Question

At the time a space ship moving with speed ν = 0.5 c passes a space station located near Mars, a radio signal is sent from the station to earth. This signal is received on earth 1,125 * later.

How long does the spaceship take to reach the earth according to the observers on earth?

Answer 1

If the space station is located at a distance d from the earth then d is fixed by the time taken by the radio signal to reach the earth is

d = ct

As observed from the earth, at t1 = 0 the spaceship was at a distance d approaching with speed 0.5c. It will arrive at time

t1 = d/βc = ct/βc = 1,125/0.5 = 2,250s