Science Puzzle
How Does Your Phone Know Where You Are?
Your phone can show where you are on a map to within a few metres, anywhere on Earth, even in a desert with no phone signal. It does it with help from satellites about 20,000 kilometres up. The satellites don't know where your phone is. They don't even know it exists; they just keep sending out signals.
How does your phone work out where it is?
The Answer
By timing the signals. Each satellite broadcasts exactly when its signal left and where the satellite was. Your phone works out how long each signal took to arrive, turns that into a distance and finds the one spot that's the right distance from every satellite.
The signals are radio waves, which travel at the speed of light, about 300,000 kilometres a second. If a signal took 0.07 seconds to arrive, the satellite is about 21,000 kilometres away. That alone puts you somewhere on a huge imaginary sphere around that satellite. A second satellite narrows it to a circle where two spheres meet, and a third to a single point. The phone's own clock isn't nearly good enough, so it uses a fourth satellite to correct its clock as well.
The timing has to be astonishingly precise. Light travels 30 centimetres in a billionth of a second, so a clock that's a millionth of a second out puts you 300 metres off. Each satellite carries atomic clocks, and even Einstein's relativity has to be allowed for: up there, the clocks run about 38 millionths of a second a day faster than clocks on the ground. Left uncorrected, that would move your dot on the map by about 10 kilometres every day, so the clocks are set to tick slightly slow before launch.
The principle: Position from timing. Knowing exactly when a signal was sent and how fast it travels gives the distance to its source, and distances to several known points pin down a single position.