The Construction of a ThirdOrder Secular Analytical JSUN Theory by the HoriLie Technique. Part II: Determination of (F_{1s}, F_{2s}, F_{3s}) and (F_{1c}, F_{2c})
Abstract
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 JupiterSaturnUranusNeptune. 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.
 Publication:

Earth Moon and Planets
 Pub Date:
 October 1993
 DOI:
 10.1007/BF00572137
 Bibcode:
 1993EM&P...63...29B
 Keywords:

 Hamiltonian Functions;
 Jupiter (Planet);
 Neptune (Planet);
 Planetary Orbits;
 Saturn (Planet);
 Uranus (Planet);
 Canonical Forms;
 Mathematical Models;
 Poincare Problem;
 Poisson Equation;
 Astrophysics