GPS would fail within a day if it ignored Einstein's relativity.

A GPS receiver estimates its location from precisely timed radio signals. Multiplying signal travel time by the speed of light gives a distance-like quantity called a pseudorange. Because radio waves travel so quickly, even a tiny timing mismatch corresponds to a substantial ranging discrepancy. Accurate clocks and a shared time model are therefore essential.

Two relativistic effects pull in opposite directions. A satellite's orbital motion makes its clock run slower relative to a comparable Earth-centered reference description, an effect associated with special relativity. Its higher altitude places it in a weaker gravitational field, making its clock run faster relative to clocks near Earth's surface, as described by general relativity.

For nominal GPS conditions, the motion contribution is roughly minus 7 microseconds per day, while the gravitational contribution is roughly plus 45. The combined result is about plus 38 microseconds daily. These rounded figures describe an important clock-rate correction, not the complete catalogue of timing and signal-propagation effects handled by the system.

Einstein published special relativity in 1905 and general relativity in 1915, long before satellite navigation became an engineering project. Atomic clocks later made their timing predictions experimentally testable. NIST describes comparisons involving airplanes, satellites and clocks at different elevations as evidence that motion and gravitational conditions affect measured clock rates.

GPS made those effects operationally important. Rather than assuming every good clock must agree everywhere, its designers incorporated a consistent relativistic timing framework. The predictable average orbital clock-rate offset is handled in the satellite clock design and frequency setting, while additional corrections address changing conditions during actual operation.

Orbits are not perfectly circular, so a satellite's speed and gravitational potential vary during each orbit. Receivers apply a broadcast-orbit-based relativistic correction for this periodic effect. Earth's rotation also matters when relating signal transmission and reception in the rotating terrestrial frame, commonly discussed through the Sagnac correction.

The familiar "GPS would fail within a day" statement captures the importance but overstates the precision of a deadline. An untreated rate offset would rapidly spoil accurate ranging, yet actual position errors depend on satellite geometry, receiver clock estimation and which corrections were removed. There is no universal instant when every receiver suddenly stops working.

Multiplying 38 microseconds by roughly 300,000 kilometers per second gives about 11 kilometers. This illustrates the light-travel distance corresponding to that accumulated timing difference. It should not be presented as a guaranteed daily displacement of the location marker on every phone, because receiver solutions estimate several unknowns simultaneously.

A receiver commonly uses signals from at least four satellites to solve for three position coordinates and its own clock offset. That clock estimation does not make relativity optional: the satellite clocks, orbit calculations and transmission timestamps must still be mutually consistent. Relativity is part of the model that makes those measurements fit together.

GPS is a timing system used to infer position, not a satellite camera looking down at a receiver. Its relativity corrections belong alongside orbital information and atmospheric modeling. Accurate navigation depends on combining these pieces rather than crediting one correction with solving every source of positioning error.