- #1
erincaldwell
- 1
- 0
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!
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!