Physics
Scientific paper
Jan 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..26...25m&link_type=abstract
(Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets, Namur, Belgium, July 28-31,
Physics
18
Asymptotic Series, Gravitational Effects, Many Body Problem, Orbit Perturbation, Planetary Orbits, Three Dimensional Motion, Coplanarity, Eccentric Orbits, Hamiltonian Functions, Orbital Mechanics, Periodic Variations, Perturbation Theory, Secular Variations, Solar Orbits
Scientific paper
For the 'planetary case' of the gravitational n-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.
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