The reason the satellite clocks run faster than the ground based clocks is because the gravitational time dilation effect is greater than the time dilation effect due to relative motion (for the GPS system case). Starting with the Schwarzchild metric (the first solution to Einstein's equation). In geometric units:
dt2=(1-2M/r)dt2 - dr2/(1-2M/r) - r2df2

Set dr=0, divide the metric by the square of bookkeeper time dt2 and set -r2(df/dt)2= -v2 to obtain for either satellite or Earth clocks

(dt/dt)2=(1-2M/r)-v2

We can write the above equation for both satellite and Earth clocks and find the ratio of time lapses recorded on the clocks.

dtsat/dtEarth=(1-2M/rsat-v2sat)1/2(1-2M/rEarth-v2Earth)-1/2

We can apply (1+d)n ~ 1+nd provided |d|

• satellite - rbwinn - May 18, 2001 - 06:56 UTC
  • As you've been told many times... - bruce - May 18, 2001 - 21:07 UTC
    • adieu - rbwinn - May 19, 2001 - 19:41 UTC
      • I would like you.. - bruce - May 19, 2001 - 20:45 UTC
        • velocity - rbwinn - May 20, 2001 - 04:36 UTC
          • The only thing you've proven.. - bruce - May 20, 2001 - 22:54 UTC
            • adieu again - rbwinn - May 21, 2001 - 23:16 UTC
              • You are a fool - bruce - May 21, 2001 - 23:35 UTC
                • You are a name caller - rbwinn - May 22, 2001 - 13:10 UTC