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Stuck on Algebra in Time Dilation Problem.

  1. Oct 17, 2011 #1
    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!
     
  2. jcsd
  3. Oct 18, 2011 #2
    This is the basic equation that you have written out.

    [tex]\frac{d}{v} = \frac{t}{\sqrt{1- \frac{v^2}{c^2}}}[/tex]

    Solving for v gives:

    [tex]v = \frac{cd}{\sqrt{d^2+c^2t^2}}[/tex]

    where
    c = speed of light constant
    d = distance in metres
    t = time (on spaceship) in seconds
    v = velocity in m/s

    At least by my reckoning!
     
    Last edited: Oct 18, 2011
  4. Oct 19, 2011 #3
    If you want me to run through the procedure that I used to get the new equation in v then I'd be happy to run through it for you.
     
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