## Cubic Earth

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Steve3007
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### Cubic Earth

Suppose that instead of being spherical the Earth was a cube. Yes, I know, it's not possible. It would immediately collapse back into a sphere. But suppose it didn't. (Perhaps it's made from some kind of super-strong material.)

The radius of our (roughly) spherical Earth is (roughly) 6371 kms.

If the cubic Earth had the same volume as the spherical Earth then each side of the cube would be 10270 kms long. That means that the centre of each of the 6 faces would be 5135 kms from the centre of the Earth. But the centre of each of the 8 edges would be 7262 kms from the centre of the Earth, and each of the 8 corners would be 8894 kms from the centre of the Earth. So the centre of each edge would be 2127 kms higher than the centre of each face.

If this Earth had water and air (and if the water and air behaved like water and air normally does) then it would pool in the middle of each of the faces in a shape which would be a slightly squared-off circle. So the deepest points of each of the 6 oceans would be in the centres of the faces. But on our (roughly) spherical Earth, the distance from the depths of the deepest ocean to the top of the highest mountain is less than 20 kms.

So on cubic Earth the edges and corners are high up in the vacuum of space. The oceans and atmospheres of the 6 faces are entirely cut off from each other, except perhaps when the occasional meteor hits a face and ejects some material hard enough that it flies over an edge and lands on another face.

Would life evolve entirely independently on each face? If intelligent life evolved on one or more of the faces and eventually got around to inventing space travel and/or extreme mountaineering would they be able to assess the probability of the evolution of life by surveying how many of the other faces became hosts for it?

What about the other 4 regular polyhedra? (the "Platonic solids"). Would their edges be high enough to make each of their faces completely cut off from each other? What's the maximum number of faces that a polyhedron would be able to have and still have all its faces completely cut off from each other such that life (if it evolved) would evolve entirely seperately on each one?

Albert Tatlock
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Joined: October 15th, 2017, 3:23 pm

### Re: Cubic Earth

What a brilliant post, I can't believe nobody has responded to it. I once wondered about this very thing myself. I didn't put as much thought into it as you have and I certainly didn't do any research and what you've come up with is fascinating. The only thing that occurred to me was that, no matter where you were, apart from the exact centres of the faces, you would always be on a hill.

Greta
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Joined: December 16th, 2013, 9:05 pm

### Re: Cubic Earth

If the object is large enough to be a planet yet not spherical then the material would be too hard to or the kind of permeability that allows the chemistry of life to happen. If there was such a soft opening for live, say, in the middle of one of the faces, then wouldn't that part of the planet be squeezed upwards like toothpaste by the gravitational pressure of the surrounding harder material?

Albert Tatlock
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Joined: October 15th, 2017, 3:23 pm

### Re: Cubic Earth

Greta wrote:If the object is large enough to be a planet yet not spherical then the material would be too hard to or the kind of permeability that allows the chemistry of life to happen. If there was such a soft opening for live, say, in the middle of one of the faces, then I expect that that part of the planet would be pushed upwards by the pressure of the surrounding hard material.
This is a purely hypothetical planet, Greta, and is therefore exempt from any laws of physics deemed to be inconvenient. If you want to put a soft opening in the middle of one of the faces so that life can evolve that's fine, but just bear in mind that it will be under water, Steve3007 has already seen to that.

Steve3007
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### Re: Cubic Earth

I am not sure if a thought experiment like this has to selectively discard the laws of physics. I suppose it has to. I was thinking that I could get away with proposing the existence of the super-hard material from which the cube is made but leave all the laws of physics as they were. But I guess if you start following through the consequences of that you inevitably have to change other things too.

Albert Tatlock
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Joined: October 15th, 2017, 3:23 pm

### Re: Cubic Earth

Steve3007 wrote:I am not sure if a thought experiment like this has to selectively discard the laws of physics. I suppose it has to. I was thinking that I could get away with proposing the existence of the super-hard material from which the cube is made but leave all the laws of physics as they were. But I guess if you start following through the consequences of that you inevitably have to change other things too.
Well you can blame Greta for that. Everything was going along swimmingly until she came along and spoilt it.

Steve3007
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### Re: Cubic Earth

It may be because, being Australian, she lives on one of the other faces of the cube is therefore an entirely different life form.

-- Updated Wed Oct 18, 2017 9:41 am to add the following --

Seriously though:

Greta:
If the object is large enough to be a planet yet not spherical then the material would be too hard to or the kind of permeability that allows the chemistry of life to happen. If there was such a soft opening for live, say, in the middle of one of the faces, then wouldn't that part of the planet be squeezed upwards like toothpaste by the gravitational pressure of the surrounding harder material?
Yes the material from which the planet is made would have to be unnaturally hard. Certainly harder than any known material, I wonder if it would be harder than anything that is physically possible using the standard laws of chemical bonds? Interesting idea to consider.

So I guess if life existed on this planet it would have to be in a superficial layer of "normal" matter, like the oceans and atmosphere I proposed.

