# Are there any theoretical size limits of man-made space stations/structures?

The question speaks for itself. If the answer is "yes", what are the problems in creating a large-scale space structure, maybe even dozens of kilometres large? What about moving & repositioning, building, handling, supplying, maintaining and repairing issues of space hyperstructures (for example, a nuclear factory in space)?

I could check only one aspect: moving and repositioning.

Theoretically, larger space structures (like space stations) don't need serious propulsion because they can be built in space (as it happened with the International Space Station: it was built piece by piece) and moving them should be necessary at repositioning - but if they could get an orbit (around a moon, a planet or maybe even a star), they are moved by the force of gravity.

EDIT: with the word structure, I mean a man-made facility that has certain functions. I wouldn't like to use the word space station, because with very large scales, a similar facility would be more than a station.

• with the word structure, I mean a man-made facility that has certain functions. I wouldn't like to use the word space station, because with very large scales, a similar facility would be more than a station. – Zoltán Schmidt Jul 29 '13 at 18:41
• AFAIK, collapsing under own gravity and turning into black hole is the only limit. Look up "Dyson Sphere" for example of something BIG. By the way, I remember at least a few ideas involving transforming asteroids into space ships. – SF. Jul 29 '13 at 19:00
• But even the Death Star wasn't so big that it'd have collapsed under its own gravity - even though that was just a fictional facility. =) – Zoltán Schmidt Jul 29 '13 at 19:06
• Death Star didn't have to follow the laws of physics, just the laws of moviegoers' imaginations. ;) – TildalWave Jul 29 '13 at 19:20
• I know, I wasn't even totally serious =) but to create black holes, enourmous concentration is necessary...I mean, like the mass of Earth in the head of a pin. (source: VSauce) It's very unlikely to happen with a man-made facility. – Zoltán Schmidt Jul 29 '13 at 19:23

Electromagnetism

To be as practical as possible, the Space Shuttle mission STS-75 experimented with a space tether. For the record, the tether did break. To be fairly exact, it did break for reasons that wouldn't have broken it if the line had been shorter. So in a certain sense (but only a limited sense), we have already seen a space tether break because of its size.

That was because of wire current interacting with trapped air from manufacturing in the line. The current was caused by movement within the Earth's magnetic field. That was 20 km long. We can't call that a limit in any meaningful sense, because NASA could make a better tether now, and the entire point of the mission was to experiment with induced current. So an insulator would fair better.

Nonetheless, induced current is still size specific. It's also specific to velocity, magnetic field, and probably a few other things.

Tidal Forces

The reason there was tension in the wire to begin with was tidal forces. There are abundant tether proposals for various cislunar systems that take advantage of the gravity gradient. It was even considered to make structures for the ISS that would use the tidal forces to help maintain orientation.

There are some qualifiers. Tidal forces only extend in one direction, so it may not actually stress your structure depending on geometry and how it's pointed.

For a basic mathematical treatment, the tidal field grows linearly with movement from the central point. If you have a mechanical member, then that is integrated over the length to give a tensile force on the order of (length)$$^2$$, I believe.

In a meaningful sense, a space elevator has to fight against tidal forces, and it would require futuristic materials. My poor $$l^2$$ approximation would be insufficient on that scale.

Self-gravitation

Something can collapse under its own weight. Of course, we'll have to assume that it's not relying on internal pressure. Planets rely on their own internal pressure to hold itself stable against self-gravitation. This is fairly unspectacular, and since we're looking for man-made structures, I'll imagine something like the Death Star.

If a spherical space station has a constant density, the gravity grows linearly from the center. Because of that, it would have the same (length)$$^2$$ scale of structural requirements, but this would be compressive. You can push materials limits further with tensile loads than compressive loads in general.

It's important to note that self-gravitation depends on the average density of the structure. Actually, it's a (density)$$^2$$ relationship. The argument for the square is that on Earth your weight is just (mass), because it's gravitation between you-Earth. Self-gravitation is between you-you. Thus, your mass term gets entered twice. This means that a very sparse structure could theoretically span a size greater than that of Earth, while not collapsing under its own self-gravitation.

