The elimination of short-periodic terms in a Uranus-Neptune general planetary theory by von Zeipel's method

Details The elimination of short-periodic terms in a Uranus-Neptune general planetary theory by von Zeipel's method The elimination of short-periodic terms in a Uranus-Neptune general planetary theory by von Zeipel's method

May 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979ap%26ss..62...79k&link_type=abstract

Astrophysics and Space Science, vol. 62, no. 1, May 1979, p. 79-116.

Astronomy and Astrophysics

Astrophysics

4

Neptune (Planet), Planetary Evolution, Planetary Mass, Uranus (Planet), Von Zeipel Method, Disturbing Functions, Fourier Series, Hamiltonian Functions, Linear Equations, Partial Differential Equations, Poincare Problem, Planets, Uranus, Neptune, Mass, Eccentricity, Inclinations, Mathematical Models, Distance, Gravity, Sun, Equations Of Motion, Orbits, Two Body Problem

Scientific paper

We eliminate by the method of von Zeipel the short-period terms in a first order - with respect to planetary masses - general planetary Uranus-Neptune theory. We exclude in the expansion terms of eccentricities and sines of inclinations higher than the third power. Our variables are the Poincare canonical variables. We use the Jacobi-Radau set of origins, and we refer the planes of the osculating ellipses to a common fixed plane, the longitudes to a common origin. The short-periodic terms arising from the indirect and principal parts of the disturbing functions, are eliminated separately. The Fourier series of the principal part of the disturbing function, is reduced to the sum of only the first three terms.

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