A rocket is traveling toward a galaxy with speed v.
a) If NASA says that distance from earth to the galaxy is d, what is the distance d' from earth to the galaxy according to the astronauts?
b) The astronauts experience a travel time to the galaxy t' and NASA records the travel time as t. For NASA, d = vt. Show that the astronauts also find that distance = speed x time.
c = 3 x 10^8
Lorentz Factor = (1-(v/c)^2)^(-1/2)
x' = 1/LF ( x - vt)
t' = 1/LF ( t - vx / c^2)
The Attempt at a Solution
Currently I only learned the equations above. I do not know the x', x, t', or t. Is this an intuitive question?