Proxima Centauri, the star nearest our own, is some 4.2 ly away. (a) If a spaceship could travel at a speed of 0.24c, how long would it take to reach the star according to the spaceship's pilot? (b) What would someone in the frame that moves along with the spaceship measure as the distance to Proxima Centauri?
d = v/t
t' = t/sqrt(1-(v/c)^2)
The Attempt at a Solution
I know this question is probably very basic, but I'm having a hard time trying to see reason in the way that the question is asked. If the pilot is moving in the frame of reference of the spaceship, would not the time taken to reach the star just be (v/d)? Wouldn't time only be dilated for a stationary observer?
As for part (b), would not a person moving along with the spaceship's frame of reference perceive the same time? Wouldn't this imply that the perceived distance is still 4.2 ly?