The Question
Your smartphone can tell you exactly where you are on Earth, to within a few meters, anywhere on the planet, at any time. This technology—the Global Positioning System—is so seamlessly integrated into modern life that we rarely stop to wonder how it actually works. The answer involves a constellation of satellites, atomic clocks, and Einstein's theory of relativity.
Detailed Explanation
GPS works through a process called trilateration. The GPS constellation consists of at least 24 satellites orbiting the Earth at an altitude of about 20,200 km, arranged so that at least 4 satellites are visible from any point on Earth at any time. Each satellite continuously broadcasts a radio signal containing two pieces of information: the satellite's precise location and the exact time the signal was sent (measured by an extremely accurate atomic clock on board). Your GPS receiver picks up these signals. Because radio waves travel at the speed of light (about 300,000 km/s), the receiver can calculate how far away each satellite is by measuring how long the signal took to arrive. If the signal took 0.067 seconds to arrive, the satellite is about 20,000 km away. With the distance to one satellite known, your position is somewhere on a sphere of that radius centered on the satellite. With two satellites, your position is on the circle where two spheres intersect. With three satellites, your position is narrowed down to one of two points (one of which is usually obviously wrong—in space or underground). A fourth satellite is needed to correct for errors in the receiver's clock, which is far less accurate than the atomic clocks on the satellites. With four or more satellites, the receiver can calculate your precise three-dimensional position (latitude, longitude, and altitude).
Going Deeper
GPS requires extraordinary precision in timekeeping. The satellites' atomic clocks are accurate to about 20-30 nanoseconds. Even a tiny error in timing translates to a significant error in position—a 1-microsecond error would result in a 300-meter position error. This is why the atomic clocks on GPS satellites must be corrected for two effects predicted by Einstein's theories of relativity. Special relativity predicts that the satellites' clocks run slightly slower than clocks on Earth because the satellites are moving fast (about 14,000 km/h). General relativity predicts that the satellites' clocks run slightly faster than clocks on Earth because they are in a weaker gravitational field (farther from Earth's center). The net effect is that GPS satellite clocks gain about 38 microseconds per day relative to clocks on Earth. If this were not corrected for, GPS positions would drift by about 10 km per day. GPS is therefore a practical, everyday application of Einstein's theories of relativity—without relativistic corrections, your navigation app would be useless within hours. The system was originally developed by the US Department of Defense for military use and was made available for civilian use in the 1980s. Russia has its own equivalent system (GLONASS), and the European Union has Galileo. Modern smartphones use signals from multiple systems simultaneously for greater accuracy.
Did You Know?
The GPS system was originally designed with "Selective Availability"—a deliberate degradation of the civilian signal to prevent adversaries from using it for precision military applications. The civilian signal was intentionally made inaccurate by up to 100 meters. This was turned off by President Clinton in 2000, immediately improving civilian GPS accuracy from about 100 meters to about 10-20 meters. Modern differential GPS techniques, which use ground-based reference stations to correct for atmospheric errors, can achieve centimeter-level accuracy. This precision is used in precision agriculture, autonomous vehicles, and surveying. Another fascinating application is the use of GPS to measure the movement of tectonic plates. By placing GPS receivers on bedrock and measuring their positions over years, scientists can track the movement of the Earth's crust with millimeter precision, providing invaluable data for earthquake research.
