Summary
Highlights
GPS is an integral part of our lives, utilizing a system of 24 orbiting satellites. It requires at least four satellites to pinpoint a location, relies on atomic clocks, and remarkably, applies Albert Einstein's theory of relativity.
GPS uses a mathematical technique called trilateration. In a two-dimensional scenario, two satellites measure the distance to a receiver (R1 and R2). The receiver's location is at the intersection points of the two circles formed by these distances. The Earth's surface helps eliminate one improbable solution.
In three dimensions, three satellites are needed. Each satellite defines a sphere around the receiver. The intersection of two spheres creates a circle, and the intersection of this circle with a third sphere yields two potential points. Again, the Earth's surface helps identify the correct 3D coordinates.
Satellites are equipped with highly accurate atomic clocks and send radio signals containing the exact time they were sent and the satellite's position. A receiver calculates the difference between the sent and received times, multiplying this by the speed of light to determine the distance to the satellite.
Receiver clocks (like those in smartphones) are not as accurate as atomic clocks, leading to a 'time offset' which causes significant errors. Since all satellites maintain the same time, the time offset of the receiver becomes an additional unknown. To solve for this fourth unknown (three spatial coordinates plus time offset), a fourth satellite measurement is required, eliminating the need for an atomic clock in the receiver.
Even with accurate time measurements, GPS would be incorrect without accounting for relativity. Special relativity dictates that fast-moving satellite clocks slow down by 7 microseconds daily. General relativity states that being higher in weaker gravity causes clocks to tick faster by 45 microseconds daily. These opposing effects result in a net 38-microsecond daily offset. Relativity equations are integrated into satellite systems to adjust for these discrepancies, preventing a 10-kilometer error per day.
GPS was developed by the US Department of Defense and is free for public use. Modern receivers often combine GPS with other navigation systems for greater accuracy. GPS does not require an internet connection, but assisted GPS (A-GPS) uses internet to download satellite location information, significantly speeding up startup times compared to direct satellite downloads.