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A Semi - Analytic First Order Jupiter - Saturn Planetary Theory. Part II

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2015

Vol. 19, nr 2

103--118

In this part we present the algebraic calculus computations related to the Hamiltonian equations of motion for the Jupiter – Saturn subsystem. Also we give a comment on the methods of the solution for the system of linear and nonlinear differential equations describing the motion of this subsystem.

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

Kamel O. M.

Mechanics and Mechanical Engineering

2015

Vol. 19, nr 1

17--22

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 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.