Science fiction has explored super-sized habitats of various kinds – Dyson Spheres, Alderson Disks, Ringworlds, Orbitals, and so forth. All of these suffer from one basic fatal flaw – they can’t exist. Solid structures that size can not be made from any known materials and oftentimes the structures are dynamically unstable. For example, both the solid Dyson Sphere and Ringworlds orbit a central star at super-orbital speeds to generate spin-gravity – unless we’re talking a Bob Shaw Orbitsville made of gravity-generating unobtainium. Now a basic fact of physics that a shell/ring will feel no gravitational effects from masses within it and so that orbital position is unstable to small perturbations – eventually it will run into its star.
So what can be built instead? And how big can it get? Karl Schroeder’s Sun of Suns features a 5,000 km wide air-filled sphere made of carbon nanotubes – which is roughly the limit based on the strength of nanotubes. And carbon is the strongest material in great abundance in the Universe. Theoretically there could exist ridiculously strong “materials” made of higgsinos, monopoles and black holes, but all require some glossing over the difficulty of making the stuff and the unknown physics behind some of the claims. For example, the Solar Queendom stories of Wil McCarthy feature a sun-spanning ring made of collapsium – material made of stabilised mini-black holes. Essentially the black holes are arranged so they eliminate their mutual gravity and inertia and they recycle their Hawking radiation – all of which is very fringey physics. Fun, but dubious.
So I wondered just how big a gas filled object could get before it got into trouble with gravity. A volume filled with a gas at constant pressure and temperature (on average) has a limiting size known as the Jeans radius – the point at which the gravitational potential of the mass of gas equals twice its kinetic energy. In equations that’s:
3/5GM^2/R = 3NkT
where G is the gravitational constant, M is the gas mass (kg), R the volume’s radius (m), N the number of gas molecules, k Boltzmann’s constant, and T the gas temperature in Kelvin. Of course the mass, M, equals N*(mu), where (mu) is the molecular mass of the gas. With a bit of rearranging all sorts of interesting bits of data fall out of the equations – a gas sphere of Earth mix, pressure and temperature starts collapsing under its own gravity when it’s 34,761 km across. If we change the gas mix – say 50:50 helium/oxygen – and lower the molecular mass, the radius goes up. If we decrease the pressure the radius also goes up. For that heliox mix at 0.4 bar pressure the sphere is about 229,000 km in radius.
Imagine a sphere containing heliox at 0.4 bar pressure and 400,000 kilometres across – enough volume to fit almost two dozen Jupiters. Interesting thing is that the sphere doesn’t have to hold the gas in by brute strength if it’s thick enough – self-gravity of the sphere and the gas mass provides the counter-pressure. If we make it from diamond (the strongest carbon allotrope, density 3.5) then it only has to be 1,345 metres thick for its gravity and the gas’s gravity to provide sufficient counterpressure.
And the mass? Just 0.4 Earth masses for the shell, and 0.655 for the gas – thus just a bit more than an Earth mass. Such masses are ludicrously large for us mere mortals to contemplate, but for the postulated Post-humanity of current SF such a project may well appeal. And if it can be done, out in the Cosmos there may be Someone who has already done so.
Such an object would be opaque – even gas and diamond at such thicknesses is opaque, though look out for interesting refraction during an eclipse – and an ideal target for a transit search. If a civilization felt the need it might totally re-engineer its star system and populate it with potentially thousands of such objects, which would be entirely stable given suitably convoluted orbital design. A Dyson Swarm – as Freeman Dyson originally meant it – rather than a solid Sphere. Such a re-engineered system would stand out like a sore thumb to distant observers, thus providing one motive for the idea – getting the Galaxy’s attention. All the habitable volume – given suitable artificial stars within – would be another motive, but beings able to disassemble planets would hopefully have tamed the urge to runaway population growth.
How about another megastructure, that I have never seemed mentioned before – an “Earth Ring.” Imagine a torus about the same composition and diameter as the Earth, going all the way around the sun. In other words, an Earthlike planet in the shape of a torus, with a minor radius of 4000 miles and a major radius of 93,000,000 miles.
This would have a mass of 1/10th of the sun, and a surface area about 80,000 times that of the Earth. A system of carbon fiber shadow squares and would provide a day/night cycle…big aluminized mirrors will reflect sunlight onto the back, making both sides habitable.
Would this be stable?
I guess since it’s a torus, the surface gravity of something with Earth’s density and 8000 miles thick would be more than that on the surface of the Earth, so maybe it will be a little thinner or less dense.
It would be built out of an early phase preplanetary disk, which may have lots of dust.
Sweetcement
“Now a basic fact of physics that a shell/ring will feel no gravitational effects from masses within it and so that orbital position is unstable to small perturbations…”
Can you explain how that happens? I’ve heard that before but never understood it. I do understand that the inverse square law means that a shell/ring will feel no gravitational effects from masses inside (and vice versa) in flat spacetime. But doesn’t that just make it neutral? What’s the instability?
Not that it isn’t just as bad, since it can random-walk into the sun if the solar wind isn’t the dominant perturbation.
