The Construction of a Third-Order Secular Analytical J-S-U-N Theory by the Hori-Lie Technique. Part 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 ofF ₁,F ₂,F ₃ and the critical terms ofF ₁,F ₂ in terms of the canonical variables of H. Poincaré neglecting powers higher than the second inH, K, P, Q.