GPS clock correction
The combined SR + GR clock-rate correction applied by every GPS satellite firmware: kinematic time dilation slows the orbiting clock by ~7 μs/day, gravitational time dilation speeds it up by ~45 μs/day, net correction ~+38 μs/day. Without the correction, position fixes would drift roughly 11 km per day.
Definition
Every GPS satellite carries a caesium or rubidium atomic clock whose ticking rate is offset before launch by exactly the amount required to compensate two relativistic effects. Special-relativistic time dilation: the satellite's orbital speed is roughly 3.87 km/s, giving γ slightly above 1, so the satellite clock ticks slower than ground clocks by about 7.2 μs per day. General-relativistic time dilation: the satellite orbits at about 20,200 km altitude, where gravitational potential is higher (less negative) than at Earth's surface, so by the equivalence principle its clock ticks faster than ground clocks by about 45.9 μs per day. The two effects partially cancel; the net is +38.7 μs per day.
If the correction were not applied, position fixes from GPS trilateration would degrade catastrophically: a 38.7-μs error per day, multiplied by the speed of light, would inject a ~11.6 km/day error into the satellite-to-receiver pseudorange. The fact that GPS works at all is a continuous, civilian-scale verification of both special and general relativity to roughly one part in 10¹⁰. Engineers building the system in the 1970s initially debated whether to bother with the correction; the Air Force operationally confirmed within hours of the first satellite launch in 1978 that without it, the system was unusable. GPS is the textbook example of relativity moving from theoretical exotica to load-bearing infrastructure.