Another pointless and naive physics question from me. I know that planets and larger things are spherical because of gravity, that is to say; the combined mass/size/strength of the material the object is made from means it’s impossible to diverge significantly from a sphere.
So, something about the size of Sedna or larger would necessarily end up spherical if it was made of some relatively massive material like iron. But what about polystyrene, for example? Its mass/volume is a lot less. There are probably even better materials to choose from, but is it possible to arrange polystyrene into a cube with the same volume as Sedna and not have it collapse into a sphere? How large could such a structure get? I’d like the structure to be stable for at least a couple of hundred thousand years, longer if possible (I imagine that in the very long run, random collisions would deform any structure you can imagine).
Please note that I’m talking about volume, not mass, with the assumption that “hollow” structures can be built on that scale. Now that I’m thinking about it, that would probably mean that any size “empty” cube would count as well.
ETA: Obviously, I’m positing this structure to be out in “open space”. Not on or near any planet/star/other massive object.
WAG here. I don’t think an empty cube with sides made of anything but heavy matter would collapse under its own gravity for couple of hundred thousand years out in open space at any size unless the sides were made unnecessarily thick. There are probably lots of materials that won’t hold together for 5 minutes, but not collapsing from their own gravity. It just doesn’t seem that you could get enough mass into something just a little thicker than a 2 dimensional area to have it’s own gravity cause a collapse. It might deform if it’s too flimsy. But you could make something light years across out of thin steel, and I don’t think the gravity from opposing sides would pull the sides together in just a couple of hundred thousand years.
If that’s the case, when you specify stable, and if you mean maintaining a cubic shape within some reasonable tolerance, I don’t know. Something like an aerogel I guess.
I think a solid cube would be a much more difficult problem.
What did you need this for by the way? Some kind of art thing? A tomb? Intergalactic billboard?
Yes it’s a solid cube and by literally back of the enevlope I mean I did the calculation on the back on an envelope.
Infact I think I mispoke, the figure for a concrete cube doesn’t sound too far off or if anything a little too large. According to wikipedia the largest object in the solar system not in hyrdostatic equilibrium has a diamter of 532 km.
Looking at the solar system, the smallest object known to be gravitationally rounded is the moon Mimas, while the largest irregular object is the slightly larger moon Proteus. You might want to check your calculations against these real-world examples. Oddly, Proteus has a higher density, but it’s thought that Mimas formed at a higher temperature, giving it greater plasticity.
That does sound pretty small - even for a solid heavy object - then again, a cube with a 500 km diameter would be pretty amazing to watch. Still waiting for someone to give some estimates for a polystyrene/aerogel cube though.
I think a big factor is heat history. Hot things deform easier than cold. Hot polystyrene deforms easily. Cold is more rigid. How about a foam made out of titanium? I don’t have to pay for it do I? Or even figure out how to make it?
4 Vesta at 529 km (mean diameter) is the largest out-of-round object in the Solar System. Most of its out-of-roundness is due to a large crater at the south pole, and the rest is thought to be round due to hydrostatic equilibrium. If that’s the case, then it must have been in equilibrium when it formed and was probablly hotter than now. If it were still in equilibrium, that crater would have slumped and filled in.