Add them up: 38 microseconds a day

Add them up: 38 microseconds a day

Speed makes the clock lose 7.2 microseconds, and gravity makes it gain 45.7 microseconds. Together, a satellite clock runs about 38.5 microseconds a day ahead. One microsecond was 300 m, so multiply and you get about 11.5 km a day. If nobody fixed this, the distance to every satellite would be measured wrong by 11.5 km a day.

Why?The two effects push in opposite directions. The lower a satellite orbits, the faster it must fly, so the speed effect grows; the higher it orbits, the weaker gravity gets, so the gravity effect grows. At GPS height, the gravity effect is about 6 times bigger, so the clock runs ahead. On the International Space Station, which orbits much lower, clocks actually run slow.

Learn moreThis calculation leaves out Earth’s spin and the slightly squashed shape of the orbits. Even so, the result is almost the same as the value GPS engineers use.

How far a satellite clock runs ahead each day

+38.5 μs

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