The Global Positioning System (GPS) is a network of 29 satellites orbiting the Earth at an altitude of ~12,400 miles. GPS was originally created by the US government to help with military navigation, but now if you are holding any type of GPS receiver you can intercept GPS signals. Wherever you are on the planet at least 4 GPS satellites are “visible” to you.
Every GPS satellite has an atomic clock on board. It is a special type of clock that is very accurate. The satellites send a signal in the form of a radio wave, travelling at the speed of light, at regular intervals. Every signal contains the time at which it was sent. When a GPS receiver gets the signal, it uses the Theory of Relativity to calculate the distance the message travelled based on how long it took the message to arrive.
The satellites’ clocks are moving at ~8,700 mph in orbits that circle the Earth twice a day. Einstein’s Theory of Special Relativity says that the rapidly moving clocks tick slower by 7 microseconds per day. Also, because the orbiting clocks are ~12,400 miles above the Earth, the gravity is four times weaker than on Earth. Einstein’s Theory of General Relativity says that gravity curves spacetime, which makes the clocks tick faster by 45 microseconds per day. Both of these facts are very important when calculating the distance between the GPS receiver and the satellites.
How do we know the exact location of a GPS receiver?
The GPS receiver needs at least 4 satellites to pinpoint your location (within 4 meters) using a process called trilateration.
Imagine you are lost somewhere in England and one friendly person comes along and tells you that you’re 39 miles away from central London. Do you know where you are? No, but you can draw a circle around London with a radius of 39 miles. You still don’t know where you are, but you’ve narrowed it down because you know you’re somewhere in the circle.
As you’re working that out, another friendly person comes and tells you that you are 23 miles from Oxford. You do the same thing and draw a circle around Oxford. You still don’t know where you are, but you’ve narrowed it down even more.
Finally, one last friendly person comes and tells you that you are 67 miles from Bristol. Now, do you know where you are? Yes! There should be a point where all of the circles overlap each other, and this is where you are. This is how trilateration works, but instead of circles there are spheres and the Earth acts as the fourth sphere.
If we didn’t use the Theory of Relativity to work out these calculations, when your satellite-navigation tells you there is a petrol station in 400 yards it would be wrong by more than five miles after only one day!
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