Class 91 - Fundamentals of Physics (Halliday and Resnick) 10th Edition - Chapter 13.

Problems from Chapter 13 of the book Fundamentals of Physics (Halliday and Resnick) 10th edition.
Problem 91
91. Two identical bodies of mass m, A and B, are accelerated toward each other from rest by the mutual gravitational force. The initial distance between the centers of the two bodies is R_i. Suppose an observer is in an inertial frame of reference that is stationary with respect to the center of mass of this two-body system. Use the law of conservation of mechanical energy (K_F + U_F = K_i + U_i) to determine the following quantities when the distance between the centers is 0.5R_i: (a) the total kinetic energy of the system, (b) the kinetic energy of each star, (c) the speed of each star relative to the observer, and (d) the speed of star B relative to star A. Next, assume that the observer's frame of reference is linked to star A (i.e., the observer is at star A). In this case, the observer sees body B accelerating toward him from rest. In this frame of reference, again use the relation K_F + U_F = K_i + U_i) to determine the following quantities when the distance between the centers is 0.5R_i: (e) the kinetic energy of star B, and (f) the speed of star B relative to star A. (g) Why are the answers to parts (d) and (f) different? Which of the two answers is correct?
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