Others

There's another way you could push this even further - use kinetic forces. You could have a rigid structure that rotates in a big ring, which avoids some self-gravitation compression. You could push that idea very far, with huge self-gravitating Dyson swarms, or something along those lines. But maybe that would fail the requirement for not being "rigid". There may be other workarounds. My creativity fails me at this point.

At this point, reaching absurdity, there are some odd and even comical limits you can think of. For instance, if you assume that our energy growth continues to grow at 1% per year, we will cook the Earth in 1000 years or so. It's not a complicated argument. Just assume we continue to exponentially grow and the conclusion is obvious. This can be applied on any boundary, including the solar system or the galaxy.

Ultimately, yes, the limit would be a becoming a black hole. It's difficult to see how that would happen sooner than the thermal limit, because it's highly sensitive to the matter density. Theoretically you could make a black hole without a catastrophic event like a supernova, because large black holes can have a "density" (defined with the event horizon) less than water. So if you were flying giant blocks of lead around in space in a carefully planned formation over many light years, you could turn into a black hole in a very novel way. But why?

• But why? BECAUSE WE CAN! Out of jokes, big +1 for the long, deep and precise answer! – Zoltán Schmidt Jul 29 '13 at 19:59
• @ZoltánSchmidt There's always hope for the feature in a future Kerbal Space Program version – AlanSE Jul 29 '13 at 20:05
• @ZoltánSchmidt - it is customary to wait at least 24 hours before accepting an answer, just to give folks from all time zones a chance to add their 0.02 dirhams. Alan's answer is all right, just thought you have to know this local custom... – Deer Hunter Jul 29 '13 at 20:06
• @DeerHunter thanks for the tip, no one have mentioned it for me yet. – Zoltán Schmidt Jul 29 '13 at 20:10
• @DeerHunter - 0.02 dirhams converts to only 1¢ US, and we all know the universally accepted standard value of user contributions is 2¢ US. :P – TildalWave Jul 30 '13 at 12:40

In simplest terms: The upper limit is the point at which the object asserts enough gravity to collapse itself, and the available limit on materaials available.

An object of sufficient mass should self-collapse into a spheroid; for silicates this is estimated to be several hundred miles diameter; note that Ceres is above the self-rounding limit, and is about 0.00015 Earths (895E18 kg), and about 590 miles diameter (about 1/13 earth diameter).

One cannot build a structure bigger than the total materials available; in the Sol System, assuming cannibalization of all rocky bodies, that limit is somewhere around 3-4 Earth Masses.

This page has a good list of designs (though these are all for the largest inhabitable structure) and explanations of the challenges. In short, gravity is the main challenge, both in restricting how big you can build a structure and how well you can live in that structure. Many of the designs take the form of big hollow spheres, or shells:

• A shell with nothing inside would give you a lot of surface area for the mass. For example, a shell with Earth's mass and an areal density of 500 kg/m2 would have a radius of 31 million km. However, it would have extremely low gravity at the surface, essentially 0 g. Whether people could live in that long-term is unknown.
• A shell around a central body, such as a planet, star or black hole, could give you a lot of surface area at higher gravity (e.g. 1 g). However, because of gravity, this design is limited by the compressive strength of the material used for the shell. A shell of diamond would have a maximum radius of 180,000 km, which could surround any planet but isn't enough for stars or black holes; for those, you would need dynamic support.
• A shell filled with gas would be kept inflated by internal pressure, so strength isn't a concern. There's still a maximum size, as past a certain point, adding more gas causes it to become compressed rather than increasing the internal volume. With hydrogen, the lightest gas, you get a maximum radius of 240,000 km. With a breathable gas mixture (mainly nitrogen and oxygen, which are denser than hydrogen), you could live inside the shell but the maximum size is smaller at 40,000 km radius. Note that this design also has low gravity (~0.002 g for the hydrogen-filled version).

Another possible design is the topopolis, which is basically an O'Neill cylinder extended in both directions until it loops around a star one or more times. This could achieve 1 g of gravity through rotation and could be almost arbitrarily large by repeatedly looping around the star, though self-gravitation would still place an upper limit.