How GPS and Satellite Positioning Actually Work
✦ Key takeaways
- GPS fixes your location by measuring how long signals take to arrive from at least four satellites.
- The GPS constellation of about 31 satellites orbits at 20,200 km and covers the entire planet.
- The fourth satellite is needed to solve for the receiver's clock error, not just altitude.
- A timing error of one microsecond translates to roughly 300 m of distance error, which is why atomic clocks are used.
- Both special and general relativity must be corrected; without them the system would drift about 10 km per day.
When you open a map on your phone and a blue dot pins you to within a few metres, you are actually receiving messages from machines circling more than twenty thousand kilometres above your head. The story behind that dot is an elegant blend of geometry, physics, and even Einstein's relativity.
The Constellation: Satellites Always Overhead
The American GPS is designed around a baseline of at least 24 operational satellites arranged across six orbital planes, though the real operational number is around 31 to guarantee coverage and provide spares. These satellites orbit at roughly 20,200 kilometres and complete one trip around Earth about every 12 hours, so that any user on the surface can see at least four satellites at almost any moment, anywhere on the planet.
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Each satellite carries a precise atomic clock and continuously broadcasts a radio signal with two essential pieces of information: the satellite's identity and exact orbital position (its ephemeris data), and the precise time the signal was sent. The classic civilian GPS signal is transmitted on a frequency known as L1 at 1575.42 MHz.
Timing to Location: Trilateration
The core idea is simple: radio signals travel at the speed of light, about 299,792 kilometres per second. If the receiver knows when a signal was sent and when it arrived, it can compute the distance to the satellite by multiplying the travel time by the speed of light. That single distance places the receiver somewhere on the surface of an imaginary sphere centred on the satellite.
Measuring the distance to a second satellite gives a second sphere, and two spheres intersect in a circle. A third satellite narrows the possibilities to just two points, only one of which normally lies on or near Earth's surface. This process is called trilateration, and it is the heart of the whole system.
Why You Need Four Satellites, Not Three
Geometrically, three satellites are enough to fix a point in three-dimensional space. The catch is time. The atomic clock aboard the satellite is extraordinarily accurate, but the clock inside your phone is cheap and never perfectly synchronised. Even a tiny offset in the receiver's clock corrupts every distance calculation at once.
The elegant solution treats the receiver's clock error as a fourth unknown. There are three unknowns for position (latitude, longitude, altitude) and a fourth for time, and solving four unknowns requires four equations, meaning four satellites. In effect, your device continuously corrects its cheap clock until it behaves as if it carried an atomic clock of its own.
Atomic Clocks and Relativity: Enter Einstein
Timing precision is everything here. To appreciate why, consider that a timing error of just one microsecond, a millionth of a second, translates into a distance error of about 300 metres, because light travels roughly 300 metres in that span. An error of one nanosecond yields about 30 centimetres. This is why satellites carry atomic clocks that drift by less than a nanosecond per day.
More surprising is that relativity genuinely matters. Under special relativity, the moving satellite clocks tick slower by about 7 microseconds per day. Under general relativity, they tick faster by about 45 microseconds per day because gravity is weaker at that altitude. The net effect is roughly 38 microseconds per day of gain; left uncorrected, that would accumulate into a positioning error of about 10 kilometres in a single day. So the satellite clocks are deliberately pre-adjusted to compensate.
| Parameter | Value |
|---|---|
| Satellite orbital altitude | ~20,200 km |
| Operational satellites | ~31 |
| Civilian L1 signal frequency | 1575.42 MHz |
| Orbital period | ~11 h 58 min |
| Typical phone accuracy | 3 to 5 m |
| Uncorrected relativity drift | ~10 km per day |
Accuracy Factors and A-GPS on Phones
GPS accuracy is not fixed; it is shaped by several factors. The biggest are signal delay in the ionosphere and troposphere, multipath errors when signals bounce off buildings and mountains, and the geometry of the visible satellites, expressed by a figure called DOP (Dilution of Precision). The more widely spread the satellites are across the sky, the better the fix, which is why performance degrades between skyscrapers or in narrow canyons.
Your phone leans on A-GPS, or Assisted GPS. Instead of waiting for the slow orbital data to trickle down from the satellites, which can take minutes, it downloads that data over the internet or cellular network. This shrinks the time to first fix from minutes to seconds. Modern phones also fuse signals from other systems such as Europe's Galileo, Russia's GLONASS, and China's BeiDou, along with inertial sensors and Wi-Fi positioning, giving you a fast, reliable location even in difficult conditions.