Question

Challenge problem. (extra credit) Suppose we are on our way to Proxima Centauri, which is 4.2 ly away (in the reference frame of the Earth). We are in a space ship which is traveling with a speed of .99148 c. When we are half-way there, we send a signal to both the Earth and Proxima Centauri. The signals travel at the speed of light c. In the reference frame of the Earth and Proxima Centauri, both signals travel 2.1 ly and thus arrive at their destinations at the same time. (a) In our reference frame, how long (years) does it take for the signal to reach Earth? Remember that in our reference frame, the distance between Earth and Proxima Centauri is less than 4.2 ly because of length contraction. (b) In our reference frame, how long (years) does it take for the signal to reach Proxima Centauri? (c) These two events (the signal reaching Earth and the signal reaching Proxima Centauri) are simultaneous in the Earth’s reference frame. How much time (years) elapses between these two events in our reference frame? Give the answers to 2 significant figures.

Answer 1