A couple of weeks ago, I had a post about how the rate at which clocks run is affected by the strength of the gravitational field in which they are in. So a clock on the surface of the moon would run faster than an identical clock on the surface of the Earth because the gravitational field there is less than the field here.
Then a couple of days ago I watched an episode of the PBS TV series Nova where they ran again a 45-minute program titled Inside Einstein’s Mind that looked at how he used thought experiments to arrive at his ideas of relativity. At the 39:00 minute mark, they show an experiment involving two identical atomic clocks, each accurate to one billionth of a second. After synchronizing them to give identical times, one is kept at sea level while the other is taken close to the top of Mount Sunapee in New Hampshire, where the peak is at a height of 831 m. After four days, the clock at the top is brought down again and compared with the other and is found to be ahead of the clock at the bottom by 20 nanoseconds, which agrees with what the general theory of relativity predicts.
The show also said that if adjustments are not made for this effect, the clocks on the GPS satellites that are at heights of about 28,000 km above the surface of the Earth would differ from the clocks on Earth and thus introduce errors into distance estimates. Over a day, the resulting error could be as much as six miles.
You can see the program below or by clicking the link for it above.