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We explore the geodesic movement on an effective four-dimensionalhypersurface that is embedded in a five-dimensional Ricci-flat manifolddescribed by a canonical metric, in order to applying to planetary orbits inour solar system. Some important solutions are given, which provide thestandard solutions of general relativity without any extra force component. Westudy the perihelion advances of Mercury, the Earth and Pluto using theextended theory of general relativity (ETGR). Our results are in very goodagreement with observations and show how the foliation is determinant to thevalue of the perihelion's advances. Possible applications are not limited tothese kinds of orbits.

Perihelion advances for the orbits of Mercury, Earth and Pluto from Extended Theory of General Relativity (ETGR)