sunearthday.nasa.gov |
Title Page
GPS Satellites Special Relativity
General Relativity
Application to GPS Satellites
Bibliography |
http://upload.wikimedia.org/wikipedia/commons/8/8d/GPS_Satellite_NASA_art-iif.jpg |
We've seen that
Special Relativity and General Relativity will both have
opposite effects on how fast or slow the clock on the
satellite is compared to our time on the surface of
Earth. Special Relativity will make the time on the
satellite go slower than our time measured on Earth since it
is traveling at a much higher rate of speed compared to
us. General Relativity will make our time on Earth
move slower compared to the time on the satellite since we
are closer to the Earth's gravitational field. So
using the equations for both Special and General Relativity,
we must adjust the time on the satellites so that they can
be used to calculate our physical positions using
trilateration. These GPS satellites must be accurate to within 20-30 nanoseconds in order for us to receive an accurate measurement of our position. According to Richard Pogge in his "GPS and Relativity", Special Relativity will cause the clocks on orbiting GPS satellites to fall behind by 7 microseconds each day, but General Relativity would cause our clocks on Earth to fall behind the satellite's time by 45 microseconds each day. A microsecond doesn't sound like much, nor does the net 38 microsecond difference in time each day that would occur between our clocks and the satellite clock. However, if that 38 microsecond difference due to Special and General Relativity wasn't corrected for, our GPS locations would be up to 10 km off after only 1 day! (Pogge) |
http://www.crownedanarchist.com/emc2/images/larson_mc2.jpg Cartoon by Gary Larson |
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