Abstract: This paper introduces a method of finding central force by derivative of the kinetic energy of a particle in a polar coordinate system to the radius vector, called the kinetic energy derivative method. The central gravity acting on a moving particle in a conic curve is obtained by this method, and then the potential energy function and the conserved total energy of the particle are obtained in this paper. The function of kinetic energy expressed as radius vector and the conservation of angular momentum are the premises of the above reasoning. Compared with Binet忆s formula method, it is found that the reasoning process of kinetic energy derivative method is simpler and the physical meaning of the energy derived is clearer. The expression of total energy is another important conclusion of this paper, which has universal applicability. The reasoning ideas and conclusions of the article may provide some reference for the teaching of related content.

Key words: conic curve, centrifugal force, kinetic energy derivative method, Binet忆s formula, advantage