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OK, so we've reached the Clarkian "sufficiently advanced technology" stage, and we can hoover up all the mass in solar system and convert it to something with the tensile strength needed to build a Dyson sphere. See, for instance, How many worlds would you need to mine in order to make a complete Dyson's sphere? Can we live in it?

Dyson spheres were originally conceived as the ultimate in energy-collection schemes (for a single solar system), but are often described in terms of livable surface area, and I think this is not supportable.

If the DS collects all the energy from the sun, and converts some or all of that energy to "usable" energy which is then used within the sphere, the waste heat has to go somewhere, and must eventually be radiated away by the surface of the sphere. Since the solar flux at 1 AU is nominally 1366 W/sq meter, the exterior must radiate a similar power. Assuming the surface is a black body, this implies a temperature of about 390 K, or 117 C. Since energy is flowing outward, the temperature of the inner surface must be at least the same, with obvious consequences for habitability, and note that if the surface is not a black body, and has an emissivity less than one it will get even hotter.

In order to keep the outer surface at 300 K, the power density needs to be about 460 W/sq meter, and this implies a radius of about 1.7 AU. At this distance, the decreased insolation will presumably cause real problems with agriculture.

Much worse, the entire interior volume of the DS is both isothermal and nominally at zero gravity (excepting the equatorial band of the spinning sphere). The atmospheric pressure gradient behaves similarly to the existing earth along the radial direction, but the pressure gradient laterally (towards the poles of the sphere) will be much less, and without the installation of Rim Mountains (a la "Ringworld", or a Dyson Ring) the amount of atmosphere required to proved a breathable habitat at the equator becomes enormous.

Since the interior is isothermal, there would seem to way to produce much of a temperature gradient in the atmosphere, and thus no way to convert water vapor to precipitation. It's true that surface-heated air will tend to rise, since it is of lower density than the layers immediately above it, but it cannot radiatively cool once its density reaches that of a higher altitude. Or rather, it will do so, but only weakly compared to the situation which pertains with radiation to the sky in our current setup. Currently the upper atmosphere radiates almost entirely to space, at a nominal 2.7 K temperature, but in the DS the sky is maintained at the surface temperature. The result would seem to be that the "habitable" portion of a Dyson sphere will be nothing of the sort, with low solar illumination (1/3 of current levels) and virtually no rain.

Or am I thinking about this wrong? And are there other effects I've missed?

EDIT - Please note several points.

1) I believe the interior is NOT habitable. I'm particularly interested in either being proved wrong, or it's even less habitable than I think.

2) At 1 AU, the surface gravity of a solar stationary sphere is 50 ug, so living on the outer surface is not on the table. Furthermore, a space-based civilization outside the sphere must live in darkness, since the peak emission for a 300 K black body occurs at 10 microns.

3) Since the only livable area is in the interior, it seems reasonable (and has seemed reasonable to a fair number of science fiction authors, too) for the civilization to inhabit the interior. While there's lots of room, you only get equivalent gravity near the equator if you spin it.

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  • $\begingroup$ This isn't really an answer, but by the time we make a Dyson sphere, I don't think we'll be human anymore. Instead, I'm sure we'll have had a pretty long time to design our new robot children to live comfortably on whatever structure we plan to build for them. $\endgroup$ – DaaaahWhoosh May 22 '15 at 13:08
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A (Qualified) Defense of Habitable Dyson Shells

Habitable Dyson Shells in the 1-2 AU range seem a bit absurd from an efficiency standpoint. I'll be defending this as being a fundamentally tractable engineering challenge (without unobtanium materials or new physics), not as something we will actually be doing.

Intro: To Begin With, Build a Dyson Sphere

The first Dyson sphere we create won't be a habitable (or unhabitable) shell, but a solar power collector that beams energy to wherever we need it.

Surprisingly, we can get started on that with something close to today's tech -- ability to harvest a bit of fuel and mass from near earth asteroids, solar sails to get around, plain old photvoltaics, rockets, lasers, and (most crucially) self replicating robotic systems. Since manufacturing systems on earth are nearly self replicating over all (i.e. they do replicate, with human help), and since no particular step in the supply chain cannot be automated in principle, this is justifiably in the "near term" category, especially if we include robotic telepresence. So this is no mere thought experiment.

To take control of the solar system's available energy, the prerequisite for this grand scheme of a Habitable Shell, we'd probably begin by making a light-supported system with a density of around 0.78 g/m^2, aka a Dyson Bubble, comprised of statites (stationary satellites). This lets us generate (or rather, take control of) large amounts of energy, which we can convert to antimatter, high-intensity lasers, high velocity kinetics, and so on. Enough that we can more or less do whatever we want with the rest of the solar system, on a scale of years to decades.

