Perihelion advances for the orbits of Mercury, Earth, and Pluto from extended theory of general relativity (ETGR)

Abstract

We explore the geodesic movement on an effective four-dimensional hypersurface that is embedded in a five-dimensional Ricci-flat manifold described by a canonical metric, to applying to planetary orbits in our solar system. Some important solutions are given, which provide the standard solutions of general relativity without any extra force component. We study the perihelion advances of Mercury, the Earth, and Pluto using the extended theory of general relativity. Our results are in very good agreement with observations and show how the foliation is determinant to the value of the perihelion’s advances. Possible applications are not limited to these kinds of orbits.