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Why does GPS need corrections from special and general relativity?

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Brian Greene sits in a living room, holding a pen, with handwritten equations m = E/c^2 and E = mc^2 on a whiteboard beside him, highlighting c^2 as the speed of light. — relativity Brian Greene kicking off his *Your Daily Equation* video series with Albert Einstein's famous equation E = mc².

The Global Positioning System (GPS) relies on precise timing to calculate location, making it essential to account for time dilation caused by both special relativity and general relativity.12

Because GPS receivers determine distance by measuring the time it takes for signals to travel from satellites, even tiny discrepancies in clock rates lead to significant positioning errors. Relativistic corrections are necessary due to two primary factors:1

Special Relativity: Satellites move at high velocities relative to observers on Earth. According to special relativity, this motion causes their onboard clocks to tick more slowly compared to clocks on the ground.2
General Relativity: Satellites orbit at a much greater distance from Earth than terrestrial receivers. Because they are in a weaker gravitational field, general relativity dictates that their clocks tick faster than those located closer to Earth's mass.12

Without applying these relativistic corrections, GPS technology would fail to achieve the high level of accuracy required for modern navigation.12