If the Earth were a cube instead of a sphere:
[ol]
[li]Would we have the longest, steepest, but completely flat ski run of all time?[/li][li]Would we need a spacesuit to ski part of this run?[/li][li]Where could you stand completely upright without having to lean?[/li][li]Would it be dangerous to stand on the edges or the corners?[/li][li]Where would the habitable zones be?[/li][li]Would there be anything strange about the place?[/li][/ol]
5: Wherever the people lived.
6: Well, yeah! It would be a cube rather than a sphere!
Wouldn’t there be only six spots on the cube (the center of each side) that didn’t resist gravity in some weird way?
Sorry! I screwed that up…
Logic would seem to suggest that the centres of the six faces would be the only places you could stand upright (perpendicular to the surface, that is), however, the corners of the cube would be quite massive and would generate gravitational attraction in their own right, but I can’t get my head around the possibilities of what might happen.
To my mind, it would be like a spherical earth with eight VERY large and evenly spaced tetrahedral mountains, this ought to mean that water from the oceans would tend to collect in an enormous blob in the centre of each of the faces, which would make standing there tricky.
dammit, forgot to turn the bold ** off, sorry
I screwed around with this idea on my own a few years ago.
The corners would be like ENORMOUS mountains. Gravity would certainly pull these down, no matter what they were made of, unless you built it out of something like the material used to construct Larry Niven’s “Ringworld”.
Gravity would pull you towards the geometrical center ONLY if you were at the center of any face or at ant of the corners. Elsewhere, the gravity vector would NOT point directly toward the geometrical center. It probably wouldn’t be far enough off for you to notice if you were there, however, and in any case gravity will always pull you to the center of the nearest face, where you’d end up with all of the loose dirt, water, and other unsecured detritus. This would end up making weird-shaped “seas” that would seem to “bulge out” from the center of each face and have surface that would be defined by very strange mathematical functions.
I’m not sure if you could have stable orbits near such a body. They’d look pretty weird in any case.
It would be a pretty hard business to construct such a cube of any size. It would tend to collapse into a sphere, given half a chance, but it would look neat.
Ooops, forgot to mention that the gravity vector will also point towards the geometrical center at the center of each edge, as well.
The mountains really aren’t “tetrahedral”, since the angle of each face is a right angle, not 60 degrees. But the description is roughly correct, in a colloquial way. I guarantee you that the “mountain peaks” would poke up above the atmosphere, whose contours, like that of the “ocean” will be defined in a weird way. BTW, if you add rotation to the gravitational effects, things will get REALLY interesting, in terms of the ocean and atmosphere shapes, and your weather patterns, which will be truly whacky. There are all KINDS to possibilities, depending upon which symmtry axis you choose as your axis of rotation – the axis running along the body diagonal? or from face center to face center? or from edge center to edge center?
Given that the faces are flat, does that mean the oceans would form immensely high bubbles at the center of each face? If you were near an edge would everything look flat but would it feel like you were standing on a very steep mountain?
Tetrahedron: a pyramid whose base is triangular, actually any solid with four flat faces
the angles of the faces would only be 60 degrees if it was a Regular tetrahedron, but that isn’t what I said.
Interesting question. You’d be standing on the underlying scrith (or whatever you called the construction material) at an angle, because the gravity vector wouldn’t be normal to the surface (you wouldn’t be standing on rocks or soil, I expect, because gravity would’ve pulled in down toward the center of the face. It should be pulling you, too. but you’ve secured yourself there somehow. Pitons, maybe). The surface of the “ocean” you’re looking at will be a weird shape defined by the strange gravity situation. As I’ve mentioned above, the surface defined probably won’t be a sphere, especially when you factor in any spin. I expect it will be uniform in all directions, to the naked eye, ayway, but it might actually appear to be bulging above you, rather than being flat.
