Time to Find Your Way
All scenes › Chapter 2 Three Strings
String two: where two spheres meet
Two sphere surfaces overlap along a single circle
View in 3DString two: where two spheres meet
The phone does the same math with satellite 2’s broadcast. This time a green sphere appears. You have to be on the red sphere’s surface and on the green sphere’s surface. The only place they overlap is one yellow circle. The possibilities just shrank from a whole sphere to a single circle.
Why?When two soap bubbles stick together, a round rim forms where they touch. The surfaces of two spheres always meet in a circle like that.
Learn moreThis circle stands around the line joining the two satellites, with a radius of about 13,700 km. Parts of it pass through Earth, and those parts are hidden on screen.
- Distance to satellite 2
- 22,889 km
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.