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The Greatest Time Traveler

  1. Nov 10, 2009 #1
    The greatest time traveler we have so far, Sergei Krikalyov, spent 803 days in space, orbiting the earth at 17,000 miles per hour. As a result of this he has traveled 1/48 of a second into the future.

    I am curious how much gravity affected the calculation of Sergei Krikalyov's fraction of a second time travel to the future?
     
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  3. Nov 10, 2009 #2

    tiny-tim

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    Hi sciroccokid! :smile:

    From the PF Library on time dilation (substitute "Krikalyov" for "clock" :wink:) …

    Gravitational time dilation in static metric:

    [tex]\sqrt{\frac{g_{00}(clock)}{g_{00}(observer)}}\ \simeq\ \sqrt{\frac{1\ -\ 2U(clock)}{1\ -\ 2U(observer)}}\ \simeq\ 1\ -\ U(clock)\ +\ U(observer)\ =\ 1\ -\ \Delta\,U[/tex]

    Schwarzschild (static metric) gravitational potential at distance r from mass M:

    [tex]U\ =\ \frac{2GM}{rc^2}\ =\ \frac{2gr}{c^2}[/tex]
     
  4. Nov 10, 2009 #3
    Thank you Sir. However, you have not taken into account the fact that you are of a vastly superior intellect then I. Is there any way to answer that equation, with some thing like "1/30 of earth's gravity."

    Sergei was traveling at 17,000 mph & traveled 1/48 of a second into the future after 803 days. I suppose we could find the "altitude" somewhere.

    Can any one out there find the solution to this?
     
  5. Nov 10, 2009 #4

    tiny-tim

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    Hi sciroccokid! :smile:
    I'm only a little goldfish. :blushing: :rolleyes:

    I just know where to look things up. :smile:
    I was expecting you would tell us what the altitude was …

    once you have that, just mulitply it by g/c2, where g = 9.81 m/s2. :smile:
     
  6. Nov 10, 2009 #5
    The altitude is about 173 Mi (278km)...
     
  7. Nov 11, 2009 #6
    Lets check: for the time delay due to special relativity, we have

    [tex] \Delta t = (\gamma -1) T [/tex]

    where T = 803 days and [tex] \gamma \simeq 1 - v^2/2c^2 [/tex]. This gives the result [tex] \Delta t = 0.02 \sec [/tex] which is what you quoted. This means that time passes more slowly for the astronaut, meaning that he 'travels into the future'.

    Now, for gravitational time dilation you have

    [tex] \Delta t \simeq -\Delta U T \simeq -0.004 \sec, [/tex]

    so special relativity makes him travel 0.02 seconds into the future and general relativity makes the rest of the world travel 0.004 seconds into the future.
     
  8. Nov 11, 2009 #7
    Notice btw, how the time dilation due to SR is proportional to v^2, and the time dilation due to GR is proportional to r (on small speeds and distances), meaning that the magnitude of the effects would be reversed for example in an aeroplane.
     
  9. Nov 11, 2009 #8
    Can you please clarify more on that please? How can he make the whole world travel to future?
     
  10. Nov 11, 2009 #9

    tiny-tim

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    Welcome to PF!

    Hi Elvin12! Welcome to PF! :smile:
    He means the surface of the Earth, not the whole universe. The stronger gravity dilates time more, and so a clock on Earth will go very slightly more slowly than a clock on the spaceship.

    This is the opposite effect to the special relativity effect … so speed makes the Earth clock go faster than the spaceship clock.
    Hi clamtrox! :smile:

    I think "travel into the future" is a bit misleading when he's actually getting comparatively yonger (and will remain so when he comes back to Earth)…

    though it enables him to travel into the future without dying!

    I think it's clearer to say that speed makes him age slightly less, but the weaker gravity makes him age very slightly more. :wink:
     
  11. Nov 11, 2009 #10
    Did you know that in the future we're all going to die?!!?

    -Stephen Colbert
     
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