Theory of the Trojan asteroids. III

Details Theory of the Trojan asteroids. III Theory of the Trojan asteroids. III

Oct 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..22..267g&link_type=abstract

Celestial Mechanics, vol. 22, Oct. 1980, p. 267-287.

Physics

13

Asteroids, Celestial Mechanics, Orbital Mechanics, Solar Orbits, Asymptotic Series, Convergence, Elliptic Functions, Hyperbolic Functions, Recursive Functions, Time Dependence

Scientific paper

Time dependence is expressed by a hyperelliptic integral in a formal long-periodic solution for the problem of motion of the Trojan asteroids treated as the case of 1:1 resonance. The function t(lambda, alpha, 0) can be expanded in a series involving standard elliptic functions with the approximation m = 0 in the integrand. The normalized period tau(alpha, m) of the motion is approximated by the Hagihara (1972) hyperelliptic integral tau(alpha, 0) corresponding to m = 0. The integral is expanded into elliptic functions. Asymptotic series are derived for the cases alpha approximately 0 and alpha approximately 1 corresponding to the vicinity of the extreme members of the tadpole branch of the family.

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