The Value of Low Lunar Orbit Space Stations

I am a fan of space guns as a means of lifting material off a planet and into space. These would work horribly for Earth, but the moon is the best place in the entire solar system to station a large-throughput launcher and catcher system… or at least that’s what I’m going to argue here.

I will indulge a little background before getting into some light math as a framework for my argument.

Background on Lunar Material Lifting

Rockets suck, and they suck uniquely when they have to carry all their propellant with them for a high Delta-V trip. The only time they suck even more than this is when the rockets have to be thrown away at the end of the trip.

I really can’t do any better to argue this than linking to the following graphics. If you read these that and still don’t see the central problem of space development, then I’m sorry, you’re wrong.

However, I want to be very clear that this vision constitutes a type of half-solution. Gas stations are very important for eventual large industries in space, but it still sucks that in most cases the gas stations would only be holding stations for the gas. The gas still has to be delivered at a tremendous cost. This results in a new kind of dismal math.

See the following for some of the “outrageous” consequences of keeping the rocket equation, but breaking the trips up into gas stations. This is a wet blanket mostly on the idea of delivering lunar propellant to low Earth orbit. It would still be workable to have EML-2 refueling for deep space missions.

This reality is self-apparent to a good number of people, but we really need to dig into the specifics. The discussion gets extremely location-specific. Near Earth Astroids can be somewhat of a panacea for small volumes of propellant production, but for larger volumes you start to get into the problem of the poor abundance vs. proximity relationship.

This is a case where I believe existing literature is wildly inconsistent. In the 1970s, among the great exuberance for the seemingly inevitable migration into space, authors wrote about mass drivers on the Moon with language such as this.

The mass-driver will be an electrically driven launcher, a sort of electromagnetic catapult. It will accelerate masses of lunar material to escape velocity, 1.5 miles per second. These masses are to be launched, one or two per second, day in and day out, indefinitely. They will fly out into space, curving in the moon’s gravity and slowing down as they go outward. Two days after launch they will reach the catching point, 40,000 miles above the lunar far side. There they will be intercepted.

Note the parts where the payloads coast for 2 days, and “There they will be intercepted.” This particular statement was truly a marvel of wishful thinking. The distances covered over are many times the size of the Earth, itself. Here, as in many other places, an aspiring space cadet hand-waves off a complicating factor that is on planetary scale, when they should have concluded that this factor rules our the entire system.

The particular distance probably refers to a trip to EML-4 or EML-5, the place for large orbital colonies which was in vogue around that time. O’Neil colonies reference this type of architecture, and when you see pictures like this:

Lunar Mass Driver, old NASA Work

The EML-4,5 destination with massive colonies tends to be what they had in mind.

Note that the more modern authors don’t even try to attempt to argue for this or anything even remotely resembling it. The vision used by David Hop tends to either go straight to reusable rocketry, or use tethers. Tethers are kind of the technology in vogue right now, but I suspect that there are precious few years left where that will be taken seriously on full planetary scales.

So, if you dive into the details of how a mass-driver targeting EML-4 or 5 would operate, exactly how would they deal with the targeting problem? One answer is that it will perform active course corrections, by essentially carrying a tiny rocket and navigation system on-board. This might work someday, there’s no scientific blocker. However, the entire problem we would like to solve is eliminating disposable rockets, and this just winds up calling for a million tiny disposable rockets with little mass payoff to justify them.

So on to my claim.

Lunar Orbital Industry

A reasonable catcher/launcher-based lunar transportation system would involve a massive LLO orbiting station. Why? Firstly, it’s cheaper than doing the same things on the lunar surface. Landing on the moon is another stage in the Delta V math. Secondly, micro-gravity is the point of going into space in the first place, and may be better suited for rocket building. Thirdly, it’s the only place in the solar system that a mass-driver makes any near-term sense.

What we don’t have is a place with microgravity and unlimited (on-demand) material resources. You can get these things by coupling a mass driver on the moon with an orbital catching station right above it. This offers vast advantages over astroid capture. It is a factory-style production machine, whereas astroids are opportunistic captures with lots of labor involved in each.

Let’s start diving into the technical details of why this scheme is so much better than the alternatives. Here is my jupyter notebook for the calculations:

Necessarily, the lunar surface mass-driver must be on the Moon’s equator, and the orbital catcher must also be orbiting exactly along the equator.

I assume that the orbiting station must be at 100 km altitude, for the simple reason that this is often quoted as the definition of low-lunar-orbit. In practice, it could be lower (and correspondingly easier), safety permitting.

