An application of KAM theory to the planetary three body problem

Details An application of KAM theory to the planetary three body problem An application of KAM theory to the planetary three body problem

Jun 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..56..197r&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 56, no. 1-2, p. 197-199.

Astronomy and Astrophysics

Astronomy

1

Hamiltonian Functions, Orbital Resonances (Celestial Mechanics), Three Body Problem, Jupiter (Planet), Saturn (Planet)

Scientific paper

A new planetary analytical expansion in canonical heliocentric variables is used to demonstrate the stability of two planets in a spatial problem, for all values of the semimajor axes. Results obtained confirm that there is stability in the general planetary spatial three-body problem. For small values of planetary mass, inclinations, and eccentricities, almost all initial conditions belong to a 4D invariant torus filled with quasi-periodic orbits which are stable over infinite time.

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