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Relativity(Light years)? PLEASE HELP!

  1. Apr 12, 2010 #1
    Relativity(Light years)??? PLEASE HELP!

    1. The problem statement, all variables and given/known data
    Imagine an astronaut on a trip to Siris, which is 8 light years from Earth. On arrival at Siris,
    the astronaut finds that the trip lasted 6 years. If the trip was made at a constant speed of .8c, how can the 8 light year distance be reconciled with the 6 year duration?


    2. Relevant equations
    E=mc^2


    3. The attempt at a solution
    I don't know how to solve this question....8 light years-> 6 years. 3/.8c??
    Please help!
     
  2. jcsd
  3. Apr 12, 2010 #2

    tiny-tim

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    Hi SAT2400! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    (e = mc2 has nothing to do with it … and i think it's Sirius :wink:)

    the astronaut's measurement of the time (on his own clock) is 6 years

    what is his measurement of the distance?
     
  4. Apr 12, 2010 #3
    Re: Relativity(Light years)??? PLEASE HELP!

    The relevant equations are:

    γ=1/root(1-v2/c2)
    t'=γt
    x=γx'

    The 6 years is measured from his frame of reference, you need to measure the distance in the same frame as well.
     
  5. Apr 15, 2010 #4
    Re: Relativity(Light years)??? PLEASE HELP!

    hmm, can you explain more easily/??:(

    Thanks !!
     
  6. Apr 15, 2010 #5

    tiny-tim

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    Hi SAT2400! :wink:

    Do you know the Lorentz transformation equations?

    (you didn't mention them in your "Relevant equations")

    If not, look them up in your book. :smile:
     
  7. Apr 15, 2010 #6
    Re: Relativity(Light years)??? PLEASE HELP!

    root of( 1-v^2/c^2) ...is this right??

    hmm...could you please explain more in detail??

    Sorry,,but I still don't know how to solve this question....:(
     
  8. Apr 15, 2010 #7

    tiny-tim

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    Sort-of …

    but how are you going to use it? :smile:
     
  9. Apr 17, 2010 #8
    Re: Relativity(Light years)??? PLEASE HELP!

    I still have no idea.......T_T

    If I knew how to do this,,I would have not come to this website.......

    SO...

    Please help!!!!

    THank you very much!
     
  10. Apr 18, 2010 #9

    tiny-tim

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    Use x and t for the coordinates in the Earth's frame (so Sirius is at x = 8, for all t).

    Use x' and t' for the coordinates in the astronaut's frame.

    Start the trip at (0,0) in both frames.

    What do you get? :smile:
     
  11. Apr 18, 2010 #10

    Matterwave

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    Re: Relativity(Light years)??? PLEASE HELP!

    For one such as yourself, who seems to have a very rudimentary understanding of SR, I wouldn't bother with Lorentz transforms. For the question all you need to utilize is Length-contraction.

    To the people traveling on the rocket, the length between Earth and Sirius is contracted to: [tex]L=L_0\sqrt{1-\frac{v^2}{c^2}}[/tex] The time that they measure is then simply: [tex]t=L/v[/tex]

    Now you will notice that since L is contracted, it is no longer 8 light years but something shorter, and hence t can be shorter than 8 years without the rocket traveling faster than c.
     
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