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

TL;DR

This paper explores deriving the general relativistic equation of planetary motion using only special relativity techniques, revealing differences in orbital parameters but matching perihelion precession results.

Contribution

It demonstrates a novel approach to obtain GR planetary motion equations solely through special relativity and perturbation theory.

Findings

Differences in mean motion and orbital radius compared to GR

Exact match in perihelion precession with GR

Provides insights into spacetime structure under gravity

Abstract

It is attempted to derive the general relativistic (GR) equation of motion for planet and its solution solely by the special relativity (SR) techniques. The motion of a planet relative to the sun and that of the sun to the planet are solved independently in special relativistic framework using the perturbation theory in the 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 PN approximation, both are different concerning the mean motion and the radius of the orbit but exactly the same as for the perihelion precession.