A GENERALIZATION OF NEWTON’S DYNAMICAL GRAVITATIONAL FIELD EQUATION AND ITS APPLICATIONS TO PLANETARY THEORY

Over the years there has been the need to generalize both Newton’s dynamical theory of gravitation and Einstein’s geometrical theory of gravitation in order to provide better agreement to all physical theories. In this research work, the Riemann’s Laplacian operator was used to generalize Newton’s dynamical gravitational field equation to construct a generalized dynamical gravitational field equation. The generalized dynamical gravitational field equation was applied to static homogeneous spherical massive bodies to obtain generalized exterior and interior gravitational scalar potentials. The generalized dynamical gravitational scalar potential exterior to the body was substituted into the well-known Newton’s dynamical equations of motion, General dynamical equations of motion and Einstein’s geometrical equations of motion to obtain generalizations of Newton’s dynamical equations of motions, General dynamical equations of motion and Einstein’s geometrical equations of motion. The generalized equations of motion (Newton’s dynamical equations of motions, General dynamical equations of motion and Einstein’s geometrical equations of motion) are applied to the motion of the planets in the solar system to obtain generalized planetary equations of motion and hence the planetary parameters such as the orbital eccentricity, amplitude, the angular frequency, period, angular momentum per unit rest mass and the perihelion and aphelion distances. The results are that the generalized dynamical gravitational field equation, dynamical gravitational scalar potentials exterior and interior, Newtonian acceleration vector, Newtonian equations of motion, General dynamical equations of motion, Einstein’s geometrical equations of motion, Newtonian dynamical planetary equations of motion, General dynamical planetary equations of motion and Einstein’s