Mmm, planets
September 13, 2016 2:24 PM   Subscribe

 
So, planet Homer or planet Wiggums?
posted by TedW at 2:27 PM on September 13, 2016 [1 favorite]


The equilibrium shapes of self-gravitating rotating ellipsoidal planets have been extensively analyzed.[link]

What!

Well, my afternoon's shot.
posted by indubitable at 2:31 PM on September 13, 2016


What would the Earth be like if it was the shape of a donut?

More importantly, could we find a cup of coffee large enough in which to dunk it?
posted by Going To Maine at 2:31 PM on September 13, 2016 [5 favorites]


There's coffee in that nebula!
posted by Halloween Jack at 2:33 PM on September 13, 2016




Could a planet in the shape of a donut exist, and could it sustain life?

FUCK, YEAH.
posted by My Dad at 2:39 PM on September 13, 2016


"There is also a lower rotation rate where the ring become unstable to tidal forces and implodes into a 'hamburger'"
posted by Kabanos at 2:42 PM on September 13, 2016 [1 favorite]


Cake or yeast donut?
posted by Thorzdad at 2:53 PM on September 13, 2016 [2 favorites]


"… implodes into a 'hamburger'"

This only happens if less than 768px, and then you can click it to expand the menu.
posted by Monkey0nCrack at 3:23 PM on September 13, 2016 [2 favorites]


What's fun is the idea of imagining a moon held stationary in the middle of the imaginary donut-world, and every denizen of this planet knows its moon's orbit is metastable and that said moon would inevitably plow into the donut-world or be kicked out into space at some point.
posted by a lungful of dragon at 3:30 PM on September 13, 2016 [2 favorites]


Still holding out for Ringworld to be a thing.
posted by Fizz at 3:34 PM on September 13, 2016 [2 favorites]


I can't tell you much, but I can tell you how many colors you'll need on the maps.
posted by cardioid at 3:38 PM on September 13, 2016 [14 favorites]


Of course donut-shaped worlds exist, anyone who has played a video game RPG has probably been unwittingly playing on a torus.
posted by Mr.Encyclopedia at 3:42 PM on September 13, 2016 [7 favorites]


Donuts: Is there anything they can't do?
posted by entropicamericana at 3:53 PM on September 13, 2016 [2 favorites]


Could a planet in the shape of a donut exist, and could it sustain life?

Not for long if I exist.
posted by srboisvert at 4:08 PM on September 13, 2016


And all the world is football-shaped. It's just for me to kick in space. And I can see, hear, smell, touch, taste. And I've got one, two, three, four, five.
posted by kurumi at 4:16 PM on September 13, 2016 [5 favorites]


Finally, a justification for strategy games with maps that wrap on all edges.
posted by ckape at 4:24 PM on September 13, 2016 [1 favorite]


My math teacher in high school had a bunch of pictures on the walls of the continents mapped onto various solids (Earth as a tetrahedron, Earth as a cube, Earth as a cylinder, etc.) One was on a torus, and as a teenaged D&D player, I paid close attention. I asked a question or two about it, pondering how one would map such a thing. Turns out my math teacher had no clue as to how to even determine the surface area of a torus.

The question is much less pressing now, but if anyone can enlighten me, I would be grateful.
posted by ricochet biscuit at 4:55 PM on September 13, 2016 [1 favorite]


The Chandrasekhar link 404'd for me. I googled it up:

Ellipsoidal figures of equilibrium—an historical account†
S. Chandrasekhar

posted by bukvich at 5:09 PM on September 13, 2016 [1 favorite]


No one has played Halo?
posted by bongo_x at 5:38 PM on September 13, 2016


The question is much less pressing now, but if anyone can enlighten me, I would be grateful.

The surface area of a torus is the surface area of a circle at some distance from the axis, spun in a circle around the access. Let's call the radius of the little circle (i.e., the cross-section of the torus) r and the radius of the big circle (the distance between the axis and the center of the torus' circular cross-section) R.

Pappus' theorum says that the area of any surface of revolution (i.e., this torus) is equal to the length of the curve generating the surface (i.e., the circumference of our little circle) multiplied by the distance travelled by its geometric centroid. In this case, the geometric centroid is the center of the little circle and the distance it travels when we spin it around the axis is 2πR. The circumference of the little circle is 2πr, and therefore the area of the torus is 2πr x 2πR or 4π2rR.
posted by Joe in Australia at 5:52 PM on September 13, 2016 [11 favorites]


And all the world is football-shaped. It's just for me to kick in space.

Given the context I would have gone with "biscuit-shaped" and "feed my face", but de gustibus etc.
posted by The Tensor at 5:55 PM on September 13, 2016


Pappus' theorum

!!

I remember seeing this question (surface area of a torus) on some Math Olympiad sort of exercise in high school and beat my head against the wall trying to find the answer using calculus for half an hour before giving up. But the answer was really, "just know this theorem"? Shit.
posted by indubitable at 6:10 PM on September 13, 2016


The surface area of a torus is the surface area of a circle at some distance from the axis....

Thanks. Now to look up Mr. Alderson and let him know.
posted by ricochet biscuit at 6:13 PM on September 13, 2016


I would think it a water form, with a backwards spiral tidal movement, that causes it to get enough sunlight on all surfaces to maintain a sorta constant temperature. Then it would be in a very flat plane around its star, or else the shape of the Torus would change to match the elliptical orbit, and other gravitational pulls. It is a fascinating idea, worlds don't have to be rocky balls, or gas balls, maybe a water torus is something that happens, in a galaxy far, far away.
posted by Oyéah at 7:54 PM on September 13, 2016


Well, sure- if you want Galactus turning up every time he feels a little peckish.
posted by TheWhiteSkull at 8:48 PM on September 13, 2016 [2 favorites]


The tags beat you to it.

One was on a torus, and as a teenaged D&D player, I paid close attention. I asked a question or two about it, pondering how one would map such a thing.

A rectangular map that wraps at the edges (something going off the top edge reappears at the bottom) is actually already a toroid, with very little distortion relative to most projections of a globe. The OP article actually links to a relevant Kotaku article.
posted by XMLicious at 9:26 PM on September 13, 2016


So I was on the middle of a dungeons and dragons game tonight with a bunch of physicists and in a little break I told them about this story.

And then this happened.

Their answer was "mmmmmaybe". But they had to get there on their own.
posted by lollusc at 3:27 AM on September 14, 2016 [2 favorites]


No one has played Halo?

Yes. And the Halos are artificial constructs not natural formations.
posted by dances with hamsters at 6:57 AM on September 14, 2016


Imagine being the first person from the outer rim to summit the incredible gravity of either pole, only to see the other half of the world rise and then arc into the sky.
posted by Eideteker at 3:45 PM on September 14, 2016 [1 favorite]


It would be obvious your world wasn't a sphere from the different curvature but I wonder if scientists could figure out whether the word was a disk or a torus without observing the centre.
posted by Mitheral at 8:35 AM on September 16, 2016


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