Global kolmogorov tori in the planetary N-body problem. Announcement of result

We improve a result in [9] by proving the existence of a positive measure set of (3n — 2)-dimensional quasi-periodic motions in the spacial, planetary (1+n)-body problem away from co-planar, circular motions. We al'so prove that such quasi-periodic motions reach with continuity corresponding (2n — 1)-dimensional ones of the planar problem, once the mutual inclinations go to zero (this is related to a speculation in [2]). The main tool is a full reduction of the SO(3)-symmetry, which retains symmetry by reflections and highlights a quasi-integrable structure, with a small remainder, independently of eccentricities and inclinations.