GPS and Relativity

I'm dawdling through a book called, The Science of Interstellar, by the physicist Kip Thorne. Here's an interesting paragraph on GPS (slightly edited):

"Our smart phones rely on radio signals from a set of 27 satellites at a height of 20,000 kilometers.... Each radio signal... tells the smartphone where the satellite is located and the time the signal was transmitted... The scheme would fail if the signal were the true times measured on the satellite. Time at a 20000 kilometer height flows more rapidly than on earth by 40 microseconds each day and the satellites must correct for this. They measure time with their own clocks, then slow that time down to the rate of time flow on Earth before transmitting it to our phones."

Einstein predicted that time moves more slowly relative to locations close to heavy gravitational objects than it does relative to locations that aren't.