How GPS Uses Relativity
Understanding Time Dilation in Satellites and Synchronization
Introduction to GPS and Relativity
The Global Positioning System (GPS) is a network of satellites that provides location and time information anywhere on Earth. What's fascinating is that GPS wouldn't work accurately without accounting for Einstein's theories of relativity.
GPS satellites orbit at about 20,200 km above Earth, moving at approximately 14,000 km/h. At these speeds and altitudes, both special and general relativity affect the satellites' clocks compared to clocks on Earth.
Time Dilation in GPS Satellites
There are two relativistic effects at play:
- Special Relativity: Due to their high speed (about 14,000 km/h), satellite clocks run slower by about 7 microseconds per day compared to clocks on Earth.
- General Relativity: Due to being in a weaker gravitational field (higher altitude), satellite clocks run faster by about 45 microseconds per day.
The net effect is that GPS satellite clocks gain about 38 microseconds per day (45μs - 7μs). Without correction, this would cause positioning errors of about 10 km per day!
How Time Dilation Affects GPS Accuracy
Here's what happens if we don't account for relativity:
- After 1 second: ~10 meter error
- After 1 minute: ~600 meter error
- After 1 hour: ~36 km error
- After 1 day: ~864 km error
This is why GPS engineers must build relativity into the system design.
GPS Relativity Simulation
Try this interactive demonstration to see how relativity corrections affect GPS accuracy:
Frequently Asked Questions
Why does GPS need relativity to work accurately?
GPS requires nanosecond-level timing accuracy. The 38 microseconds per day difference due to relativity would cause positioning errors of about 10 km per day if not corrected. Relativity provides the framework to understand and compensate for these timing differences.
How is relativity built into GPS systems?
GPS accounts for relativity in three ways:
- Satellite clocks are pre-adjusted to run slightly slower before launch
- Ground stations continuously monitor and correct clock drift
- GPS receivers apply additional corrections based on satellite data
