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I'm trying to design a cube world while sticking somewhat closeish to real physics, but am not entirely sure about the physics involved with objects of non-uniform density, specifically as relates to increasing gravity near the corners and edges. Is it possible to make a cube world (with rounded edges) that has a mostly uniform, earth-like surface gravity, assuming you can make it out of indestructible materials of any density, including negative densities (antimass)? If so, would there be any gravitational features preventing travel to other sides of the cube?

Additionally, would the rotation of the planet have a strong affect on gravity when nearing the corners and edges of Cubeworld, and would it be to such an extent that it made having a uniformish surface gravity substantially harder?

While the setting does not include true static or directional artificial gravity, materials exist that have densities (both positive and negative) that allow for creating things like a hollow spherical world with people living on the inside (using a sphere of antimass in the center).

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    $\begingroup$ Any magic used to justify a weird effect has more unintended consequences than just justifying the weird effect with magic. Negative mass in particular will have some really, really weird consequences that you probably don't want in your setting. $\endgroup$
    – g s
    Commented May 15 at 1:43
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    $\begingroup$ For example: time contraction, spatial dilation, self-accelerating systems, virtually infinite gravitational potential energy, inconsistencies with the Einstein field equations, etc. etc. etc. Negative mass is bad. Certainly an interesting tool in sci fi, but it causes a lot more harm than good in most circumstances. (Not to diss the question, which I found interesting and +1ed.) $\endgroup$ Commented May 15 at 12:32
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    $\begingroup$ Yes, I would also ditch the negative mass as well. At the very least, you do not need it for your cube world as I explained in my answer. But your hollow sphere world, while true no positive mass could create such a world, I'm sure there are better ways than with gravity to have people attracted the walls. Inside a hollow sphere, there is no force of gravity whatsoever anyway, so you could have just about anything else push things to the outside and it would have nothing to fight against. Things won't fall to the center on their own, just float around inside a hollow sphere. $\endgroup$ Commented May 15 at 16:55
  • $\begingroup$ Thanks, I'll almost certainly ditch the antimass, Especially now that I know the gravity is doable with mass only. $\endgroup$
    – DDriggs00
    Commented May 15 at 21:08

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I suspect the answer is yes (for a rounded-edge cube), no anti-mass required, but it is in fact a surprisingly difficult calculation to deal with. You can search up questions about the gravitational field from a uniformly dense cubical planet, and already those calculations are quite hard to model.

Let's start with thinking about a uniform cube first though, and how exactly the gravity is different. The centers of the faces of the cube work normally for free, gravity is pointing to the center of the cube which would be perpendicular to the ground, and the pull from the corners are symmetrically distributed and so even out. However, if we have a cube where we have 1g of gravity on the centers, by the time we reach an edge the gravity is going to drop to around 0.7g due to the increased distance from the center of mass, and also more importantly, that gravity is going to be pointing at almost 45 degrees to the ground, so that near the edges it would feel like you were actually on a 45 degree slope, not level ground at all! And this effect is even more pronounced at the corners.

To compensate for that, the planet would need to get more and more dense near the edges and corners. On a perfect cube, they would need to be infinitely dense on the edges, in order to have gravity remain perpendicular to the ground. Thus rounded edges would have to be used.

I would have to make a computer model to verify if you could get uniform gravity at every point on the face of a cube, or if you would only be able to normalize a subset of points. It may be the case that a distribution that gets normal-to-ground gravity on the edges, while keeping it normal in the centers of the faces, could be possible but the spaces between the centers and edges are still misaligned. But on the face of it (pun intended), if you are already supposing super materials like antimass and indestructible materials, in terms of believability I think you can get away with an explanation as vague as the one above just fine, no one is going to check your math on this one.

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    $\begingroup$ beveling (roughly rounding) cube's edges to the max leads to an octahedron, beveling octahedron's edges to the max leads to a cube. inbetween should be a sweet spot $\endgroup$
    – user110814
    Commented May 14 at 21:54
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    $\begingroup$ What about the travel question, though? If everything is finely calibrated to deliver constant gravity on the surface, wouldn't their still be weirdness with flying a plane or climbing a tree? $\endgroup$
    – Robertiton
    Commented May 14 at 22:46
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    $\begingroup$ Yes, but the fact it's almost spherical means gravity pulls toward the middle of the planet whether you're at sea level or 30,000 feet up, no matter where you are on the planet. I don't think that will be true on the cube planet. Imagine you're 30,000 feet above a (rounded, extra-dense) corner. Surely that won't have the same gravity as being 30,000 feet up somewhere else. It's not even clear what 30,000 feet up means, because you can be equidistant from more than one point. $\endgroup$
    – Robertiton
    Commented May 14 at 23:14
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    $\begingroup$ @Robertiton good point, stable low lunar orbit is already problematic due to mass concentrations, even if the moon is already pretty spherical. No clue what would happen on that cubic Earth, even considering free falling objects. $\endgroup$
    – user110814
    Commented May 15 at 0:33
  • $\begingroup$ @user721108: If we presume that the gravitational flux is uniform across the entire surface of the cube, and that the orbit is much higher than the Earth's center-to-corner distance (e.g. in real life the Moon's orbit is about 60x the Earth's radius), then I find it difficult to imagine a significant gravitational anomaly at that distance. Low orbits would definitely be messier. $\endgroup$
    – Kevin
    Commented May 15 at 5:50
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Something that should be noted: with the appropriate distribution of antimass, you can make your Cubeworld behave (gravitationally) exactly like a spherical planet.

The whole reason Cubeworld’s gravity would be off is because of the edges, not because of the cube-ness of it. Being a cube creates a deviation from being a sphere that changes up the surface gravity. Assuming your cubeworld is made of standard-alloy unobtainium, that should be fine, but people on your world might be a bit confused around the edges.

Still, your cube can be considered an extension of a sphere: imagine cutting out a sphere from the middle of Cubeworld. What you’re left with is the “extra” material, which has its own gravitational field. If you weave columns of antimass into the extra material so that its total mass is 0, then it won’t have any effect on Cubeworld’s gravity.

You will still have to deal with the fact that the surface gravity on the edges will be lower than at the center of one of Cubeworld’s faces. You can do this by removing the antimass from certain areas of the extra material, slightly increasing the surface gravity there to account for the increased distance from the spherical “core” of Cubeworld.

What effect will all this negative mass have on spacetime? Absolutely none. So long as the total mass in any region is greater than or equal to zero, there are no problems; issues arise when you cross the threshold from 1 kg to 0 kg to -1 kg. What you’re actually doing is just inertial dampening of the extra material; also not allowed under regular physical laws, but less-not allowed than negative mass, I suppose.

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  • $\begingroup$ Your third paragraph undos all the effects from the first two. You can't have both a 0-mass cube structure and have the surface gravity on the corners be the full gravitational pull of the centers of the faces. Its not a slight amount of anti-mass that would need to be removed, the surface gravity on the edges is signficantly lower if your corners are 0-mass as you say. At the extreme, on the corner the gravity is 1/3rd of the center face. $\endgroup$ Commented May 15 at 17:08

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