In the solar system, it is reasonable to regard the motion problems of the major planets, minor planets and satellites (including natural and artificial ones) as the perturbed two body problems, and the perturbing sources are mainly the third body.

An application is done with a solution of the two-body problem.

Based on the fundamental theory of celestial mechanics and the discussion of two body problem under the action of universal gravitation ,the general model which can be continuously used to calculate the apparent place of celestial body in the solar system was derived.

This paper analyses the two body problem of kinematical equation and discusses the elastic collision between two particles in the center of mass system.

This paper discusses perturbations problem with relation to a speed of the balanced development,a proportion of the balanced development and a period of crisis, and obtains some important conclusions with practical economic background.