How GPS makes use of General Relativity

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I recently went to a show at the Dow Planetarium that dealt with relativity. Like most science shows designed for the general consumer, it told me little I didn’t already know. I don’t mean that to sound arrogant, I’ve simply been studying astronomy and relativity since grade school. But, it did bring up an intriguing point that I had never considered: without the theories of General and Special Relativity GPSwould be of no use at all.

History of GPS

GPS was developed in the 1960s by the US DoD but its stewardship was later transferred to the IGEBcommittee on which sits members of the Joint Chiefs of Staff, NASA, Department of Defense and the Department of Transportation, among other agencies.
From its inception, GPS had–and still has–the ability to intentionally provide corrupted solutions to receivers through a mechanism called Selective Ability:

SA was a technique implemented by the DOD to intentionally degrade a user’s navigation solution[…]The net result of SA was about a five-fold increase in positioning error. DOD achieved signal degradation by altering (also known as dithering) the satellite clock. Another means designed by DOD to degrade GPS performance was to broadcast less accurate ephemeris parameters.
The DOD-authorized users were able to undo SA. However, due to the fact that SA is spatially correlated, civil users were able to eliminate SA through the implementation of Differential GPS (DGPS), albeit an additional expense on the part of the users.
SA was used to protect the security interests of the U.S. and its allies by globally denying the full accuracy of the civil system to potential adversaries.

A presidential order in May 2001 discontinued the active implementation of SA; though it still remains an option, the military has preferred the tack of locally impeding GPS reception where desirable, rather than diluting the global network.
Something to keep in mind is that it is wholly owned, operated and maintained by the US government. Like a driver’s license, its use by any civilian is a privilege, not a right, and like a driver’s license, most do not understand this.

The Orbital Assets

At any given time there are, as a baseline, 24 satellites in orbit around the Earth, though at the time of this writing there are actually 29 in service. They orbit in such a pattern and altitude (approximately 20 000 km) as to ensure that at least four satellites are visible from a clear horizon from any location on Earth. The group of orbiting GPS satellites is known commonly as the “GPS constellation”.
The GPS constellation is not actually made of a series of satellites in geosynchronous or geostationary orbit–they instead have a period of about half a day. How, then, can we determine our position, one may ask?
For the most simplistic co-ordinate triangulation on Earth, we use a single emitter and at least two receivers. These receivers then compare the times that they received the signal from the common emitter and from that determine its position. What may not be immediately apparent is that this works not because both receivers are stationary but because their relative positions are known at the time of signal acquisition. It is just as easy and reliable to tri-angulate with two receivers on jeeps moving in a random pattern as long as the instantaneous position of both jeeps is known at the time of signal acquisition.
This is precisely how GPS works. The ephemeral data transmitted by the satellite, along with the time from an atomic clock are used to compute the receiver’s position. Though in the previous example we had one emitter and many receivers, many emitters and one receiver work just as well if the emitters broadcast not just a ping but their own co-ordinates and time, as in GPS.

The Role of Relativity

To achieve a navigation resolution of a few metres, the time of the satellites must be known to an accuracy of approximately 30 nanoseconds. However, relativity intervenes to predict that because the satellites are orbiting with a velocity of around 14 000 km/h a ground-based observer will perceive the atomic clocks on the GPS satellites tick more slowly than their own, losing slightly less than 10 microseconds a day. However, because the constellation maintains an extremely high orbit, General Relativity predicts that the weaker distortion of space-time in high orbit compared with the stronger one at the surface of the Earth will cause the clocks on the GPS satellites to tick faster than those on the ground, gaining slightly less than 50 microseconds a day. This leads to a net imprecision of about +35 microseconds that accumulates every day.
Since the time of each satellite must be known to an accuracy of 30 nanoseconds, but the satellites’ clocks gain 35 000 nanoseconds a day, the system becomes useless by the time it takes to start-up most hand-held GPS receivers.

The Simple Remedy

The designers of the GPS constellation took into account the faster atomic clock-ticking predicted by General Relativity and slowed the clocks down so that the observer’s time would appear correct.
As Ohio State University professor of astronomy Richard Pogge put it

Relativity is not just some abstract mathematical theory: understanding it is absolutely essential for our global navigation system to work properly!


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