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Most of us use satellite navigation every day without giving it a second thought. A phone can tell us within a few metres where we are standing, almost anywhere on Earth. The system behind this, the Global Positioning System or GPS, was developed by the United States military and became fully operational in 1995. Today it is used by everyone from farmers to delivery drivers.
GPS relies on a group of around thirty satellites orbiting about 20,000 kilometres above the Earth. Each satellite carries extremely accurate atomic clocks and constantly broadcasts a signal that says, in effect, "This is satellite number such-and-such, and the time is exactly this."
A GPS receiver, such as the one in your phone, does not send anything back to the satellites. It simply listens. Because radio signals travel at the speed of light, the receiver can work out how far away each satellite is by measuring how long its signal took to arrive. If a signal took a tiny fraction of a second longer than another, that satellite must be further away.
Knowing the distance to one satellite only tells you that you are somewhere on a huge imaginary sphere around it. With signals from several satellites, however, the receiver can find the single point where these spheres meet. In practice, a receiver needs signals from at least four satellites: three to fix its position and a fourth to correct the small errors in its own clock, which is far less accurate than those in space.
Remarkably, the system must also take Einstein's theories of relativity into account. Because the satellites are moving fast and are further from the Earth's gravity, their clocks run very slightly faster than clocks on the ground, by about thirty-eight millionths of a second per day. That sounds insignificant, but if engineers ignored it, positions would become wrong by roughly ten kilometres every day.
GPS is no longer the only system of its kind. Europe, Russia and China have each built their own, and many modern phones use signals from several systems at once, which makes them faster and more accurate, especially in cities where tall buildings block part of the sky.