Two identical hard spheres, each of mass m and radius r, are released from rest in otherwise empty space with their centers separated by the distance R. They are allowed to collide under the influence of their gravitational attraction. (a) Show that the magnitude of the impulse received by each sphere before they make contact is given by [Gm3 (1/2r ─ 1/R)] 1/2. (b) What If? Find the magnitude of the impulse each receives if they collide elastically.