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| 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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