Infinite Powers: How Calculus Reveals the Secrets of the Universe

by Steven H. Strogatz

gravity could have a strange effect on time: The passage of time could speed up or slow down as an object moves through a gravitational field. Bizarre as this sounds, it really does occur. It needs to be taken into account in the satellites of the global positioning system as they move high above the Earth. The gravitational field is weaker up there, which reduces the curvature of space-time and causes clocks to run faster than they do on the ground. Without correcting for this effect, the clocks aboard the GPS satellites wouldn’t keep accurate time. They’d get ahead of ground-based clocks by about 45 microseconds per day. That may not sound like much, but keep in mind that the whole global positioning system requires nanosecond accuracy to work properly, and 45 microseconds is 45,000 nanoseconds. Without the correction for general relativity, errors in global positions would accumulate at about ten kilometers each day, and the whole system would become worthless for navigation in a matter of minutes.