Since Schwarzschild’s first solution of the Einstein field equations, the simple model of a single, point mass gravitating source has encompassed an impressive array of phenomena that have provided confirmation for Einstein’stheory of General Relativity. These include gravitational time dilation and spectral redshifts, gravitational refraction of light, perihelion precession of planetary orbits, innermost stable orbits of accretion disks and, recently, the shadows of the photon spheres of extremely compact masses. These phenomena are associated with the geodesic motions of material particles or photons in the immediate vicinity of large masses that can be regarded as point sources of gravity. The limited purposes of this article are to present the underlying physicsof the exponential metric of Yilmaz and to demonstrate that it correctly encompasses the observed phenomena. As an isotropic metric, It may be the only one also in accord with the observed isotropy of inertia.