Relativity in the Global Positioning System

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.

Figure 1

Typical Allan deviations of Cesium clocks and quartz oscillators, plotted as a function of averaging time τ.

Figure 2

Net fractional frequency shift of a clock in a circular orbit.

Figure 3

TOPEX clock bias in meters determined from 1,571 observations.

Figure 4

Rms deviation from mean of TOPEX clock bias determinations.

Figure 5

Comparison of predicted and measured eccentricity effect for SV nr. 13.

Figure 6

Generic eccentricity effect for five satellites.