A quantum mechanical model for gravitational forces is proposed, based on an assumption that virtual graviton exchange occurs between units of mass or mass-energy. A formula for the Newtonian gravitational constant G can then be derived using Heisenberg's uncertainty principle, showing that it is proportional to the product of Planck's constant and the speed of light. Furthermore, this formula can be rearranged to show that G is also proportional to the product of the Compton wavelength of a mass unit and its mass-energy. The substitution of this formula for G in various classical equations of Physics can provide a novel quantum mechanical interpretation, including for the field equation of General Relativity. It can also provide an explanation of why constant radial velocity profiles of... stars have been observed in most galaxies, and therefore, why modified Newtonian dynamics can match observation on a galactic scale.