The construction of a third-order secular analytical J-S-U-N theory by the Hori-Lie technique. II: Determination of (F1S, F2S, F3S) and (F1C, F2C)

We expand both parts, the principal and indirect, of the Hamiltonian function up to the third order in the masses for the four major planets Jupiter-Saturn-Uranus-Neptune. Accordingly we write down the secular terms of F 1 , F 2 , F 3 and the critical terms of F 1 , F 2 in terms of the canonical variables of H. Poincare neglecting powers higher than the second in H, K, P, Q