A ground-based GPS unit would keep operating "normally" for six months to a year at least, I hope
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I always assume apocalypse means everyone’s dead, so about 0 seconds.
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GPS satellites are not people though
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Many phone GPS units would die immediately because they rely on the cell network to get the almanac. The satellites would lose accuracy over the course of weeks due to lack of calibration, but keep "working" for decades. The errors could be fixed in software, but it'd be hard.
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By "in software" I mean - set up a base station to measure satellite positions, compute a new almanac from those, and your GPS is good as long as you've updated it within ~4 hours. By "hard" I mean where are you going to find a GPS expert after the apocalypse?
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What flavor of apocalypse? Can you still charge your phone/receiver? Have tectonic plates moved significantly? Is the sky on fire?
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If apocalypse is man-made, then 0 seconds -- the US military will turn it off immediately. If it's "natural", then depends on how it happens -- a solar flare or gamma ray burst will wipe every satellite; a comet will probably leave most satellites intact.
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There are other "GPS" systems like Galileo (EU), GLONASS (Russia) and BeiDou (China). Look at the page for GNSS on Wikipedia.
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Literally not long at all, it drifts a lot. I heard it's something like 60 days worth of ephemeris data is stored in case of problems, in 4 hour chunks. So I guess within 3 months it's basically unusable...
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