Application of the Restricted Problem of Three Bodies to Space Mechanics

The most celebrated problem of dynamics, the problem of three bodies, is defined in the first chapter and it is shown how the problème restreint is obtained from the general formulation. This is followed by a historical review of the restricted problem from the point of view of space dynamics applications and the present state of the art is described in some detail. The third and final chapter reviews the major activities in the field of space mechanics and their relation to the restricted problem are pointed out. The purpose of this compte rendu is to demonstrate two theses. Firstly, based on the history of the restricted problem of three bodies, it will be shown that combining recent advances in computer technology and in analytical dynamics with modern topological techniques, a terra firma exists for a new attack on this classical problem. The second thesis is that the restricted problem of three bodies plays a central role in celestial mechanics and in space dynamics. From the second thesis it follows that progress in the solution of this problem will further the case of the entire field of space dynamics. An outline of a combined theoretical and experimental program, leading to possible significant contributions to this pièce de résistance of dynamics, completes the paper.