The Physics Inside GPS Satellites
Every time your phone finds your location, it is running an experiment in Einstein's relativity. GPS satellites carry atomic clocks, and without correcting for both special and general relativity, your position would drift by kilometers within a day.
Special relativity — moving clocks run slow
GPS satellites orbit at about 3.9 km/s. Special relativity says their clocks tick slower than Earth clocks by roughly 7 microseconds per day. Ignore this and positions drift.
General relativity — gravity slows time
At 20,200 km altitude, gravity is weaker, so satellite clocks tick faster — about 45 microseconds per day. This effect wins over the special-relativity slowdown, for a net gain of ~38 microseconds per day, which engineers correct for.
Trilateration with light-speed signals
Each satellite broadcasts its position and the exact time. Your receiver measures signal travel times, multiplies by the speed of light (299,792,458 m/s), and intersects spheres from at least four satellites to fix your 3D position plus clock error.
Atomic clocks
Satellites carry cesium and rubidium atomic clocks stable to nanoseconds per day. A single nanosecond of timing error equals ~30 cm of position error — precision timekeeping is the whole game.
Try this yourself
- Time how long your phone takes to get its first GPS fix after being indoors — that's it downloading satellite orbit data.
- A 38-microsecond daily drift × c ≈ 11 km of error per day: compute it yourself to feel why relativity matters.