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Time dilation in gravitational field

  1. Apr 19, 2009 #1
    1. The problem statement, all variables and given/known data
    I recently had a test in the theory of relativity, and there was one task which I could not solve. This one has bothered me since the day I had the test.
    It was a compound task about GPS-satellites.
    There is no tricky calculations, or anything like that. The task aims at proving an expression.

    [tex]\frac{{t_e }}{{\sqrt {1 - \frac{{2\gamma M}}{{c^2 r}}} }} = \frac{{t_s }}{{\sqrt{1 - \frac{{2\gamma M}}{{c^2 (r + h)}}} }}\[/tex]

    Where [tex]{t_e }\[/tex] is the time on earths surface, [tex]{t_s }\[/tex] is the time for the satellite, r is the radius from the center of earth to the surface.

    2. Relevant equations

    [tex]\tau = \sqrt {1 - \frac{{2\gamma M}}{{c^2 r}}} t\[/tex]

    3. The attempt at a solution
    I've tried a lot of editing these expressions, but it didn't get me anywhere. I really do not now how to prove the expression. I do imagine that there are some theory I need to figure, so that I can do something quirky with the expressions or something.
     
  2. jcsd
  3. Apr 19, 2009 #2
    Oh. It looks like something happened to the LaTex-codes. Any ideas of what to do?
     
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