Every GPS satellite is launched with a clock deliberately set to run slow, because Einstein's relativity speeds it up by about 38 microseconds a day once in orbit — and without that built-in correction, your phone's location would drift by roughly ten kilometres a day.

Every satellite in the GPS constellation carries atomic clocks, and before launch those clocks are deliberately set to tick at the wrong rate. They are adjusted to run slightly slow. The offset is small and precise, and it is built in on the ground, on purpose, by the engineers who designed the system.

The reason is relativity. Once a GPS satellite is in orbit, its onboard clocks run fast relative to clocks on the ground. Left uncorrected, that drift would make accurate navigation fail within hours. The deliberate slow-setting is the fix, applied before the satellite ever leaves Earth.

Two effects, pulling opposite ways

The 38-microsecond figure often quoted is not a single effect. It is the net result of two relativistic effects working against each other.

The first comes from special relativity. A GPS satellite moves fast, several kilometres per second relative to the ground. Special relativity says that a moving clock, observed from the ground, ticks slow. On its own, this effect would make a GPS satellite’s clock lose about 7 microseconds a day.

The second comes from general relativity. A GPS satellite orbits roughly 20,000 kilometres up, where Earth’s gravity is weaker than at the surface. General relativity says that a clock in weaker gravity ticks fast. On its own, this effect would make the satellite’s clock gain about 45 microseconds a day.

The two do not cancel. One subtracts 7, the other adds 45, and the satellite clock ends up gaining roughly 38 microseconds a day as seen from the ground. The gravitational effect wins. A GPS clock in orbit runs fast, and it runs fast by a specific, calculable amount.

Why 38 microseconds matters so much

Thirty-eight microseconds is 38 millionths of a second. It is an almost meaninglessly small interval by the standards of ordinary life. For GPS, it is enormous.

GPS works by timing. A receiver, in a phone or a car, works out how far it is from a satellite by measuring how long the satellite’s signal took to arrive, and multiplying by the speed of light. The speed of light is about 300,000 kilometres per second. That is the number that makes timing errors so costly. Light travels about 300 metres in a single microsecond. An error of a millionth of a second in the clock becomes an error of hundreds of metres in the distance, and the position fix is only as good as those distances.

So a clock error that accumulates at 38 microseconds a day does not produce a small navigation error. According to the Ohio State University physicist Richard Pogge, whose explanation of GPS and relativity is widely cited, an uncorrected system would produce position errors growing at about 10 kilometres each day. Pogge’s account also notes that a navigational fix would be measurably wrong after only about two minutes. The system would not degrade gracefully. It would fail quickly.

How the correction is actually done

The headline version of this story is that the clocks are “set to run slow,” and that is true, but it is worth being precise about what that means.

The correction is built in as a frequency offset. A GPS satellite clock is meant to operate at a fundamental frequency of 10.23 MHz once in orbit. To achieve that, engineers set the clock, on the ground, slightly lower, to about 10.22999999543 MHz. The relativistic speed-up then brings it up to the intended rate once the satellite is in orbit and moving. The clock is wrong on the ground so that it will be right in space.

This handles the large, steady part of the effect, the part that is the same for every satellite in a roughly circular orbit. It is not the whole correction. GPS orbits are not perfectly circular, and the small variations in speed and altitude around each orbit produce smaller relativistic wobbles that change through the orbit. Those are dealt with separately, by a calculation in the receiver itself. The pre-launch frequency offset is the main correction, not the only one.

What the system demonstrates

It is sometimes said that GPS proves Einstein right. That is a fair claim, with one qualification worth keeping.

Relativity was well tested long before GPS. The system did not provide the first confirmation of either special or general relativity. What GPS does provide is something a little different and, in its own way, just as persuasive. It is a working demonstration, running continuously, that relativity is not only correct but quantitatively correct, accurate enough to engineer around. The designers did not treat relativity as a theory to be respected in principle. They treated it as a number to be subtracted, and the system works because the number is right.

Every position fix a phone produces is, in that sense, relativity being used as a tool. The 38 microseconds are not a curiosity attached to the system. They are designed into it, and the system would not function without the correction having been made.