An Extended Newtonian Theory for Gravitational Bound Systems

A physical fundament was derived to support the empirical correction to the balance between the force given by Newton 2^nd law and Newton gravitation introduced previously by the author to account for the perihelion precession of Mercury. An equation was obtained that coincided in sign and magnitude with the Einstein perihelion shift when the 3^rd law of Kepler was used to express the orbital period in term of the semi-major axis and the same level of accuracy was demanded. Other more accurate equations for the intrinsic perihelion shift were obtained that resulted in a relative deviation of about 1% or less.