Well, it will be a gravitational isopotential, so we would probably see it as flat. It won’t be a section of a sphere – as I’ve pointed out, the cubical shape will exert a weird gravitational pull that will not, in general, point towards the geometrical center. Each facal “ocean” will have fourfold symmetry. But it will be so big that the horizon will likely look the way it does here. So, as think about it, I think you’re probably correct that the ocean will be perceived as a flat surface, and the “beach” will seem to angle down into it. (Unless our perception s really thrown by the situation, and both the beach and the cean seem tilted). That’s assuming that the dirt that’s slid down from the walls doesn’t build up along the water’s edge.
Wow, what a weird coincidence. I just finished reading a collection of short stories that includes a story based on this exact scenario. I even have the book here with me at work, because I’m returning it to the person who lent it to me. It’s called “Vaccuum Diagrams” by Stephen Baxter. The short story in question goes by the same name.
Basically, it’s as everyone here as put it. The atmosphere pools in a blob in the center of the inhabited face. From the center, it’s uphill in all directions. In the story, they take a tram to the Edge, then another tram to the Corner, which is like a huge mountain.
What about the inhabitants of this world? If not just the corners but the edges are out of the atmosphere then presumably 6 different races could form independantly. They would only meet when one or more had developed the technology to survive without an atmosphere for a period of time.
This situation would be similar to us Earthlings developing ocean-going ships and meeting other civilisations. However, the “Cublings” (ha) would be much more developed when they finally encountered another race; making the contact much more interesting.
It’s conceivable that if we can get martian bacteria here (fossil evidence still uncertain) via meteorites, the same thing could happen between faces on the cube. So some smaller life forms or even plant seeds or insect eggs could be transferred on rare occasions in this way.
While I’m thinking about other planetary bodies, wouldn’t any moon(s) play havoc with this bubble-shaped mass of water on a flat plane?
Well, in this story, it was actually an artifact sailing along through space. The bubble of air was provided by the humans who’d landed. But y’all are free to speculate beyond the story.
I think we’ve now conclusively proven that there are bigger Trekkies than I on the boards. I’m humbled. By the way, I presume that Doc Smith’s use of the material is in Children of the Lens? I’ve read all the others…
But regardless, neutronium is still a lousy building material.
What about Niven’s planet Jinx? It’s described as egg shaped (prolate sphereoid?), such that the poles stick out of the atmosphere. Could such a planet form naturally, or would the Funky Custom Planets Corporation have to build it?
No, it’s in that self-parody that Smith has Kinnison write (in Second Stage Lensman, I think). The one involving Qadgop the Mercotan. In fact, our own SDMB Qadgop frequently puts that text in his signature. I’m sure you’ve seen it.
Nope, it’s not in Second Stage Lensmen. I’ve read that one, and I was looking for any references to Qadgop. There also wasn’t any sort of self-parody in that one.
As for a prolate planet, it could not exist naturally if it’s big enough to hold an atmosphere. Even if you artificially formed a big chunk of rock into that shape, it wouldn’t be strong enough to stay in that shape. On the other hand, it could potentially have been made of some exotic substance that Niven used in his books (ringworld substrate or GP hull come to mind).
Niven’s Jinx is a tight-orbit satellite of a gas giant, and the prolateness is supposed to be from tidal effects due to the huge gravitational pull of the gas giant (Niven, of course, is fond of attributing things to tidal effects). Whether he has that remotely right or not, Jinx isn’t maintaining its shape due to its own internal structure.
Niven’s known space also housed Plateau and Canyon, of course. Niven seemed to be fascinated with constructing planets with extreme atmospheric gradients.
I’ve nothing to add to the physics of this discussion.
But in high school one of my teachers had decorated his walls with “maps” of Earth if Earth were of various non-sperical shapes.
Cupical, pyramidal, torus, dodecahedron, etc. They were interesting pictures.
Seems a journey along one edge from corner to corner would be a weird experience. You’d be travelling down one mountain, then up another one. But you won’t have been through a valley.
My head hurts.
My math teacher had the same posters. My fave was the torus. The text mentioned that normal polar conditions would exist at the top and bottom of the ring, but that it would be extra-cold on the inner surface, due to lack of sunlight. I often wished they’d taken it farther, like this thread has, and discussed the gravitational effects. It seems like on the ‘inner equator’ you’d lose gravity entirely, due to the sum of the attraction of the planet under your feet and the much larger (but more distant) mass above your head.
Oops, I think I’ve just started a whole 'nother discussion.
> 3.Where could you stand completely upright without
> having to lean?
Everywhere. Standing upright and not leaning are the same things.
> 4.Would it be dangerous to stand on the edges or
> the corners?
As much as it is on regular mountaintops, plus any problems you might have not being able to breath and being bombarded by cosmic radiation. But the edges would absolutely not be like cliffs that you could fall off of. They’re symmetrical 45 degree slopes, thus the worst you could do is slide down one, not freefall to your doom. (Of course, any mountaineer will tell you that a long slide is potentially fatal too)
A cube of uniform density has the identical moment of inertia about any axis through the center (just like a sphere). This means that all axes are equally stable, and the spin axis and angular momentum always line up perfectly. Anybody know if this is true for the other regular polyhedra? It’s been years since I took Classical Mechanics.
Cubes spinning on a table rise onto their corners due to friction effects. Because in this case they are not free bodies, the rules for free body rotation and conservation of angular momentum do not apply.
Rick (reformed physicist)
[nitpick]
Of course, the Earth is not a perfect sphere.
[/nitpick]
So does that mean it wouldn’t be a perfect cube?
I didn’t mean to imply that it was. I was talking about abstract, mathematically-ideal cubes and spheres. Earth is not of uniform density, either. But without knowing the details of this hypothetical, cubical planet’s construction, it’s a best first approximation to assume it is uniform, and my answer to the stability problem stands.
For any real material, there would certainly be distortion due to gravitational effects, but material capable of supporting planet-sized mountains without slumping is probably pretty darn rigid.
Rick
Quoth Saltire:
Please, nobody answer that yet. I’m being greedy here, but I’d like for there to still be something left to discuss when my Staff Report on the matter gets posted.
Sheesh… That question was two years old at the time I picked it up, and when does somebody choose to ask about it on the boards?
On Jinx: Yes, tidal effects could cause a planet to become prolate, but they’d also effect the atmosphere. Either you’d get a fairly uniform atmospheric density at the surface, or a significant “leak” at the extreme ends. There’d be nothing stopping air from flowing from the central regions to the ends. I’m surprised that Niven would make that mistake; he’s generally much better about the physics details.
Back to our cube: The extreme of the apparent slope (angle between the gravitational vector and the inward-pointing normal) would be right at the corner “mountain peaks”. I’m not up to doing the calculation right now, but it would be a little steeper than 45[sup]o[/sup].
Well, you’d be upright wherever you stand, it would be the surfac that would be crooked!