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TorusWorld

Cross "Ringworld" with a doughnut...
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A doughnut, or a bagel, or a tire's inner-tube, all have the same generic shape. "Torus" is the generic name for that shape.

A torus has a "major diameter" and a "minor diameter". The way a bagel is typically sliced allows us to talk about the "major diameter". Looking at half a bagel, we see a circle of bread-stuff with a circular hole in the middle of it. Halfway between the edges of those two circles, we can draw a "average" sort of circle. The width of that circle is the major diameter.

Now take a nice large bite out of a doughnut, and look at what remains. From one point of view, it might look something like the letter "C". From another point of view, you will see two badly-shaped circles of exposed bread-stuff (thanks to bite-marks). The diameter of either of those circles is the "minor diameter" of the torus. Note that the center-point of this diameter, when followed all the way around the large circle of the doughnut, specifies the major diameter.

So, how about a TorusWorld that has a major diameter equal to the Earth's orbit, and a minor diameter equal to the Earth?

Constructing such a monster will not be easy. For starters, it would be rather more than 73000 times the mass of the Earth (because Earth's orbit is big enough to hold 73000 spheres the size of the Earth, touching each other --and we want to fill the gaps between those spheres to make a smooth torus).

The next problem has to do with the self-gravitation of the torus. While it could be built as a thing normally orbiting around the Sun, that's actually not enough for the end-product!

Construction has to be done carefully. Assuming we don't want to do this in our Solar System, (which would mean destroying Planet Earth), we first find a likely star, similar to the Sun, and second gather up (and gather up, and gather up...) appropriate materials.

Third, we construct an Earth-sized sphere in orbit around the star. We do NOT want it to rotate yet! Fourth, we construct a second sphere on the opposite side of the star, in the same orbit. Then, halfway between both, we simultaneously construct two more spheres (for a total of 4, at 90-degree intervals around the star). The basic idea is to keep the spheres gravitationally affecting each other equally.

Then we construct 4 more spheres simultaneously, halfway between each pair of the first 4. Then we construct 8 more spheres, then 16, and so on, until we are finally filling in all the gaps simultaneously, between adjacent spheres.

Gravitationally, even though it was constructed in a balanced manner, I would not want to claim that a TorusWorld is inherently stable. For one thing, it can be computed that the gravitation on the surface of the TorusWorld varies with location. There is rather more gravitation on the "outside" of the TorusWorld (where you can't see the central star) than on the "inside" (where the central star is directly overhead).

I suspect the entire TorusWorld needs to be spun up sort-of like Niven's RingWorld, but not to such a degree as the RingWorld. We only want to spin it enough so that centrifugal effects increase the APPARENT gravitation on the "inside", and reduce the apparent gravitation on the "outside", so that they become equal.

This leads to a problem it will now share with the Ringworld, in that by being spun up, it is no longer truly in orbit around the central star, and so additional technology must be employed to ensure that the star stays in the center of the TorusWorld. Here I will assume that if we have enough tech to build a TorusWorld, this other problem will be relatively minor. (Heh, the star might be only 4 times as massive as the TorusWorld!)

Next, now that gravity has been balanced, we want a day and night cycle. Here is where we can compare the Minor Diameter to the Major diameter, and conclude that the Minor Diameter is trivial. That means the 12000-km Minor Diameter is insignificant, less than 1/23000 of the diameter of the orbit in which the TorusWorld was built. Its surface can be rotated without unduly stressing the TorusWorld. The particular rotation can be imagined by starting at any and all points where the star is directly overhead, and paying attention to the "plane" occupied by the TorusWorld. Let all those points simultaneously move as if trying to go "above" the plane of the torus. Further rotation carries all those surface points to the outside of the TorusWorld, where the star cannot be seen. Further rotation carries those points back toward the side where the star can be seen again. Now just arrange this so it happens once every 24 hours.

Apply atmosphere, and start colonizing. If it was built with a hot core, then there will be volcanic activity and plate tectonics, sufficient to balance long-term erosion of continents into the seas, just like we have here on Earth.

Vernon, May 22 2008

About Larry Niven's "Ringworld" http://en.wikipedia.org/wiki/Ringworld
For anyone who didn't read his novel of that name. [Vernon, May 22 2008, last modified May 23 2008]

About "Klemperer Rosettes" http://burtleburtle...hysics/kempler.html
Niven also gets a Bad Science tag, so you're in good company [lurch, May 22 2008]

[link]






       What's the advantage of the Torusworld over the Ringworld, other than you don't lose atmosphere over the sides?
phoenix, May 22 2008
  

       The lack of shadow squares, and all that dang Sinclair-chain wire.   

       [Vernon], I kind of gag on all the points where, during construction, nothing is affected by gravity until you want it to be affected. You're trying to hide a magic wand up your sleeve - a wand which would make a pool cue to put Arcturus in the corner pocket.   

       Bypassing all that, though, I do find it interesting that the twist-rotation providing the day-night cycle deforms the surface on a scale which answers pretty well to thermal expansion and contraction - it may well end up solar driven, much like a weather system.
lurch, May 22 2008
  

       What's wrong with shadow squares? You always see the "arch", but that's not so bad.   

       I'm just thinking about how much more material this needs. Then you have to twist it! Seriously - if you have that sort of technology, why bother with a sun?   

       I wonder what the weather would be like. Flying an airplane along the axis of the torus would be like performing one long corkscrew. You'd eventually get to see *all* the constellations (both northern and southern hemispheres - not that that word would have any meaning).
phoenix, May 22 2008
  

       [lurch], there is somewhat less magic than you are implying. Look up "Klemperer Rosette". While most such rosettes are imagined as involving a modest number of orbiting planet-sized bodies, in theory it can be expanded as described here.
Vernon, May 22 2008
  

       I think you may not have linked what you thought you had.   

       Klemperer rosettes are (sorry, Larry, missed again...) stable in certain sets of even-numbered polyhedral groupings, but they do have an upper membership limit. The upper limit gets reached before your OuterSpaceInnerTube world gets much of a foundation.
lurch, May 22 2008
  

       That's 50,000'ish earth-sized planets
FlyingToaster, May 23 2008
  

       [lurch], thanks, I hadn't noticed that. Something happened to the two links I posted. Nevertheless, I'd say that the point where we have maximized a Klemperer Rosette is also the point where instabilities would appear if we want to add more spheres to the TorusWorld-under-construction, then we need to start increasing the orbital velocities of all those spheres. Trickier to do, but not necessarily impossible.
Vernon, May 23 2008
  

       Um, halfbaked already. Check out "Moonbow" by J.P. Boyd from the May 11, 1981 edition of Isaac Asimov's Science Fiction Magazine. Yay for eclectic book collections!
Hive_Mind, Jun 09 2008
  
      
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