5.9 Exercise 39

(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy $12.0 \times 10^{9} \text{ly}$ away is receding from us at 0.900c, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990c as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)