A Semi-Analytic First Order Jupiter-Saturn Planetary Theory Part I : Outline

Osman Kamel
2015 Mechanics and Mechanical Engineering   unpublished
Herein we lay the broad lines for the construction of a first order w.r.t planetary masses Jupiter-Saturn theory-giving the orbital elements of the two planets at any epoch. This is implemented by the evaluation of the R. H. S. of the original first order Hamiltonian equations of motion. The first order Hamiltonian is composed of the first order secular terms and the first order periodic terms. We restrict the periodic terms to be the commensurate ones for the J-S (Jupiter-Saturn) subsystem. We
more » ... give throughout the text an idea to the extension of the theory to the case of the four major outer planets J-S-U-N. The original first order Hamiltonian equations of motion, in terms of the variables of H. Poincare' for the J-S subsystem is given by dLu dt = ∂F1 ∂λu dλu dt = − ∂F1 ∂Lu dHu dt = ∂F1 ∂Ku dKu dt = − ∂F1 ∂Hu (1) dPu dt = ∂F1 ∂Qu dQu dt = − ∂F1 ∂Pu