Moving clocks run slow.
Einstein's special relativity says a clock moving relative to you ticks slower than yours — by nanoseconds a day on a jet, by microseconds a day in orbit, and dramatically once speed nears light itself. GPS satellites have to correct for exactly this, every single day.
Speed v
v → c ⇒ γ → ∞
≈0denser resolution as v → c0.999 c
Time gap after 1 year (moving clock's own time)
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The Lorentz factor γ = 1/√(1−v²/c²) comes from special relativity, the theory Albert Einstein published in 1905. A clock moving at speed v ticks slow by a factor of 1/γ as measured by a stationary observer — so over τ seconds of the moving clock's own (proper) time, the stationary clock counts γ·τ, an extra (γ−1)·τ. This page only models that velocity term. GPS satellites' real onboard clock correction (about +38 µs/day, running fast overall) also includes general-relativity gravitational time dilation — clocks run faster higher up in a weaker gravity well — which is a separate, larger effect this page does not model; don't read this page's velocity-only −7 µs/day figure as the real GPS correction on its own. The "1 year" reference duration is a Julian year (365.25 days = 31,557,600 s). Orbital speeds (ISS, GPS) are treated as constant for this estimate, using the standard instantaneous-velocity time-dilation formula even though orbital motion is technically accelerating, not inertial.