In this paper we use a dynamic form of modified Newtonian gravity to reformulate the equations for gravitational time dilation. Here we introduce the generic equations for gravitational time dilation. It is shown that these equations agree exactly with gravitational time dilation in satellite navigation systems. The equations are also in agreement with a reanalysis of observations of gravitational red shifts in black hole accretion discs. Using these equations, we translate the time dilation into a finite value at the black hole event horizon. Thus this reformulation resolves the difficulties of the existence of black hole singularities. Importantly these dynamic gravitational equations provide testable predictions in the vicinity of black holes.