Convergence of classic expansions of celestial mechanics

Details Convergence of classic expansions of celestial mechanics Convergence of classic expansions of celestial mechanics

Jun 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984azh....61..556k&link_type=abstract

(Astronomicheskii Zhurnal, vol. 61, May-June 1984, p. 556-563) Soviet Astronomy (ISSN 0038-5301), vol. 28, May-June 1984, p. 325

Astronomy and Astrophysics

Astronomy

Celestial Mechanics, Convergence, Many Body Problem, Perturbation Theory, Series Expansion, Solar Orbits

Scientific paper

The hypothesis that for a several-body problem the region of convergence may be wider than those found previously, since the average value of the rate of change of the semimajor axes equals zero, is proved. It is demonstrated that the classic series of perturbation theory in typical nonresonance problems of celestial mechanics converge for /mu/ less than C/t/ to the -kappa, where mu is a small parameter, t is time, and kappa equals one. A wider range of convergence (kappa less than one) can be encountered only in exceptional cases.

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