Megastructures 05 Shellworlds

## Transcript

Last time in the Megastructures Series we looked at building artificial worlds whose gravity was supplied by rotating them. Today we’re going to look at building ones which have their gravity supplied normally, by sheer mass. Now, building a planet is obviously a pretty serious endeavor and uses up a lot of material, but in of itself it’s not high tech. Like a lot of these it’s really more of resource intensive affair. Here on Earth, for every square foot of land there’s about a megaton of rock and magma underneath you, for a rotating habitat, even a pretty elaborate and bulky one, a couple tons a square foot works. So artificial planets of this variety are usually considered impractical, but they are a lot more appealing to a lot of people so today we’re going to talk about a variation of this concept that is a bit more practical, Shellworlds.

The concept behind a Shellworld is that you don’t need to make the whole thing out of rock and metal, which are rare compared to other things like hydrogen and helium. Done as a thin skin of rock and water and air around some filler material, a Shellworld wouldn’t use anymore material than a rotating habitat except for the filler, which could be hydrogen or helium in a low tech version, or could be stuff like artificial black holes or dark matter, which we’ll get to in a bit. The other advantage of ShellWorlds is they let you build your artificial planets at different sizes and still have Earth-normal gravity. You can tailor the gravity to be higher or lower than Earth’s own but the real appeal of the ShellWorld is that you can replicate Earth for all practical purposes.

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So let’s start with a quick look at gravity. When you’re outside a spherical object the gravity on you is linear to its total mass and inverse-square to its radius. Which is to say if you double the mass, you double that force, triple the mass, triple the force. Alternatively double your distance and the force falls to a quarter, triple it and it drops to a ninth, get ten times further away and it’s just 1%. But if you just scale up something like Earth, doubling its radius, you won’t have the same gravity at the surface. Volume rises with the cube, so it’s got 2-cubed or eight times the mass and so eight times the gravitational force, but the distance has also risen by double, so the force drops to a quarter. Eight divided by four is two, so this scaled up Earth has twice the surface gravity. We don’t want that, so the fix would be to use a filler that was half as dense, so it had half the mass.

Similarly if you wanted a planet half the size of Earth but with the same gravity you’d need a filler that was half as dense. That’s why gas like hydrogen and helium comes in so handy, you can change its pressure and density. Do it right and you can even have a hot and pressurized gas counteracting the weight of the shell so it needn’t be super strong. I sometimes think of this subset of a shellworld as a balloon world. The inside of a balloon is at a higher pressure than the air outside it to counteract the tension in the balloon and this is the same concept. In fact done right you could even get away with a magma layer and tectonic plates.

 Saturn
 Water
 Earth
 Lead
 Osmium
 White Dwarf
 Neutron Star

But the key thing is that your filler’s density, to get the same gravity as Earth, is inverse to its size compared to Earth. Whatever the diameter or radius is in comparison to Earth, the density of your filler material is inverse to that. Triple your diameter and you need a third the density for your filler. Build a planet a tenth the diameter of Earth and you need a filler ten times denser. The other aspect is that regardless of how big or small you build one of these things you use the same amount of mass per square foot, one megaton. Whether your shellworld is a few dozen miles across or as big as Saturn, your living area costs you one million tons of matter per square foot. Saturn’s a great example of this because it is about a hundred time’s Earth’s mass, and ten times the diameter, if you built a shell around Saturn the gravity would be Earth normal and you’d have a planet with a hundred times the living area of Earth.

All that actually matters is that average density, the matter can be all crunched up in one spot, like if you dumped an artificial black hole somewhere and built a shell around it. If you are building a shell that isn’t being supported by internal pressure it has to be very strong though. If you’ve got some very rigid and strong material you’re fine, but in many of these cases the strength needed way exceeds what any known material can handle. This where the orbital rings we discussed way back in the first megastructures video come into play. By using a stream of particle orbiting a planet normally, just like a planet ring, you can magnetically levitate material over that. You can go back and review that video if you want the details on how that works. So you build a ring, it appears as a solid object that is not moving though in reality it’s got its own filler of material orbiting the planet akin to a hose turned into a donut full of moving water. The more mass you pile onto that ring the faster the material inside needs to go. Now you build another ring at a different angle running a hair lower or higher. These don’t actually have to be perfect circles either, than can be ellipses, but circles would be preferable by and large and we’re building a sphere anyway. You build another ring at a different angle, and another, and another until you’ve got a grid mesh big enough to comfortably handle your shell and dump dirt and water and air on it.

