Astropolis

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    In classic science fiction, when Humanity expands into space people build their cities on other planets and/or their moons. The idea of a major city floating free in interplanetary space had not occurred yet, certainly not as a proposal for an achievement of the near future. The idea of habitats in space did not really take hold until the 1970's, when Gerard O’Neill and his students devised their L-5 Project.

    O’Neill had asked his students whether it would be feasible to use the spacefaring technology of NASA’s Project Apollo to construct a fleet of solar-power satellites. He received an affirmative answer and in 1976 he published a book, "The High Frontier", that laid out the plan that he and his students had devised. Part of the plan consisted of building a town at the Earth-moon Lagrange-5 point (the point sixty degrees ahead of the moon on the moon’s orbit). One concept, the Stanford Torus, resembled a bicycle wheel 8 kilometers in diameter with a cross-sectional diameter of several hundred meters. The other consisted of two counter-rotating cylinders, each perhaps 8 kilometers in diameter by 32 kilometers long. That town would have housed the people who used lunar-derived material to build, deploy, and maintain the powersats.

    As impressive as that achievement would have been, it was still a very small town. If Humanity is to spread into space and make the entire solar system its home, we will want much larger cities. Can we build them? If so, is there a limit on the size?

    With current technology and development we would be hard pressed to build anything really big, but as we get more people into space and communities multiply, the cities will get bigger. Think of how cities in the United States have developed from just a few small villages along the coasts. Eventually, if our descendants have the desire and the willingness to construct a carbon-fiber floor nearly 200 meters thick and 1000 kilometers long, they can build a city the size of France and Spain combined.

    That kind of construction is possible through the use of a material that did not exist in the 1970's. It’s a carbon fiber called Thornel™: it ponders 1.76 tonnes per cubic meter and it can endure as much as 3.2x109 newtons per square meter of tensile stress without breaking. Long ropes of this fiber will serve as the main load-bearing structures in the miniworlds that our descendants will build in interplanetary space. To see how this will work let’s reinvent the wheel.

    The stereotypical space station, popularized in the 1950's, resembles a bicycle wheel. It revolves about its unique axis of symmetry to mimic gravity through the inertial reaction commonly known as centrifugal force: as revolution makes the wheel’s parts move in circles, the outer wall presses against objects trying to move in straight lines and thereby creates the illusion of gravity. The outer part of the station resembles an inner tube, a torus, built that way to minimize the amount of material needed to hold in the pressure of a breathable atmosphere.

    Imagine that the rotational axis of the station lies in a flat plane, which we call the axial-radial plane. That plane cuts the torus of the station into two circular cross sections. The material manifestation of those cross sections must have enough strength to hold in the pressure of an atmosphere, so we look at one of the circles, bisect it, and ask how thick do the walls have to be to resist the force acting to pull the two halves apart. It’s an easy calculation: after dividing out unnecessary factors, we find that we need only multiply twice the diameter of the circle by the internal pressure and divide by the yield strength of the wall material (expressed as a pressure) to get twice the thickness of the wall. That gives us a minimum thickness of the wall, though we will want to make the wall thicker for safety.

    For example, give our space station a minor width of 20 meters, making the torus the equivalent of a six- or seven-storey building. We want to fill our station with air at normal pressure (1.01325x105 newtons per square meter, equivalent to the weight of 10.33 tonnes of matter pressing down on one square meter under normal Earth gravity) and make our structure out of an aluminum alloy listed as 2014-T6 (with a density of 2.8 tonnes per cubic meter and a yield strength of 414x106 newtons per square meter). The above calculation tells us that we need to make the walls at least 9.8 millimeters thick in order that they will hold in the pressure without bursting.

    If we have a radial-longitudinal plane that passes through the center of the station, it will show us two concentric circles, 20 meters apart in our example, with the inner one penetrated in several places by the cross sections of the wheel’s spokes. The concentric circles represent the floor and ceiling that must hold the torus structure together against the forces acting to pull the wheel apart. Those forces consist of the internal pressure pushing in all directions on the wall, floor, and ceiling of the tube and the centrifugal force of the wheel and its contents.

    Let’s now specify that our space station has an effective radius, from its axis of rotation to the midline of the torus, of one hundred meters. To create one gee (9.81 meters per second per second) on that midline, the wheel must rotate at an angular speed of 0.3132 radians (17.95 degrees) per second, equivalent to about 3 rpm. That inertial reaction makes the structure of the torus and its contents (equipment, people, and supplies) exert a force that acts to tear the torus apart. Imagine cutting the station into two identical halves with an axial-radial plane through any diameter of the wheel. The force that the structure must resist without breaking equals twice the pressure exerted on the two cross sections of the torus (twice 628 square meters in this case) plus the projection of the total centrifugal force onto that plane. For the latter number we need only calculate the centrifugal force per meter of the torus’s length and multiply it by the diameter of the station (the cosine relation of the projection makes that calculation correct).

