Category Archives: Human Settlement of the Solar System

LEOHive

leohive1

Modestly sized structures in space can be diaphanous. That’s because they’re not subject to particularly powerful gravitational effects or other forces. This fact enables contemporary geostationary satellites to deploy solar arrays longer than the wingspan of a 737 that weigh only a few hundred kg. So why spend weight on making them strong? One reason is that the process of in-orbit assembly might require it. Partly built structures may collapse unless they’re strengthened during the construction process.

These forces can be large in the case of large structures. For example, they can be strong enough to prevent the construction of space elevators with any conceivable materials. So, what if we work with the orbit mechanics instead of against them? It turns out that we could construct very large space structures that can be assembled with the help of spaceflight physics. Let’s look at one example, which I’ll call a LEOHive, to suggest its use as a large-scale habitat in low Earth orbit.

The key innovation here comes from research that Ben Reinhardt and I are conducting at Cornell. We found this interesting principle that tells you where it’s safe to stand on the outside of the space station, among other things. I mean “safe” in that you, as an astronaut, can stand with your feet planted on certain surfaces while the physics of orbits presses you into that surface, albeit very gently. That’s awfully good to know if you find yourself in a Sandra Bullock sort of situation or if you’re just interested in wing-walking.

By the way, those of you who are already fans of the Clohessy-Wiltshire equations will wonder if there’s anything new to this. I’m telling you that both Ben and I have looked, and we can’t find any references that talk about reaction forces on the surface of orbiting bodies, despite that it’s a very simple consequence of these venerable equations.

northsouthorbits

To be clear, two objects in orbit don’t attract one another because of a gravitational pull between them. Let me explain with a thought experiment that involves two astronauts. Say they’re both orbiting in the same circular orbit, more or less around the Earth’s equator. An equatorial orbit lets me say “north” and “east,” and you’ll know what I mean, but the same principle applies regardless of where above the earth these things orbit. Let’s tilt one of the orbital planes away from the other, but keep it identical in every respect. Once they’re in these two intersecting orbits, the two astronauts encounter each other twice per orbit. If one begins north of the other, he or she will eventually pass the other astronaut toward the south, and back up again half an orbit later, forever. The figure above shows these two paths.

Here’s where the Reinhardt principle comes in. If the southerly astronaut extends an arm up to the northerly astronaut, the northerly one can stand on it. The arm reacts the forces that would tend to pull that astronaut southward, without the need for the bottom one to grip the top one at all. In this case, both astronauts now travel on a single circular trajectory that averages the two earlier orbits. If they ever lose contact, they’ll return to their north-south dance.

astronauts

The Reinhardt principle applies to many more situations than only this north-south oriented pair of objects in orbit. In fact, Ben has come up with equations and a convenient picture that shows where, on the surface of an orbiting sphere, an object always feels some inward acceleration. He’s also working on a 3D plot that shows all the places on the International Space Station where something can park in this way.

In particular, the Reinhardt principle simplifies building a large, delicate structure in Earth orbit. It tells you where to place elements of this structure relative to a perfect circular reference orbit so that the components stay put while the glue dries, cement hardens, epoxy cures, genetically modified lichens grow, water freezes, astronauts attach 3D printed rivets, what have you.  Here are the rules:

  • Any component that we place above or below a surface—again, in this north-south sense—wants to press itself into that surface.
  • Any component we place inside or outside a surface—in the direction toward the Earth or deep space —wants to accelerate away from that surface. However, a component placed on the Earthward side of a surface that is outside the orbit (toward deep space) wants to stay on that side, as does its counterpart placed on the spaceward side of a surface that is Earthward of the reference orbit.
  • Any component that we place ahead of or behind a surface—in the east-west sense—feels no need to accelerate toward or away from the surface at all. However, all these rules apply simultaneously. So this rule in combination with the others still allows us to adhere components to one another.

So, consider a sort of rover that assembles truss elements or other large components. It does so autonomously, moving from component to component, adhering them together and moving on while some time-consuming chemical process hardens the structure. Again, that could be any one of a number of ways to adhere structures together. The LEOHive built this way takes shape first in a north-south direction and then extends outward in the other two dimensions leaning on interlocking connections made possible by the placement of earlier components.

Quite a few subtleties remain. As the structure takes shape, its mass distribution should conform to the principles of gravity-gradient stabilization. Long story. Ask me another time. Also, as the rover adds components, the mass center shifts, possibly changing how the rules apply across the structure. Planning the assembly to accommodate these subtleties doesn’t seem like a show-stopper to me, although coming up with a general algorithm will require the attention of at least one interested graduate student.

We do the same sort of thing on Earth, although we don’t typically think very hard about it. We assemble buildings from the ground up, parallel to gravity, because it just makes sense that way. The Reinhardt principle provides the insight we need to establish an analogous process for in-orbit construction.

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