How can I prevent a cube world from going spherical

Question

Cube worlds are cool and many people like them but unfortunately, they are less than feasible. Does this have to be this way though?

What factors could lead to the creation of a roughly cube shaped world? What could prevent it from going spherical?

Answer 1

Here are some thoughts to the matter. Don't consider it a complete answer, but more like guidelines when building your world.

1- Size and composition

As you know already, gravity gets stronger as you increase the size/mass of your world. So you would want to keep your world as small as possible when you want to keep gravity to the minimum. I read somewhere that an object made of rock and metal would start turning spherical when its mean radius approaches 300 km. The limit is 200 km for icy objects. (reference)

Since we can support larger sized bodies with rock, I would suggest making your body rocky/terrestrial. Since your world is not spheroid, so you would naturally want this size in cubic km. That would be 282743 km$^3$.

So now we know your world should be composed primarily of rock and have a volume no larger than 282743 km$^3$.

Note: I am nearly certain that a body made of mammalian bone material would be able to support even larger volumes without succumbing to its gravity, but I don't have the exact numbers on bone density versus bone strength to do the math.

2- Electricity and magnetism

These forces are much stronger than gravity, but turn to lose importance as we increase the distances. Keeping strong repelling magnetic/electrostatic poles at the planes of your world would help somewhat in reducing the effect of gravity.

A cube has 6 planes/faces. Let's say you form all the planes from very strong magnets (made of something like Alnico) and have the north pole of each magnet face inwards towards the cube, it would make a strange case where all the cube would be a powerful magnet with south pole originating outwards from each side. The very strong repulsive magnetic force would further help keeping gravity at bay.

Answer 2

The real simple idea is to cut mass, not volume. This is like the space elevator problem, but instead of going super high with really high tensile strength, we go super wide with really high compressive strength. To that end, when dealing with lightweight, high compressive strength problems, any good engineer would say:

Fill it with foam

A ball of foam

Using aerographite, of decent structural strength, an earth sized ball (cubes are coming in a minute), with r = 6378km would have a mass slightly larger than Pallas. Gravity on the surface would be only 0.000321 N/kg, and a 6,378 km column of the material would mean that the top is being pulled down with only - $368 Pa$ of pressure, well within the limits for even the low density material.

A coating of dirt

We want a planet that has 10km or so of soil on top - we want our foamy inside to stay seperated from the surface by a nice insulation layer so it doesn't shatter. I did mention that these foams shatter, right? One crack and the whole planet might implode. Good plot element there.

Back to the math, with .000321 N/kg gravity at the surface, the aerogel on the inside would have an additional 4 kPa of pressure to face. Since we're using the heavy aerogel now, we're fine. Note though - this dirt layer is thirty times more massive then the foamy core we started with! Final surface gravity of this ball is still only 0.1% of earth's gravity, so we've got plenty of room to build.

Adding some mountains on top

With such little gravity, we'd just need to build 6 giant mountains on this sphere that stretch out to make this look like a cube. To be conservative for this analysis, I'll considering each to be a tetrahedron, the surface area of all 6 of these mountains would be about the area on earth that the oceans cover. This area, again covered by 10 km of dirt, would add another 30% of pluto's mass to the planet. We'd then fill the volume of the tetrahedron with the foam, which would add 0.3% of pluto's mass. Taking that mass, dividing it evenly across our plant's spherical surface area, and we'd have 81 kPa of force - about half the ultimate strength for our foam, and thus the planet design is plausible. Adding some stress concentration factors and what not would probably put us near the edge of this material's strength characteristics with an earth sized planet and 10 km of dirt. 8 km of dirt would probably function just as well and keep the design a bit more plausible in terms of stress, but it's up to you.

Answer 3

I was excited to see this question because it harkened back to my childhood, and the glories of Bizarro World. But since you want science, let's consider the possibilities.

If you have artificial gravity, you can make the world any shape you want. Since gravity reshapes space itself, however, we could get into arguments about whether or not it is really cubical, or simply flat. From my perspective, I don't care: artificial gravity is the easy way out, so I'm going to ignore it.

As mentioned before, the relationship of gravity to the strength of your world is critical in defining the stability of any cubical world. How strong depends significantly on the size of your world, which (per the IAFA definition) cannot be a planet no matter its size:

"A celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit."

A cube cannot be "nearly round" by any definition I consider valid (though particle physicists may disagree. Moreover, the surface of your world will of necessity be boring.

Specifically, consider the gravity of your world near the edge of the cube. "Down" will still point towards the center of the cube (not with mathematical precision, but that's the limit as your approach the edge. The bigger your world, the less the difference matters). But the surface of the world near that same edge is lifted 45° from "down", which means that any liquid poured onto the surface of your world would flow towards the middle of any given side.

