GPS satellites would give increasingly inaccurate locations without Einstein’s theories of relativity because their clocks tick at a different rate from clocks on Earth. Although the difference is only a few millionths of a second per day, even such a tiny timing error can translate into substantial positioning errors. Without corrections for relativity, GPS measurements would drift by several miles each day, eventually making the system unreliable for navigation.
This happens because GPS depends on extremely precise measurements of time. Satellites transmit signals containing information about their positions and the exact times those signals were sent. Receivers on the ground use the time it takes for the signals to arrive to calculate their distances from the satellites. Since radio signals travel at the speed of light, even a tiny error in timing produces a significant error in distance.
The surprising part is that GPS works accurately only because engineers account for two effects predicted by relativity: special relativity, which describes how motion affects time, and general relativity, which explains how gravity affects time.
Why GPS depends on extremely accurate clocks
The Global Positioning System (GPS) is a network of satellites orbiting Earth that provides positioning, navigation, and timing information. It is widely used in smartphones, vehicles, aircraft, ships, surveying equipment, and many other technologies.
Each GPS satellite carries highly accurate atomic clocks. These clocks measure time using the predictable vibrations of atoms, allowing them to maintain exceptionally precise time standards.
To determine a receiver’s location, GPS relies on a technique called trilateration. This method calculates a position by measuring distances from several known reference points.
A GPS satellite broadcasts a radio signal that includes its orbital information and the time at which the signal was transmitted. A receiver compares that transmission time with the signal’s arrival time. Multiplying the elapsed time by the speed of light gives the approximate distance between the satellite and the receiver.
For example, light travels approximately 300,000 kilometers per second. In just one microsecond, it travels about 300 meters. That means a timing error of one-millionth of a second can produce a distance error of roughly 300 meters.
A GPS receiver generally needs signals from at least four satellites to determine its three-dimensional position and correct for its own clock error. The accuracy of the entire calculation depends on knowing when each signal was transmitted and received.
This is why even tiny differences in how clocks measure time matter so much.
How special relativity affects GPS satellite clocks
Einstein’s special theory of relativity, published in 1905, explains how measurements of time and space depend on relative motion.
One of its central predictions is time dilation: a clock moving relative to an observer ticks more slowly than a clock at rest in that observer’s reference frame.
GPS satellites orbit Earth at approximately 14,000 kilometers per hour. Because they move so quickly relative to clocks on Earth’s surface, their onboard clocks experience time dilation.
From the perspective of an observer on Earth, the satellite clocks tick slightly more slowly than they would if they were stationary relative to Earth.
The effect is extremely small but measurable. Special relativity causes GPS satellite clocks to lose approximately 7 microseconds per day compared with clocks on Earth’s surface.
That may seem insignificant, but GPS cannot ignore it. If engineers failed to account for this difference, the satellite signals would gradually become inconsistent with the timing expected by ground-based receivers.
The resulting distance calculations would become increasingly inaccurate.
How general relativity affects GPS satellite clocks
Special relativity is only part of the explanation. General relativity introduces another effect that is even more important for GPS.
According to Einstein’s general theory of relativity, gravity affects the passage of time. Clocks in stronger gravitational fields tick more slowly than clocks in weaker gravitational fields, when their rates are compared under the appropriate conditions.
Earth’s gravitational field is stronger near its surface than it is at the altitude where GPS satellites orbit.
Consequently, GPS satellites experience weaker gravity than clocks on the ground. Their onboard clocks therefore tick faster than ground-based clocks.
This is known as gravitational time dilation.
GPS satellites orbit at an altitude of approximately 20,200 kilometers above Earth’s surface. At this height, the gravitational effect is weaker than it is on the ground.
General relativity predicts that satellite clocks gain approximately 45 microseconds per day compared with clocks on Earth’s surface.
This is a larger effect than the approximately 7-microsecond daily loss caused by the satellites’ orbital speed.
The two effects work in opposite directions: special relativity slows satellite clocks, while general relativity speeds them up.
What happens when the two relativistic effects are combined?
The practical accuracy of GPS depends on accounting for both theories.
The daily effects can be summarized as follows:
| Relativistic effect | Change in satellite clock rate |
|---|---|
| Special relativity | About 7 microseconds slower per day |
| General relativity | About 45 microseconds faster per day |
| Combined effect | About 38 microseconds faster per day |
The combined result is that GPS satellite clocks gain approximately 38 microseconds per day relative to clocks on Earth’s surface.
This difference might appear too small to matter. However, because GPS signals travel at the speed of light, the timing discrepancy creates a substantial positioning error.
Light travels approximately 300 meters in one microsecond. Therefore, a timing difference of 38 microseconds corresponds to roughly 11.4 kilometers of signal travel distance.
If the relativistic effects were ignored, the resulting positioning errors would accumulate rapidly. Within a day, the system could develop errors on the order of 10 kilometers, or about 7 miles.
