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Spaceship Question

  1. Dec 9, 2004 #1
    How fast must a spaceship be traveling relative for one day on the spacecraft to equal 2 days on Earth? I'm pretty sure that t(0) = 172,800 seconds, and t = 86,000 seconds. Do I just need to use ∆t = t – t(0), simplify that to t = γt(0), and then since γ = 1+ (1/2)(v^2)/(c^2); take the resulting equation and just resolve for v?
  2. jcsd
  3. Dec 9, 2004 #2
    If I remember correctly, you will want to use the relativistic equation for gamma and not the approximation for speeds much lower than the speed of light. So,
    gamma = 1/(sqrt(1-(v^2/c^2))) Otherwise, using the aproximation will yeild a speed faster than the speed of light which is not possible.
  4. Dec 9, 2004 #3
    I'm ending up with v = sqrt{(((t(0)^2)(c^2))/(∆t^2))-c^2} Can someone please check my math?
  5. Dec 9, 2004 #4
    Close, it may be easier to notice that gamma = (earth time) / (spaceship time)

    So, gamma = 2 in your case. Should be easy from here . . .
  6. Dec 9, 2004 #5
    How does gamma equal earth time/ spaceship time or 2? Is this just though simplification?
  7. Dec 9, 2004 #6
    So I can just set gamma equal to 2, and solve for v!
  8. Dec 9, 2004 #7
    Yes, that should do the trick.
  9. Dec 9, 2004 #8
    Thanks a bunch Olaf.
  10. Dec 9, 2004 #9
    If gamma =2, then 2 = 1/(1+(v^2)/(c^2)), thus leaving you with a negative value when you simplify for v.
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