did you know your GPS needs Einstein to keep good time?

GPS works by timing signals from satellites. their clocks tick at a different rate from clocks on Earth's surface because both speed and gravity affect time. the system has to account for that difference.

a radio signal travels at the speed of light. knowing how long it travelled tells you a distance. combining signals from multiple satellites lets a receiver solve for position and its own clock offset.

the satellites' motion slows their clocks relative to Earth-based clocks by about seven microseconds per day. weaker gravity at their altitude speeds them up by about 45 microseconds per day.

the net effect is about 38 microseconds per day faster. this is built into GPS timing corrections; it is not a tiny optional improvement added to an otherwise accurate clock.

light travels about 300 metres in one microsecond. multiplying 38 microseconds by light speed gives about 11.4 kilometres of range-equivalent timing error per day without correction. actual position error also depends on the satellite geometry and receiver solution.

range error = light speed × timing error; 300 m/μs × 38 μs ≈ 11.4 km

• no. atmospheric delays, orbital information, and other clock errors also matter to the receiver's solution.
• relativity is measurable engineering here: everyday navigation depends on a theory that changes how we understand time.