# Time dilation in gravitational field

1. Apr 19, 2009

### Wingeer

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.
There is no tricky calculations, or anything like that. The task aims at proving an expression.

$$\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)}}} }}\$$

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

2. Relevant equations

$$\tau = \sqrt {1 - \frac{{2\gamma M}}{{c^2 r}}} t\$$

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. Apr 19, 2009

### Wingeer

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