Moreover, the tendency of matter to liquefy under pressure means that the surface of your cubical world would either need to be sufficiently small that this process would not occur, or it would need to have a solid surface made of whatever material is strong enough to keep it square. Indeed, if you do the math, you'll find that any world big enough or hot enough to support a liquid mantle will be pressing up on the sides, and the forces are strongest in the middle of each face. Since most solids are stronger in compression than in tension, the tensile strength at the surface is probably the limiting requirement for your planet.

If you're willing to go with fictional materials, Larry Niven's scrith would do the job -- its tensile strength is roughly equal to the nuclear strong force. If you want a real material, however, you're going to have to work at it:

• Consider the asteroid/dwarf planet Ceres. It is roughly 945 km (587 miles) across, with a surface gravity of 0.27 m/s². If our space engineers rework it into a cube, it would be approximately 760 km across.
• Let's assume that the force twisting our cube out of square would be roughly equal to the pressure exerted by (945 - 760)/2 = 92) km of missing mass at the center of each face. This isn't precisely true because surface gravity on a cube is different, but it's close enough IMHO for an envelope calculation.
• Pressures beneath the earth go up by 7300 psi per mile of depth, or 31.5GPa per km of depth. Even at Ceres' gravity (I'll assume it scales linearly), that's 542 KPa per km of depth. At 92 km deep, we're talking about a pressure of almost 50 GPa.
• The strongest known substance is graphene, with a theoretical maximum strength of 300 GPa. This is good - but your world probably isn't made of graphene, not if it's a natural satellite. Also, you'd have to be working with a pure carbon asteroid to make a pure graphene object. Also, since graphene is flexible, it would have to be structured into some kind of three-dimensional arrangement to keep the surface rigid.
• An alternative to consider is silicon carbide. It is tougher than graphene, and almost as strong under tension. Since you need a surface that not only won't break, but also won't bend, you may want to look into this. Whether or not it will break depends, I think, on how much of the planet is structure and how much is creamy filling, but at least you'll be able to use up any silicon dust you have lying around to make the structural part.

Note that even this case of extreme engineering still gives you a relatively small world, unable to hold any significant atmosphere, and it can't have surface water either. Artificial gravity, or post-transuranics, or some other unobtanium with previously unknown material characteristics may be required.

Answer 4

In other earlier answers I have designed a cube that’s a constructed alien megastructure.

it's clearly an engineered world, so it will be built to work more effectively.

Imagine it's hollow. Six huge squares. But, need gravity. You can have hyperdense material in a thick circle inscribed on each face. The corners are left light and mostly decorated without living geological processes.

The dense plates require less total mass than a solid sphere for the same surface gravity since you are very near to all of it. It will fall off rapidly as you rise off the surface since the distance squared is measured from 100 km underground, not 4000 km to the center.

It doesn't collapse because the corners are a lightweight (relativily speaking) skin and strut arrangement.

Answer 5

There's no real way for such a shape to exist long enough no matter what it's made of but if you allow some pseudo-science, then how about this - The planet is tidally locked with 6/8 identical satellite around it. The satellites are located exactly where the corners of the cube would be resulting in them able to constantly have the 8 corners of the planet poking out. The surfaces of the cube planet would be somewhat concave instead of flat but can be close enough to a cube.

Basically, we compensated for the gravity pulling the corners of the cube inwards by the gravity of the tidally locked satellites. And the idea of 6/8 moons sounds like a fun story element.

In real life, such a setup will collapse in short order (or at least not be able to exert enough tidal pull) but in a fantastical setting more pseudo-science can be added. For example, the corners of the cube can be oceans to explain why the planet is not getting ripped apart (meaning that it's mostly the water that's creating the corners). Or that the planet acquired that shape while still in molten state and cooled that way and now the gravity is not strong enough to overcome the satellite's pull; so it's really not a just sphere below the oceans. You can hand wave the improbability of so many satellites locked in those positions by introducing a repelling force (let's say same poles of magnets at the very metal heavy cores of the satellites) that force the satellites to be equidistant from each other while still locked in by the cube planet. Lots of handwavium but in theory it'll work as long as one doesn't sit down and does the maths, it can't work realistically anyway unless it's very tiny.

The cool part is that this setup means that dry land will be at the center of the faces of the cube and there'll be "mountains" of water around the land. If you want to go to the other faces of the cube, you just take a boat! Thinking about it all, I'm fascinated by the idea of the flaura, fauna, society and what not in such a planet (as implausible as it is).