- 02-331 Luca Biasco, Luigi Chierchia, Enrico Valdinoci
- Elliptic two-dimensional invariant
tori for the planetary three-body
problem
(588K, PostScript)
Jul 29, 02
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Abstract. The spatial planetary three-body problem (i.e., one ``star" and two ``planets", modelled by
three massive points, interacting through gravity in a three dimensional space) is
considered. It is proven that, near the limiting stable solutions given by the two planets
revolving around the star on Keplerian ellipses
with small eccentricity and small non-zero mutual inclination,
the system
affords two-dimensional, elliptic, quasi-periodic
solutions, provided the masses of the planets are small enough compared to the mass of
the star and provided the osculating Keplerian major semi-axes belong to a two-dimensional
set of density close to one.
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