الفهرس 
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Abstract
The present dissertation is concerned with the solution of the main prob- lem of the motion of a satellite in orbit around the moon. The perturbation considred are those due to the a sphericity of the moon and the attraction of the Earth. The work consists of five chapters presented as follows • Chapter I is an introduction describing the subject and surveying, briefly, previous works in the subject and describing the main features of the present work. • In chapter, II the problem is formulated. The equations of motion are formed with the orbitor referred to a rotating selenocentric frame with Z-axis along the spin axis of the Moon, and X-axis through the Moon’s longest meridian. The disturbing function is developed in terms of the orbital elements. Then the equations of motion are derived in canonical form in terms of Delaunay elements. • In chapter III, we describe, in some details, the perturbation approach used in this work which is based on the Lie-Deprit-Kamel transform. The Lagrange plenetary equation method is described in details. Also, we outlined the Von-Ziepel technique, • The aim of chapter IV is to study frozwn orbits around the Moon on the basis of an averaged Hamiltonian. The gravitational field of the Moon is considered up to the seven zonal harmonic,J7 plus the third body perturbation. The third body is assumed to move in an elliptic inclined orbit. The averaging procedure is performed through iv transformation method. We studied, for a lunar probe, both moderate and high altitude orbits. • In , we analyze and identify moderate-altitude frozen orbits for lunar probe. The force model comprises the lunar gravitational field up to the ninth zonal coefficient J9, besides attraction of a third body (Earth) moves in an elliptic inclined orbit. After removing the short period terms of the system we used the Lagrange plenetary equations to capture the long-period dynamics of the problem.