Physics
Scientific paper
Nov 1966
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1966saosr.229.....m&link_type=abstract
SAO Special Report #229 (1966)
Physics
5
Scientific paper
We eliminate, by von Zeipel's method, the short-period terms of a first order general planetary theory. The disturbed planet is referred to the orbital plane of the disturbing planet and the longitudes are counted from the longitude of the ascending node of the disturbed planet. The short-period terms arising from the indirect part Fli of the disturbing function and those arising from its principal part Flp are eliminated separately. The first terms are calculated using Newcomb operators, the second using Newcomb operators and Laplace coefficients. The powers of eccentricities and mutual inclination higher than the third are neglected. This elimination reduces the system of canonical equations whose Hamiltonian is Fli to a system whose Hamiltonian Fli is identically equal to zero. It reduces the system of canonical equations whose Hamiltonian is Flp to a system whose Hamiltonian Flp is the sum of four secular terms and one long-period term. A numerical check of our formulas has been carried out in the two particular cases of Jupiter perturbed by Saturn and Mars perturbed by the Earth.
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