Global Positioning System satellites orbiting the Earth have to continuously adjust their internal clocks to account for Albert Einstein's theory of relativity.

Why GPS Needs Einstein’s Clock Math

A GPS receiver does not locate itself by measuring signal strength. It measures how long radio signals take to arrive from satellites whose positions and transmission times are known. Because radio waves travel at the speed of light, even a tiny timing error becomes a large distance error.

Two effects of relativity pull satellite clocks in opposite directions. Their high speed makes them tick slightly slower than clocks on Earth, as described by special relativity. But satellites are farther from Earth, where gravity is weaker, and that makes their clocks tick faster, as described by general relativity. The gravitational effect is larger, so the combined result is that a GPS satellite clock gains about 38 microseconds per day relative to a ground clock.

Turning Time Into Distance

A microsecond is one-millionth of a second. Light travels roughly 186,000 miles in one second, so a timing mismatch of 38 microseconds corresponds to about seven miles of apparent travel distance. If the system treated the satellite clocks as though they ticked at the same rate as clocks on the ground, that discrepancy would accumulate day after day, and location estimates would drift badly.

GPS accounts for the difference in the clocks’ operating rates and keeps track of their timing so receivers can use the signals correctly. The correction is not a cosmetic refinement: timing is the measurement. A receiver can only calculate a useful position if the timestamps behind its satellite distances stay synchronized closely enough.Relativity is built into GPS because a clock in orbit is part of the navigation instrument, not merely a way to display the time.