Halliday, Resnick & Walker — Gravitation: Problem Problem_60

In Fig. 13.30, two satellites, A and B, both of mass \( m = 125 \text{ kg} \), 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?