Wingeer
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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 Earth's 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.