-492.
Other
2
Asymptotic Methods, Celestial Mechanics, Many Body Problem, Three Body Problem, Earth-Moon System, Mathematical Models, Partial Differential Equations, Position Errors, Solar System, Stellar Motions, Stellar Systems
Scientific paper
A three-body problem is considered in which two masses, forming a close binary, orbit a comparatively distant mass. An asymptotic solution of this problem is presented in which the small parameter (epsilon) is related to the distance separating the binary and the remaining mass. Accepting certain model constraints, this solution is accurate within a constant error of the order of epsilon to the 11th power and uniformly valid for time intervals of the order of the inverse cubic of epsilon. Two specific examples are chosen to verify the literal solution: one relating to the sun-earth-moon configuration of the solar system, the other to an idealized stellar system where the three masses are in the ratio 20:1:1. In both cases, close agreement is found when the analytical solution is compared with an equivalent numerically-generated orbit.
Barkham G. D. P.
Modi V. J.
Soudack A. C.
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