  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, in order 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 (ETGR). 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.
