I wonder about gravitational interaction between two bodies of any shape (not necessarly symmetrical). I would like to predict the motion of their centers of mas if they don't interact with any other bodies. Can I assume that mass of each body is located only in the center and compute the gravitational force as if the bodies were punctual? (In fact I should compute double vector integral over volume of each body.) I know that it's true in case of bodies with spherical symmetry (one can prove this using e.g. Gauss theorem). Is it always true for all shapes of bodies.