We watch two identical astronomical bodies, A and B, each of mass m, fall toward each other from rest because of the gravitational force on each from the other. Their initial center-to-center separation is Ri. Assume that we are in an inertial reference frame that is stationary with respect to the center of mass of this two-body system. Use the principle of conservation of mechanical energy (Kf + Uf = Ki + Ui) to find the following when the center-to-center separation is 0.5Rri:

(a) The total kinetic energy of the system,

(b) The kinetic energy of each body,

(c) The speed of each body relative to us, and

(d) The speed of body B relative to body A. Next assume that we are in a reference frame attached to body A (we ride on the body). Now we see body B fall from rest toward us. From this reference frame, again Kf + Uf = Ki + Ui to find the following when the center-to-center separation is 0.5Ri:

(e) The kinetic energy of body B and

(f) The speed of body B relative to body A.

(g) Why are the answers to (d) and (f) different? Which answer is correct?