Satellites high above you each shout, over and over, 'it is exactly this time, and I am here.' Your phone hears each message a tiny bit late, because the signal took time to travel down, and that delay tells it how far away that satellite is. One distance puts you somewhere on a huge sphere; two narrow it to a ring; three pin you to a point. That's it: GPS is finding where a few distance-spheres cross.
Most people think your phone transmits its location to satellites. In fact GPS is receive-only: each satellite broadcasts its position and the time, and your phone works out its distance from how late each message arrives.
What's actually happening
There is something almost magical about a little phone knowing, anywhere on Earth, exactly where it is. But there is no magic and, surprisingly, no transmitter in your phone reporting its location — GPS is entirely a listening exercise. High above you, a fleet of satellites does one simple thing forever: each broadcasts a message that says, in effect, "I am satellite number seven, here are my exact coordinates, and the time right now is precisely this." Your phone just listens.
The trick is that the message arrives slightly late. Radio waves travel at the speed of light, fast but not infinite, so a signal from a satellite 20,000 km up takes about a fifteenth of a second to reach you. Your phone compares the time stamped in the message with the time it actually arrived, and that tiny delay, multiplied by the speed of light, is exactly how far away the satellite is. Knowing your distance from one satellite places you somewhere on an enormous sphere around it. A second satellite's sphere cuts that down to a circle where the two overlap. A third narrows it to a point. The simulator shows it directly: two range-rings leave you guessing between two spots, but three rings cross at one place — you.
There is one beautiful catch that makes GPS far cleverer than it first appears. Measuring distance from time only works if your phone's clock agrees with the satellites' to the nanosecond — and a billionth of a second of error is about 30 cm of position error. Satellites carry atomic clocks; your phone has a cheap one. The fix is to use a fourth satellite: with four spheres and four equations, the receiver can solve not just for its three coordinates but for its own clock error too, correcting itself on the fly. That's why GPS needs four satellites in view, not three. And because the satellites move so fast and sit so deep in Earth's gravity, their clocks must be corrected for Einstein's relativity, both special and general, or GPS would drift kilometres off within a day. Your morning commute quietly runs on the theory of relativity.
GPS finds you by listening to flying clocks and crossing distance-spheres — and a nanosecond of timing error is 30 cm, so your commute quietly runs on Einstein's relativity.
- 1On paper, mark three friends' houses. Imagine someone tells you only "I'm 2 km from Anna, 3 km from Ben, 1.5 km from Cara."
- 2Draw a circle of each radius around each house. The single point where all three circles cross is the only place that satisfies all three distances.
- 3That point is the mystery location — and it's exactly what your phone computes, except with spheres in 3D and satellites instead of friends.
Common questions
Three spheres fix your position, but only if your phone's clock matches the satellites' to the nanosecond. A fourth satellite lets the receiver solve for its own clock error too, correcting itself on the fly.
No. GPS is receive-only — your device listens silently and does the sums locally. The idea of satellites tracking you is backwards.
Yes. The satellites move fast and sit high in Earth's gravity, so their clocks must be corrected for both special and general relativity, or GPS would drift kilometres off within a day.