Abstract By discussing the existent equations of mass-velocity relation, an equivalent polar coordinate equation and its Binet equation of the mass-velocity relation are given, and expressions of the mass-velocity relation and mass-energy relation are given too, which include forms of superluminal (also faster-than-light or FTL) motion. Subsequently, using the mass-energy relation, the general expression of the solution of the energy equation on the medium shell curve method is discussed, and general expression of Binet equation and its approximate solutions about orbits of the celestial bodies motion in weak and strong gravitational field are given. Further more, analysis solutions of the advance of the perihelion of planets and bending of light for the gravitational force are given.
Keywords orbit of the celestial bodies motion, equations of mass-velocity relation, Binet equation, superluminal motion, advance of the perihelion of planets, bending of light, gravitational frequency shift |