(a) Show that the gravitational force on the small star due to the two large stars in Example 12.3 (Section 121) is not directed toward the point midway between the two large masses.
(b) Consider the two large stars as making up a single, rigid body, as if they were joined by a rod of negligible mass. Calculate the torque exerted by the small star on the rigid body for a pivot at its center of mass.
(c) Explain how the result in part
(b) Shows that the center of mass does not coincide with the center of gravity. Why is this case in this situation?