Attempt to obtain the general relativistic planet's motion by special relativity techniques

Abstract

It is attempted to derive the general relativistic equation of motion for a planet and its solution solely by the special relativity techniques. The motion of a planet relative to the Sun and that of the Sun to the planet are solved independently in a special relativistic framework using the perturbation theory in celestial mechanics. The solution reveals a nature of the structure of the spacetime under the gravitation of the Sun, and then its effect on the planet's motion is examined.When the motion thus examined are compared with the one obtained by the general relativity theory in post-Newtonian approximation, both are different concerning the mean motion and the radius of the orbit but exactly the same as for the perihelion precession.