GPS and Time Dilation

Time dilation is written in stone now.

Nowadays everybody knows what GPS is, but several decades ago it was for militaries and airlines only. Quick introduction into the subject from FAA:

from FAA website

Airplanes, advanced military shells, and our smartphones take signals from 3–4 nearest satellites (of the 24 satellites on the orbit) and triangulate the position by deriving distance from each satellite using time delay of the received signal. Clocks on the GPS satellites should be extremely precise, because to get the distance from a satellite, time delay is multiplied by the speed of a signal, which is 300,000,000 m/sec. Thus, even one millionth mistake in time leads to 300-meter error in position. In the early 1980s, despite clocks being very accurate, within the first 24 hours clocks were so off that error in the positioning was hundreds of meters, even miles. Turns out it is because time on the orbit runs faster than on the Earth, the phenomenon known as Einstein’s time dilation. And although time offset was minuscule (the order of its magnitude was about billionth of a second per second), it was accumulated fast, and led to incorrect distance measurements even within the first 24 hours:

24 hours × 3,600 sec × one billionth time dilation × 300,000 km/sec = 26 km/day = 16 miles/day error.

Actually, because GPS satellites are not too far from the Earth, time dilation rate is lower than one billionth, but even with 1/10 of one billionth, error is accumulated by 1.6 miles per day (in a month it will be about 50 miles).

That problem was fixed by making clocks for GPS satellites run a bit slower, so that when they are on the orbit (where time runs a bit faster) they still stay in sync with the clocks on the Earth.

Here is a good explanation on how time delay is used in distance calculation and the need for a 4th satellite signal (due to the error of cheap clocks in receivers):

https://youtu.be/QK1lDsinMwk

Long time ago, even great Newton believed in Absolute Time — that time pace is everywhere and always the same. Not anymore: time dilation is taken into account in modern hardware and software.

Question: Signal delay between GPS satellites and our smart phone should be timed extremely precisely, but clocks in our phones are small and cheap, then how is triangulation possible at all? Answer in

Atomic Clock in Your Pocket

Next 👉1.000000000445 Seconds Pass in GPS Satellite, in 1 Earth-Second.