We’ve seen that it’s pretty easy to determine your latitude using the sun as a reference point. All you need is a shadow and chart that was easily available to sailors of previous centuries and you’re set. Finding your longitude is another story. The reason for the difference in difficulty is one of time. The sun varies very little in its north-south position from day to day, but it varies enormously in its east-west position by virtue of the whole “rising and setting” thing. It’s easy to look up on a chart to find a correction factor that varies day-by-day, but when you need a correction factor that varies minute-by-minute you’re in deep trouble especially if you live in the age before reliable clocks.
It was the work of John Harrison shortly before the American Revolution that first gave the world a clock accurate enough to navigate by. With a good clock you can determine to the second where the sun should be at a given longitude and thus reconstruct the longitude you’re actually near.
Modern GPS uses almost this same method. All a GPS satellite does is eternally broadcast two continuously updated pieces of information: its position and the time on its atomic clock. Knowing that light travels at about 1 foot per nanosecond, we can calculate how far we are from the satellite to the foot, as long as the GPS clock is accurate to the nanosecond and we have a receiver that can handle such a precise signal. One satellite is not enough, because simply knowing a distance doesn’t tell you direction. If you have two signals, you can eliminate some possibilities. Imagine I know how far I am from Houston and how far I am from College Station. In most cases this narrows down the possibilities to two, which we can see schematically for one hypothetical pair of distances:
I could be in Conroe or in a field north of Highway 90. One more position signal would eliminate the wrong possibility. In 3d we need four satellites, but in practice you’ll be able to get signals from many more than that at a given time if you have a decent view of the sky.
All this relies on having a good clock. While a clock isn’t usually thought of as a position-finding tool, we would be much the worse without them.