TorusWorld

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.