Beautiful Science: The Physics Behind GPS

Today’s Global Positioning System (GPS) is an indispensable technology that has found its way into our cell phones. But how exactly does GPS work so flawlessly in giving you information about locations? What is the science behind it? This post provides brief answers to these questions that may leave you quite surprised.

The Basics of GPS

GPS tap in broadcasts from a collection of satellites located high above the Earth. Currently there are more than thirty of these satellites strategically placed around the globe. Their radio broadcasts don’t translate into talk or music. Instead, they broadcast locational data such as time stamps, specifying when the signals were sent. The atomic clock that is onboard each satellite ensures that the signal time stamps are highly accurate.

The Physics of GPS

Key to the success of GPS are various physical theories that we learnt in high school and university. First, let’s go through the main steps GPS uses in transmitting location signals from satellite back to Earth:

1. Your GPS receiver picks up some of the satellite signals. The unit, which also has access to signals from an extensive network of ground-based clocks, computes how long the different signals took to arrive. Since those signals arrive at a known speed – the speed of light – the transit times can be used to determine the satellites’ distances.

2. Using those distances, the positions of the satellites, and Euclidean geometry, the computer determines a unique position of the source (i.e., you) by triangulation.

3. The computer reports that result, and you learn where you are.

Now comes the physics part of GPS. The orbital satellites monitor their motion using onboard gyroscopes and accelerometers, like the ones in your iPhone. From the observed response of those instruments, the satellite’s computer can read out the satellite’s acceleration using the physics of Newtonian mechanics. From that input, using calculus, it calculates how much the satellite has moved. Indeed, Newton invented calculus to solve problems like this.

The engineers who designed the GPS built it on many assumptions. The system relies on the idea that the speed of light is constant (as proved by Einstein). It uses atomic clocks, whose design and interpretation rely on advanced principles of quantum mechanics to do accurate timing. As mentioned earlier, it uses the tools of classical mechanics to calculate the position of the satellites it deploys. In addition, it makes corrections for the effect based on Einstein’s Theory of General Relativity which predicts that the rate of clocks depends slightly on their elevation above Earth (specifically, clocks run slower on Earth’s surface where its gravitational field is stronger).

In short, the GPS that is our everyday tool relies on numerous scientific facts, established over a period of many centuries by brilliant scientists. The moral of the GPS story are many. First, we should never dismiss “basic” research as ivory tower stuff, because you never know how practically useful they may be one day. Second, the most glorious and adventurous scientific achievements rely on tangled webs of underlying theories. And when those adventurous experiments hold up, they increase our confidence in the individual theories and their interactions. Third, we should not dismiss a model just because it is incomplete. Euclid’s geometry fails to provide a complete model of reality. But, as GPS shows, it still plays a pivotal part in the overall workings when combined with later scientific advancements.

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