GPS
or: how we used Einstein to find the DoorDash guy
We built clocks so precise they count a cesium atom wiggling 9 billion times a second, strapped them to rockets, flung about 30 of them into orbit at 8,700 mph, then had to fix them with both of Einstein’s theories because time literally runs faster up there. They scream the exact time at Earth nonstop, so a slab of glass in your pocket can hear four at once, do some algebra, and figure out where you’re standing on a spinning rock.
How it works, badly
We put really, really good clocks in space.
Time runs faster up there, so we fix the clocks on purpose.
Your phone listens to four of them and does algebra.
Then we use it to watch our burrito get lost.
Wait, is that real?
Yes, almost all of it.
How your phone finds you
About 31 working GPS satellites orbit roughly 12,550 miles up, circling Earth twice a day at about 8,700 mph; the exact count shifts as new ones launch and old ones retire. Each one broadcasts its exact time and position. Your phone measures how long each signal took to arrive, and since the signals travel at the speed of light, that delay becomes a distance. Four satellites are needed because there are four unknowns: your position in three dimensions, plus the error in your phone’s own cheap clock.
The Einstein part
The satellites move fast, which by special relativity makes their clocks run about 7 microseconds a day slow. They also sit farther from Earth’s gravity, which by general relativity makes them run about 45 microseconds a day fast. The net is roughly 38 microseconds a day fast. Left alone, that would drift your position by about 6 miles a day, so the clocks are tuned to tick slightly slow before launch.
The clocks
GPS satellites carry cesium and rubidium atomic clocks. A cesium atom flips between two energy states at exactly 9,192,631,770 cycles per second; that number is how the second itself is officially defined.
The fine print
A phone under open sky usually lands within about 16 feet, not inches, and it rarely listens to just four satellites; it grabs as many as it can, including other countries’ systems like Galileo, and leans on Wi-Fi and cell towers too. And “mostly” is a joke: GPS timing quietly keeps cell networks, banks, and power grids in sync, which is less funny but more important than your burrito.