100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

Relativity in the Global Positioning System 273Fractional Frequency Shift x 10^126004002000-200ShuttleGPS GeostationaryGLONASS20000 40000 60000 80000 100000Radial distance in kilometersFig. 2.Net fractional frequency shift of clock in a circular orbit.by general relativity, then the synthesizer could be turned on, bringing theclock to the coordinate rate necessary for operation. After the cesium clockwas turned on in NTS-2, it was operated for about 20 days to measureits clock rate before turning on the synthesizer. 13 The frequency measuredduring that interval was +442.5 parts in 10 12 compared to clocks on theground, while general relativity predicted +446.5 parts in 10 12 . The differencewas well within the accuracy capabilities of the orbiting clock. Thisthen gave about a 1% verification of the combined second-order Dopplerand gravitational frequency shift effects for a clock at 4.2 earth radii.Additional small frequency offsets can arise from clock drift, environmentalchanges, and other unavoidable effects such as the inability to launchthe satellite into an orbit with precisely the desired semimajor axis. Thenavigation message provides satellite clock frequency corrections for usersso that in effect, the clock frequencies remain as close as possible to the frequencyof the U. S. Naval Observatory’s reference clock ensemble. Becauseof such procedures, it would now be difficult to test the frequency offsetpredicted by relativity.When GPS satellites were first deployed, the specified factory frequencyoffset was slightly in error because the important contribution from earth’s