The gravitational two-body potential generated by binary systems

We evaluate the {\em three-dimensional}, {\em non-axis-symmetric}, {\em time-dependent} Newton potential generated by a pair of mutually orbiting objects such as pairs of ordinary or neutron stars and, in some approximations, black holes, spinning around each other. The `vertical component' of the gravitational force (that is, that orthogonal to the plane of their orbit) is also evaluated, along with the other components of the field. The pseudo-Newtonian Paczy\'{n}ski-Wiita form of the potential is also computed. The effect of the asymmetry due to the more common case of different masses is stressed.