Construction of a general planetary theory of the first order

All the necessary formulae for constructing a general solution for the motion of a planet, in rectangular coordinates, at the first order of the disturbing masses, in purely literal form in eccentricities and inclinations, are given. The authors present the transformation formulae in the two-body problem which give the correspondence between the constants of integration introduced in the theory and the classical keplerian elements. The practical elaboration of the algorithm and some partial results for the couple of planets Jupiter and Saturn are described.