1. The problem statement, all variables and given/known data The International Space Agency is designing a spaceship to reach the star Proxima Centauri, 4 cyrs (light years) away so that the on-board crew will age 4 years from departure to arrival. How fast must the ship travel? 2. Relevant equations t(moving clock) = t(stationary clock)*sqrt(1-V^2/c^2) t(between ship light clock ticks to us) = 2D/(sqrt(c^2-V^2)) = t(between ticks of our own light clock)/(sqrt(1-V^2/c^2)) 3. The attempt at a solution We must identify which frames we are in. We are wondering how fast the ship must travel, V, to people on Earth. The crew must age 4 years, so we take t' = 4 years, the time it takes for the crew to age (ship frame). The ship must travel a distance of 4 c*yrs, which is in the Earth frame, so we say L = 4c*yrs. This seems like insufficient information. L = 4c*yrs V = ?? unknown, need. t = unknown t' = 4 years V' = ?? L' =??? I suppose, if I can say L' = 4 c*yrs, then I can say that the speed the ship is going at is c (speed of light), but then the equations start to break down so that seems like a dead end. I know that the time of the clock on the ship must be a shorter time change than that of Earth frame. Is there anything that I am stating as false?