Yeah, I intentionally broke any non-anonymous URLs when the board went searchable. (Actually, perhaps mods can deal with this by editing links in old posts?)
In any case, here are the three posts from this thread that had links in them, now with new links. More details in the thread itself.
[QUOTE=Pasta]
In any case, here are the three posts from this thread that had links in them, now with new links. More details in the thread itself.
[/QUOTE]
In your computations, did your cubical Earth have a uniform density?
Yes.
:eek: You don’t still turn it, do you? Sliding gravitational singularities through other gravitational singularities might generate gamma waves or worse.
Or something.
Pasta, that is the awesome.
Pasta – Can you add atmosphere? (It’s harder, because unlike water, air is not close-enough-to incompressible). But it would be interesting.
Also, I noted an error in the original thread. If the axis of rotation is through the center of a face, and no tilt, the north and south faces are going to be frozen solid of course, but the other four faces are going to have exactly 12-hour days, with the sun going directly overhead (just like a spot on the equator on a spherical Earth with no tilt).
If there is a tilt, with face-centered axis, I think days are still 12 hours everywhere, but the sun’s path is now directly overhead only on the equinoxes. There are only two seasons, repeated twice each year, with the hot season at the equinoxes, and the cool season at the the solstices; and the solar climate is identical everywhere on each face. The pole faces have one-year days, and do have distinct winter and summer.
Still working out the case for the vertex-centered axis.
That’s how my ‘anti-gravity’ device works. You simply suspend an object with the same approximate mass of the Earth a few inches over your head. It would be like walking around in zero G conditions. That is if the object moves with you, maybe a tether on a hat or something. Anyway, I never really got into the idea, so feel free to run with it.
Somebody didn’t read Neutron Star.
Only Gene Ray, the wisest human, can answer this!
So if I happened to be on a boat in the center of one of the six seas of this planet, and pulled out my binoculars (or telescope if need be) Would the face of the planet visually appear to be flat all the way to each edge and corner, or would it appear to be four steep mountain peaks rising between parabolic valleys 90 degrees apart?
Bearing in mind that my boat would lift me a fair ways above the surface/ocean floor of the planet, and that I’d be in the center of the plane’s atmosphere looking out past the edge of it into space at the edges and corners.
Assuming your height above the face is very small compared to the size of the face, the apparent difference between the “center-of-edge horizon” and the “corner horizon” is going to be very tiny. Basically, both of those points will fall short of the theoretical infinite horizon by a tiny angle — perhaps a few hundredths of a degree — and the ratio of those angles will be about 1.4 (√2).
Would you be able to notice that effect anyway? I doubt it, but I’m not sure. However, you should (or at least might) be able to notice the different appearance made by the perimeter of the round ocean — where it falls short, by different distances, from the square horizon of the land. The overall horizon would seem a little darker in the directions of the corners.
Possibly. This is my best guess for a Friday afternoon anyway.
I have spent way too much time on this. I worked out the formula for the potential function for a cube, and after a few calculations and plots, I think Cecil made a simplifying assumption in his response:
“If you weigh 200 pounds at sea level back on spherical earth, you’ll discover when you finally reach the peak that you weigh just 103.”
This assumes that the cube and person are point masses, which as others in this thread have pointed out, is not a safe assumption. You would actually weigh closer to 130; I wrote up details here. (For example, as is also mentioned in this thread, the gravity vector does not always point toward the center of the cube; in fact it can deviate from this by nearly 14 degrees.)
Interesting. The gravitational potential formula you ended up with is not symmetric when you interchange x, y and z. That seems worrying - why should the gravitational potential be so clearly coordinate dependent?
Hmmm. I double-checked my LaTeX transcription, and I did miss the parentheses around the sum, which I corrected. But perhaps you are referring to the intermediate function w? You are correct that this function is not symmetric in the coordinates, but U is, being a sum over three “rotated” valuations of w.
Earth should always be capitalized when associating it with the planet to show respect for the world that provides for us. When talking about dirt as earth it doesn’t need to be.
THere are some problems with your column. Firstly, you fail to calculate the mass of the corners/edges, which, being as much solid matter as the center of the cube, also exhibit their own gravitational fields, which will deform the six central seas of each face into a sort of oblated square like a cathode ray tube face.
Another issue you fail to consider is that this CubeWorld may exist in a different sort of timespace geometry, in which mass does not deform timespace with curves, but instead does so with angles. Rather than a gravity “well”, a massive body in CubeWorld timespace creates a much more box-like depression in the spacetime metric, and people and objects that move around the corners and edges do so naturally.
If that’s the case, why didn’t you capitalize “planet” or “world”? Or “us”, for that matter—don’t you respect me?
I would guess that the two people here who modeled Cubeworld by computer were modeling it as a large cube of uniform density, with one Earth’s mass (or thereabouts), in a universe with classical Newtonian gravity. So, no need to consider any spacetime at all, curved or otherwise, unless you just want to make your life harder.
That is to say, I think the intent of the original question is to explore what an actual cubical planet might look like in our universe, should such a thing ever form or be built somehow. You’re certainly free to speculate about spacetime geometries other than our own, but I don’t think the question is really about alternate universes as such.
Would it be possible to construct a cube of non-uniform density such that, at least for one of the surfaces, the gravitational pull is always perpendicular to the surface? If so, I imagine this would radically change the article’s depiction of walking on the surface.
Almost certainly that could be done for at least a portion of the surface. It would be more difficult as you approached the edges of the surface. You’d need higher and higher density.
Also, the height above the surface where the pull could be perpendicular would be smaller near the edge. For example, if you wanted perpendicular pull for at least 10 feet above the surface, it might be impossible to achieve that within 10 feet of the edge.
ETA: Actually, you should be able to do this on all six surfaces simultaneously, again, with restrictions near the edges.