Why do GPS satellites tick precisely 38 microseconds faster than clocks on Earth?
The GPS satellite clocks actually need to tick over 38 microseconds per day (!) slower than terrestrial clocks in order to compensate for relativistic time dilation and contraction effects – at least, they would tick that much slower if they were still on the ground. They do indeed speed up by that amount in orbit, so they’re designed to run slower on the ground in order to compensate for that.
There are two things going on simultaneously here, and they work against each other, but don’t quite cancel each other out, resulting in that 38-microsecond difference.
It’s all Einstein’s fault:
According to his special theory of relativity, clocks onboard the satellites should be running slower due to their high relative motion. It’s essentially the story of the twins, one of which boards a fast spaceship for a round trip around the galaxy and returns having only aged a few years, while his brother has been dead for centuries upon his arrival. For the speeds of the satellites, this translates into the clocks losing about 7 microseconds per day.
The general theory of relativity, on the other hand, predicts that clocks in a strong gravity field run slower, like how time slows down as you approach a black hole. This effect causes the clocks in the satellites to run faster than they do here on the ground, due to the fact that they don’t feel the Earth’s gravity as strongly as clocks on the ground do. This effect speeds the clocks up by about 45 microseconds per day.
45 – 7 = 38 microseconds per day too fast.
Note that GPS requires you to be able to measure time differences in the order of nanoseconds. 38 microseconds = 38,000 nanoseconds (per day). Ignoring such a clock drift introduces position errors within minutes, and add up to about 10 km of position drift per day.