Hi sweetcement & rillian
That a shell of mass or charge has no net gravitational effect on what lies within takes a little bit of explaining – imagine a tiny segment of the shell and its attraction on a mass within it, and a segment symmetrically opposite to the first segment. Their forces add together vectorially – direction matters – and cancel because they oppose each other. Because the shell is symmetrical from all directions the net attraction sums to zero – if the internal mass is in the centre that’s immediately obvious.
What if we move the mass off centre? Thus one side of the shell is closer, but a smaller area of shell is on that side, and the other side is further away, but has a larger area. The increase in area cancels out the decrease in attraction caused by increasing the distance. The attraction of any component is counteracted by another segment of the shell – and the shell’s net attraction is zero.
Similarly for rings & disks – though only in the ring/disk plane.
It’s amazing to me that people still don’t get the implications – for example that hollow planets have no felt gravity on the inside surface. Inner shell planets would on their outsides, but not on their under-surfaces. Which, when you think it out, makes sense. After all gravity on Earth’s surface only points inwards.
Now sweetcement that toroid – where would you find 33,000 Earths of solid material? And at that size its material strength is irrelevant – solid diamond will flow as easily as solid butter. Gravity will only work on its anti-Sun side – consider it a 6.28 AU “wide” bridge-span.
My physics isn’t that strong, but I know a sphere or rapidly spinning ring would not be stable so sliding into the sun.
But the torus I discussed is actually in orbit around the sun. I’m not sure the torus (in orbit) would not be stable. A torus rotating faster than orbit would be unstable, but why would a torus in orbit be unstable? Is so, then why are Saturn’s rings, which could be modeled as a large number of concentric toruses (tori?) stable? Sure, they’re not solid tori, but they can be considered as “tori” of disconnected particles in circular orbits.
The torus would be in orbit around the sun, so material strength is irrelevant…Saturn’s rings are in orbit around Saturn, and a section of Saturn’s rings at a certain distance from Saturn can be considered a uniform ring – and it won’t slide off center…so therefore, by analogy, the torus would be stable, too…or it would be if it were broken up into a mass of particles…like Saturn’s rings. Are you telling me if a section of Saturn’s rings condensed onto a torus, it would be unstable to perturbations, so it would slide into Saturn?
The torus is symmetrical in the X-Y plane, but there’s no counteracting mass in the Z direction, so therefore I’d think that the gravity (or charge) would not cancel.
This whole exercise is an attempt to imagine a long-lasting megastructure that could actually exist for millions of years. Dust clouds and early stage preplanetary disks where protostars are forming have plenty of mass, in the form of dust, to be coralled into the form of a giant torus over a long period of time (swarms of free-space replicators?), and terraformed into livability over millions of years.
Though I’m still not sure about the gravity situation.
Is there a way to model this?
Sweetcement
Hi sweetcement
The problem isn’t orbital stability, but structural. Nothing solid can be made that size without basically collapsing on itself from its self-gravity. The toroid will break up into “beads” – basically planets – which will eventually coalesce into one giant planet. At the scale you’re talking about there’s nothing strong enough that can remain rigid.
What can be done is a whole toroidal cloud of orbital habitats that circulate in a stable ever-changing configuration. But there’s nothing composed of known materials that can be +6 AU in size and remain rigid.
What possible use is a gigantic enclosed sphere of gas? Unless you spin it for gravity, its still not permanently habitable by mammals.
But if you spin it for gravity, keeping your civilization on the equatorial band, why would you need all those cubic km of air that remains unoccupied? Unless you’re interested in some kind of weather system inside, or some kind of airborne recreation . . . I can’t think of any purpose whatsoever.
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Hi hamsterbaffle
Karl Schroeder’s Virga is populated by people in spin-gravity structures, so the sphere itself doesn’t have to rotate. The point is that a 3-D civilisation becomes possible in such an environment.
Adam,
sweetcement is (mostly) right about the ring. You’ve flip-flopped the concepts of strength and stability. You write:
”
The problem isn’t orbital stability, but structural. Nothing solid can be made that size without basically collapsing on itself from its self-gravity. The toroid will break up into “beads” – basically planets – which will eventually coalesce into one giant planet. At the scale you’re talking about there’s nothing strong enough that can remain rigid.
”
Believe me, I’ve worked on this problem. I have the actual 3D vector field of gravity around the ring. The ring may exist, requiring no material strength. It could be made out of any ordinary matter.
Now, it could break up into beads. Just consider a small portion being cut out. Obviously the “ends” will retract since they are more attracted to the direction with more matter, and this would most likely cause a chain reaction throughout the rest of the torus, creating many planets. I have still not figured out if this is an instability of the torus in a differential sense, meaning that any small deviation would destroy it, or if it’s locally stable and will only break up with a large disturbance. It’s not a trivial problem and I’ve spent a lot of time working on it. There are academic papers published on similar problems and their respective stability. For instance, there was one paper that addressed the stability of rings held together by surface tension. This is more practical to test since surface tension is a significant force on the human scale, but it is a characteristically different force from gravity. Coincidentally, that paper only addressed the problem with experiments. The actual problem we’re talking about with the torus stability or instability is actually much much larger.
Nonetheless, the fact that the torus is balanced is indisputable.