A cubic world?

February 17, 2005 1:29 PM

What would a cubic world be like?

What if there was an object, like a planet, that was the size and mass of the earth, except that it was a perfect cube, with perfectly flat edges and perfectly cut corners. What would the gravity and the experience of living on this object be like? What would the horizon look like? Could something orbit it without hitting the corners? And most interestingly, what would happen if one stood at the very edge: what would it look like? What would happen if you stepped off? What would the sky look like?

posted by ac to science & nature (24 comments total)

Well, the world would have to be made out of something exceptionally rigid to stop it collapsing in to a sphere.

Assuming that, you'd have to do some heavy calculus to figure out the direction of gravity at any given point on the surface of the world. "Down" wouldn't always be towards the surface of the world, due to it's not uniform shape.

My (completely unjustified) gut feeling is that water would pool in a deformed hollow circle on each face of the world.
posted by Capn at 1:37 PM on February 17, 2005

Probably like this and this
posted by dirtylittlemonkey at 1:39 PM on February 17, 2005

The gravitational field outside the cube would basically be the same as that generated by a point mass located at the center of the cube with the same mass. So, gravity would decrease as you moved toward the edges, and decrease the most as you got near the corners. But, except at the center of the faces, it would not point 'down'. It would point at the center of the cube.

Yes, something could orbit it without hitting the corners. If it were far enough away, the orbit wouldn't be much affected by the shape.

A cubic shape would wreak havoc on things like the atmosphere, ocean currents, and plate tectonics. We'd probably get monster storms, huge earthquakes, and volcanoes. Also, the flat faces would mean much greater temperature variations between day and night. The earth's water would flow to the points with higher gravity. It probably wouldn't be much fun.
posted by driveler at 1:49 PM on February 17, 2005

if you picture each 'corner' of the cube as a really big, straight, mountain, you'd get some idea. the horizon would look bowed.
posted by sauril at 1:51 PM on February 17, 2005

as for gravity, the center of gravity of a cube is the middle, so that's where you would be pulled.
posted by sauril at 1:51 PM on February 17, 2005

It would be populated by imperfect duplicates of Superman and Lois Lane.
posted by COBRA! at 1:52 PM on February 17, 2005

It'd be extremely unpleasant, I'd guess. I hope a physicist can step in and answer this, but wouldn't such a planet be subjected to a significant amount of wobble and instability?

This aside, I dare say you'd end up with nearly all the population living in the center of each face, and the verticies being almost impossibly scalable mountains which would be subjected to extremes of temperature.
posted by wackybrit at 1:54 PM on February 17, 2005

The earth's water would flow to the points with higher gravity. It probably wouldn't be much fun.

This is a good point. The rapidly freezing and unfreezing vertices would probably result in deluges of water flooding towards the habitable face center sections, making such a planet inhabitable. That said, perhaps the vertices would remain frozen permanently, but that's for a geologist to correct me on :)
posted by wackybrit at 1:56 PM on February 17, 2005

uninhabitable, of course.. I'll shut up now.
posted by wackybrit at 1:57 PM on February 17, 2005

So you couldn't easily walk to one of the corners then. You would be pulled toward the center of whatever particular face you were on. If you did reach the corner, and stepped over, you'd then be pulled toward the center of that face. So it is somewhat like climbing a mountain, but the shape is different.
posted by knave at 1:57 PM on February 17, 2005

If by "size of the Earth," you mean the length of an edge is the same as the diameter of the Earth, then it's 12,742 km on a side. The gravity at the center of any side would still be 1 g, but it would decrease the further away you went until at an edge it would be .5 g. Capn is right that water, flowing downhill, would collect there. (If by same size, you mean same overall volume, the numbers would be different.)

The edges would be sort of like very narrow mountain ranges extending almost 3000 km high (as compared to Everest at under 9 km). Like Capn says, it would have to be extraordinarily sturdy stuff to not collapse immediately. But if you arranged this, it would totally wreak havoc with atmospheric pressure and weather. (As such, I'm not going to attempt to guess what the sky would look like.)

The horizon most places would look normal (just as people here took the world to be flat). Near the edges, it would look like you're approaching a cliff. On the edge, it would look like you were atop a very steep, very high mountain (not that a human could survive there unprotected.) Nothing very interesting would happen as you walked around the edge (assuming the faces aren't so smooth you couldn't find purchase) -- one side would rapidly disappear from view.

