The Construction of a Third Order Secular Analytical J-S-U-N Theory by Hori-Lie Technique

We construct the outline of a third order secular theory for the four major planets. We apply the Hori-Lie technique to solve the problem. We take into consideration both parts of the perturbing function. Our canonical variables are those of H. Poincaré. Our periodic terms are the only 2:5 and 1:2 critical terms of J-S and U-N respectively. Terms of degree higher than the second in the Poincaré canonical variables H, K, P, Q are neglected.