Now that we can easily access location and directions from our smartphones, it’s even more amazing to consider the measures that ancient explorers had to take to find their way around, especially at sea when out of sight of land. Early navigation relied on astrolabes and then sextants to measure latitude. By the late 1800s, chronometers were widely used with astronomical observation to determine longitude for marine navigation. Satellites came into the navigation picture in 1964, with the Transit system (also called NAVSAT or NNSS). Today, a network of 31 satellites orbiting the Earth at an altitude of 20,000km serves as the U.S. Global Positioning System (GPS), providing directional guidance to anyone in the world with a GPS receiver.

The basic principle of the GPS system is that radio signals are transmitted from satellites to receivers on or close to the Earth. The positions of the satellites at any given instant are known, and the distance or “range” from the receiver to each satellite can be calculated from the propagation delay of the radio signal from that satellite. Knowing the distance to each of several reference points (i.e., satellites) allows calculation of the receiver’s spatial coordinates.