Modified gravity: gravitationally coupled bodies displace the center of mass of each other

Abstract

Abstract Empirical observations have revealed that Newtonian dynamics do not correspond with the amount of visible matter in galactic scales. This imply that there is a vast amount of unseen matter or failure of the theory of gravity in galactic scales or something else. This paper demonstrates that gravitationally coupled bodies offset the center of mass of each other from either very center. Gravitational interaction among particles composing gravitationally coupled bodies lead to displacement of their (bodies) centers of mass towards each other. The magnitude of displacement of the center of mass of a body depends on its mass density, separation distance between the bodies, and mass of the body exerting the gravitational pull. This phenomenon reduces the separation distance between the bodies, thus increasing the net gravitational force between them (bodies).