How Does Gravitational Time Dilation Affect Clocks on Earth and Satellites?

[Seedling]

Homework Statement

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

Homework Equations

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

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

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?

 

[tiny-tim]

Hi Seedling!

(try using the X² and X₂ tags just above the Reply box )

T = T0 / (1 - 2gR/c^2)^.5
…
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?

The ratio, rather than the difference …

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