Relation GPS and relativity theory S1150048 Takefumi Ogata
Outline●Introduction●GPS●Sagnac effect●How to calculate●Consideration●Result and Conclusion
IntroductionThe Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without carefully accounting for numerous relativistic effects, the system would not work. This paper discusses the conceptual basis, founded on special and general relativity, for navigation usingGPS. Relativistic principles and effects which must be considered include the constancy of the speed of light, the equivalenceprinciple, the Sagnac effect, time dilation, gravitational frequency shifts, and relativity of synchronization. Experimental tests of relativity obtained with a GPS receiver aboard the TOPEX/POSEIDON satellite will be discussed.
GPS GPS is a space-based global navigation satellite system thatprovides reliable location and time information in all weather and at all times and anywhere on or near the Earth when and where there is an unobstructed line of sight to four or more GPSsatellites. It is maintained by the United States government and is freely accessible by anyone with a GPS receiver. In addition toGPS other systems are in use or under development. The Russian GLObal NAvigation Satellite System was for use by the Russian military only until 2007. There are also the planned ChineseCompass navigation system and Galileo positioning system of the European Union. GPS was created and realized by the U.S. Department of Defense and was originally run with 24 satellites.It was established in 1973 to overcome the limitations of previous navigation systems
Sagnac effect The Sagnac effect named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams aremade to follow a trajectory in opposite directions. To act as a ringthe trajectory must enclose an area. On return to the point of entry the light is allowed to exit the apparatus in such a way that an interference pattern is obtained. The position of the interference fringes is dependent on the angular velocity of the setup. This arrangement is also called a Sagnac interferometer.
ConsiderationIn the ECEF frame used in the GPS, the unit of timeis the SI second as realized by the clock ensemble ofthe U.S. Naval Observatory, and the unit of length isthe SI meter. This is important in the GPS because it means that local observations using GPS areinsensitive to effects on the scales of length and time measurements due to other solar system bodies, that are time-dependent.
Result and Conclusion GPS can be used to compare times on two earth-fixed clocks when a single satellite is in view from both locations. This is the ¡Ècommon-view É method of comparison of Primary standards, whose locations on earth¡Çs surface are usually known veryaccurately in advance from ground-based surveys. Signals from a single GPS satellite in common view of receivers at the two locations provide enough information to determine the timedifference between the two local clocks. The Sagnac effect is very important in making such comparisons, as it can amount to hundreds of nanoseconds, depending on the geometry.
Conclusion In 1984 GPS satellites 3, 4, 6, and 8 were used in simultaneous common view between three pairs of earth timing centers, to accomplish closure in performing an around-the-world Sagnacexperiment. The centers were the National Bureau of Standards in Boulder, CO, Physikalisch-Technische Bundesanstalt in Braunschweig, West Germany, and Tokyo Astronomical Observatory . The size of the Sagnac correction varied from 240to 350 ns. Enough data were collected to perform 90 independentcircumnavigations. The actual mean value of the residual obtained after adding the three pairs of time differences was 5 ns, which was less than 2 percent of the magnitude of the calculated total Sagnac effect.