Twenty thousand kilometres above the Earth, a fleet of atomic clocks is racing time itself. The 31 operational satellites of the Global Positioning System each carry caesium or rubidium oscillators accurate to a few nanoseconds a day, orbiting at roughly 14,000 kilometres per hour. And every day, each of those clocks ticks about 38 microseconds faster than an identical clock sitting on the ground. That drift is not a defect. It is exactly what Albert Einstein predicted in 1905 and 1915, and if the engineers who built GPS had not baked the correction into the hardware itself, the system would be useless for navigation within a single afternoon.
The number sounds small — 38 millionths of a second. But GPS works by measuring how long a radio signal takes to travel from a satellite to a receiver, and radio waves move at the speed of light. Light covers about 30 centimetres in a nanosecond. A timing error of 38 microseconds translates, at the speed of light, into a positional error of roughly 11 kilometres. Left uncorrected for 24 hours, your phone’s little blue dot would not just drift down the street. It would leave the city.
Two effects, pulling in opposite directions
The 38-microsecond figure is actually the sum of two separate relativistic effects, and they push against each other.
The first is special relativity, from Einstein’s 1905 paper. A clock in motion, seen from a stationary observer, ticks more slowly. GPS satellites move at about 3.87 kilometres per second relative to the ground. Plug that into the time-dilation formula and the satellite clocks run roughly 7 microseconds per day slower than clocks on Earth.
The second is general relativity, from 1915. A clock deeper in a gravitational well ticks more slowly than one further out. Earth’s gravity is weaker at the altitude of the GPS constellation (about 20,200 km up) than at the surface, so the satellite clocks run faster — by about 45 microseconds per day.
Add them: +45 from gravity, −7 from velocity, and the net result is that the satellite clocks gain approximately 38 microseconds every 24 hours. This is not a theoretical estimate. It is measured, continuously, and it matches Einstein’s predictions to within the precision the hardware allows.
How the correction is baked in
The engineers behind GPS knew about this before the first satellite ever flew. When the Block I satellites were being designed in the 1970s, some physicists inside the programme were sceptical that the relativistic corrections were real enough to matter. So the first satellite, launched in 1977, carried a switch: the onboard frequency synthesiser could be run either at its nominal rate or at a rate offset to compensate for relativity, and mission controllers could flip between them.
The physicists were right. When the satellite was run at the un-corrected rate, its clock drifted from ground clocks by the predicted amount almost exactly. After that, every GPS satellite has had the correction built in at the factory. The atomic clocks on board are not tuned to 10.23 MHz, their nominal operating frequency; they are tuned to 10.22999999543 MHz, a deliberately slower rate on the ground so that once the satellite is in orbit and the relativistic effects kick in, the clock ticks at the nominal frequency as seen from Earth.
It is one of the very few pieces of consumer infrastructure — because that is what GPS became — whose designers had to solve for the geometry of spacetime before they could ship the product.
The corrections that never stop
The 38-microsecond-per-day figure is only the average, and only the largest piece of the picture. The corrections do not end once the satellite is switched on.
GPS orbits are not perfectly circular. They are slightly elliptical, so each satellite’s altitude and speed vary a little over each 12-hour orbit. That means the gravitational and velocity effects both fluctuate. This adds a periodic correction, called the eccentricity term, of up to about 46 nanoseconds — small, but at the speed of light that is still 14 metres of position error, and GPS receivers apply the correction themselves. The equation for it appears in the official GPS Interface Specification (IS-GPS-200) that governs how every civilian receiver on Earth talks to the constellation.
Ground stations at Schriever Space Force Base in Colorado and around the world track each satellite’s clock continuously, comparing it to a master ensemble of atomic clocks at the US Naval Observatory. Corrections are uplinked to each satellite roughly once a day, and each satellite broadcasts a small set of clock-correction coefficients — a bias, a drift, and a drift rate — that your phone uses to trim the timestamps it receives. The whole architecture assumes relativity is true and treats the corrections as routine engineering.
Why 10 kilometres, and why so fast
The “10 kilometres a day” figure that circulates in physics textbooks is not an exaggeration; it is close to arithmetic. A 38-microsecond timing error, multiplied by the speed of light (299,792,458 metres per second), gives about 11,400 metres. And because GPS positions are calculated by trilaterating from at least four satellites at once, the error does not average out — it compounds, because every satellite’s clock is drifting the same way relative to your receiver.
Modern receivers get sub-metre accuracy in good conditions, sometimes centimetre accuracy with differential techniques. That precision is only possible because timing at the nanosecond level is treated as sacred. It is the same reason that chip designers now worry about how far light travels in a single clock cycle: at the timescales modern electronics operates on, the finite speed of light is no longer an abstraction. It is a budget.
An experiment that pays rent
General relativity was, for most of the twentieth century, an exotic theory. It explained the anomalous precession of Mercury’s orbit, the bending of starlight around the Sun during the 1919 eclipse, and a handful of laboratory results with mercury vapour and Mössbauer spectroscopy. None of these affected daily life.
GPS changed that. It is, in a very practical sense, the first piece of Einstein’s physics that ordinary people carry in their pockets. Every time a phone locks onto a satellite fix, the calculation that lands the blue dot on the correct side of the street includes a term for the curvature of spacetime around the Earth. Turn relativity off and the system dies within hours.
The engineers who built GPS did not set out to test general relativity. They set out to build a navigation system, and they discovered that they could not do so without inheriting the whole of twentieth-century physics. In that sense, the constellation overhead is doing two jobs at once: telling drivers where to turn, and running, in perpetuity, one of the most precise tests of Einstein’s theories ever devised. Every satellite pass is another data point. So far, the theory has not missed.
