The satellites that tell a phone where it is are moving fast and sitting high. Each of the roughly 31 operational spacecraft in the Global Positioning System orbits at about 20,200 kilometres above the Earth’s surface, travelling at close to 14,000 kilometres per hour. Aboard each one is an atomic clock — usually a rubidium or caesium standard — accurate to within a few nanoseconds a day. That accuracy is not a luxury. It is the entire trick.
GPS does not measure position directly. It measures time. A receiver on the ground listens for signals from at least four satellites, notes how long each signal took to arrive, multiplies by the speed of light, and solves for a location. Light travels roughly 30 centimetres in a nanosecond, so a timing error of a single microsecond translates into a positional error of about 300 metres. If the satellite clocks and the receiver clocks disagree about what time it is, the map is wrong.
Which is where Einstein walks in. Two separate effects from relativity pull the satellite clocks in opposite directions, and neither of them is small enough to ignore.
Two clocks, two theories, one problem
The first effect comes from special relativity. A clock in motion runs slower, as seen by a stationary observer, than a clock at rest. The GPS satellites are moving at nearly 4 kilometres per second relative to the ground, and that motion slows their onboard clocks by about 7 microseconds per day compared to identical clocks on Earth’s surface.
The second effect comes from general relativity. Clocks deeper in a gravitational well run more slowly than clocks higher up, where spacetime is less curved. The satellites, floating 20,200 kilometres above the planet, sit in a much weaker gravitational field than a receiver on the ground. Their clocks therefore run faster than ground clocks by about 45 microseconds per day.
The two effects don’t cancel. General relativity wins by a wide margin. Net result: each GPS satellite clock ticks roughly 38 microseconds per day faster than an identical clock on Earth. That figure — 38 microseconds — is quoted in the technical literature by physicists including Neil Ashby of the University of Colorado, whose Living Reviews in Relativity paper on relativity in GPS remains the standard reference on how the corrections are actually applied.
Thirty-eight microseconds sounds negligible. It isn’t. That daily clock error works out to more than eleven kilometres of light-travel distance, and left uncorrected it would send GPS positions drifting by roughly ten kilometres every 24 hours. Within a couple of hours the system would be unusable for navigation. Within a week it would be pointing users at the wrong city.
The fix is baked into the hardware
The engineers who designed GPS in the 1970s knew this. Rather than correcting for relativity in software after the fact, they solved it at the factory. The atomic clocks that fly on GPS satellites are deliberately tuned before launch to tick more slowly than a ground clock at their nominal frequency of 10.23 MHz. Specifically, they are offset downward by about 4.465 parts in ten billion, so that once the satellite is in orbit and relativity speeds them up, they end up ticking at the correct rate as seen from Earth.
This detuning is documented in the GPS Interface Specification (IS-GPS-200), the public engineering document that defines exactly how the satellites broadcast time and position to receivers. The specification also builds in a smaller, periodic relativistic correction for the fact that GPS orbits aren’t perfectly circular — as a satellite dips slightly closer to Earth and speeds up, both special and general relativity nudge its clock a little differently, and the receiver has to account for it.
There is a persistent piece of internet folklore that the first GPS satellites were launched without the correction, and that the U.S. Air Force was quietly skeptical of Einstein until the drift showed up on orbit. The reality is more careful. According to Ashby, NTS-2 — the Navigation Technology Satellite launched in 1977, and the first spacecraft to carry a caesium atomic clock in orbit — had a frequency synthesiser that could switch the relativistic offset on and off. Engineers ran the clock without the correction for about three weeks, confirmed that it drifted at the predicted rate, and then switched the correction on. As Physics Today recounts, Einstein passed the test before the constellation went operational.
Why the number is exactly what it is
The 38-microsecond figure is not a rough estimate. It falls out of two equations that any physics undergraduate can write down.
For special relativity, the time dilation from orbital velocity is approximately v²/2c², where v is the satellite’s speed and c is the speed of light. Plug in about 3,874 metres per second and the result is a fractional slowdown of roughly 8.3 × 10⁻¹¹, or about 7 microseconds a day.
For general relativity, the fractional speed-up from being higher in Earth’s gravitational field is approximately ΔΦ/c², where ΔΦ is the difference in gravitational potential between the satellite’s altitude and the Earth’s surface. That works out to about 5.3 × 10⁻¹⁰, or roughly 45 microseconds a day.
Subtract 7 from 45 and there is the famous 38. It is one of the cleanest, most testable predictions of general relativity ever operated at industrial scale, and it has been running continuously — through 31 satellites, dozens of hardware generations, and roughly three decades of civilian use — without ever meaningfully disagreeing with Einstein’s 1915 theory.
What this means for everything else
GPS is now embedded in far more than navigation. The same timing signal that a phone uses to find a coffee shop is used to synchronise cellular base stations, timestamp stock market trades, coordinate the electrical grid, and align the sampling clocks of scientific instruments across continents. The U.S. National Institute of Standards and Technology distributes precise time in part by leaning on GPS. In each of these applications, relativity is silently in the loop. Turn it off, and the grid desynchronises, trades get out of order, and telecommunications networks lose lock within hours.
There is a certain elegance to it. Einstein published general relativity in 1915 on the basis of thought experiments about falling elevators and the bending of starlight during an eclipse. He never imagined a swarm of atomic clocks orbiting the planet, quietly correcting themselves so that a delivery driver could find the right driveway. And yet the same equations that describe a photon skimming past the Sun describe, to eleven decimal places, why the satellite overhead has to be told to tick slow.
For readers who enjoy the theme of quiet, distant hardware doing improbable things on very little power, Voyager 1 is still transmitting from roughly 24 billion kilometres away on less than 250 watts of decaying plutonium — a signal from a different era of engineering, but the same trick: trust the physics, and build the machine around it.
GPS works because someone, decades ago, took Einstein at his word and shipped the correction in silicon. Every time a map on a phone snaps to the right street, that decision is being re-validated, 38 microseconds at a time.
