1. The problem statement, all variables and given/known data Using natural units with c=1. We have our Sun and a star at rest relative to it one light year away. A space ship travels from our Sun to the star with v=1/2. During the journey how much time passes on the space ship's clock? How much distance does the captain of the space ship think has been traveled during the journey? 2. Relevant equations -1 < v < 1 t' = gamma(t - vx) x' = gamma(x - vt) y' = y z' = z gamma = 1/sqrt(1-v^2) 3. The attempt at a solution The space ship and both Sun start with t=0, x=0. (0,0) In the Sun's frame the star is at (0,1), and the space ship will reach the star at (2,1). To get the space ship's view of the amount of time passed, we perform the Lorentz transform on (2,1). t'=gamma(2-1/2) x'=gamma(1-1)=0 y=0 z=0 gamma=1/sqrt(3/4)=sqrt(4/3) So by the ship's clock the space ship has reached the star in sqrt(4/3)*3/2=sqrt(4/3)*sqrt(9/4)=sqrt(3). That seems reasonable. How about the distance the ship's captain believes have been traveled. At t=t'=0 the star is at t=0 x=1. So if we perform the Lorentz transform on this we should get the distance perceived in the moving frame. t' = gamma(0 - 1/2) x' = gamma(1) y' = 0 z' = 0 so x'=sqrt(4/3) which is greater than one. That seems unphysical to me. But the captain will calculate his velocity as gamma/(gamma3/2) = 2/3 which seems reasonable. As a check I redid the problem with v=0.9 and the captain calculates his velocity as 4.73 which seems unphysical. What am I doing wrong?