Gravitational time dilation

  1. 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. jcsd
  3. tiny-tim

    tiny-tim 26,053
    Science Advisor
    Homework Helper

    Hi Seedling! :smile:

    (try using the X2 and X2 tags just above the Reply box :wink:)
    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. :smile:

    (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 :wink:).
     
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