Abstract: In this paper, the equation of the positive ellipse in polar coordinate system with the center as the pole is derived first. Then, from Newton忆s second law in rectangular coordinate system, Binet formula and energy conservation, it is proved that the orbit of a particle under the action of gravity proportional to distance is an ellipse, and the expressions of the specific parameters, energy and angular momentum of the ellipse orbit are given. Finally, the comparison of these three methods is made, and the choice of some symbols in the calculation process is explained.Although simple, the detailed reasoning process and conclusion given in this paper may provide some reference for the teaching of relevant content.

Key words: direct proportion, gravitation, ellipse, orbit, proof method