General planetary theory in elliptic functions

Details General planetary theory in elliptic functions General planetary theory in elliptic functions

May 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..59....1b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, vol. 59, no. 1, p. 1-36

Astronomy and Astrophysics

Astronomy

4

Eccentricity, Elliptic Functions, Planetary Evolution, Planetary Orbits, Quadratures, Fourier Series, Hypergeometric Functions, Kepler Laws, Planetary Mass, Solar Longitude, Solar Orbits

Scientific paper

It is shown that the first-order general planetary theory, i.e. the theory without secular terms, developed in (Brumberg and Chapront, 1973) may be re-constructed and presented by the series in powers of the eccentricity and inclination variables with the closed form coefficients expressed in terms of elliptic functions. The intermediate solution of the zero degree in eccentricities and inclinations has been given explicitly with the aid of elliptic functions and the Hansen type quadratures with trigonometric function kernels. In determining the first and higher degree terms in eccentricities and inclinations one meets the Hansen type quadratures with elliptic function kernels. The secular evolution is described by the autonomous polynomial differential system.

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