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Time dilation in gravitational field

  • Thread starter Wingeer
  • Start date
  • #1
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Homework Statement


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.

Homework Equations



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

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.
 

Answers and Replies

  • #2
76
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Oh. It looks like something happened to the LaTex-codes. Any ideas of what to do?
 

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