In 1971, two scientists borrowed four atomic clocks from the Naval Observatory and flew them east and west around the globe. Comparing these atomic clocks with those left behind on the ground showed that those flying East experienced a slowing of time (Einstein’s Theory of Relativity) equal to 59 nanoseconds, and those flying west had time slow for them by 273 nanoseconds, the difference being caused by the fact that the Earth is rotating to the east.

Can you imagine the complexities involved in the GPS system? General relativity states that clocks tick slower the nearer it is to a gravity source. Clocks on Earth are slower than one in space, and one on a mountain top is faster than one in the valley.

Yet, special relativity states that, on faster moving bodies, the clock will tick slower than on slower moving bodies. One traveling in space ticks slower than one on Earth.

Thus, the atomic clocks on a GPS satellite traveling at speed will tick slower than one stationary on Earth, BUT atomic clocks on a GPS satellite in weightless space will tick faster than one in the gravity well of Earth. These two factors do not cancel each other out completely, but, obviously, they do to some extent.

Yet, there are other factors! The Earth spins! This plays a part in relativity as well. Elliptical orbits cause havoc in figuring out the relationship of relativity. Tidal potentials of the moon and sun, which are not always a consistent distance away, should also be considered. What elevation are you at with your GPS?

There is a lot that goes into this! Nanoseconds are important! Nanoseconds mean being off of your correct position by meters (one nanosecond, or one billionth of a second, is equal to one foot of position error in your GPS). Of course, corrections are figured out and made. They use the Earth's geode at mean sea level as the position in which to correct these relativistic errors. The corrections with WAAS are in the order of about 2.4 meters, but I'm sure it must be ever changing.

But, can you imagine what a mind-bending thing to figure out all of this? And, it is only a small fraction of what goes into the GPS system.