Time Dilation and GPS: How Relativity Keeps Your Navigation Accurate

GPS Clocks Gain 38 Microseconds Every Day Due to Relativity — Uncorrected, Navigation Would Drift 10 Kilometers

The Global Positioning System depends on extraordinarily precise timing. Each GPS satellite carries between one and four atomic clocks, accurate to within a few nanoseconds. To determine a receiver's position, the system measures the time a signal takes to travel from multiple satellites to the receiver and triangulates the result. An error of one microsecond in timing corresponds to roughly 300 meters of position error. If relativistic effects were not continuously corrected, GPS clocks would drift by approximately 38 microseconds per day — producing position errors exceeding 10 kilometers by the end of a single day, compounding further with each passing day. The GPS system is, among other things, a real-world experimental confirmation of Albert Einstein's theories of relativity, running continuously since 1978.

Two Competing Relativistic Effects

Two distinct predictions from Einstein's theories of relativity affect GPS clocks, and they push in opposite directions. Both must be calculated and corrected to maintain system accuracy.

Special relativity: velocity-based time dilation. Einstein's 1905 special theory of relativity predicted that a moving clock runs slower than a stationary one from the perspective of an observer at rest. The effect is described by the Lorentz factor. GPS satellites orbit Earth at approximately 14,000 kilometers per hour (3.9 km/s). At this speed, special relativity predicts that satellite clocks run slow by approximately 7 microseconds per day relative to ground-based clocks. Time slows for moving objects.

General relativity: gravitational time dilation. Einstein's 1915 general theory of relativity predicted that clocks in weaker gravitational fields run faster. GPS satellites orbit at approximately 20,200 kilometers altitude, where Earth's gravitational field is significantly weaker than at the surface. Clocks in a weaker gravitational field tick faster. General relativity predicts that satellite clocks run fast by approximately 45 microseconds per day relative to ground-based clocks.

How Engineers Compensate

GPS engineers address relativistic time dilation through two mechanisms. First, before launch, the frequencies of the satellite atomic clocks are deliberately adjusted — they are manufactured to tick slightly slower than the target frequency, so that once in orbit (where they speed up due to gravitational effects) they arrive at the correct rate relative to ground clocks. The target frequency for ground-based clocks is 10.23 MHz; satellite clocks are pre-adjusted to tick at 10.22999999543 MHz on the ground. This accounts for the expected combined relativistic offset.

Second, continuous monitoring and correction by ground control stations accounts for remaining eccentricity-related variations. GPS orbits are not perfectly circular. As a satellite moves through the slightly elliptical portions of its orbit, its altitude and velocity both change — producing small periodic variations in clock rate that the pre-launch frequency adjustment cannot fully address. The satellite's on-board navigation message includes relativistic correction parameters that GPS receivers use in their position calculations.

The Atomic Clocks That Make It Work

The atomic clocks aboard GPS satellites are cesium or rubidium beam clocks. The current generation GPS III satellites carry three rubidium clocks and one cesium clock per satellite. Cesium atomic clocks define the SI second — the internationally agreed unit of time based on 9,192,631,770 oscillations of the cesium-133 atom. The accuracy of these clocks is approximately 1 part in 10¹³ — meaning they would drift by less than one second over three million years without relativistic effects.

• Cesium frequency standard: Accuracy of approximately 3 × 10^-14; primary frequency standard defining the SI second
• Rubidium frequency standard: Accuracy of approximately 5 × 10^-13; smaller, lower power, used as backup and in modern satellites
• Hydrogen maser: Used in European Galileo navigation satellites; accuracy of approximately 1 × 10^-15; most accurate but larger and more expensive

Experimental Verification History

The GPS system was not the first verification of relativistic time dilation — that came from laboratory experiments and earlier satellite observations — but it provides continuous, operationally critical confirmation at unprecedented scale. The Hafele-Keating experiment of 1971, in which physicist Joseph Hafele and astronomer Richard Keating flew cesium atomic clocks around the world on commercial aircraft, measured time differences consistent with relativistic predictions to within experimental uncertainty. Later experiments with the Gravity Probe A rocket in 1976 confirmed gravitational time dilation to within 70 parts per million of Einstein's prediction. GPS has since confirmed both effects with even greater precision through its operational requirements.

Beyond GPS: Relativity in Other Navigation and Communication Systems

GPS is not unique in requiring relativistic corrections. The European Galileo system, Russia's GLONASS, China's BeiDou, and Japan's QZSS all require the same relativistic accounting. The Galileo system's highly accurate hydrogen maser clocks require corrections for both special and general relativistic effects, as well as the Sagnac effect — a consequence of Earth's rotation that introduces additional corrections as signals travel in the rotating reference frame of the Earth's surface.

The fact that every operational satellite navigation system on Earth requires daily relativistic corrections derived from Einstein's 1905 and 1915 theories is perhaps the most mundane and most profound proof of those theories' accuracy — encoded into every navigation calculation made by every smartphone, aircraft, and ship in the world.