If, as you've suggested, there might be some kind of opening in the surface of the cube, I don't think the material in it would be squeezed upward by gravity because there would still be lots of the hard matter below it. Although the gravitational field of this planet would be a different shape from that of a spherical planet. Hence the slightly squared off shape of the oceans.

By the way, this is far from being an original idea. (Nothing new under the sun). I googled it and found somebody else with nothing better to do had actually worked out the shape of the gravitational field.

Greta
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Joined: December 16th, 2013, 9:05 pm

### Re: Cubic Earth

Poor Albert. I am a professional wet blanket.
Steve3007 wrote:It may be because, being Australian, she lives on one of the other faces of the cube is therefore an entirely different life form.

-- Updated Wed Oct 18, 2017 9:41 am to add the following --

Seriously though:

Greta:
If the object is large enough to be a planet yet not spherical then the material would be too hard to or the kind of permeability that allows the chemistry of life to happen. If there was such a soft opening for live, say, in the middle of one of the faces, then wouldn't that part of the planet be squeezed upwards like toothpaste by the gravitational pressure of the surrounding harder material?
Yes the material from which the planet is made would have to be unnaturally hard. Certainly harder than any known material, I wonder if it would be harder than anything that is physically possible using the standard laws of chemical bonds? Interesting idea to consider.

So I guess if life existed on this planet it would have to be in a superficial layer of "normal" matter, like the oceans and atmosphere I proposed.

If, as you've suggested, there might be some kind of opening in the surface of the cube, I don't think the material in it would be squeezed upward by gravity because there would still be lots of the hard matter below it. Although the gravitational field of this planet would be a different shape from that of a spherical planet. Hence the slightly squared off shape of the oceans.

By the way, this is far from being an original idea. (Nothing new under the sun). I googled it and found somebody else with nothing better to do had actually worked out the shape of the gravitational field.
There's an irony. Some material that is hard enough could be found on neutron stars, and are apparently amongst the most perfectly smooth spheres in nature, with "mountains" a couple of millimetres high.

The closest object we know would be Hyperion nasa.gov/jpl/cassini-sends-final-close- ... n-hyperion. However, its very low gravity would, I suppose, mean that its poles would be more precarious to stand on.

Steve3007
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### Re: Cubic Earth

Is neutron star material hard in the sense that we need it to be here? Or just dense? To make our cubic Earth we'd need it to be hard in the sense that it would resist forces that change its shape. I suppose that would mean shear strength.

Still, if it was a choice between neutron star material or Hyperion, I guess that's one gravitational extreme to the other.

LuckyR
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### Re: Cubic Earth

Greta wrote:If the object is large enough to be a planet yet not spherical then the material would be too hard to or the kind of permeability that allows the chemistry of life to happen. If there was such a soft opening for live, say, in the middle of one of the faces, then wouldn't that part of the planet be squeezed upwards like toothpaste by the gravitational pressure of the surrounding harder material?
Great point. I was reminded of the age old question, why do mermaids have such luxurious hair when everyone knows that their conditioner would immediately wash off in the salt water?
"As usual... it depends."

Steve3007
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### Re: Cubic Earth

LuckyR:

Surely you're not suggesting that the various questions raised by my carefully crafted topic are all moot because cubic planets couldn't possibly exist? Like the hair care problems of mythical beings?

Perhaps it's a modern equivalent of questions about how many angels can dance on the head of a pin.

-- Updated Wed Oct 18, 2017 6:31 pm to add the following --

Incidentally: it's 42.

Chili
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Joined: September 29th, 2017, 4:59 pm

### Re: Cubic Earth

How deep is the atmosphere? Are germs allowed to float from one face to the next?

LuckyR
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### Re: Cubic Earth

Steve3007 wrote:LuckyR:

Surely you're not suggesting that the various questions raised by my carefully crafted topic are all moot because cubic planets couldn't possibly exist? Like the hair care problems of mythical beings?

Perhaps it's a modern equivalent of questions about how many angels can dance on the head of a pin.

-- Updated Wed Oct 18, 2017 6:31 pm to add the following --

Incidentally: it's 42.
No, not me... but now that you mention it...
"As usual... it depends."

Steve3007
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Location: UK

### Re: Cubic Earth

Chili:
How deep is the atmosphere? Are germs allowed to float from one face to the next?
Not that deep. The actual Earth is (famously) as smooth as a billiard ball. So the edges and corners or a cubic Earth would be thousands of miles further from the centre than the middles of the faces would be. So for germs to be able to float across the edges the atmosphere would have to be Jupiter-like.

So, for all we know, maybe there's a cube in the middle of Jupiter? If the cube was the size of Earth, I wonder if the non-isotropic shape of its gravity would mean that Jupiter's overall shape, as defined by the top of its atmosphere, would be noticeably irregular?

Interesting.

But more importantly: Do mermaids take two bottles into the shower? Or do they use Wash 'n' Go?

Albert Tatlock
Posts: 183
Joined: October 15th, 2017, 3:23 pm

### Re: Cubic Earth

Steve3007 wrote:Chili:
Do mermaids take two bottles into the shower?
That would point to quite a drink problem.