The Semi-Analytical Motion Theory of Major Planets of The Solar System

The semi-analytical motion theory for the eight-planetary problem is constructed in this paper. The Hamiltonian of the problem is written in the Jacobi coordinate system and expanded into a Poisson series in powers of the small parameter and the orbital elements of the second Poincare system. The Hamiltonian is averaged by the Hori - Deprit method to the second order in the small parameter. The analytically constructed equations of motion are numerically integrated by various methods to study the orbital evolution of eight major planets of the Solar System on long-time scales. The obtained results are compared with different motion theories.