The energy density of a Newtonian gravitational field is shown to be −g2/8πG, whereg is the local acceleration due to gravity andG the universal constant of gravitation. In the case of a spherically symmetric object this causes a departure from the inverse square law forg. Allowance for this gravitational energy also introduces to objects a critical radius of sizeGM/2c2, whereM is the mass. Allowance for the gravitational energy of the Sun produces a classical advance of the perihelion of a planet at the rate 1/12 of that found in general relativity. It is also shown that direct application of Sommerfeld's fine-structure theory to gravitation shows an advance of the perihelion of a satellite orbit which is 1/6 that found in general relativity. The theory defines a gravitational fine-structure constant αG=Gm2/ℏc, wherem is the mass of a hydrogen atom. αG determines the rate of perihelion advance for an orbit in Sommerfeld's theory.