In the version I posited, with edges 3000 km further from the center of the planet than the centers of the faces, satellites would have to be very far away to orbit. Low earth orbit is 320 to 800 km from the surface -- a lot closer than those edges.
posted by Zed_Lopez at 2:00 PM on February 17, 2005

The center of each face would be the "lowest" point from a gravitational perspective. This means:

As you walk away from the center you will lean forward to stay upright. As you walk up to an edge, you will be at a 45 degree angle to just stay "upright"

The ocean at the center of each face would actually look (from space) like some big bulging drop of water. Anything dropped into the ocean would roll or slide toward the center of it.

I dont know what the weather would be like but conceivably the corners could jut out outside the atmosphere, essentially being in outer space. If the atmosphere were thin enough, there could also be just one per face - sort of like six separate worlds.
posted by vacapinta at 2:27 PM on February 17, 2005

If by "size of the Earth," you mean the length of an edge is the same as the diameter of the Earth, then it's 12,742 km on a side. The gravity at the center of any side would still be 1 g...

Actually, since said cube would have ((2r)^3)/((4/3)pi*r^2) times the amount of mass as the Earth, and since the force of gravity varies with the mass of the objects, the gravity would be roughly 1.91g at the center of each face, 0.95g at an edge, and 0.63g at the corner.
posted by Plutor at 3:04 PM on February 17, 2005

I think the gravity would be less than 1g at the corners, and also less than 1g in the center of a side, and probably higher somewhere in-between. For a reasonable definition of "the same size" that is, such as volume or diameter equal to diagonal length. The gravitational field should look the same as any other shape with the same center of gravity, anywhere *outside* a sphere that encloses the entire mass; so that would include the corners; which are further from the center than the surface would be on a spheroid planet; therefore less g-force there. Inside that imaginary sphere, things would be different. My intuition says gravity would be less than maximum at the center of a side, since much of the mass of the cube is at approximately the same "altitude" as the observer, so wouldn't contribute much to the gravity. Consider that the gravitational field is weaker on Earth when you're underground. So, gravity would be highest somewhere between the corner and the center. That's where the tricky calculus would come in.

"Downhill" would be towards the center of the side you're on, but "down" would not always be straight towards the center of mass, I think. Atmosphere or water would pool in the center of the faces, like everyone else said. Since the surface of each face would always be entirely at the same angle to the sun, there's not that much differential heating except because of the atmosphere being pooled up in the middle, blocking the light on the far side. So, I think you'd get weather circulating in a ... um... circular pattern around the center of each side. I bet it'd be very boring compared to earth weather, though. Assuming similar amounts of water and atmosphere, that is. Sunrise and sunset would be rather abrupt. Depending on how the cube is rotating (or not) the climate could be very different on some of the cube's faces.

The "horizon" would look almost perfectly flat from the inahbitable part of the cube, except you wouldn't be able to see that far. Standing on a corner it'd just look like standing on the top of any big tetrahedron. Oh, and if there is a big ocean in the middle of a side, and it's sitting on the surface of a flat cube, um... I guess it'd look round like earth's water. It'd be a really long, shallow, slightly curved beach. The horizon looking out over the water would be very slightly higher than elsewhere.

(Plutor: he didn't specify the density.)
posted by sfenders at 3:09 PM on February 17, 2005

I assume you wouldn't be satisfied with something like this.

Do you care if the earth would be rotating or not? Because rotation around its own axis would force it to be errr... more spherical. Or -more precisely-to acquire the geoid (the shape the earth we sit on has). Then again a not rotating earth.... is not earth at all!
posted by carmina at 3:14 PM on February 17, 2005

Also, if the climate around the edges was right for snow, it'd make for some really nice downhill skiing.
posted by sfenders at 3:29 PM on February 17, 2005

FAQ: Weather on a Cubical Earth (USA Today)

Ran across this today when looking for a different cube
posted by Hlewagast at 4:19 PM on February 17, 2005

The ocean at the center of each face would actually look (from space) like some big bulging drop of water. Anything dropped into the ocean would roll or slide toward the center of it.

