Abstract: The motion of a celestial body around a central celestial body is to study the dynamics of two celestial bodies that can be regarded as particles under the action of universal gravitation. It is also the basic two body problem in celestial mechanics. Therefore, it is of great significance. In this paper, the motion of the central force field is simply solved by using the principle of conservation of mechanical energy. The orbit, speed and time of the celestial body moving around the central celestial body are systematically studied. The algebraic relations of orbit eccentricity, position coordinates, speed and time are established for the first time. At the same time, the derived formula has also passed the actual test of the orbit of Halley's comet, showing good accuracy.

Key words: central gravitational field, elliptical orbit, conservation of mechanical energy, operating velocity, running time