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Abstract
The thesis is organized so as to include a general introduction and four chapters: they are ordered as follows:In the introduction the history of the restricted problem of the three bodies is outlined in a chronological manner beginning from the early works due to the brilliant scientists. Lagrange1281, EuIer71, Jacobi1231, Hill1201’ 1211, [221 Poincarét371, Levi-Civita1301 .. etc. and continues to the up to date references. Also the main features of the present work are summarized. In the first chapter the basic scientific materials relevant to the topic of the thesis subject. e.g. the restricted three body problem, the equations of motion in the rotating frame of reference have been formulated. The Lagrange’s points, computation of their locations and investigating their linear stability are addressed, The curves of zero relative velocity and the permissible motions in the field of the restricted three-body problem are explained in the light of the Jacobi integral. In chapter two the post-Newtonian approximation is presented and suited to be applicable for the three body problem. The equations of motion of the relativistic restricted three body problem are derived from the post-Newtonian Lagrangian upon using the Euler Lagrange equation.