Every human on Earth vanishes, except for one random person in the US. A button is placed on the summit of Mount Everest that can be pressed to undo this change. Can humanity be restored?

[u/ThePriestofVaranasi]

Every human on Earth vanishes without a trace, except for one random survivor: Ethan from the United States. Moments after the disappearance, a mysterious device materializes before him, displaying a message:
"Humanity can be restored. To activate revival, you must press the button housed at the highest point on Earth—the summit of Mount Everest."

Ethan essentially has as much of a prep time as he wants to gather all the essentials like food, water, weapons, vehicles and everything else that has been suddenly abandoned. He can raid supermarkets, libraries, military depots, and pharmacies for supplies. Ethan can still die of old age so this prep time isn't unlimited.

Now, Ethan faces an impossible gauntlet:
He must travel to Nepal and ascend to the summit of Mount Everest without dying.

Can Ethan survive long enough to reach the button and restore humanity?

[u/guyblade]

This is flagrantly incorrect.

GPS works by each satellite knowing the precise time and where it is going to be at that time. Given the precision needed, that information is computed on the ground and uploaded to satellites based on ground-based observations of them (e.g., laser & radar range-finding + models). Generally, those satellites only have a few weeks of forward-looking data on them at any time.

If humans aren't doing those uploads, then the system breaks down within a month.

[u/Leninlover431 → u/guyblade]

My understanding was that GPS is calculated solely from time-of-flight of the signal, and its the various correction services that rely on the ground-based observations (SBAS). So the accuracy of the system will degrade, yet it will remain functional as long as the GPS sats remain in orbit with functional clocks.

[u/guyblade → u/Leninlover431]

Flight time is important to the calculation, but you have to know where you're measuring from with high accuracy. That's the ephemeris data.

If you look at the GPS spec, it includes an error budget relative to how old the data (ephemeris and other) is on page A-12. Notice that after the ephemeris is only 15 days old that the error is over 200 meters.

[u/EncabulatorTurbo → u/guyblade]

to miss getting a boat to china you need a good deal more substantial drift than 200 meters

[u/guyblade → u/EncabulatorTurbo]

It is important to keep that 200m in context. This image from page A-7 of the doc shows that the degradation seems to get exponentially worse as time goes on.

That section also references this document. While I'm not certain that I'm interpreting the table properly, it seems like the table on page 135 of that document implies that a (block IIR or later) GPS satellite just won't have ephemeris data past 62 days after its last upload. If that's true, there would be a slow degradation, then a complete loss of function at ~2 months.

[u/IEatGirlFarts → u/EncabulatorTurbo]

You could also correct with your compass and heading.