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A setting where we still have the rest of our technology, but for reasons - alien space bats, basically - there are no longer any stable orbits around Earth with an altitude higher than about 1000 km.

Could we build a replacement GPS based on satellites in low orbit? I know the existing system is based on geosynchronous orbit, but is that an absolutely necessary quality of any such system, or would using LEO just make the engineering more expensive?

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    $\begingroup$ That would be like creating a restaurant that serves both dinners AND desserts. It already works that way. It's higher than 1000km but could be lower, no problem. So, great idea :) $\endgroup$ – Harper - Reinstate Monica Jul 28 '17 at 2:54
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Global positioning is not dependent on geosynchronous orbit - as covered in the wikipedia article:

Orbiting at an altitude of approximately 20,200 km (12,600 mi); orbital radius of approximately 26,600 km (16,500 mi), each SV makes two complete orbits each sidereal day, repeating the same ground track each day.

As illustrated in the excellent animation accompanying the article, a lower orbit would necessitate more satellites, to ensure that at least four were visible at any point on earth, but a similar constellation of satellites would still work.

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  • $\begingroup$ This pretty much sums it up, but it's also important to note that your orbital period for LEO satellites would be much smaller (spacecraft moving faster) so that the increase in satellites needed wouldn't be overly dramatic. (For reference a polar orbiting satellite with an average altitude of ~500 miles has an orbital period of ~100 minutes, making ~14 orbits per day) $\endgroup$ – Miles Engel Jul 28 '17 at 18:10
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Our GPS system isn't based on geosynchronous orbit, only on knowing the orbits of the satellites with a high level of precision.

Consider this illustration, which demonstrates multiple different orbits on different planes (none equatorial, it would seem); geosynchronous orbit is only possible on the equatorial plane. (Edit: As pointed out in the comments, this only applies to geostationary orbits. Geosynchronous can occur on any plane, but at any rate as noted in the next paragraph our GPS satellites use neither anyway.)

So a constellation of GPS satellites in LEO is absolutely plausible. They'll finish each orbit a lot faster than the ones we use today (orbiting at about 20,200 km -- roughly half the altitude of geosynchronous orbit), but while that affects the numbers being crunched it shouldn't affect the actual functionality of the system.

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    $\begingroup$ That's not quite true. Geosynchronous orbits are possible in any plane- its only geostationary orbits, a subset of geosynchronous, which are restricted to the equator. $\endgroup$ – Logan R. Kearsley Jul 28 '17 at 4:28
  • $\begingroup$ Oops! Good catch, thank you @LoganR.Kearsley! $\endgroup$ – Kromey Jul 28 '17 at 17:10
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Have a look at aviation beacons from the pre-GPS era. Look at NDB's and VOR's. There was even older technology, Omega, (https://en.wikipedia.org/wiki/Omega_%28navigation_system%29). Have few of these land-based systems, and then triangulate their signals to obtain your position.

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    $\begingroup$ The problem is that you need a lot of VORs, given that the usable range is roughly 100 miles/160 km. (For light aircraft: commercial jets fly at higher altitudes and so might pick up the signal at a somewhat longer range.) That's assuming you're high enough to have line-of-sight to the VOR: intervening mountains can block the signal. $\endgroup$ – jamesqf Jul 25 '17 at 5:45
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    $\begingroup$ Don't forget Loran. Which has the advantage of being harder to interfere with then GPS. $\endgroup$ – Firelight Jul 25 '17 at 10:50
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There is nothing stopping satellites from giving your GPS coordinates even if they aren't Geostationary, the only problem is that satellites that aren't geosynchronous will move away from you and be unable to communicate to you when they rotate away from above your location.

The solution is a network of satellites that cover the whole planet and all share their information so at any time there is three or more satellites over head to communicate your coordinates to you.

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All thought not GPS until the Mid 2010s the US maintained Loran-C.

I have used it on a couple of boats back in the late 1980s before we had access to GPS. It was not as accurate as GPS but it used huge ground based antennas and allowed you to use a FANCY box to find your current lat long and then plot the course you wanted.

I remember a US Coast Guard flyer about "Why does the USCG have a base in the Kansas?" and it explaining how to Loran-C and how to Navigate safely in storms with it.

As I recall The Obama Administration decided it was not worth maintaining. Though my gear has all switched over to GPS so I did not follow it much.

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