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Time dilation problem

  1. Nov 13, 2012 #1
    The distance to Alpha Centauri is 4,3 light years. How fast would a space ship have to travel to get there in 10 years, according to the crew?

    The answer *should* be 0,395c. So far I've gotten all sorts of answers but not much close, so I seem to be approaching the problem the wrong way.
     
  2. jcsd
  3. Nov 13, 2012 #2

    Doc Al

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    Staff: Mentor

    Show what you've done so far.

    Hints: What's the basic idea of time dilation? What's the definition of velocity?
     
  4. Nov 13, 2012 #3
    The first part of the assignment asks for the time required when traveling at 30% of light speed. Given a gamma factor of 1,048 I get ~13,7 years, which is correct (so the gamma factor must be correct as well).

    velocity = distance / time

    But...

    for t = 10 and d = 4,3

    v = 4,3 / 10
    v = 0,43, which is wrong

    taking length contraction into account gives

    4,3/1,048 = 4,1

    v = 4,1 / 10
    v = 0,41, which is still wrong
     
  5. Nov 13, 2012 #4

    Doc Al

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    Staff: Mentor

    Good. Keep going.

    From Earth's viewpoint, you have the distance. What's the time?
     
  6. Nov 13, 2012 #5
    Hmm... i don't know. :/

    The distance is 4,3 ly but I don't know the speed, so how do I find the time?
     
  7. Nov 13, 2012 #6
    Hang on... the time for the crew is 10 years so the time for the observer is t/gamma

    10/1,048 = 9,54 years

    Edit: no that's not right....... I have no idea what I'm doing

    Edit2: the time from earths viewpoint is d * gamma = 4,3 * 1,048 = 10,48 years, while the time is 10 years for the crew
     
  8. Nov 13, 2012 #7

    Doc Al

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    You have that reversed. If the ship time is 10 years, then to earth observers it will be longer: t*gamma, not t/gamma.

    In addition to what I already pointed out, do not use the gamma from the previous part of the question.

    So continue with that velocity equation, v = d/tearth.
     
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