Now you would probably never build a shellworld like this unless you had figured out controlled fusion, both because you need access to that kind of energy source to build such a thing and keep it’s rings stable, but also because that’s what first justifies such a mass-expensive process in comparison to Rotating Habitats. If you’ve got controlled fusion, or artificial black holes, then hydrogen and helium become very important to you and you’d like to be able to keep your stockpiles in nice accessible chunks. I’ve mentioned earlier that you need a megaton of matter per square foot of living area on these things regardless of size, and to put that in terms of energy if you started off with a filler made entirely of hydrogen and converted it to helium you’d get about 6.3×1023 Joules of energy per megaton. Now the average solar illumination on Earth is about 30 Watts per square foot, or about a billion joules per year. So that means your filler mass would provide fusion fuel to run your world for about 600 trillion years, more than a hundred thousand times longer than our sun has left to its life. You basically are using your filler mass as your power supply, either by using very tall lighthouses or a fake sun actually orbiting your planet. When that’s over you’ve lost about 0.7 percent of your mass so your surface gravity would only be 99.3% of what it was six hundred trillion years ago. That’s a very long time to adapt to a miniscule gravity difference but if you really want it to stay the same you can slowly shrink your world just a little to keep it the same. Now if you can tap into black holes or raw matter to energy conversion you can extend that lifespan a hundred fold and keep shrinking your world to keep the gravity the same. Which would also reduce the power it needs, extending that life time even further.

So Shellworlds, while way more mass-intensive than rotating habitats, actually aren’t over sufficiently long times since if you’re building for the very long term your mass requirement is mostly for energy supplies. I mentioned in the discussion of rotating habitats that you’d keep your fusion fuel in non-rotating tanks around the habitat that also provided shielding from radiation and meteor impacts, but if you are building for a trillion year civilization then you might as well keep your fuel inside where it can provide gravity. You might also use shellworlds on pre-existing worlds like Earth or Mars, since it lets you slowly extract the rocky material inside and replace it with pressurized tanks of gas or buried orbital rings to be switched on. A lot of times when we talk about doing Dyson Spheres or Dyson Swarms I get asked if I think we’d eventually disassemble Earth to provide more material and I would actually bet the answer is no, that we’d hollow it out instead.

But this brings up the Matryoshka variant of a shellworld. In this every shellworld has many layers instead. I would actually bet that Earth itself is destined for some version of this, because we are likely to be pretty attached to our homeworld. You just construct another shell around the first, then another, then another, and you could also go down too. Keeping gravity at the same everywhere isn’t all that hard either. The interesting thing about a spherical shell of matter is that if you’re inside it you don’t feel any gravity at all. It all cancels out. So every layer above you, that you build, has no effect on the gravity of shells below you. Alternatively the mass of that shell does effect people living on it or above it on higher layers. So you just need to make sure each layer has the right total mass based on its distance.

As an example, ignoring air for the moment, if I built a shell forty miles over Earth, which is about 1% of its radius, we’d expect gravity to drop by about 2% meaning we need to add about 2% of the Earth’s mass to that shell to keep the gravity right. Another layer, 80 miles up, would need about 4% of Earth’s mass to work, but you can count that lower layer against that total. A Matryoshka Shell can get very large indeed, just so long as your average density is decreasing to match that. Since air is about five thousand times less dense than the Earth, and about a thousand times less dense then water, you can build some pretty monstrously big worlds before this becomes an issue. Now you can’t just build a big globe of air without it compressing to higher densities, but if you’ve got layers of shells you can prevent that, and you can even have lower densities near to vacuum if those layers are far enough apart, same as our natural atmosphere decreases in density as you get up higher. Your individual layers can be a few hundred feet high or a few hundred miles high, dependent on what you’re aiming for.

