I'm working on a simple time dilation problem: Astronomers discover a planet orbiting around a star similar to our sun that is 20 LY away. How fast must a rocket ship go if the round trip is to take no longer than 40 years in time for the astronauts aboard? I have set up the problem: T= L/v=T[o]/√(1-v^2/c^2) where v is velocity and c is the speed of light and T[o] is proper time. So: = [2*(20LY)*(9.5*10^15 m/LY)]/v = 40 years/√(1-v^2/c^2). Now I need to solve for v. I don't know how to get v alone. I tried squaring both sides and ended up with an equation like T[o]^2/L^2 + c^2 = v^2 , but that doesn't get me the right answer. Please help! I'm going crazy!