Time to Find Your Way
From the clocks in the sky to your spot on the map
Your phone finds where you are by listening to satellites announce the time. Draw three spheres from the distances to three satellites to find your spot, then use Einstein’s relativity to see why satellite clocks run 38 microseconds a day fast. Follow it in 16 scenes.
Watch from the start in 3DChapter 1 · How Does Your Phone Know?
Even in an empty field with no signs, the dot on your map lands right on you. How?
- 1 How does your phone know where you are?
Even in a field with no signs, the dot on your map lands right on you
View in 3D → - 2 Your phone only listens
Satellites broadcast the time, and your phone just listens
View in 3D → - 3 The satellites circling Earth
About 30 satellites, 20,200 km up, twice around Earth a day
View in 3D →
Chapter 2 · Three Strings
If you know how far away the satellites are, three spheres can pin down where you are.
- 4 String one: a distance makes a sphere
Knowing the distance to one satellite puts you somewhere on a sphere
View in 3D → - 5 String two: where two spheres meet
Two sphere surfaces overlap along a single circle
View in 3D → - 6 String three: two points remain
Three spheres all meet at just two points
View in 3D → - 7 One in space, one on the ground
Throw out the point in space; the one on the ground is you
View in 3D → - 8 Old strings: the height of stars
Sailors found their way by drawing circles from the height of stars
View in 3D →
Chapter 3 · A Clock Is a Ruler
Distances to satellites are really measured with clocks. What if a clock is a little off?
- 9 A millionth of a second = 300 m
A clock off by a millionth of a second puts the distance off by 300 m
View in 3D → - 10 String four: your phone’s clock
A fourth satellite also solves for the error in your phone’s clock
View in 3D →
Chapter 4 · Satellite Clocks Run Differently
Do clocks in the sky tick at the same pace as clocks on the ground? Einstein said no.
- 11 Fast-moving clocks run slow
Because of its speed, a satellite clock loses 7.2 μs a day
View in 3D → - 12 Clocks run fast where gravity is weak
Because of gravity, a satellite clock gains 45.7 μs a day
View in 3D → - 13 Add them up: 38 microseconds a day
A satellite clock gains 38.5 μs a day → 11.5 km of distance
View in 3D →
Chapter 5 · Einstein Shows the Way
Now that we know why satellite clocks drift, it’s time to set them right.
- 14 If nobody fixed it
Distances would drift 11 km a day, and the spheres would stop meeting at one point
View in 3D → - 15 Einstein shows the way
Satellite clocks are set slightly slow on purpose, before launch
View in 3D → - 16 Try it with your phone
Use your own phone to pin where you are right now on the globe
View 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.