Einstein’s field equations are approximated, keeping a notion of simultaneity and of flat space, based on a finite propagation speed of the (Newtonian) gravitational force. This leads to the modification of Newton’s equation by an implicit state-dependent delay. We first present the gravitational potential due to a point mass in motion, prescribed by a trajectory, \(\textbf{r}_p(t)\) . The gravitational force at \((\textbf{r},t)\) is obtained as the (usual) gradient of the potential and a gravito-magnetic effect emerges. Next we predict the kinematics of gravitating binaries with unequal masses, thus generalizing our findings in [9, 12]. In particular, Newton’s results for the orbital speeds hold if the masses are replaced by the relativistic ones.