String one: a distance makes a sphere

String one: a distance makes a sphere

The phone picks up satellite 1’s broadcast. Subtract the send time written in the message from the time it arrived, and you get 0.0732 seconds. Radio waves travel about 300,000 km every second, so multiplying gives the distance to the satellite: 21,943 km. But the phone doesn’t know the direction. So you could be anywhere 21,943 km from satellite 1, somewhere on the surface of the red sphere.

Why?Imagine a friend on the playground tells you only, “You’re ten steps away from me.” Then you’re somewhere on a circle around your friend. Out in space there’s also up and down, so the circle becomes the surface of a ball.

Learn moreFinding a position from distances alone is called “trilateration.” It’s different from “triangulation,” which uses angles. The sphere on screen is true to scale: its radius is about 3.4 times Earth’s radius.

Distance to satellite 1

21,943 km

Time the broadcast took

0.0732 s

× speed of radio waves

299,792 km/s

= distance to satellite 1

21,943 km

textbook formulas