GPS would no longer provide the reliable location information that people expect from modern navigation systems.
Why GPS engineers must correct clocks before satellites begin operating
GPS engineers do not simply launch satellites and allow their clocks to run without adjustments. Relativistic effects are incorporated into the system’s design and operation.
Before launch, satellite atomic clocks are adjusted so that, once the satellites reach their intended orbits, their average rates match the GPS system’s reference time as closely as possible.
This requires accounting for the predictable difference between time on Earth’s surface and time at satellite altitude.
The system also applies ongoing corrections to account for smaller variations in satellite clock behavior and orbital motion.
For example, satellite clocks are not perfectly identical. Even highly accurate atomic clocks experience small changes in frequency over time. GPS control stations monitor satellite performance and determine corrections that can be included in the navigation messages transmitted to receivers.
There are also additional relativistic effects associated with the shape of satellite orbits. GPS satellites do not travel in perfectly circular paths, so their distances from Earth and their speeds vary slightly throughout each orbit.
These variations produce small periodic changes in clock rates. GPS receivers and satellite systems account for these effects through relativistic correction calculations.
Relativity is therefore not merely a theoretical consideration added to explain GPS after its development. It is an essential part of the engineering that makes the system function.
Why the speed of light makes tiny timing errors so important
The relationship between time and distance is central to understanding why GPS needs relativistic corrections.
GPS signals are electromagnetic waves that travel at the speed of light in a vacuum. Their travel time is used to estimate the distance between satellites and receivers.
Because the speed of light is so enormous, a small timing error can correspond to a considerable distance.
Consider what happens when a satellite clock runs slightly faster than expected. Its transmitted timestamp will gradually become inconsistent with the reference time used by the GPS system.
A receiver may interpret that difference as evidence that the signal traveled a longer or shorter distance than it actually did.
The receiver then uses these incorrect distances to calculate its position.
The problem is not that the satellite has moved to the wrong place or that its radio signal has changed direction. The problem is that the receiver is using inaccurate timing information to interpret the signal’s journey.
This distinction is important. GPS does not directly measure physical distance with a ruler. It calculates distance from signal travel time, making accurate timekeeping fundamental to accurate positioning.
Does relativity affect GPS receivers on Earth too?
Yes, although the effects on ground-based receivers are different from those on orbiting satellites.
A GPS receiver on Earth’s surface is also subject to relativistic effects. Its clock experiences gravitational time dilation and time dilation associated with Earth’s rotation.
However, GPS receivers generally do not need atomic clocks of their own. Instead, they use signals from multiple satellites to estimate and correct their internal clock errors.
The receiver calculates four unknowns: its three spatial coordinates and the offset of its clock relative to GPS system time.
Using signals from at least four satellites allows it to solve for these values simultaneously.
The satellite clocks, meanwhile, must be maintained and corrected with much greater precision because their timing information forms the foundation of the positioning calculations.
This arrangement allows relatively inexpensive devices, including ordinary smartphones, to determine their locations using signals from satellites equipped with sophisticated atomic clocks.
Why GPS provides a practical demonstration of Einstein’s theories
Relativity is often associated with extreme situations, such as objects traveling close to the speed of light or the intense gravitational fields surrounding black holes. GPS demonstrates that its predictions also matter in everyday technology.
The satellites do not travel anywhere near the speed of light, and Earth’s gravitational field is not exceptionally strong compared with those found around compact astronomical objects. Nevertheless, the combination of orbital speed, altitude, and extraordinary timing precision makes relativistic effects impossible to ignore.
GPS is particularly interesting because it depends on both major branches of Einstein’s relativity.
Special relativity explains why the motion of satellites makes their clocks run slower. General relativity explains why the weaker gravitational field at orbital altitude makes those same clocks run faster.
Neither correction alone is sufficient. The system needs both to maintain accurate synchronization.
This principle extends beyond GPS. Other satellite navigation systems, including Europe’s Galileo, Russia’s GLONASS, and China’s BeiDou, also account for relativistic effects in their designs.
Relativity is not an optional refinement for satellite navigation. It is part of the physical reality that engineers must accommodate.
The importance of getting time right
GPS works because it combines precise satellite positioning, radio communication, atomic clocks, and carefully calculated corrections. Its accuracy depends on treating time as a physical quantity that can change depending on motion and gravity.
Without special relativity, engineers would overlook the slowing of satellite clocks caused by their orbital speed. Without general relativity, they would miss the faster ticking caused by the weaker gravitational field at satellite altitude.
Together, these effects produce a net clock-rate difference of approximately 38 microseconds per day. That tiny interval corresponds to more than 11 kilometers of light travel distance.
The lesson is straightforward: accurate navigation requires accurate time, and accurate timekeeping requires understanding how the universe actually works. Einstein’s theories make that understanding possible, helping GPS deliver reliable location information to billions of people around the world.