Abstract

The 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 using GPS. Relativistic principles and effects which must be considered include the constancy of the speed of light, the equivalence principle, 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. Recently frequency jumps arising from satellite orbit adjustments have been identified as relativistic effects. These will be explained and some interesting applications of GPS will be discussed.

Highlights

  • The Global Positioning System (GPS) can be described in terms of three principal “segments”: a Space Segment, a Control Segment, and a User Segment

  • The GPS is a remarkable laboratory for applications of the concepts of special and general relativity

  • GPS is valuable as an outstanding source of pedagogical examples

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Summary

Introduction

The Global Positioning System (GPS) can be described in terms of three principal “segments”: a Space Segment, a Control Segment, and a User Segment. The Space Segment consists essentially of 24 satellites carrying atomic clocks. Tied to the clocks are timing signals that are transmitted from each satellite. These can be thought of as sequences of events in spacetime, characterized by positions and times of transmission. Associated with these events are messages specifying the transmission events’ spacetime coordinates; below I will discuss the system of reference in which these coordinates are given. Additional information contained in the messages includes an almanac for the entire satellite constellation, information about satellite vehicle health, and information from which Universal Coordinated Time as maintained by the U.S Naval Observatory – UTC(USNO) – can be determined

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