Dear Evil Engineer: Just how big a structure could I build in space?

Dear Evil Engineer,

I have been unable to get climate change off my mind. Watching our leaders utterly fail to decarbonise with the urgency scientists warn us is necessary makes me more certain by the day that Earth’s ecosystems face collapse in my lifetime and billions of people will die. It got me thinking – what a once-in-a-lifetime business opportunity this presents!

My fellow high-net-worth villains are building private bunkers and mouthing off about the need to terraform Mars as a back-up planet, but I have an alternative proposal. I’d like to build a habitable megastructure in space that people – that is, those willing to pay a very reasonable resettlement fee – can live inside indefinitely while Earth succumbs to climate change. Could you advise me approximately how large a structure I might be able to build? Would I be limited to around the size of the ISS, or could I go much larger: as large as the Moon? The Earth?

Yours,

An opportunistic villain 

Dear villain,

I’m always delighted to hear that a correspondent is thinking outside the box when it comes to climate change. This is the perfect moment for big, ambitious plans.

Substantial space structures that humans could spend extended periods of time in are not out of the realms of possibility for an individual with ample means. I would not be shocked, for instance, to read that a Bezos or a Musk is making plans to construct a private space station for use as a luxury hotel.

In many ways, building in space offers an opportunity to go bigger than when building on the surface of Earth. There is the obvious advantage of unlimited, er, space, but also of microgravity or zero-gravity conditions. This means that many of the usual structural engineering concerns that restrict the size and shape of structures on Earth can be ignored. Building in orbit, too, can negate the need for a single complex, expensive and risky launch – structures such as the Tiangong space station are increasingly being assembled in orbit. 

Looking ahead, there is also real interest in going beyond merely assembling structures in space, and actually building them out there too. Florida-based start-up Made in Space, for instance, has been operating a 3D printer on the ISS, and aims to launch a 3D printer into orbit which can manufacture almost anything, even a 100m-long space telescope. Former CEO Andrew Rush commented in 2018: “We can manufacture a structure that couldn’t support its own mass if it were on Earth. The only practical limitation you have is how much material you’re providing to the system.”

OK, so additive manufacturing looks like a good scalable option for construction. But if you aim to build a structure that can permanently support a community, you’ll be thinking on the scale of kilometres, not metres. Is this feasible?

This question has actually received a lot of attention. The concept that probably matches your specification best is a ‘Bernal Sphere’. First suggested in 1929 by the Irish physicist John Desmond Bernal, this is a mostly hollow sphere of around 16km in diameter, filled with air and containing a human colony of 20,000 to 30,000. A sphere is an ideal shape, being stable and providing the largest possible internal volume to surface area ratio. Bernal suggested that it could be built mainly from materials mined from asteroids, the ring of Saturn and other planetary debris handy. “Owing to the absence of gravitation, its construction would not be an engineering feat of any magnitude,” he wrote. This might be taken as something of an exaggeration, but perhaps we might take from it that there is – in theory – no unassailable technical barrier to its construction.

You asked me how large a structure it would be possible to build. Could we go beyond the 16km hollow sphere proposed by Bernal? Yes. Slightly counter­intuitively, there is, theoretically, no limit for how large a hollow sphere can get before it collapses under its own weight.

Imagine a shell with radius r and thickness << r. If you increase its size by an increment, dr, its volume and hence mass increase by dr2. Meanwhile, according to Newton’s law of gravitation, the gravitational force at any point on the shell decreases in proportion to dr2. In other words, when a sphere grows larger, it grows heavier, but the surface is also further from the centre of mass. As a result, there is no net change in gravitational force; it does not vary with r. If a hollow sphere doesn’t collapse under its own weight at a small radius, it doesn’t at any radius.

Strange as it may seem, there is no theoretical limit to how large a hollow sphere you could build in space. The limit, then, is set by the practicalities of construction. For example, if you plan to source your building materials from the asteroid belt, you might find yourself hindered by: the quantity available (there is estimated to be around 2.3x1021kg of material in the asteroid belt, about 3 per cent the mass of the Moon), the difficulty of transporting those materials across astronomical distances, and how to process those materials for 3D printing.

Yours,

The Evil Engineer

PS: Building a number of smaller hollow spheres, on the scale of Bernal Spheres or smaller, would significantly reduce risk. For instance, if a stray asteroid hits a structure, you would lose just one of many, rather than risking your megastructure being ripped apart by sudden decompression.

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