Relativistic effects in the global positioning system

The Global Positioning System (GPS) uses accurate 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 properly accounting for relativistic effects, the system would not work. As a practical matter, therefore, many individuals who use the GPS need to understand how relativistic effects are accounted for in the system. This paper discusses relativistic effects arising from both special relativity and general relativity, and how these effects are incorporated in GPS operations. Two introductory sections on kinematics in special and general relativity, respectively, are followed by a section which describes how relativistic effects should be accounted for. The concept of synchronization in the Earth-Centered Inertial frame is discussed in detail. Numerical and experimental examples are given, showing the sizes of the various effects. The treatment of special and general relativity is sufficiently complete that a person should be able to follow the development without much reference to external material, except that a few standard results have been quoted from textbooks without derivation.