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The expansion of the inverse of the mutual distance between two planets raised to any real integer using Taylor theorem and elliptic expansions Part I, Theoretical results

Elmabsout B., Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2018

Vol. 22, nr 4

1175--1195

We introduce in this part the method to obtain the literal expansion of the mutual distance between two planets of the solar system raised to any negative real integer.

A First Order Jupiter Saturn Planetary Theory. Numerical Results

Kamel O. M., Soliman A. S., El Mabsout B.

Mechanics and Mechanical Engineering

2016

Vol. 20, nr 1

59--73

We present the numerical analysis solution of the eight ordinary non linear differential equations of a first order secular J – S planetary theory. There is no general solution for these equations. We deal with the Poincare’ variables Hu, Ku, Pu, Qu; u=1,2 only. The solution is approximative, since we confine our treatment to a first order secular theory and truncate the Poisson series expansions at the fourth power in eccentricity – inclination.