Walker, Halliday & Resnick — Gravitation: Problem 9

9 In Fig. 13-23, two satellites, A and B, both of mass \(m = 150 \text{ kg}\), move in the same circular orbit of radius \(r = 7.87 \times 10^6 \text{ m}\) around Earth but in opposite senses of rotation and therefore on a collision course. (a) Find the total mechanical energy \(E_A + E_B\) of the two satellites + Earth system before the collision. (b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass \(= 2m\)), find the total mechanical energy immediately after the collision. (c) Just after the collision, is the wreckage falling directly toward Earth’s center or orbiting around Earth?