What Would Life Be Like on a Hypothetical Cube-Shaped Earth?

[DiracPool]

A cubic Earth is not a flat Earth

Yes it is. There's just more "flat" there. In fact, there's 6 TIMES as much flat on a cubic Earth than your "regular" flat Earth. I did the math

 

[ImATrackMan]

Yes it is. There's just more "flat" there. In fact, there's 6 TIMES as much flat on a cubic Earth than your "regular" flat Earth. I did the math

No, it's flat³, silly.

 

[krash661]

Good question! Now I'm going to be asking everyone I know this question.

I also thought it was, it's kind of a good thought experiment if you think about it.

 

[SW VandeCarr]

The gravity vector field for an ideal cube is pretty straightforward. How about an ideal torus? Where can you have an ocean on an Earth mass/volume torus? (only undergrads please).

 

[collinsmark]

The gravity vector field for an ideal cube is pretty straightforward.

Are you sure about that?

I tried to find the vector field representing the force on a given point an any particular face last night, but needles to say I was not successful. Setting up the triple, definite integral is easy enough. But evaluating it is a bear. Even Mathematica gave up when evaluating it directly. As Micromass said, "well, if Mathematica can't solve it..."

Maybe it's easier to work with gravitational potential first like these folks did:
http://possiblywrong.wordpress.com/2011/09/09/if-the-earth-were-a-cube/. (I haven't checked their math yet, btw. Instead I gave up and went to sleep. Maybe later.) Once the gravitational potential is calculated, the vector force field can be found by taking the gradient.

Here is something else that might come in useful:
http://arxiv.org/pdf/1206.3857.pdf

 

[SW VandeCarr]

Are you sure about that?

haven't checked their math yet, btw. Instead I gave up and went to sleep. Maybe later.) Once the gravitational potential is calculated, the vector force field can be found by taking the gradient.

Here is something else that might come in useful:
http://arxiv.org/pdf/1206.3857.pdf

Sorry. I was only thinking of the direction of the vector, not it's length (representing the acceleration on a test mass). In line with OP, I was only concerned the perception of "tilt'. Given an ideal cube with uniform density, I just assumed all vectors point toward the center of mass.

That's not true for a torus.

EDIT: Thanks for the link. It seems there is some directional distortion of the vectors due to the mass around the vertices. This does doesn't surprise me. I didn't consider it important wrt the OP's question.

 

[I_am_learning]

I wonder

Just like spherical Earth isn't perfectly smooth and that there are horizontal plains where people live even in the mountainous regions, In the cube earth, there will be cities built on plains that are perpendicular to the gravitational vector fields at that place.
But as you move from cities on the center to cities towards the edges, you will always need to travel steep highways.
But the gravity in the cities that lie on the edges will be much lower (or will it be?)
Basketball baskets will be placed higher there because people can jump higher.
Oceans will be only located at the centers, rivers will be very steep and enormous potential for hydro-power. The edges are like enormous mountains.

How would an artificial satellite fly?

 

[collinsmark]

I think the most profound characteristic of the cube Earth would be its atmosphere. The only natural, survivable atmosphere would not extend to the cube corners or even the edges. (The same is true with water.)

Neglecting microbes that might rarely traverse faces via meteor impacts (and if they survive that), all of life on a given cube face is completely isolated from all other faces of the cube planet.

The natural, biological evolution of all species on the planet would be completely isolated between cube faces (again, except perhaps for those rare microbes that might survive a meteor blast).

Serious technology would have to first be created by any intelligent species before attempting to traverse faces. Airline travel is obviously right out (there is no air at the edges, so there can be no airplanes at the edges). Space-suits would have to be invented. Also, one couldn't drive a unmodified, conventional car to the edges either, since internal combustion engines require air to operate. Traveling from one face to another would be something sort of akin to an Apollo mission.

Resulting life on one face could/would be absolutely different than on other faces. Traveling from one face to another would be like traveling to an alien world.

How would an artificial satellite fly?

That's a good question. Low-earth-orbit satellites are right out. On our Earth, the International Space Station is only about 230 miles (370 km) above the surface. On a typically sized globe, that's to scale with about the width of a finger or thumb. It goes without saying that that wouldn't work for a cube.

Perhaps satellites farther out, such as geosynchronous satellites might be possible/practical. But it would be tricky.