prize7-9, Exercise 1: How GPS finds a position

Model answer (check the details):

Principle: each satellite broadcasts its position and the exact time of the signal. The receiver notes when the signal arrives. The delay, multiplied by the speed of light, gives the distance to that satellite.

One satellite: the receiver could be anywhere on a sphere of that radius around the satellite.
Two satellites: the spheres intersect in a circle.
Three satellites: the circles meet at two points, one of which is usually absurd (in space or far from the Earth), so a position is fixed.
Four satellites: needed in practice, because the receiver's own clock is not accurate enough. The fourth signal lets the receiver solve for the clock error as well as for the three coordinates (latitude, longitude and height).

Why time matters: light travels about 300,000 kilometres per second, so a clock error of one millionth of a second is a distance error of about 300 metres. The satellites carry atomic clocks.

Link: this is the longitude principle of Chapter 7 (position from time) applied with extremely good clocks.