GPS Satellites Must Account for Relativity

The incredible accuracy of the Global Positioning System (GPS) is a direct, real-world application of Albert Einstein's theories of relativity. Two powerful relativistic effects are at play: special and general relativity. Special relativity predicts that because the GPS satellites are moving at about 14,000 kilometers per hour relative to an observer on the ground, their onboard atomic clocks should appear to tick slower by about 7 microseconds each day. This is a consequence of time dilation, where time moves slower for a moving object from the perspective of a stationary observer.

However, a much larger effect comes from general relativity, which describes how gravity warps spacetime. The satellites orbit far above the Earth, where the planet's gravitational pull is weaker. According to general relativity, clocks in weaker gravitational fields tick faster than those in stronger ones. For GPS satellites, this means their clocks run about 45 microseconds faster per day compared to clocks on the Earth's surface.

When these two effects are combined, the net result is that the clocks on GPS satellites tick about 38 microseconds faster than ground-based clocks each day. While this might seem like an insignificant amount of time, it is crucial for a system that relies on timing signals to determine position. If these relativistic effects were not accounted for, the entire GPS system would be rendered useless, with navigational errors accumulating at a rate of roughly 10 to 11 kilometers every single day. To counteract this, the satellite's clocks are precisely engineered to run slightly slower in space, ensuring they remain synchronized with clocks on Earth.