All scenes › Chapter 5 Einstein Shows the Way
Distances would drift 11 km a day, and the spheres would stop meeting at one point
View in 3DWhat happens if the satellite clocks are left alone? A clock that runs ahead puts a time in the broadcast that is also ahead, so the phone measures the distance to that satellite about 11.5 km too short every day. On top of that, each satellite’s clock was set at a slightly different moment, so each one drifts by a different amount. Then the spheres no longer meet at a single point. On screen, after one day, the point where three spheres meet is about 19 km from where you really are.
Why?If every satellite were off by exactly the same amount, the phone could treat it as an error in its own clock and fix it. The trouble is that each satellite is off by a different amount. It’s like a test where every page is graded by a different rule: you couldn’t trust the score.
Learn more“11.5 km a day” is how much the measured distance to a satellite drifts. It doesn’t mean the dot on your map slides exactly 11.5 km sideways. How far the dot actually wanders depends on where the satellites are and when their clocks were set. The differences in when the clocks were set are just an example here.
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.