Of course if you have a layered shell world like this you need to provide artificial lighting and you’d have to worry about getting rid of heat. Neither plants nor human eyes need the level of lighting provided by noon-time clear sky sunlight so you can dim that down a lot. You can also pump heat outwards. A lot these designs use a variation of the Space Fountain we discussed back in the third video to hold up the sky in addition to orbital rings, and you can channel heat up that way too. Your actual top layer could be just a normal landscape but you might want to abandon that layer to a highly reflective heat pump with a bumpy surface to maximize how much heat you’re radiating away. In some versions of these with black holes in the middle you might go the other way and pump your heat into the black hole but that would depend a lot on how the thermodynamics of black holes actually work and we don’t know for sure if you can just dump heat into a black hole like that. If it is doable then there’s no real limit on your layers. If you need to vent heat via infrared radiation then you can only do so many layers and you’d probably be capped out at under a hundred.

Sometimes we kick around the notion of the largest possible artificial world you can build, and this is an example since you could do this around, for instance, a white dwarf or neutron star and use them for power. Or even around a galactic core black hole, since those are about a trillion times more massive than Earth you’d get a trillion times more area on your shell, whereas even a Dyson sphere only provides about a billion times the living area, and each layer would double that. Such a structure would be wider than the orbit of Pluto but it does have the mass energy of a million suns to run it so it could also stay powered for time increments way long than stars normally live. I’ve always liked this concept because the notion of some massive world with many trillions of times the living area of Earth located at the center of a galaxy just seems like the ultimate galactic empire capital.

Now a common theme to these is always their longevity, even their natural gravity helps to prevent leakage of gases from slowly losing material. That’s why I mention white dwarf stars and neutron stars and black holes in context to these a lot. You really don’t gain much by building these unless you’re aiming for very long lasting civilizations, ones that outlast normal stars. Of course, if we ever find a way to manipulate dark matter, which is the supermajority of matter in the universe and far larger in quantity then rocky matter, it would also make a superb filler material. We don’t know much about dark matter yet besides that it generates gravity so if you could gather and contain it then it might have all sorts of useful purposes but the one we do know of for sure would be using it for filler material to generate gravity. It’s entirely possible that might be its only use, though sweeping it up and keeping it inside a shell is something we can’t do at the moment and may be outright impossible.

Shell worlds are fun for fiction, though rather underused even there, and this particular video series is as much about fiction concepts as pure science so they are worth looking at. Usually they get dismissed as something you’d never actually build just because they use so much mass compared to something like a rotating habitat, but if you are building for the super long term or if you want a place like Earth to remain essentially intact but be bigger, they do start becoming realistically practical. They aren’t limited to examples of things you’d only ever build just because you can. Next time we’re going to take a look at something that you really only would ever build just because you can, by taking a look at flat earth Discworlds, and we’ll try to show that they aren’t actually all that impractical after all. If you want a reminder of when that and other videos come out, click the subscribe button. And don’t forget to like and share the video if you enjoyed it. Thanks for watching and we’ll see you next time.

1. ↑ Approximate Mass of Earth (6×1021 tons) / Approximate Area of Earth (6×1015 sq.ft.) = 1,000,000 tons/sq.ft.
2. ↑ Steel wouldn't really cut it, though Diamond or Carbon Nanotubes might.
3. ↑ Matter to Energy, E=mc2. Hydrogen to Helium Fusion converts 0.7% of the mass to energy. One megaton ~ 6.3×1023
4. ↑ 6.3×1023 Joules/megaton / 109 J/sq.ft/year = 630 Trillion years
5. ↑ Geocentric Fake Suns will be even more amusing when we get to Flat Earth Discworlds in the next episode
6. ↑ You might recall from the Dyson Dilemma video how I mentioned that even if you didn't want to build solar collectors around stars you would still want all that mass for big projects. Building tons of these would be an example.
7. ↑ Named for the Doll-inside-a-doll.
8. ↑ Each successive shell must contain enough mass to compensate for the loss of gravity from distance. Too much or too little would raise or lower the gravity on that layer.
9. ↑ That's why Gas Giants are very dense as you get deeper.