String four: your phone’s clock

String four: your phone’s clock

Satellites carry atomic clocks, but your phone’s clock isn’t nearly as accurate. If the phone’s clock is off by just 10 millionths of a second, every sphere grows by about 3 km. Then the point where the three spheres meet ends up about 5 km underground. And the fourth satellite’s yellow sphere doesn’t pass through that point. So the phone adjusts its own clock until all four spheres meet at exactly one point.

Why?Like trying keys one by one until a lock opens, the phone nudges its clock value until the four spheres meet at a single point. Only one clock value makes all four fit, so that value is the right time. The phone finds where you are and what time it is in one go.

Learn moreThat’s why GPS needs four or more satellites in view. There are four unknowns: east–west, north–south, height, and your phone clock’s error. As a bonus, your phone’s clock gets set to GPS time. The 10 μs on screen is just an example.

Also solves for your phone clock’s error

4 satellites

textbook formulas