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Comment by thatcherc | Hacker News Reader

A challenge there is that there are very few stable lunar orbits! High orbits are perturbed by Earth's gravity (3-body problem) and low lunar orbits are perturbed by the lumpy distribution of mass in the Moon's interior [0]. Lunar GNSS satellites with a little bit of onboard propulsion could probably correct for some of these perturbations but once they ran out of fuel they would have a limited orbital lifetime.

[0] - https://en.wikipedia.org/wiki/Lunar_orbit#Perturbation_effec...

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Technically, satellite positioning only needs 1 satellite. GPS requires several but one of its forerunners was Transit[1] which I believe only needed a signal from a single satellite at a time. It worked by measuring the doppler shift of the signal coming from the satellite. Of course that only works if the orbit can eventually cover all (or much of) the surface and for all I know there is no such frozen orbit for the moon. Also, it would still presumably require extensive surface-based tracking and correction.

[1] https://en.wikipedia.org/wiki/Transit_(satellite)

I wonder if lunar space elevators might be the fix here. If I understand correctly, such an elevator would not be as subject to the perturbations since the tension would keep it's orbit stable (is it still an orbit if it's tethered?).

Another option might be a LORAN style system put up on towers. With lower gravity and no atmosphere I imagine we could stick transmitters up very high without super complex construction, maybe even just a giant carbon fiber tube with a transmitter at the top.

Let’s put a high power laser on the end to send advertisements in Morse code to anyone looking towards the moon.

Raster-scan it to deliver persistence of vision ads!

Oh wow, good reading in that link.

I had no idea the moon was that lumpy. The wiki entry says that despite the mascons there are 4 known stable orbital inclinations?

That is correct. The NASA page link (now 404) has a bit more on the orbits and their history.

https://web.archive.org/web/20210307002503/https://science.n...

And they're very lumpy.

> The mascons' gravitational anomaly is so great—half a percent—that it actually would be measurable to astronauts on the lunar surface. "If you were standing at the edge of one of the maria, a plumb bob would hang about a third of a degree off vertical, pointing toward the mascon," Konopliv says. Moreover, an astronaut in full spacesuit and life-support gear whose lunar weight was exactly 50 pounds at the edge of the mascon would weigh 50 pounds and 4 ounces when standing in the mascon's center.

That is a great link. Do you know if any of it is outdated now?

It is still all completely correct. There may be some new findings, but the lunar prospector ( https://en.wikipedia.org/wiki/Lunar_Prospector ) did all the work and this was written after that.

could the legrange points work? dealing with the 3 body orbits would be a pain, but they would give you nice separation

You need signals from 3+ different locations to navigate, and the two stable Lagrange points, L4 and L5, are as far from the moon as Earth is: https://en.wikipedia.org/wiki/Lagrange_point.

But-- GPS already produces an okayish fix. Improving it with another signal from somewhere else would make a big difference.

> and the two stable Lagrange points, L4 and L5

We have plenty of spacecraft hanging out around L1, etc. It's possible to orbit it without too much issue. Having one broadcast a navigation signal synchronized with GPS would not be too bad.

> are as far from the moon as Earth is

The issue isn't that they're far away-- it's that they're all in pretty much the same direction. There's very small uncertainties in orbits and measured path length, but if they're all in the same direction you get very poor lateral position.

This is the same effect you can get if you can only see a little tiny bit of the sky with GPS. You might have enough satellites to navigate, but since they're all close to the same direction the navigation solution is much worse.

I meant the earth/moon, not earth/sun Lagrange points.

Is the 3 body problem mostly meaningful above a certain mass? If you had small satellites could you deal with it?

The mass of a satellite is already trivial compared to the mass of the moon.

The restricted three-body problem deals with the case when the third mass is trivial and the orbits are circular. The new solutions in this case are the Lagrange points. That's helpful, but doesn't make finding dynamic solutions much easier on it's own.

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