Elimination of the critical terms in a first-order general planetary theory

Details Elimination of the critical terms in a first-order general planetary theory Elimination of the critical terms in a first-order general planetary theory

Apr 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981m%26p....24..137k&link_type=abstract

Moon and the Planets, vol. 24, Apr. 1981, p. 137-155.

Mathematics

4

Astronomical Models, Celestial Mechanics, Planetology, Solar System, Canonical Forms, Equations Of Motion, Hamiltonian Functions, Partial Differential Equations, Poincare Problem, Transformations (Mathematics)

Scientific paper

A first order canonical general planetary theory is constructed, assuming the solar system to be composed of eight planets excluding Pluto, referring to a common fixed plane, and applying the Jacobi-Radau set of origins. The 2:5 and 1:2 critical terms of Jupiter-Saturn and Uranus-Neptune inequalities were eliminated by von Zeipel's method. The variables are those of Poincare, and the eccentricities and sines of the inclinations were expanded up to a power of three.

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