How GPS Satellites Correct for Relativity

The Global Positioning System (GPS) is perhaps the most practical, everyday application of Einstein's theories of Relativity. Without precise corrections for both Special and General Relativity, the GPS in your phone would fail by several kilometers in just one day.

The Two Competing Effects

GPS satellites experience time differently than we do on the surface of Earth due to two distinct relativistic phenomena:

1. Velocity Dilation (Special Relativity)

Satellites orbit the Earth at approximately 14,000 km/h. According to Special Relativity, clocks in motion tick slower than stationary ones. This velocity causes the atomic clocks on GPS satellites to lose about 7 microseconds per day relative to a clock on Earth.

2. Gravitational Shift (General Relativity)

Satellites orbit at an altitude of about 20,200 km, where Earth's gravitational pull is weaker. According to General Relativity, gravity warps spacetime and slows time down. Since the satellites are in a weaker field, their clocks tick faster by about 45 microseconds per day.

The Maintenance Solution

The net effect is that the atomic clocks in orbit run faster than Earth-bound clocks by precisely 38 microseconds per day (45 minus 7). While this sounds small, the speed of light is so fast that 38 microseconds translates to an error of about 10 kilometers per day in location tracking.

To solve this, engineers don't adjust the satellites after launch. Instead, the clocks are designed to tick at a slightly different frequency (10.22999999543 MHz instead of 10.23 MHz) pre-launch. Once in orbit, the relativistic effects bring the frequency back into perfect sync with Earth-based receivers.

Conclusion

Every time you navigate to a new coffee shop using your phone, you are benefiting from the successful application of 100-year-old physics. The GPS constellation is a living laboratory proving that time is not a constant, but a variable that must be managed with extreme mathematical precision.