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Problem dealing with a chapter on relativity

  1. May 1, 2006 #1
    I think I know how to do this problem, but need to make sure... so...

    1) In an earth reference frame, a star is 82 light years away. How fast would you have to travel so that to you the distance would only be 35 light years?

    First I have two simple questions:

    1. Light years is in a unit of time or length?

    2. How to convert light years?

    So I would use either:

    a) L = Lo x sqroot(1-v^2/c^2) ~~~> 82 light years = 35 light years x sqr(1-v^2/(3.0 x 10^8)^2)

    or

    b) to = t x sqroot(1-v^2/c^2) ~~~> 35 light years = 85 light years x sqr(1-v^2/(3.0 x 10^8)^2)
     
  2. jcsd
  3. May 1, 2006 #2

    Hootenanny

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    Light years is a unit of length, therefore, you would use Lorentz length contraction. A light year is the distance light can travel in the period of one year.

    ~H
     
  4. May 1, 2006 #3

    mrjeffy321

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    A light year is a unit of length/distance.

    If the distance between the Earth and the star (as seen from Earth) is 82 ly, how much of a contraction would be needed to make the distance only seem like 35 ly in the frame of someone traveling at relativistic velocities?

    Lenth = Proper Length / gamma

    where gamme is the lorentz factor,
    gamma = 1/ sqrt(1 - v^2/c^2)

    If we call "proper length" the length in the Earth's frame of reference, then we solve for gamma to be 82 ly / 35 ly = 2.3429

    Now how fast must an object be flying fast Earth in order to have a lorentz factor this hight?

    2.3429 = 1/ sqrt(1 - v^2/c^2)
    solve for v.
     
    Last edited: May 1, 2006
  5. May 2, 2006 #4
    (also so you cannot use L = Lo x sqroot(1-v^2/c^2)?) Look below.

    could you also have said --> 85 = 35 x sqroot(1-v^2/c^2) and then solve for V?
     
    Last edited: May 2, 2006
  6. May 2, 2006 #5

    Hootenanny

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    You have applied L = Lo x sqroot(1-v^2/c^2) here, which is the correct thing to do. However, I am confused as to why you have used 85 lightyears.

    ~H
     
  7. May 2, 2006 #6
    I mis typed it the first time.
     
  8. May 2, 2006 #7

    Hootenanny

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    Then you are correct, apply lorentz's length contraction and solve for v.

    ~H
     
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