How big can a carbon nanotube structure get?

Question

I am making a "structure" out of carbon nanotubes in deep space. This structure can be any shape or design, I just want it big. Big in just one direction is cheating (so no long thin structures), this has to be big in all three dimensions.

Approximately how big can I make this structure before its own mass and gravity becomes strong enough to collapse the structure in on itself and form a sphere?

How big can I go, before gravity makes it a no?

EDIT:

This is not the same as How big can a space ship be before it collapses on itself?, and for these reasons:

• This is not a space station, and doesnt require anything to be functional on or in the structure - it is simply a structure made from carbon nanotubes - for all intents and purposes think of it as a work of art. It has no function other than to be appreciated from afar - I just want to know how big it can get.

• The question talks about a solid body of rock and it also talks about metal. The accepted answer talks about pre-stressed steel. My structure is made almost exclusively from carbon nanotubes.

• The question explicitly rules out a Dyson Sphere, as it should have an internal structure. My question doesn't rule out any shape or design, and it has no requirement for any internal structure (although internal structures are welcome if you want them).

I simply want to know how big I can go with a carbon nanotube structure before its own mass pulls it in on itself. The structure has to be strong enough to hold together for at least a hundred years (ignoring any impacts with astral bodies, asteroids etc).

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Just to give you an idea of the scales I am thinking of - I first considered making a cylindrical structure about 50 kpc in diameter (for comparison, our galaxy is about 30 kpc wide).

I am guessing a carbon nanotube structure that was 50 kpc in diameter and 0.2 kpc tall would be too big, have too much mass to maintain its structure and would collapse in on itself. Am I wrong in this assumption? If so, what are my limits?

Answer 1

How much carbon do you have?

Gravity is a very weak force, when compared to other forces, and its influence rapidly diminishes with distance. What this means is that a single bar of carbon nanotube can be infinitely long without its own gravity having much effect on it. So, what if we fold that bar a few times so you have a rectangle? Say we now have a square that encompasses the galaxy. Branch a few times, now we have a cube that encompasses the galaxy. The local gravity on an individual 1 foot length of a carbon nanotube is still trivial, even though the full structure probably outmasses any star.

Your structure can be any shape, assuming no exterior forces, as long as the density is low enough for the local gravity of any individual length of carbon remains low.

Really, the problem's going to be the gravity of other celestial objects (aka, external forces). If you're building this within a galaxy, you'll have to worry about stars and planets mucking about your structure, especially since stars and planets have a habit of moving around. This means within a galaxy, you'll need a structure small enough that it can move within the galaxy without any solar systems crashing into it.

Your other options are to have your structure encompass a galaxy (so that all the stars and black holes and whatnot move entirely within it, without threatening the structure) or outside any galaxies, where very few external forces would influence your structure and it can be basically as big as you like (until you run out of carbon).

Answer 2

A dense structure (similar to a space base, planet or whatever else) will very quickly be at it material limit, and then collapse by its own mass. You could assume the size of a medium star as the maximum (disregarding the material used).

To achieve something bigger, vacum is required: the structure need to be empty enough to disperse the gravity effect.

Imagining a bar of infinite length, the gravity compression on a specific point tend to a constant.

A simple estimation is: Assuming each Km of this bar to weight only 1Kg, and using Newton gravity formula, we achieve approximately.

$F = G * \sum_{i=1}^{\infty} \frac {1*1}{(1000*i)^2} = \frac{\pi^2}{6000000}$

This is far below the limit of any material.

However, you ask for volume structure.

When we think about Kpc structure, any bar section could be ignored. For this reason, each bar of the structure will offer zero resistance to bending. For little that the traversal effect of gravity is, it will bend structure up to the point in which the total mass will collapse, returning to the sphere case.

Considering assumptions, does not really matter the material you use, you will be limited to about the size of a medium star ( ~1 billion Km of diameter).

EDITED:

As suggested a comment, external forces could be used to compensate gravity:

• Rotation if the structure is planar
• Some engines or active compensation
• etc.