The Great Inequality In A Hamiltonian Planetary Theory

Details The Great Inequality In A Hamiltonian Planetary Theory The Great Inequality In A Hamiltonian Planetary Theory

1993-11-30

arxiv.org/abs/chao-dyn/9311011v2

Nonlinear Sciences

Chaotic Dynamics

6 pages, PostScript, compressed and uuencoded, 150KB, figures included, hard copy available upon request

Scientific paper

The Jupiter-Saturn 2:5 near-commensurability is analyzed in a fully analytic Hamiltonian planetary theory. Computations for the Sun-Jupiter-Saturn system, extending to the third order of the masses and to the 8th degree in the eccentricities and inclinations, reveal an unexpectedly sensitive dependence of the solution on initial data and its likely nonconvergence. The source of the sensitivity and apparent lack of convergence is this near-commensurability, the so-called great inequality. This indicates that simple averaging, still common in current semi-analytic planetary theories, may not be an adequate technique to obtain information on the long-term dynamics of the Solar System. Preliminary results suggest that these difficulties can be overcome by using resonant normal forms.

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