How GPS works: how your phone knows where you are
How GPS measures distance with nothing but a clock
A GPS satellite never measures how far away you are. Your phone works it out alone, with a clock and no ruler. How do you measure 20,000 km with a clock?
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Back on the trail, your phone hears satellite 7: "I sent this at exactly 10:42:05." By your phone's own clock, the signal arrives a tiny moment later: 0.07 seconds late.
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The signal is a radio wave, and radio travels at the speed of light: about 300,000 km every second. In 0.07 seconds, it covers about 21,000 km. That is how far away satellite 7 is. It is a bit more than 20,000 km, because satellite 7 is not straight above you.
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But how can a phone time something so short? The signal carries a pattern of short pulses, on and off, and each satellite has its own. Your phone makes the same pattern itself, then slides its copy until the two line up. How far it had to slide is the delay.
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One distance is not yet a place. You could be anywhere at 21,000 km from satellite 7. On a map of the world, all those places make a huge circle, and you are somewhere on it.
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There is a catch. Light is so fast that a clock wrong by one millionth of a second makes the distance wrong by 300 m.
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The satellites carry atomic clocks, far better than any watch. Your phone has a cheap clock, often wrong by far more than a millionth of a second. So how can it time light at all?
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