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We give a constructive proof of the existence of lower dimensional elliptictori in nearly integrable Hamiltonian systems. In particular we adapt theclassical Kolmogorov's normalization algorithm to the case of planetarysystems, for which elliptic tori may be used as replacements of elliptickeplerian orbits in Lagrange-Laplace theory. With this paper we support withrigorous convergence estimates the semi-analytical work in our previous article(2011), where an explicit calculation of an invariant torus for a planar modelof the Sun-Jupiter-Saturn-Uranus system has been made. With respect to previousworks on the same subject we exploit the characteristic of Lie series giving aprecise control of all terms generated by our algorithm. This allows us toslightly relax the non-resonance conditions on the frequencies.

On the convergence of an algorithm constructing the normal form for lower dimensional elliptic tori in planetary systems