Abstract
Using new expansions of the planetary Hamiltonian in Poincaré canonical elliptic variables, Arnold's theorem for the existence of quasiperiodic orbits in degenerated cases is applied to the general spatial planetary three body problem. The existence of quasiperiodic motion is demonstrated for almost all values of the ratio of semi-major axis α in ]0, 0.8] and almost all values of the mutual inclination up to about 1 degree. This extends the previous result of Arnold (1963).
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Robutel, P. Stability of the planetary three-body problem. Celestial Mech Dyn Astr 62, 219–261 (1995). https://doi.org/10.1007/BF00692089
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DOI: https://doi.org/10.1007/BF00692089