Legacy · Direct Application
GPS and Satellite Navigation
The clocks on navigation satellites tick at a different rate from clocks on the ground. Without Einstein's corrections, your position would drift by kilometers a day.
How GPS Works
Each GPS satellite carries atomic clocks and continuously broadcasts the time and its own position. A receiver picks up signals from several satellites and measures how long each took to arrive. Since radio waves travel at the speed of light, travel time gives distance, and distances to four or more satellites give your position.
Light covers about 30 centimeters in a billionth of a second. The whole system therefore depends on clocks that agree to within a few billionths of a second.
Two Effects, Opposite Directions
The satellites orbit about 20,200 kilometers up, moving at roughly 14,000 kilometers per hour. Both facts matter.
- Special relativity. Because the satellites are moving fast relative to us, their clocks run slow, by about 7 microseconds per day.
- General relativity. Because they are higher in the Earth's gravitational field, where gravity is weaker, their clocks run fast, by about 45 microseconds per day.
The net result is that a satellite clock gains about 38 microseconds per day on an identical clock on the ground.
The Fix
Thirty-eight millionths of a second sounds like nothing. Multiplied by the speed of light it is about 11 kilometers. Left uncorrected, ranging errors would build up at roughly ten kilometers per day, and the system would quickly become useless for navigation.
So the correction is built into the hardware. Before launch, each satellite's clock is set to tick very slightly slower than its nominal frequency, 10.22999999543 megahertz in place of 10.23, so that once in orbit it keeps pace with clocks on the ground.
How Direct Is the Link?
As direct as it gets. Engineers apply the equations of special and general relativity to make the system work. Every time a phone shows a blue dot on a map, it is using both theories.
In Numbers
The constellation had 31 operational satellites as of 2023, each circling the Earth twice a day. A 2019 study sponsored by the US National Institute of Standards and Technology estimated that GPS had generated about 1.4 trillion US dollars in economic benefits for the US private sector between 1984 and 2017.