The Elimination of the 1:2 Critical Terms of a First Order Theory of Uranus Perturbed by Neptune Through Von-Zeipel Method

In this paper we eliminate in a first order U-N theory the 1 : 2 critical terms up to the third degree with respect to eccentricity — inclination in both parts, main and indirect of the U-N planetary Hamiltonian. We operate the Von Zeipel technique. We adopt, in this theory, the Jacobi-Radau coordinates, and the Poincaré canonical variables. We neglect powers higher than the third in the eccentricity-inclination. This paper is related to the two previous articles (Kamel, 1982; 1983).