If the Earth was a perfect cube, what would the gravitational effect be at the edges? Could you casually step over the 90-degree bend onto an adjacent face?
— Victor Allen
The Straight Dope research department debated how to deal with your question, Victor. Una thought we could have a little fun with it, pointing out the numerous opportunities for sublime comedy about Bizarro World (the cubical planet of the Superman comics, inhabited by blockheads) and similar topics. My own feeling was we should jump on you with both feet, since a cubical Earth was impossible, and encouraging belief to the contrary was the same road to perdition that had given us the Tea Party and Charlie Sheen.
I reasoned that one of the official criteria for planethood was that the body had achieved hydrostatic equilibrium, meaning it was sufficiently massive for its gravity to have pulled it into a round shape. The largest known nonspherical object in the solar system is Neptune's moon Proteus, an awkward lump with a diameter that varies from 390 kilometers to 424 kilometers. The pull of gravity on Proteus' surface is 1/140th that of Earth's, meaning a typical human standing on it would weigh a little more than a pound. In short, assuming Proteus marks the upper bound sizewise, the main gravitational effect you'd have to be concerned about on a cubical planet would be how to keep from accidentally jumping off.
"I know that," said Una. "All I'm saying is, let's suppose."
"Suppose what?" I replied. "That you could have an Earth-size cubical planet? Not possible. Earth-scale gravity is so strong that a cube made of the strongest rock would soon be deformed into a ball."
"Define soon," said Una.
"Within a very short period of time," I said. "Probably less than a billion years."
"I think that allows enough time for a hypothetical experiment without violating the laws of the cosmos," Una said.
"Fine," I said, "let's imagine your damn cubical planet. Even better, let's imagine you on it, standing on one of the six square faces. Your assignment: Journey from there to one of the planet's corners. Not to alarm you, but at the very least you'll want a couple ham sandwiches, a lifetime supply of pitons and a spacesuit."
The first thing you notice on being teleported to cubical Earth is that you're at the edge of a vast body of water we'll call the Central Ocean. The land rises steeply away from the shore — apparently the ocean lies in a basin. This strikes you as odd, since you'd think the sides of a cubical planet would be flat. Patience. All will soon become clear.
Turning from the ocean and looking out over the land, you discover something else — you can see vast distances. On spherical Earth the horizon on average is a little more than three miles away. On cubical Earth you can, in theory, see to the edge of the planet, potentially a distance of thousands of miles. Up the slope you're standing on, impossibly far off, you can make out a gigantic mountain peak — one of the corners, you realize, of your cubical world.
Time to get hiking. I hope you're in good shape, since the path literally becomes steeper with every step — you'll have the impression of climbing up the inside of a round bowl. Worse, the mountain is stupefyingly high. How high? Well, the tallest known mountain in the solar system is Olympus Mons on Mars, 14 miles high from base to peak. In contrast, the vertical rise from low point to high point on cubical Earth is about 2,300 miles.
Soon you see why you needed that spacesuit — the atmosphere gets progressively thinner until there's none at all and you're in the blackness of space. One consolation is that your weight steadily decreases. 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.
But here you are, on top at last. You don't have the sense of walking around 90-degree corners that our letter-writer naively imagines. Rather, the peak looks like the tip of a three-sided pyramid. The three sides fall away steeply — if you lose your footing you'll have a wicked drop.
On the plus side, the view is like none on Earth, or on any planet anywhere. You can sight down one edge of the cube to a far corner, a distance of some 6,400 miles. Even more strikingly, you see all the atmosphere and water has been concentrated by gravity into a blob in the middle of each face, with the corners and edges poking out into space. You realize your cubical planet isn't one world but six, each face's segment of the biosphere isolated from the others by the hopeless climb.
Bizarre? Yup. Impossible, too. You may want your planet to be cubical. Just about every other force in the universe wants it round.
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