## How does a GNSS account for relativity?

Among the inevitable problems with any global navigation satellite system, relativistic effects such as time dilation, gravitational frequency shift and eccentricity effects all have to be accounted in order for the system to function correctly.

As explained by the theory of relativity, the clocks on each satellite will run fractionally faster than those on Earth because of their constant movement and height relative to the Earth-centred nonrotating reference frame.

Gravitational frequency shift due to general relativity dictates that a clock close to a massive object (ie the Earth) will run slower than a clock farther away. Therefore, the clocks in GNSS receivers on the Earth's surface will run slower than those in the satellites in orbit around the Earth.

The combined effect of the time dilation and gravitational frequency shift amounts to about 38 microseconds per day. And were this discrepancy not compensated, pseudorange errors of roughly 10 km/day could accumulate.

Finally, as GNSS satellite orbits are elliptical, rather than perfectly circular, both the time dilation and gravitational frequency shift effects will vary with time. This eccentricity effect causes the clock rate difference between a GNSS satellite and a receiver to increase or decrease depending on the altitude of the satellite.

To compensate for the discrepancy, the frequency standard on board each satellite is given a rate offset prior to launch, making it run slightly slower than the same frequency on Earth.