All scenes › Chapter 3 A Clock Is a Ruler
A clock off by a millionth of a second puts the distance off by 300 m
View in 3DNobody measures the distance to a satellite with a tape measure. You take the time the broadcast took and multiply it by the speed of radio waves. So if the clock is wrong, the distance is wrong too. In a millionth of a second, radio waves travel about 300 m. A clock off by just a millionth of a second shifts the red sphere’s surface by 300 m.
Why?A blink takes about a tenth of a second. A millionth of a second is a hundred thousand times shorter than that. You could never feel it, but light covers 300 m in that time. That’s why GPS only works with extremely accurate clocks.
Learn moreA millionth of a second is called a “microsecond,” written “1 μs.” GPS satellites carry atomic clocks so accurate they would drift only about a second in hundreds of thousands of years. This view zooms way in on a few kilometers around the car. Up this close, even the surface of a sphere more than 20,000 km across looks almost like a flat board.
textbook formulas
View this scene in 3D →More in the series
Orbits, distances and clock differences are calculated with textbook formulas (Kepler’s laws and simple forms of special and general relativity). The 30 satellites follow the real GPS layout but are not the real satellites or positions. In the 3D view, the satellite models are drawn huge and radio waves move far slower than in real life.