    Let’s assume that the contents of the torus ponder ten tonnes per meter of length. We thus calculate 5.197x107 newtons as the force trying to rip the torus asunder. Dividing that number by the yield strength of the aluminum alloy tells us that we need a minimum total cross section of 0.1255 square meter of aluminum to withstand that load. Distributed evenly around the minor circumference of the torus, that figure yields a wall 1.998 millimeters thick. If we use Thornel™, the wall will need an average thickness of 0.26 millimeters.

    The comparison of 1.998 millimeters to the 9.8 millimeters that we calculated for holding atmospheric pressure in the torus (and 1.27 millimeters if we use Thornel™) tells us that we can extend the torus in the axial direction, but that we must increase the thickness of the wall to compensate the altered stress. In this case, if we give our torus a rectangular cross section with semicircular end caps, we must calculate the thickness needed to contain the pressure using the major diameter of the torus rather than the minor diameter. In the present case we will need almost two centimeters of aluminum or 2.6 millimeters of Thornel™.

    What I have described above is fine for a research station, but for an actual city in space, a place where people live (not merely reside) and work, we need something bigger. When I was growing up there in the 1950's and early 1960's, the City of Visalia, in California’s Central Valley, held 15,000 people in an area that measured roughly eight miles (12.8 kilometers) by eight miles. What would it take to build a flederstadt (flying city) big enough to contain that small town? With a radius of two kilometers, the torus will have a length of 12.57 kilometers and we can make the axial width the same. If we want normal gravity on the outer wall of the torus (the floor), the wheel must rotate at a rate of 7x10-2 radians per second, making one revolution every 1-1/2 minutes. We then put the inner wall of the torus (the ceiling) one hundred meters closer to the axis to give the inhabitants a sense of roominess.

    The atmosphere presses down on the floor with the equivalent of 10.33 tonnes of mass per square meter. To that force we must add the weight of the contents of the town. We want a layer of soil so that we can grow lawns and bushes and, perhaps, some small, shallow-rooted trees. Buildings, streets, and other structures will add their own weight, though the builders will make them as light as possible (perhaps something like the traditional Japanese house made of lacquered paper). For construction, bricks will be made of ceramic foam and wood will come from specially-evolved trees, whose wood is as light as balsa, as tough as live oak, and as fireproof as redwood. If we budget a little over three tonnes per square meter (about one meter of soil or three meters of water if we have a lake or swimming pool), then we can call it 14 tonnes per square meter and calculate the minimum thickness of the Thornel™ comprising the floor at 343.35 centimeters (at 5'11", I stand 180 centimeters tall), which requires over 95.6 million tonnes of Thornel™ just for the floor.

    The ceiling holds the atmosphere in place with its weight, derived from 10.33 tonnes of glass per square meter. Window glass has a density of about 2.5 tonnes per cubic meter, so those people will have 4.132 meters of solid glass floating overhead, held up by air pressure. If it weren’t for the presence of the atmosphere, the builders would need a band of Thornel™ 253 centimeters thick to hold up that ceiling. As a safety measure that amount of Thornel™ will be distributed throughout the glass in cords and the glass will be so made that it will channel sunlight around the cords (as in an optical fiber) and provide proper illumination to the city without overheating the cords. With the glass supported by Thornel™, the builders can spin up the city before introducing the atmosphere, 19.3 million tonnes of air, but they will likely carry out the spin-up and the inflation simultaneously, depending on the Thornel™ as a backup support in case something goes wrong.

    The builders will likely make an improvement before they start building large towns. Experimenters have observed samples of diamond with yield strengths as high as 60x109 newtons per square meter, 18.75 times as strong as Thornel™. Diamond is denser than Thornel™, pondering 3.50 tonnes per cubic meter, but the extra strength makes its use worthwhile. Using the Omnifex technology, our builders could make fibers and cords of diamond with that much strength (the theoretical maximum strength of diamond lies between 90x109 and 225x109 newtons per square meter.). If we use cords of diamond fiber, call it Atlasite, then our town’s floor must be 18.3 centimeters thick and the cords supporting the ceiling must have a collective thickness of 13.5 centimeters.

    O’Neill’s students determined that a space colony would have to be surrounded by four tonnes per square meter of dead mass to protect the inhabitants from radiation and meteoroid impacts. The ceiling will certainly meet that requirement, especially in the blocking of ultraviolet radiation. In the floor, 18.3 centimeters of Atlasite won’t be sufficient shielding, so we must add extra mass, thereby increasing the required thickness of the Atlasite to 23.5 centimeters. If we make the radiation shield as a kind of linear foam with the Atlasite cords distributed throughout it, then we can have solar-powered microbots moving through it, carrying out maintenance and repairs.

    At the north and south edges of the city the builders must construct semicircular walls to hold in the atmosphere and provide protection from radiation and meteoroids. If we put the ceiling 100 meters (about the height of a thirty-storey building) above the floor, then the walls must consist of Atlasite 0.17 millimeter thick. For every meter of wall along the edge of the city that thickness corresponds to 187 kilograms, light enough that the city’s internal pressure will keep the wall from sagging. The radiation/meteoroid shield forms a separate structure that doesn’t rotate with the city, but floats several tens of meters from the wall, held in place by cables connecting it to the city’s hub.

