Asymptotic series for planetary motion in periodic terms in three dimensions View Full Text


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Article Info

DATE

1982-01

AUTHORS

P. J. Message

ABSTRACT

For the ‘planetary case’ of the gravitationaln-body problem in three dimensions, a sequence of Lie series contact transformations is used to construct asymptotic series representations for the canonical parameters of the instantaneous orbits in a Jacobi formulation. The series contain only periodic terms, the frequencies being linear combinations of those of the planetary orbits and those of the secular variations of the apses and nodes, and the series are in powers of the masses of the planets in terms of that of the primary, and of a quantity of the order of the excursions of the eccentricities and inclinations of the orbits. The treatment avoids singularities for circular and coplanar orbits. It follows that the major axes are given by series of periodic terms only, to all orders in the planetary masses. More... »

PAGES

25-39

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01233180

DOI

http://dx.doi.org/10.1007/bf01233180

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1001757038


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