How GPS Works — The Science Behind Your Location

GPS — the Global Positioning System — tells your phone exactly where you are on Earth within a few metres, using signals from satellites orbiting 20,000km above you. The underlying principle is elegant geometry, but the practical implementation involves some impressive physics and mathematics.

The Basic Principle — Trilateration

GPS works through trilateration — finding a position by measuring distances from known points. Imagine you know you're 5km from London, 7km from Oxford and 10km from Birmingham. There's only one point on Earth at all three of those distances simultaneously. GPS works the same way, but in three dimensions using satellites instead of cities.

The Satellites

The GPS constellation consists of at least 24 operational satellites, orbiting in 6 different orbital planes. This arrangement ensures that at least 4 satellites are visible from any point on Earth's surface at any time. (Four, not three, because the third dimension — altitude — requires an extra satellite.)

Each satellite broadcasts a signal containing two things: its precise location, and the exact time the signal was sent, according to an atomic clock accurate to nanoseconds.

Measuring Distance with Time

Your GPS receiver calculates how long the signal took to arrive. Since the signal travels at the speed of light (299,792,458 m/s), the distance to the satellite is simply: distance = speed × time.

A signal taking 0.067 seconds to arrive means the satellite is 0.067 × 299,792,458 ≈ 20,000km away. With four satellites, your receiver can solve for four unknowns: latitude, longitude, altitude, and clock error.

Why Four Satellites?

With three satellites, you'd have a position but your receiver's clock error would introduce significant inaccuracy. The fourth satellite allows the receiver to solve for its own clock error, effectively synchronising itself to atomic clock accuracy without needing an expensive atomic clock of its own. This is the clever trick that makes cheap GPS receivers practical.

Relativistic Corrections

GPS provides one of the most striking practical demonstrations of Einstein's relativity. GPS satellites experience two competing effects: special relativity (moving fast relative to Earth makes their clocks run slow by about 7 microseconds/day) and general relativity (being further from Earth's gravity makes their clocks run fast by about 45 microseconds/day). Net effect: satellite clocks run fast by 38 microseconds per day. Without corrections for this, GPS positions would drift by about 10km per day.