A Tiny Clock Error Becomes a Large Position Error
A GPS receiver figures out where it is by comparing the arrival times of signals from several satellites. Because those signals travel at the speed of light, even a small timing mistake changes the apparent distance: an error of one millionth of a second corresponds to about 300 meters.
The satellites’ clocks do not tick at quite the same rate as clocks on Earth. Two effects pull in opposite directions. Their high orbital speed makes their clocks run slightly slower, as described by special relativity. But they are farther from Earth’s mass, where gravity is weaker, so general relativity predicts that their clocks run faster. The gravitational effect is larger; together, the two effects make a satellite clock gain about 38 microseconds per day relative to a clock on the ground.
How GPS Keeps the Timing Useful
GPS accounts for this difference when its satellite clocks are configured and when the system processes their signals. Without that adjustment, the timing mismatch would steadily distort the distances calculated from satellite signals. The resulting position error could grow to roughly 10 kilometers a day—not because the satellites suddenly moved off course, but because the receiver would be measuring their signals against clocks that had drifted out of sync.
That is why relativity is not merely an abstract correction in this system. GPS works as a practical positioning tool because its engineers treat the satellites’ clocks as part of the navigation hardware—and account for how gravity and motion change their timekeeping.