Meaning that, over time, debris would collect to bulge out the sides. As the edges eroded, you'd get closer to a sphere.
posted by hydrophonic at 4:24 PM on February 17, 2005

The edges wouldn't erode much if the atmosphere there was thin. Anyway, we already have a remarkably rigid planet-sized cube, so I don't see why it shouldn't be impervious to erosion as well.

Somehow, I find it much easier to imagine a planet-sized cube than to believe that "what would the weather be like on a cube" is a question frequently asked of USA Today.
posted by sfenders at 5:42 PM on February 17, 2005

Wow, this is fascinating! Thanks for all the responses. I would assume a cube big just big enough to fully contain the earth, solid throughout. What I am having a hard time picturing is the experience of standing on an edge. If you are looking down off of a huge mountain, normally stepping over the edge causes you to fall. But in this case... what would happen?? Would it seem like your whole sky, horizon etc just spun around?

A bunch of other stuff that came to me:

Another idea, what if the earth was the same as it is now but became enclosed in a very lightweight but extremely strong and rigid cube, so that all the mass was in a sphere-shape inside the cube, but everyone was living on the outside of the cube - then would one fall off the edge?

What if earth was an ultraflat pancake, would it be possible to fall off the edge?

I know celestial bodies are spheres because of gravity - so what if 8 ultra small and insanely small objects were linked together by some sort of framework, to form a wireframe cube, could a cube-shaped planet develop? Would the gravity be any different from a solid cube?
posted by ac at 5:57 PM on February 17, 2005

The rising sun would be an interesting thing to watch, assuming this cube-planet rotated like Earth does. The sun would flash into the sky immediately for an entire face, the area of which would exist in a single timezone.
posted by odinsdream at 7:23 PM on February 17, 2005

Not exactly.... It would still creep over the horizon and have its light refracted by the atmosphere (if there is one). The time zone comment is interesting though, because the light will hit the surface at (essentially) the same angle, no matter where you are on the face...
posted by knave at 10:14 PM on February 17, 2005

What I am having a hard time picturing is the experience of standing on an edge. If you are looking down off of a huge mountain, normally stepping over the edge causes you to fall. But in this case... what would happen?? Would it seem like your whole sky, horizon etc just spun around?

No, there's no abrupt shift in the direction of gravity at an edge. Recall what vacapinta said:

As you walk away from the center you will lean forward to stay upright. As you walk up to an edge, you will be at a 45 degree angle to just stay "upright"

As you then reach the edge, it will be like standing on the top of a mountain ridge where "down" bisects the angle made by the two faces. Anywhere sufficiently near the edge (and sufficiently far from the corners), "down" is essentially parallel to the line bisecting this angle. You could fall off the edge, but you wouldn't fall straight down--it's a 45° slope down either way.

As you go from the center of a face to an edge (er, ignoring for a moment, as others have pointed out, that the center of the faces are under water) the direction of gravity gradually shifts over the course of your journey. It's not as if gravity is perpundicular to the face the entire time, then abruptly shifts at the edge.

Also, if the faces were sufficiently flat, you'd be able to see all of both adjacent faces while standing on the edge. Except what's blocked by that giant bulging sea in the middle of each face. All of all three adjacent faces while standing at a corner. If you brought your space suit, since you're well outside the atmosphere there.

Another idea, what if the earth was the same as it is now but became enclosed in a very lightweight but extremely strong and rigid cube, so that all the mass was in a sphere-shape inside the cube, but everyone was living on the outside of the cube - then would one fall off the edge?

No, it would be more or less the same as what's already been described. The math would work out slightly different (i.e., scientists would be able to tell by gravitational measurements the difference between a solid cube, and a hollow cube with a solid sphere inside), but the broad qualitative strokes we've been painting here would essentially be the same.

Hey, I just thought of something. Since there's this big bulging sea--possible hundreds of miles high at the center--in the middle of each face, everyone can have an ocean view. Even if you live nowhere near the ocean, you can still see the ocean.
posted by DevilsAdvocate at 8:18 AM on February 18, 2005

What if earth was an ultraflat pancake, would it be possible to fall off the edge?

Yes, if you could get up to the edge in the first place, seeing as how it's practically equivalent to a vertical wall to climb it near the edge. Gravity at the edge will pull you towards the center of the disk.
posted by DevilsAdvocate at 8:24 AM on February 18, 2005