You don’t need such strange situations to have weird perceptions of the horizon, BTW. It has been remarked several people that if ou are well above the ground – say in a balloon – then it looks as if you’re in a great bowl, because the ground directly below you is obviously far below you, but the horizon appears to be at eye level – it certainly doesn’t appear to be below your level – so the flat ground looks like it’s shaped like a bowl that slopes upwards towards the horizon. Edgar Allen Poe remarked on this in “Hand Pfall”, and Mark Twain talked about it in one of his travel books.
Being in a truly weird gravity potential like that of a cubical planet will result in weird shapes for the oceans to begin with, but your perceptions of it will be further distorted by your instincts and expectations.
Which were planted there by the Devil to fool the Faithful into heathen beliefs about the origin of the Earth.
Have faith, Brothers & Sisters ! [sub]And don’t look at that fossil evidence, either.[/sub] :wally
This place am sounding like me home, the Bizzaro World. :D:D
Quoth Squink:
Sigh. Star Trek used to be somewhat reputable, and the original series would never have spread a piece of misinformation this far. Neutronium (the stuff of which neutron stars are made) is just about the absolute worst material you could possibly use for such a job. First of all, it’s not a solid. It’s not only a fluid, but a superfluid, which means that it’s about as far from solid as you can get. Its shear strength (ability to resist forces causing it to slide against itself, the sort of strength most relevant for this sort of job) is exactly zero: Air would be stronger. Furthermore, the only reason that neutronium is stable is the humongeous gravitational fields present in a neutron star. You’ve heard the figures that a teaspoonful of the stuff would mass as much as a mountain? Well, if you got that teaspoonful away from the star somehow, it would expand to about the size of a mountain, at least, as well. I don’t think I need to point out that this would probably have destructive effects. Stick with Ringworld substrate: That has the tremendous advantage that we don’t know what it is.
Sorry… This was a bit of a hijack, wasn’t it?
Now that I think about it, if you were standing on an edge and fell off wouldn’t this be like falling off a cliff?
And if you built a house next to the ocean wouldn’t you have to angle it upwards in order to have a correct feeling of up and down? If you wanted to go swimming it seems you’d have to dive into a cliff of water. Pretty weird stuff - does anyone know of a place like this? Might be fun.
Ummm… The Doomsday Machine. Not quite neutronium girders, but still neutronium.
Anyway, not only would the corners of Earth-Cubed (trademark pending) be above the atmosphere, the edges would be also (assuming the same volume of atmosphere as Earth). So there would be six completely independent ecospheres. I don’t know the volume of the Earth’s oceans off-hand, but I’m suspecting the angle between gravitational down and the normal to the cube at the edge of the oceans will be smaller than we’re imagining, maybe just a couple degrees.
There are three symmetric ways of rotating a cube: axis through the face centers, axis through the edge centers, and axis through the opposite corners. Anyone know if one way is more stable than the others?
Actually, the original series did, twice. In The Doomsday Machine, the title referred to a huge gadget with a hull of pure neutronium. It couldn’t be phasered, so they had to dive a starship inside to destroy it. In A Piece of the Action one of the gangsters is said to be “mad enough to chew neutronium.” Of course, neutronium also was said to make up the shell of the Dyson sphere in the Next Generation episode Relics.
Obviously, the word doesn’t refer to neutron star matter in the 23rd and 24th centuries, but rather to some superalloy. After all, none of these shows explained the term, so they quite easily may not have been referring to the same stuff we mean when we talk about burned out stars.
I wonder if neutronium was the common term for collapsed starstuff in the late sixties, or if it was more recently adopted by those cosmologists and physicists that needed a term for it.
Sorry to continue the hijack, but I had to let my trek geek flag fly.
Which spin axis is most stable ?
Wouldn’t putting the spin axis through two opposite corners maximize the angular momentum at a given spin rate ? That would make it more stable than the edge centered or face centered spin at the same rpm.
I have not integrated the function for mass vs distance from axis for a cube, but I have noticed that a cube of pyrite, or a die for that matter, will climb onto one of its corners when it is spun on a table.
I think that the water would look perfectly level and flat (even though it would be part of a sphere, like it is on the earth we have presently) and the ground that you were standing on would seem to be sloping sharply toward the water’s edge.