Oh yeah I forgot about the death squads…
Erm, I need to make an addition to what I said before: I now realize Cecil is 100% infallible.
(Since I’m phrasing it as an addition, it doesn’t count as a U-turn ;))
Yes.
Anyone reading the column does not necessarily have a moderate understanding of physics. The column therefore provided a way to slightly educate all the idiots who read the column, while still answering the actual question.
More than once has someone asked in General Questions, “Why are so many celestial things round?” with the hint that maybe they’ve found proof of God/gods.
In his “Known Space” series of stories, Larry Niven postulates a planet (actually a moon of a gas giant) that is egg-shaped due to orbital forces during its formation.
The important thing to realize is that your mental picture of how you would walk on the face of a massive cube is wrong. You would not be walking at a ninety-degree angle to the face of the cube you’re on. Gravity will be pulling you to the center of the cube’s mass not perpendicular to the surface. The only place where you would appear to be standing upright would be if you were at the exact center of a cube face. Everywhere else, you’re going to appear to be leaning.
So people standing on the surface would look like this:
\\\__ | _____ ///////____
… and assuming the “planet” has water, like Cecil does, you’d also be standing underneath miles of it. The only realistically habitable point would be at the edge of the “central sea” and you’d live your entire life on a slope of a few degrees.
Gravity does not always act towards the centre of mass of an object, in fact it’s quite easy to think of a graviational system where at some points it acts directly away from the centre of mass.
Unfortunately the graviational field of a fixed homogenous cube is not simple, but I doubt that on the surface of the cube it would always act towards the centre of mass. Though at certain points it would do due to symmetry (for example at the exact centre of one of the faces).
You’re imagining that gravity is perpendicular to the surface at all points. What Cecil was trying to point out is that gravity pulls towards the center at all places. So as you move farther away from the center of the face toward an edge or the vertex, you will find more and more leaning required to remain vertical to gravity. The ground under you will appear to become more sloped.
That is also why the water piles up at the center of each face. Because that point is physically closer to the center of the cube, it has a lower gravitational potential. It is “lower” in common vernacular. Thus water (at atmosphere) piles up there.
FYI, the tone Cecil takes in the columns is broader than the forums allow. There are stricter rules here for addressing one another, including Cecil.
Sorry to spam-up the forum, but I draw a quick-and-dirty image to illustrate the planet, and what it would look like if you were standing at the center of one of the edges (I can’t figure out how to embed images in this forum, so click the link):
http://schend.net/images/photoshops/cube_planet.png
The top part of the image illustrates the planet from a distance, as if you were looking at it from a spaceship and space was white for some reason. The dark grey is rock/dirt, the light grey cloudy pattern is atmosphere, and the blue cloudy pattern is water. Excuse the screwed-up perspective on the non-front-facing faces, you need a 3D drawing program to do this diagram properly.
The bottom image is the view from the center of one of the edges between two faces, looking across the face. You are standing in space, but in the distance you see a dome-shaped pocket of atmosphere and inside of it you see another dome-shaped pocket of water (the central ocean). Space is still white for some reason, maybe it’s Bizarro-universe.
I would not say that was correct, as looks to me to suggest that the graviational field of a cube is spherically symmetric which it most definitely is not. I also think it;s wrong to assume that the oceans would be circular in their shape in the plane of the face of the cube.
This is true, but it’s still probably a pretty good first approximation for the case here (and certainly a far better approximation than assuming it’s always perpendicular to the faces).
And in one of the previous threads, someone did actually construct an equivalent of Blakeyrat’s diagram from a numerical simulation. Digging it up, the links are dead now, but Pasta (who made them) is I think still around; maybe he could re-post them?
Well, for a few minutes doodling on a lunch break it’s pretty good. 
What we really need is a physicist to crunch the numbers, figure it out, and feed the data into a 3D renderer to create a good image. I don’t have the time, inclination, or skillset for that unfortunately.
I’m aware that the center of mass and the center of gravity are not identical. But I can’t imagine a gravitational system where gravity acts directly away from the center of mass. How would that work? (I’m assuming were talking about the center of mass of the whole system and not some object in the system.)
One example would be a torus-shaped planet. The gravitational field will always point towards the torus itself (though not necessarily perpendicular to the surface), so on the inner edge of the torus, the field would be away from the center of mass.
An even simpler example would be two identical spheres, separated by some distance. The center of mass would be at a point midway between them, but if the separation between the spheres were large compared to their size, gravity on each one would behave just like on a single planet.
You’llprobably kick yourself as it’s in fact a very simple example.
Take two identical fixed point masses seperated by some distance. The centre of mass of the system is at the midpoint between them. However any test particle lying on the imaginary straight line between both masses that is not at the centre of mass will be attracted away from the centre of mass and towards one of the point masses.
I’ll admit it’s a fairly crude example, but I just use it to illustrate that it should never be taken as given that gravity always acts towards a single point.
In the cube example you however have 26 points on the surface of the cube where gravity will be directed towards the centre of mass. In between these points the direction of gravity on the surface will probably not be directed towards the centre of mass, but in a slightly different direction.
I don’t mean to be overly critical, the gravitational potneital of a cube is not simple, so to produce a more accurate disgram would be very involved. The only thing I could say about the ocean is that it would have two axes of symmetry.
For anyone who’s interested the equation for the graviational potential of a fixed homogenous cube lies on page 20 of this paper (warning PDF):
One way I was able to wrap my mind around the concept of a cubical planet was to, instead of a solid planet-size cube, imagine the spherical Earth being surrounded by a cubic box with the sphere (Earth) only touching the box sides at their midpoint. That way, I was able to more easily imagine myself walking away from the center of gravity, and the difficulties that would entail. I would envision the “central ocean” of the cube’s side to rise up above an observer on its shoreline, like a drop of water on a sheet of glass.
A cube the extent of a sizeable planet is something that really stretched the mind, with consequences that are not intuitive, so use are we living on a large sphere. Maybe that’s why Cecile was seemingly so reluctant to tackle the concept.
Okay, I see your point.
But effectively, I think my post makes a valid point. Gravity wouldn’t be perpendicular to the surface at most points on a cubical planet. Suppose you were walking from the center of one face to the center of another. Standing at the center of the first face, you would be perpendicular to the ground. But as you began walking, gravity would have you leaning more and more forward. By the time you reached the edge, you’d be leaning forward at a forty-five degree angle. Then when you stepped across the edge, you’d be leaning backwards at a forty-five degree angle. (Of course, it wouldn’t feel like you were leaning, you’d always feel like you were standing upright and the ground was tilted.) As you continue walking, you gradually become more upright until you reach the center of the other face, where you would once again be perpendicular to the ground.
May I point out a short story from 1987 by Henry H. Gross, “Cubeworld”? Originally published in the collection Mathenauts, edited by Rudy Rucker (Arbor House, 1987).
In order to avoid a colossal negative space wedgie (of great power), the entire Earth is reformed as a cube. The oceans are used to alter Earth’s orbit so that it gravitationally protects the Solar System at large. (Yes, I know, a great deal of handwavium was used in this story.)
Gross covers most of the issues, such as the still-spherical oceans and atmosphere, the increasing slope towards the edges, and so forth. Several illustrations show the result, including the fact that the corners would poke out of the atmosphere.
Fred
A Rubik’s cube has rounded corners, not sharp.
Powers &8^]
Maybe yours does, but after I found I wasn’t able to solve mine I polished it to the point that it’s a lethal weapon.