Construction of Kolmogorov's normal form for a planetary system

We describe an algorithm constructing an invariant KAM torus for a class of planetary systems, such that the mutual attractions, the eccentricities and the inclinations of the planets are small enough. By using computer algebra, we explicitly implement this algorithm for approximating a KAM torus for the problem of three bodies in a case similar to the Sun–Jupiter–Saturn system. We show that, by reducing the masses of the planets by a factor 10 and with a small displacement of the orbits, our semianalytical construction of the torus turns out to be successful.