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Comment by tecleandor | Hacker News Reader

Oooooh. I guess that although the signal will be fainter, as they're ~21x further away than usual (240k miles vs 20k), they'll have the advantage of having less noise and practically no signal bouncing.

What I don't know is: Even when receiving a good signal... how difficult would be calculating location when satellites are going to be all concentrated in a really small portion of the sky, and all of them in a proportionally small distance between them, compared to the distance of the receptor?

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The geometry will reduce the accuracy of the fix though as all the satellites will be in the same 8 degrees of the sky.

I wish they had said in the article what the accuracy is!

Is 8 degrees the angular size of the Earth from the moon? Aren't GPS satellites in relatively high orbit, so it could potentially be a larger patch of sky.

I hadn’t realized it, but you are right.

- Orbit height: 20,200 km

- Earths diameter: 12,760 km

https://www.gps.gov/systems/gps/space/

https://science.nasa.gov/earth/facts/

It’s the satellites’ size.

The satellites are 20 Mm high above the ground so their spread is 53 Mm, which is 4.4 times the diameter of the Earth (12 Mm). So yes, the angular size of the satellite cloud (7.896°) is quite a bit larger than the Earth (1.785°) from the moon PoV.

Although since the GNSS satellites use directional antennae pointing at Earth, this experiment only picked up signals where the satellites are on the other side of Earth and close enough to its edge for some of that directional signal to leak past the edge of Earth and get to the Moon. So, the satellites that are nearly 4° away from the centre of Earth cannot be detected because they are beaming their signal nowhere near the Moon, and the detectable angular size is much less than 7.896°.

Geometric dilution of precision (GDOP, or just DOP) is used to evaluate the quality of a GPS satellite configuration; on the back of an envelope any moon-based solution is going to be quite a bit worse relative to terrestrial ones.

At any location on the moon that has a clear view of the Earth, you'll have access to >= half the GPS satellites -- so 15-16+. On Earth that number is as low as 4. The logic would be different (having to pick the farthest apart to get the clearest data to work with) but I can't imagine that it would be problematic for determining location.

I suspect the usable number is much lower and would be just those satellites mostly opposite the Earth but with some signal reaching the moon? I recall the beam width of GPS antennas being like 30 deg (?), so almost all of the signal is directed at Earth.

They'll be using sidelobes. This is what's done at geo altitude which is also above the GPS orbits.

At geo the commercial satellite I worked with had position accuracy within about ten meters, and we always had access to 6-8 GPS satellites at a time. Obviously at the moon the signal is much fainter but my understanding is that it's essentially the same just harder to detect

Most receivers on earth aren't only using the GPS constellation. There's also Galileo, BeiDou, and GLONASS.

Just pointing out that the typical "GPS" accuracy we're used to seeing isn't happening with only 4 satellites in view.

I suppose you also know where the moon is, how it’s rotated and possibly your altitude on the moon.

So you could treat that as a virtual satellite in the other direction.

How do you know those?

besides altitude: you'd just need to know the time which the GPS signals give you. From there it's just calculating rotations.

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