# Time dilation earth

1. Jul 31, 2008

### Zman

I have calculated the clock rate difference between the surface of the sun and at the position of the earth’s orbit relative to the sun.

$$t_0 = t_f \sqrt {1 - \frac{{2GM}}{{rc^2 }}}$$

I hope the LaTex equation above is displaying correctly. In the preview it is picking up some other equation.
Should be t0=tf(sqrt(1-2GM/rc^2))

Mass of Sun 2x10^30 kg
Radius of Sun 0.7x10^9m

Radius of earth’s orbit 1.5x10^11
G = 6.67x10^-11 and c=3x10^8

I used the equation for gravitational time dilation and found that the sun lags the earth by approximately 180 ms per earth day.
I ignored all velocity issues as I was only interested in GR issues. I haven’t used any properties of the earth except its distance from the sun.
This is more of a sun question with a satellite at the distance of the earth.

The request that I have if somebody could independently do the calculation to corroborate my result (180 ms per earth day).

Last edited by a moderator: Jul 31, 2008
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