    From several places in the habitat spokes will rise like 600-storey skyscrapers, connecting the city to the hub around which it revolves. They won’t rest on the floor, but will hang from Atlasite cables that cross the hub so that one spoke holds up the one opposite it. The spokes will contain the elevators that carry goods and people to and from the city. They may also include structures where low-gravity work may be done.

    One important factor in the design and construction of the flederstadt is balance. Consequently the builders will want to distribute the mass of the city and in the spokes as evenly as possible. Even though the city spins at 3 rpm or less, they still don’t want it to vibrate or spin off center. When the inhabitants erect a new building, then, they must erect something pondering the same mass on the opposite side of the wheel. Cities in space will be remarkably symmetrical.

    Getting light into a flederstadt is a straightforward exercise in basic optics. This is only a problem because the light must enter the city from the direction of the city’s axis of rotation and it must come into the city steadily, rather than gyrating as the city rotates. To make the solution simple, the builders establish the flederstadt with its axis of rotation parallel to the axis of the city’s orbit around the sun. A flat mirror tilted 45 degrees from the city’s axis will reflect sunlight parallel to that axis so that secondary mirrors can reflect it through the city’s ceiling. Nicely enough, the glass ceiling will block the deadly ultraviolet component of raw sunlight.

    Sunlight will also provide energy, in the form of electricity, to drive the machinery of the flederstadt. Giant solar panels will float in space near the flederstadt, tethered to it by spindly cable-bearing trusses. Spread widely, the panels will give the flederstadt the aspect of a flat tree. The entire array will rotate slowly, pacing the flederstadt’s motion around the sun and keeping the panels always facing sunward.

    As long as humans are chemically-fueled creatures, they will need food. Far from other human settlements, in terms of both distance and delta-vee, each flederstadt will have to produce enough food for its population and do so in all appropriate variety. Each flederstadt must be a self-contained world.

    There likely won’t be any livestock larger than chickens. By the time Humanity is ready to move into space in a big way, meat will come from vats, where it will be grown artificially. Already some experiments are showing some small success in this endeavor. When the inhabitants of a flederstadt go grocery shopping, they will likely see packaged meat that looks no different from what we see in our supermarkets today.

    Fruits and vegetables will grow in zero-gee greenhouses floating in space on the side of the flederstadt opposite the solar-power farm. Those greenhouses will be attached to the flederstadt’s hub through a rigid frame of tubes that will facilitate movement of material between them and the city. Many of the plants will result from total genetic engineering, a combination of traditional selective breeding and of direct manipulation of DNA and RNA. Fruit trees, for example, don’t need thick trunks in weightlessness: they will look more like bushes or vines.

    The flederstadt will use an hydroponic system, of course. The plants will grow on thin sheets, with the plants’ stems and leaves on the sunward side and the roots projecting onto the opposite side, where they will be bathed in a thin mist containing nutrients. The bees necessary to pollinate the plants should have no problem with zero gee in their activities around the plants, but the hives will have to be built in rotating sections attached to the greenhouses (and if the bees evolve a species that prefers zero-gee hives, so much the better).

    Robots, both natural (the bees) and artificial, will tend the crops and harvest them, bringing food from the farm to the hub of the flederstadt and thence down one of the spokes and into the city. Other robots will take pre-processed garbage and sewage up another spoke to where it will be rendered into nutrients for the farms. The flederstadt will thus be a closed ecological system, entirely self-sufficient.

    Trade will occur, of course. It was trade on Earth that united tribes into states and states into nations and which will ultimately yield a completely unified Humanity. Luxury items, such as wine, will pass among the flederstädte and help ensure that the bonds of affection that hold Humanity together do not fray and endanger the most important institution of all, the rule of law.

    By the time we’re ready to start building these interplanetary cities, a fully unified Humanity will have spread the rule of law over the entire solar system. The authority charged with enforcing interplanetary law will also charter orbits for the flederstädte in a way that ensures that there are no conflicts or collisions. Each orbit will have to be circular (so that it won’t cross other orbits) and its radius so chosen that the orbital period won’t resonate with those of the outer planets, especially Jupiter and Saturn. That non-resonance ensures that perturbations will, over time, cancel out, as they do for the asteroids, which have been following their orbits with little change for billions of years.

    Once a group of people has obtained a charter, they can begin to build their flederstadt. They will draw building material from one or more asteroids and obtain water and gases from comets. Indeed, the first of these cities may play a role analogous to the part that Nantucket played in American history, sending out ships to hunt whales and bring the whale oil back to fuel a growing American civilization. Our cosmic Nantucket (or, for Murray Leinster fans, the Whaling Asteroid) will play a similar role, sending out ships to hunt comets and bring volatiles back to provide for a growing civilization in the Asteroid Belt and the Inner Solar System.

    Century by century the cities will become more numerous, larger, and more sophisticated. The Asteroid Belt, the Kuiper Belt, and the Oort Cloud will be emptied out as the builders sweep up all the debris they can find, eventually leaving the solar system clean. One million years from now the sun with its major planets and their moons may be the only natural bodies left. Earth may have been long ago restored to its original role as a laboratory of life in a solar system aglitter with millions of giant floating cities.

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