# Gravitational time dilation

1. Feb 15, 2010

### Seedling

1. The problem statement, all variables and given/known data

Calculate the difference in time after one year between a clock at Earth's surface and a clock on a satellite orbiting at 300 km above the surface

2. Relevant equations

T = T0 / (1 - 2gR/c^2)^.5

That is, this:
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/imgrel/gtim3.gif

3. The attempt at a solution

I don't understand how to use this equation to get the difference between the clock on the satellite and the clock on the surface. Do I just take the value of T with R = Earth's radius, and again with R = Earth's radius + 300 km, and take the difference?

2. Feb 16, 2010

### tiny-tim

Hi Seedling!

(try using the X2 and X2 tags just above the Reply box )
The ratio, rather than the difference …

T0 is the time on a clock "at infinity", and TR is the time on a clock at radius R, so TR/T0 is the ratio of their "speeds", and TR=h/TR is the ratio you want.

(But remember that this formula only gives you the general relativity time dilation … there'll also be an ordinary Lorentz time dilation, in the opposite direction ).