A topopolis (plural: topopoli) is a stellar-scale megastructure sometimes referred to as cosmic spaghetti. It consists of an enclosed tubular habitat wrapped completely around a star. The concept was created by Pat Gunkel and mentioned in Larry Niven's essay "Bigger Than Worlds." One is also described in the novel Matter Iain Banks and another is featured in the Orion's Arm online project.
A topopolis habitat is constructed very much like an O'Neill space habitat. Its circular, with a cross-sectional radius that can measure anywhere from a few hundred meters to a few hundred kilometers. The inner, open surface is sculpted to be as Earth-like as possible, with an atmosphere, soil, freestanding water, plantlife, towns, roads, and so on. Large windows set in its surface allow sunlight to pour through. Then the whole thing is set spinning on its short axis in order to produce centrifugal gravity on its inner surface.
The only real difference between an O'Neill Habitat and a Topopolis is length. An O'Neill habitat can be up to several hundred kilometers long. The length of a topopolis can reach into the millions or even billions of kilometers, usually looped around a central star.
A topopolis need not form just a simple hoop around its sun. Any coiled configuration can do as long as the loop is ultimately closed. Twirling spring-like coils, kinked star loops, and even intertwined 'braids' that loop around a star many times are all possible.
The 'dayside' of a topopolis tube would be the inner surface opposite the sunward side, which would be receiving the sunlight pouring through its windows. Depending on how far away the topopolis is from the sun, these windows may also have large angled mirrors on the outside to help focus sunlight into the interior. These mirrors could also close over the windows if need be, in case of an emergency like a major solar storm.
The windows on the interior would likely have high angled walls (tens or even hundreds of meters high, depending on the interior habitat's dimensions), to prevent too much diffraction of the incoming sunlight. This way, light doesn't 'leak' near the windows and allows the 'nightside' to enjoy something similar to a true dark. However, reflected light from the dayside would still likely lend it a twilight character, like perhaps that on Earth during a full moon.
Even though the topopolis is curled in on itself, the spinning of the habitat does not foul the integrity of the structure nor 'kink' seams between sections of the habitat. This is because the topopolis is constructed on such a huge scale length-wise that even tight-seeming curves seen from far off would actually be perceived as perfectly straight as far as the naked eye could see by a human observer close up. Its is very similar to twirling a looped string--the curls and curves of the string will not stop the twirling of the string itself along its length.
Topopoli do not need to rotate length-wise around a star like a Ringworld, as centrifugal gravity is provided by spinning along its short axis. It may pick up some small rotational velocity around the star for a variety of reasons (structural stability issues, momentum gained from the sun's movement through the galaxy, etc) but not usually enough to be felt by its inhabitants. However, like a Ringworld, it would prove unstable in the plane of its orbit, meaning it could slide about over a long enough period of time, to the point that it could even brush up against the surface of its hosting sun. In order to prevent this, the topopolis would need many large attitude thrusters to help it maintain its position from time to time.
Unlike a Ringworld, a topopolis does not necessarily need to be constructed in the parent star's life zone. Any distance at which its building materials and technology could tolerate the increased solar radiation would be doable. If closer than the life zone, the windows that let in sunlight would have to be polarized or filtered properly to avoid letting in too much damaging heat, radiation, or light. However, as the topopolis is assumed to use sunlight both for power and for maintaining its biosphere, placing the topopolis too far away from the sun could greatly reduce its operating efficiency. Generally, for a Sun-like star, a topopolis can be created anywhere from within the orbit of Mercury out to about the orbit of Jupiter. Topopoli can be constructed even further out, if they use power sources other than their hosting sun to maintain living conditions within.
Because it does not need to rotate at a high rate around its star, a topopolis does not need to be made of uber-strength material like a Ringworld often is. This is not to say that its hull will be flimsy, only that known real world materials such as graphene can be used to construct it.
If the hull is inset with conducting or superconducting material, and if set spinning close enough to a sun, a topopolis could also generate power simply by moving through its parent star's magnetic field.
A topopolis' inner habitat is usually depicted as being completely open all through its immense length, but this need not be the case. It can be sectioned off so that different areas could have different habitats and conditions to support different kinds of ecologies or cultures. It could also be a completely open habitat but with sections designed to be closed or cut off fairly rapidly in case of an emergency, such as a catastrophic hull breach.
An interesting feature the interior may have is an endless spiraling river. The water way would wind its way along the inner surface of the structure, looping itself around in a spiral that would eventually meet back with itself after a course of what may be several hundred millions miles or more. The centrifugal force of the spinning habitat would keep the water flowing. Attempting to sail all the way down such an immense waterway would likely take millennia.
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