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Time Dilation relativity

  1. Mar 17, 2009 #1
    1. The problem statement, all variables and given/known data
    The Voyager 1 space probe, launched in 1977, is moving faster
    relative to the earth than any other human-made object, at 17,000
    meters per second.
    (a) Calculate the probe's
    . p
    (b) Over the course of one year on earth, slightly less than one year
    passes on the probe. How much less?


    2. Relevant equations
    [tex]\gamma[/tex]=1/[tex]\sqrt{}1-(v/c)^2[/tex]


    3. The attempt at a solution
    I calculated the [tex]\gamma[/tex] but i dont know how to get answer (b)
     
  2. jcsd
  3. Mar 17, 2009 #2

    Doc Al

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    Staff: Mentor

    What's the time dilation formula?
     
  4. Mar 17, 2009 #3
    What it says for the formula. On my first post.[tex]\gamma[/tex]=1/[tex]\sqrt{}1-(v/c)^2[/tex]
     
  5. Mar 17, 2009 #4

    Doc Al

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    That's just the definition of gamma, a factor that appears in many relativistic formulas. What's the formula for time dilation? (It will certainly involve gamma, but also T and T'.)

    Look here: https://www.physicsforums.com/showpost.php?p=905669&postcount=3"
     
    Last edited by a moderator: Apr 24, 2017
  6. Mar 18, 2009 #5
    [tex]\Delta t = \gamma(\Delta + v\Delta /c^2)[/tex]
    By the way what does [tex]\Delta[/tex] mean?
     
    Last edited: Mar 18, 2009
  7. Mar 18, 2009 #6

    Doc Al

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    That's not the one you want. (Look for "time dilation".)
    Δ means "change"; Δt represents a time interval.
     
  8. Mar 18, 2009 #7
    [tex]T[/tex]=[tex]\frac{}{}t/\sqrt{}1-(v/c)^{}2[/tex]
    This is the one in my text book.
     
  9. Mar 18, 2009 #8
    If thats the right formula I think I got the right answer, T= 31000000.05 seconds have passed for the 31000000 seconds on earth.
     
  10. Mar 18, 2009 #9
    I think you have the values of T and t_0 mixed up. Remember time dilation would mean that slightly less time passes for the probe.
     
  11. Mar 18, 2009 #10

    Doc Al

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    Yes, it looks like you mixed things up. The rule to remember is that moving clocks run slow by a factor of gamma. Viewed from earth, the earth clocks read a longer time than does the moving probe clock.

    Since the speed is quite a bit less than c, I suggest using a binomial approximation for gamma.
     
  12. Mar 18, 2009 #11
    So i just redid it and i got 30,999,999.95 seconds passed on the probe. Is that right?
     
  13. Mar 18, 2009 #12

    Doc Al

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    Figure out how many fewer seconds passed on the probe, not the total number of seconds.
     
  14. Mar 18, 2009 #13
    .05 seconds?
     
  15. Mar 18, 2009 #14

    Doc Al

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    Sounds good.
     
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