Error analysis for the Global Positioning System: Difference between revisions

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m Selective Availability: Add data to reference
m Kinetic time dilation: Inserted absent comma, as in the subsequent "That is, the combination of Special and General effects ..."
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: <math> -8.349\times 10^{-11}\times 60\times 60\times 24\times 10^9\approx -7214 \text{ ns} </math>
 
That is, the satellites' clocks are slower than Earth's clocks by 7214 nanoseconds a day due to their velocity.
 
: Note that this speed of {{val|3874|u=m/s}} is measured relative to Earth's center rather than its surface where the GPS receivers (and users) are. This is because Earth's equipotential makes net time dilation equal across its geodesic surface.<ref>{{Cite web |last=S. P. Drake |date=January 2006 |title=The equivalence principle as a stepping stone from special to general relativity |url=http://www.phys.unsw.edu.au/einsteinlight/jw/2006AJP.pdf |website=Am. J. Phys., Vol. 74, No. 1 |pages=22–25}}</ref> That is, the combination of Special and General effects make the net time dilation at the equator equal to that of the poles, which in turn are at rest relative to the center. Hence we use the center as a reference point to represent the entire surface.