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Imagine a hoopworld spinning in free space, far from any star. Without tidal forces from rotating near a star, there is no dynamic limit on its size.

I worked up the gravitational physics for such an object some time ago as an ISO in a story about a traumatized and possibly insane S:4 entity, but I think the ISO is still a cool idea in physics, with or without the entity, so I'm dusting it off as a proposed megastructure, and if you like it, you can imagine that somewhere in the MPA somebody might have decided to build one.

So, the version of the structure that I've actually worked up the numbers on is this:

It's a hoop, 40.85 AU in diameter. It is 13.66 solar masses. It has a mass density of 1.0 tons/m3, which is substantially less than a rocky planet like Earth and a minor (cross section of the hoop) diameter of 42361 kilometers, which is 3.32 times the diameter of Earth. It rotates around its own center of mass to balance centripetal force against gravity.

Working out all the foof, I get a surface gravity of 8.82 meters per second squared. (note, there is some variation in experienced surface g and some deviation from roundness, due to only part of the surface field potential being due to self-gravitation. In round approximations, it's small enough to ignore).

If you want 9.82 m/s, you can simply increase the low mass density a bit.  With its low mass density, it's bound to have a lot of hollow inside spaces. But, I think 1 ton/cubic meter is achievable.

This gives it a surface area a bit over 5 million times that of earth. There is enough gravity and a deep enough gravity well to hold an atmosphere.

Unless something inside is using a lot of power, it's cold enough that any breathable atmosphere would fall as snow.  If something inside is using a lot of power, then there could be a breathable atmosphere and comfortable temperatures on its surface.  But it would be very, very dark, and any local ecology would probably live on heat rather than light.

If it's intended as a habitat, then its surface would be sectioned off into 'cells' a few thousand kilometers wide separated by atmosphere walls.  That way if you have a some sections that are inhabited and getting heat/power and some sections that aren't, the moisture and atmosphere doesn't just blow away from one to fall as snow in the other.  But at least anything that escapes over an atmosphere wall doesn't wind up dissipating out in the void; it just goes to the neighboring cell.

OTOH, if lacking such atmosphere walls, de-powering a few sections and bringing the surface temperature there lower than the freezing point of the atmospheric gases would continually suck the air and water away from everywhere else around the whole ring, MAKING an atmosphere wall by building up ice and air to an altitude where the air's too thin to continue condensing on it.

If relatively unmodified people were living on it, it would be illuminated by artificial lighting - probably like enormous 'streetlights' in the sense of very bright lights, probably with reflectors directing light down, mounted on very tall towers.  Or, in areas near an atmosphere wall, the lights would probably be mounted on the walls.
That’s a neat idea! (Do they still say “neat”? ) I can see some Hiders liking it. Until someone else detects its heat signature, anyhow. That’s a lot of physical resources to take advantage of!

You mention “it rotates around its own center of mass...” Have you figured out how fast that might have to be? (I have not the slightest idea how to determine what forces the resulting magnetic field, if any, would apply to the structure.)

It seems to me that it has to rotate fast enough that the net “gravity” on its exterior side, the outermost circumference of the doughnut, farthest from the center of mass, would be zero or negative. Otherwise, I’m guessing, it’d eventually crumple into a sphere. That’d result in a complicated shape for the apparent surface gravity, I think. I’m also assuming no transapient structural support like magmatter. I dunno if that’s a reasonable assumption, though.

Am I overlooking something?
Grant Hutchison worked this out, but the details escape me. The Hoopworld I described in OA is based on his calculations, but he has since indicated it would need a lot of active management to stop it from coalescing into separate beads.
https://orionsarm.com/eg-article/49142c044cba7

Anders Sandberg has described a significantly more stable hoopworld,
http://www.aleph.se/andart/archives/2014...earth.html
which is also represented in OA here.
https://orionsarm.com/eg-article/59b109574cb45

In most respects, for hoopworlds, small is better, unless you have very good control over matter.
Yes, it would require a active maintenance, so it would need some amount of power and frequent adjustments. Probably a lot less power with a transapient seeing to the task, but till some.

The rotation period would be a leisurely 70.6 years.
Couple of thoughts:

a) Given the scale in comparison to pretty much all the rest of the Terragen megastructures in the setting, I'd suggest either having this (as of Y11k) being in the early stages of construction, or be a proposed (rather than created or under construction) megastructure - possibly with a model - perhaps a very popular model - existing in virtuality in the Cybercosm. Perhaps even have the virtual model exist even if this is under construction.

b) I'd suggest actually having this be geared to the IR based ecosystem and exotic cold and dark optimized lifeforms and sophonts. If its not yet built or only partly built or the like, perhaps have the design of the future lifeforms (including the sophont inhabitants) be the subject of multiple ongoing competitions. We have very few really exotic hab environments described in the setting in terms of not being habitable for baseline humans, especially those focused on adaptations to living in deep space. This would make a very nice addition toward fixing the existing imbalance IMHO.

My 2c worth,

Todd
The mass requirements of this structure are very large. Even if we disassemble 13.66 Sunlike stars, that only gives us ~13.6 solar masses of hydrogen and helium, and a few percent of other materials. Could this structure be made from a hollow balloon, like a toroidal Edersphere?

And perhaps the Terragens would build a smaller version first, as proof of concept? Even a toroidal Edersphere in deep space with a radius of 1 AU would be a major achievement. The larger version could be in the earliest stages of construction.
When I was considering it, I imagined it as having a fairly high relative velocity compared to the surrounding stars; It requires a stupid amount of mass to construct, and bringing mass up to some velocity just to match its vector as it goes by is probably easier than bringing it up to some velocity for shipment, waiting years while it gets there, and then slowing it down again on the far end.  So during the (LONG) course of planned construction you get to draw on the resources of a few thousand solar systems where the Rogue Ring is going to be passing within half a lightyear, but without making it necessary to fully deplete them.

The 'big score' in terms of construction material would be a course that passes by several young stars with dense accretion disks.  Depleting them to the point of being "ordinary" habitable star systems could be a mutual win for both the builders and real estate developers who'd be, up to that point, too worried about dynamical and navigation hazards to build anything.

Anyway, take whatever you consider a "normal" speed for in-transit interstellar shipments of building material, and posit that the Rogue Ring under construction is moving maybe 150% that fast.  - As a compromise between 'we save about 33% of the delta-vee we'd normally use on shipping, in exchange for 50% extra speed bringing us near more places where we can get building material.'

And, if high relative velocity is a feature of the construction method, then we can imagine it as something that's intended to go someplace or traverse some space - it could be 'the million-year tour of the Galaxy' or depending on the builder's degree of ambition 'the intergalactic ISO,' but whatever it is, it should be fairly clear that it's "outbound" in the sense that by the time it's built it's going to be traversing places that weren't Terragen space when its construction began.
Well, if its velocity is sublight, it’d always be in Terragen space, wouldn’t it? Assuming Terragen space keeps expanding, of course, with nothing preventing expansion in that direction.
Terragen space seems unlikely to expand at any great speed beyond the edge of the Milky Way galaxy, or far out of the galaxy's primary plane of rotation.  I presume that something traveling at less than 10% c will remain in Terragen space for as long as it's traversing something that Terragen space wants to expand into.
Given the large section of such an object would it possible to build rings nested inside each others to better use the total space/volume?
Maybe using a central ring of black holes for artificial gravity?
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