GPS satellites run their clocks slow on purpose

The atomic clocks on GPS satellites would gain 38 microseconds a day on clocks on the ground. Left alone, that tiny slip would push positions off by around ten kilometres a day.

A GPS receiver finds you by timing. Each satellite carries an atomic clock and keeps broadcasting the time and where it is. The receiver compares signals from several satellites, works out how long each one took to arrive, and turns those delays into distances.

Radio waves travel at the speed of light, about 30 centimetres in a billionth of a second, so tiny timing errors become large errors in distance. To place you within a few metres, the satellites' clocks have to be known to within 20 to 30 nanoseconds.

The satellites orbit about 20,000 kilometres up, at roughly 14,000 kilometres an hour, going round the Earth about twice a day. Both the height and the speed change how their clocks run, compared with clocks on the ground.

Two effects pulling opposite ways

Einstein's special relativity says a moving clock ticks more slowly than one at rest. At the satellites' speed, their clocks fall behind ground clocks by about 7 microseconds a day.

General relativity says clocks closer to a large mass tick more slowly. The satellites are much farther from the Earth's mass than we are, so their clocks run faster than ours, by about 45 microseconds a day.

The second effect wins. Together, a satellite's clock would gain about 38 microseconds a day on a clock on the ground.

That sounds negligible until you remember the speed of light. In 38 microseconds, light travels more than 11 kilometres. Without correction, a position fix would be wrong within about two minutes, and the error would keep growing, by around ten kilometres every day.

So the engineers build relativity in. Each satellite's clock is set before launch to tick slightly slow, at 10.22999999543 megahertz instead of 10.23, so that once it is in orbit it keeps pace with clocks on the ground. Because the orbits are slightly elliptical, the effect also varies a little around each orbit, and that is corrected in the calculations.

Relativity can seem far removed from daily life. Every time a phone finds its place on a map by GPS, it depends on both of Einstein's theories being right.