A space craft, travelling at 0.51c, is just passing the Earth when the light from a Supernova which is travelling in exactly the opposite direction to the ship, reaches it. According to an observer on the Earth the star which caused the explosion was 897 light years away (1 light year = distance travelled by light in one year). According to an observer on the spaceship how long ago did the star explode?
what I did is :
time = d/v
897 light years / (0.51 * 3.0e^10)
= 5.86e^-6
therefore
time in the person on the earths reference frame is
5.86e^-6/(1-((0.56c)^2/(3.0e^8)^2))^(1/2)
to get 7.076e^-6 and I would then add that to the original 897 light years
but this is not correct