How GPS Works: Satellites, Signals, and Atomic Clocks

The remarkable thing about GPS is not that it exists but that it works at all at the precision it does. Locating a point on Earth to within a few metres using signals from satellites 20,000 kilometres overhead requires solving an engineering problem whose tolerances are almost absurdly tight. The key insight is that position can be derived from time — specifically, from measuring how long a radio signal takes to travel from a satellite to you.

The geometry: trilateration

Suppose a satellite broadcasts a signal at a precisely known moment, and your receiver picks it up a few milliseconds later. You know the speed of light (about 300,000 kilometres per second), so you can calculate the distance: time multiplied by speed. That distance tells you that you are somewhere on the surface of a sphere centred on the satellite.

One satellite gives you a sphere. Two satellites give you two spheres, and you are somewhere on the circle where they intersect. Three satellites give you three spheres that intersect at two points — one of which is usually obviously wrong (it might be underground or deep in space), leaving your position determined. This is called trilateration; it is similar to triangulation but uses distances rather than angles.

In three dimensions, you need a fourth satellite to solve for altitude as well, and also to handle the clock error problem described below.

Why timing is everything

Light travels about 30 centimetres per nanosecond. If your timing is off by even a microsecond (one millionth of a second), your calculated position is wrong by 300 metres. If it is off by a millisecond, you are off by 300 kilometres. The entire system stands or falls on the accuracy of its clocks.

Each GPS satellite carries multiple atomic clocks — typically caesium and rubidium standards — that are accurate to a few nanoseconds per day. These are continuously monitored and corrected by ground stations. Your phone does not carry an atomic clock; it uses a much cheaper quartz clock that drifts significantly. This is why a fourth satellite is necessary: the receiver can solve for its own clock error as a fourth unknown, alongside latitude, longitude, and altitude.

The constellation and the signal

The United States GPS system consists of at least 24 operational satellites arranged in six orbital planes, with several spares. At any point on Earth’s surface, at least four satellites are typically visible above the horizon. Other countries operate competing or complementary systems: Russia’s GLONASS, Europe’s Galileo, and China’s BeiDou. Most modern phones use signals from multiple constellations simultaneously, which improves accuracy and resilience.

Each satellite continuously broadcasts two things: the precise time at which the signal was sent (from the satellite’s atomic clock) and a description of the satellite’s exact position in its orbit (called the ephemeris data). The receiver compares the timestamp on the received signal to its own clock, calculates the travel time, and converts that to a distance. Doing this for four or more satellites simultaneously yields a precise position fix.

Relativity is not optional

One of the more striking facts about GPS is that it would not work without applying corrections from Einstein’s theories of relativity. Two effects act in opposite directions.

Special relativity predicts that a clock moving fast relative to an observer will tick more slowly. GPS satellites orbit at about 14,000 kilometres per hour, which causes their clocks to run slower than Earth clocks by about 7 microseconds per day.

General relativity predicts that a clock in a weaker gravitational field runs faster. At 20,000 kilometres altitude, gravity is weaker than at Earth’s surface, causing the satellite clocks to run faster by about 45 microseconds per day.

The net effect is that satellite clocks gain about 38 microseconds per day relative to ground clocks. If uncorrected, this would introduce a position error of roughly 10 kilometres per day. To compensate, the satellites’ clocks are deliberately set to run slightly slow before launch, and ongoing corrections are applied by ground control.

Sources of error and how they are managed

Even with atomic clocks and relativity corrections, several factors degrade accuracy in practice. The signal travels through the ionosphere and troposphere, where variations in electron density and atmospheric moisture slow it slightly and unpredictably. Signals can also reflect off buildings before reaching the receiver — a problem called multipath error that is particularly acute in dense urban environments.

These errors are addressed in several ways: differential GPS systems use ground stations at known locations to measure and broadcast corrections; the government has disabled the deliberate degradation (Selective Availability) that once limited civilian accuracy; and receiver algorithms increasingly use multiple constellations and signals on multiple frequencies to model and cancel atmospheric delays.