Radio Signals; Revolution Unit

Question

A distant star has been measured as moving at a speed of 0.59c away from the Earth. If a planet of this star sends radio signals to Earth every 17 seconds (according to their time scale), how often would we receive them (according to our time scale)?

Answer 1

There are two effects in the case, one is the time dilation due to the special relativity, and the other is the Doppler effect due to the source moving away to moving towards the receiver. Combine with these two effects the ratio of the periods in both systems is:

, where and when the source is moving away.

Therefore, the receiving period is sec.