How many microseconds per day do GPS satellites gain due to relativity?

GPS satellites gain about 38 microseconds per day relative to clocks on Earth because of relativity.

Two effects combine to produce this offset. Special relativity says a moving clock runs slow: GPS satellite motion makes its clock lose about 7 microseconds per day. General relativity predicts that a clock in the satellite’s weaker gravitational field runs fast, adding roughly 45 microseconds per day. The net effect is therefore 45 minus 7, or about 38 microseconds gained each day.

That tiny interval is crucial because GPS determines position from the arrival times of signals. Light travels about 300 metres in one microsecond, so an uncorrected 38-microsecond daily error would quickly create position errors of many kilometres. Engineers account for the relativistic rate shift when GPS satellite clocks are designed and operated.

A common mix-up is to answer 45 microseconds, which is only the gravitational contribution, or 7 microseconds, which is only the motion-related contribution. The quiz asks for the combined relativistic effect.