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Re: Re: Re: Re: Re: Re: Re: Re: One More Thought

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Posted by Bruce on February 7, 2001 04:51:50 UTC

Your the one who thinks absolute truth comes from a bible. I happen to know that GR is right. Alexander gave you a simple formula to calculate the expected differences in wristwatch time due to position in the gravitational well. I'm going to go one step further and show you how to calculate the difference between the rate of atomic clocks in GPS satellites and Earth based GPS atomic clocks. This is the same thing as your tower but it also includes difference in clock rates due to speed.
This is a solution of Einstein's equation called the Schwarzchild solution.
dt2=dt2shell=(1-2M/r)dt2-dr2/(1-2M/r)-r2df2
shell can be viewed as a orbit around the center of mass.
v2=r2df2
The orbit of the GPS satellite clock
dtsat
The orbit of the Earth clock
dtEarth
From there we can build a formula for predicting (using relativity) the difference in clock rates for GPS satellite and ground based clocks.
dtsat/dtEarth=[1-2M/rsat-v2sat]1/2/[1-2M/rEarth-v2Earth]1/2
Doing a small number thingy and multiplying out
dtsat/dtEarth=1-M/rsat-v2sat/2+M/rEarth+v2Earth/2
This is in geometric units so
M=.00444meter
rsat=26.655x106meter
rEarth=6.4x106meter
vsat=.000012923c
vEarth=.000001551c
plug the numbers into the formula and the answer will be that the GPS satellite clocks will run faster than GPS Earth clocks by 38,407 nanoseconds per day. This is what Einstein predicts and this is what actually happens. If the correction wasn't made the GPS system would immediately decrease in accuracy to the point it would be useless within minutes. Continuous validation or GR prediction and observation.
http://vishnu.nirvana.phys.psu.edu/mog/mog9/node9.html


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