Time to Find Your Way
All scenes › Chapter 2 Three Strings
String three: two points remain
Three spheres all meet at just two points
View in 3DString three: two points remain
Now add satellite 3’s blue sphere. The yellow circle pierces the blue sphere’s surface in exactly two places. Those are the two points where all three spheres meet. Three broadcasts have narrowed it down to two points. Which one is you?
Why?Push a ring through a ball and it meets the surface twice: once going in and once coming out. That’s why three satellites leave two points, not one.
Learn moreThe two points mirror each other across the flat surface through the three satellites. If the satellites are bunched in one part of the sky, the spheres meet at shallow angles and small errors move the point a lot. So phones prefer satellites spread widely across the sky.
- Where all three spheres meet
- 2 points
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.