Air-filled habitats 400,000 km across
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.