← Theory of RelativityPart 2 — General Relativity · 18

How GPS Actually Works

▶ DRILL

Your phone finds you by timing the ticks of clocks on GPS satellites — so those clocks must be perfect. But relativity bends them two ways at once: the satellite's speed makes its clock run slow (special relativity, ~7 µs/day), while its altitude — higher in Earth's gravity — makes it run fast (general relativity, ~45 µs/day). The net, +38 µs/day, sounds tiny, but it would push your position off by ~11 km a day if engineers didn't correct for it. They do — so every map pin is quietly running on both of Einstein's theories. Use the Explain it for a kid / a grown-up switch to set the depth.

EXPLAIN IT FORsimple words & pictures
ALTITUDE20,200 km (like GPS satellites)
SLOW-MOnormal
🛰️ how relativity hides inside your GPS🌍📱 Liza🛰️ground clock: steadysatellite clock vs ground — drift per day← slowerfaster →speed −7.2height +45.7net +38.5 µs/dayuncorrected → you'd be ~11 km off after a day

The big idea — your phone finds you using satellite clocks, and relativity bends those clocks two ways at once: speed slows them (time dilation) and height speeds them up (gravity). For GPS the net is about +38 millionths of a second fast per day — which would throw your position off by ~11 km a day if engineers didn't correct for it. They do — so every map pin on your phone is quietly running on both of Einstein's theories. Slide the altitude down to the Space Station and watch the balance flip the other way (down low, the slowing wins).

# breakdownat 20,200 km: −7.2 µs/day (speed, SR) + 45.7 µs/day (altitude, GR) = +38.5 µs/day net
# consequenceuncorrected, +38 µs/day × c ≈ 11 km/day of position error — so satellite clocks are pre-tuned before launch
# crossoverthe two effects cancel near 3,200 km; below that (e.g. the ISS at ~400 km) the net is negative — the clock runs slow
# the pointGPS is everyday, working proof of both special and general relativity — this whole series, in your pocket