Half a croissant, on a plate, with a sign in front of it saying '50c'
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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 23 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 23 2008]


       What's the advantage of the Torusworld over the Ringworld, other than you don't lose atmosphere over the sides?
phoenix, May 23 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 23 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 23 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

       "One thing I've found out, over the years, is that, anytime you think that you were the originator of some new idea, ' I was the first to do that, ' you'll find some old fellow who did it around 1895. Every darn time. " Edward Hamilton, 1904 - 1977, in "The Space Opera Renaissance", TOR Books, 2006
normzone, Nov 27 2017

       Helix - Eric Brown (2007)   

       In that one the day/night issue is solved'ish by having cylinder-shaped oceans between cylinder-shaped Earths : the whole thing spins. Nifty.   

       And it's a continuous spiral from a Pluto'ish orbit down to a Venus'ish orbit, with interstitial space-elevators.   

       At which point, pretty a picture as it is, my suspenders of disbelief came undone.
FlyingToaster, Nov 27 2017

       I’m not exactly sure how a torus-shaped core remains stable...
RayfordSteele, Nov 27 2017

       [phoenix], one significant advantage of a TorusWorld over a RingWorld is that its integrity is much less susceptible to the effects of meteor damage. Also, only ordinary materials can be used in its construction, not special super-materials such as a RingWorld requires.   

       [normzone], it can often (not always) be OK to claim one has independently originated an idea. This type of claim never tries to supersede an originality claim made by anyone else.   

       In reviewing this Idea, it occurs to me that a TorusWorld might be better built in free space, away from any star. One could then start with a smallish-diameter tube of appropriate length, which is then bent into a circle and given a slight spin. Additional material can be vacuum- welded to it, to thicken it gradually, until it produces enough local gravitation to allow large masses at a time to be added.   

       When the TorusWorld is finished and rotating/revolving as desired (possibly as a result of directional impacts of arriving masses during the final stages of construction), now take the nearest suitable star and use electromagnetic fields to convert its "stellar wind" into the equivalent of a rocket exhaust, to move the star into the center space of the TorusWorld. This automatically also provides a means for maintaining the star's relative position over the long term.   

       Finally, it can be noted that we can use smaller and longer-lasting stars than any similar to the Earth's Sun for a Torus World. For an ordinary world orbiting a small red star in the habitable zone, tidal effects can be expected to stop the world's rotation. Not good. But a TorusWorld should be much less susceptible to that phenomenon, largely because it is likely to be rather more massive than a small red sun.
Vernon, Dec 05 2017


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