How GPS Knows Where You Are and What Role Einstein Plays
GPS determines location with meter accuracy, but the system must account for effects from Einstein's theory of relativity. Satellite clocks on orbit run faster than Earth clocks by 38 microseconds per day due to differences in speed and gravity. Without correction, navigation errors would reach kilometers.
GPS determines location with meter accuracy, but for this the system must account for an effect that people don't even notice. Satellite navigation has become an everyday technology. GPS helps plan car routes, find addresses, track transport, and locate smartphones. However, behind the familiar point on the map lies a complex system of calculations that must even consider Albert Einstein's theory of relativity. At the heart of GPS is a constellation of satellites constantly transmitting radio signals. These signals contain information about the satellite's position and the exact time the signal was sent. Extremely accurate atomic clocks are used on board, because even a tiny time error can significantly affect coordinate determination. A smartphone or navigator receives signals from several satellites simultaneously. Since radio waves travel at the speed of light, the device can determine the distance to the satellite by the time it took the signal to travel. For reliable positioning, signals from at least four satellites are usually needed. This allows calculating the receiver's three spatial coordinates and simultaneously correcting the error of its own clock. This is where the problem arises that cannot be solved without modern physics. Time on Earth's surface and in orbit flows slightly differently. According to special relativity, the satellite's high-speed motion causes its clock to run slightly slower relative to Earth clocks. This effect is about 7 microseconds per day. Simultaneously, an opposite effect described by general relativity occurs. GPS satellites are about 20,000 kilometers above Earth's surface, where the gravitational field is weaker. Therefore, their clocks run faster than Earth clocks by about 45 microseconds per day. After accounting for both effects, the difference is approximately 38 microseconds per day: satellite clocks without correction would lead Earth clocks. At first glance, a few dozen microseconds seem completely insignificant. However, for a system that determines distances by the speed of light, this is a huge error. Light travels about 300 meters in just one microsecond. If relativistic effects were not accounted for, navigation errors would quickly accumulate and reach many kilometers. GPS as we know it would be practically useless for precise location. Therefore, satellite clocks are pre-corrected, and the system accounts for the differences between time in orbit and on Earth. As a result, effects that cannot be felt in everyday life become critically important for navigation. Other factors also affect GPS accuracy. The signal passes through the atmosphere, can reflect off buildings and other objects, and the satellite positions relative to the receiver constantly change. Modern devices use additional correction methods to reduce errors. GPS has become one of the most vivid examples of practical application of fundamental physics. A theory that over a century ago explained the nature of space, time, and gravity now works unnoticed every time a person opens a map on a smartphone and tries to determine where they are.