The mass driver launches payloads exactly horizontally, giving it slightly more velocity than it needs than to just orbit at surface altitude. This causes the payload to gradually drift upward as it moves downrange from the mass-driver.

How do we get the timing of the launch right? Well, because the mass-driver is putting the payload into a similar orbit of the orbiting station, the station is actually in sight of the mass-driver at the exact moment of launch. I tried to illustrate this the best I can.

Local Industrial Environment Around Time of Firing

The exact angle it is launched at doesn’t need to be perfectly aligned, but the muzzle velocity must be tremendously accurate. The accuracy needed is unlikely to be accomplished by the mass-driver itself (whether it be a rain-gun of a gauss-gun). Thankfully, there is plenty of downrange space for stationary equipment that can take correction actions.

Fine Velocity Adjustment

Downrange from the mass-driver, there could quite easily be stationed a integrated system of sensors and dusters. The dusters could simply toss up a bunch of lunar dust in front of the payload. The payload hits some dust particle and slows down, the sensor would determine the quantity of dust to throw up, which determines how much velocity is shed. The dust might need additional separations to assure particles are small enough. The sensors could easily measure exact speed deviations on the order of 0.01 m/s, considering the long distances between each stations (much smaller deviations than this, in fact).

This means that the mass-driver would need to impart slightly more energy than the payload needs, so that the right amount of velocity could be shed as it passes by the stations doing the fine-tuning.

I went into detail in the linked notebook what tolerances are needed in order to get the payload to the station. Some summaries:

  • An anomaly of just 0.01 m/s in the muzzle velocity will cause the rendezvous location to shift by 44 meters. This is considered to be on the borderline of acceptability.
  • A 0.1 degree right/left misalignment in the mass-driver would only add roughly 2.5 m/s to the rendezvous velocity.
  • Variations in the timing would have very little impact on the rendezvous location, roughly approximating a parabolic free-fall trajectory of 1/2 a t², where a is the lower 1/6th lunar gravity.
  • Variations up/down in the angle which the mass-driver acts at are very easily minimized (by a simple level), and will have a very small effect on the rendezvous location by a similar argument to the timing — the orbit is nearly circular and the altitude changes very little with respect to angle around apogee.

This is an extremely concrete set of constraints, and we see exactly 1 critical metric, for which we have an obvious solution by means of a scheme similar to the sensor and duster sequence illustrated above.

In the event of a failed launch, this scheme has simply the case of Newton’s Cannonball. If velocity is insufficient, it just hits the ground. If velocity is too much, the payload will hit the shield behind the mass-driver.

This is unlike other proposed uses of a lunar mass-drivers, which would almost certainly leave the failed launch payloads floating around as space debris. The constraint of LLO removes this from consideration entirely.

What it would be used for? If we would ever want to do zero-gravity manufacture of spacecraft parts, this would be the place to do it. Material availability and proximity is ideal. You would only export high-value items out of the lunar gravity well (things which will ultimately make many trips, so the maiden trip is no big deal), although the station itself could take on a massive amount of mass.

Lunar ice would certainly be a major fraction of all payloads, and this could be processed in lunar orbit to make propellant. This has direct use for the rest of space development, and the location isn’t a bad place to start out with, especially since there are nearly 0% losses going from mining output to propellant in orbit.

In my notebook, I also calculated roughly a payoff time for the scheme. This answer depends heavily on assumptions, but it could be anywhere from 5 hours to 1 year.

We should also consider the possibility to use in-situ lunar materials to produce the solar panels, in which case, it doesn’t even necessarily count toward the mass payoff equation.

There are more questions that I don’t want to quite get into here. For instance, if you had material in low-lunar orbit, then how can you get that to other destinations? I believe this is answerable, although probably somewhat more advanced and later in technological development.

EDIT:

Subsequent to posting this, I realized that I missed a full scientific prefix in the calculations for mass-payback time. I have updated the notebook to reflect this. Without considering attenuation factors for sunlight duration and angle, the mass-payback time considering just the solar panels (and considering just delivery into LLO) is somewhere between 0.2 and 1.6 days. If you add the weight of batteries needed to store the charge over the course of a full orbit, this increases the time by 0.12 days more. You could easily argue a factor of 4 for the solar angle factor. Additionally to that, you could argue to reduce the mass payoff by the mass-fraction involved in getting to and from LEO (at the absolute worst). Even if I combine these very stingy assumptions with the most punishingly poor power to energy ratios for terrestrial solar panels, the payoff for delivery of mass back to LEO comes within spitting range of 1 year.

The payoff time is actually quite a fascinating topic and is a very compelling technical argument for a LLO catcher in itself.

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