We need to process about 200 quadrillion tons (200 exatons) of matter (the mass of Pallas, one of the biggest asteroids) to create this form of power collector if we want to do it near 1.0 AU. On the other hand, at 0.3 AU, it is closer to 20 eT, which is the mass of a medium sized asteroid. This seems to be far enough out from the Sun that we can probably engineer working systems without devoting excessive amounts of effort to cooling and radiation shielding. For mass, we can disassemble Mercury (which is ~300,000 eT), and have lots more left over (which can go towards producing large numbers of robots, habitats, and any other infrastructure we want/need in the mean time).

Energy wise, it appears feasible to disassemble Mercury even if we assume fairly dismal launch and construction efficiency. The energy requirement to pull a kilogram from Mercury's surface, given escape velocity of 4.24 km/sec, is about 18 MJ. Assuming that is being spread out to 0.78 g/m^2, the energy payback time (once you have converted it into solar collector) is only a little over a second! Also note that as we pull more matter from Mercury, the launch energy requirement diminishes, and the total gravitational binding energy is 1.8×10^30 J (an amount which could be harvested in a matter of hours if we had a whole DS).

The thin-film form of Dyson bubble might need more mature tech than we can get to right away -- such lightweight, fragile plates might be hard to control and so on. So there's the thought that maybe we would want to use thicker collection surfaces to begin with. Also there could be a lot of robotic equipment involved in fabricating it, which we might leave in a more traditional orbit rather than spreading it over the whole sun. So maybe we need to start out with 10g/m^2 or so, set up a slightly offset Dyson "ring" (with reflection angle used to modify the orbit of each component slightly so we can spread them out and ensure they never block the light from the earth). In that case, 18 MJ launch cost results in 100m^2 of collection surface, which takes more like 20 seconds to pay for itself. Not really a big deal even so. In fact, we can posit substantial efficiency losses (assume we need 100 times that much mass for the manufacturing robots, etc.) and still make progress on the sphere as a whole in a matter of weeks or months.

The next phase in my mind, after a few months to decades of disassembling Mercury, or partway through that process, ends up being the development of a Saturn-like ring consisting of Mercury's mass mostly converted to asteroids, a razor thin line as seen from earth, with the major solar energy collector systems stretching north and south along the sun's equator (remaining out of line-of-sight from the planets), just far enough to harness 1-10% of the total solar energy. This collected energy gets beamed to sites within the ring that are optimized for reception.

The ring (which I think of as a "manufacturing belt", being 20 times as massive as the asteroid belt and far denser, but still fairly diffuse, and populated with a large number of self replicating robots) could be a decent place to live. Habitats with people in them can be set up to be shielded from radiation with several kilometers of rock, with smaller structures on the inside for gravity. However, really the only reason we'd want people out here is in case some tasks require active telepresence, so we can get to sub-second response times. If too many tasks need human oversight for too long, the project eventually hits a bottleneck until we can either reproduce our way out of the problem or automate them better.

Finally, at some point the manufacturing belt starts churning out a large number of lightweight graphene-reinforced panels that can float over the polar areas. At this point, we can cover the whole sun fairly quickly.

Creating a Shell

Now that we have a whole sun's worth of energy to play with, plus an obscene number of high throughput manufacturing systems capable of self replication, it's a matter of getting enough of the right materials into a shell.

Jupiter has plenty of matter, but as noted it's largely hydrogen. We might have to move Jupiter (or it's atmosphere) out of the way to avoid gravitational stresses on the sphere. Whether we can transmute the materials of that atmosphere to solids within a reasonable time is open for question. One thought is that, if we can get enough carbon together, we might be able to encapsulate "bricks" of highly pressurized metallic and/or liquid hydrogen within smaller shells of diamond or graphene, which can work as building blocks. It should also be possible to contain large stocks of pressurized H2 inside a series of smaller rocky bodies held together in spherical shapes mostly by their own gravity (gravity balloons).

In any case, if stick with the inner planets, we can build a shell a few centimeters thick (42 g/m^2). This shell could be held in place using ion jets, kinetic slugs, and so on, temporarily, but is nowhere near thick enough to hold against its own weight as a shell if we assume it's made of standard materials. Luckily, holding against its own weight isn't actually going to be necessary. We can instead create a system of strain relief mechanisms that use various forms of energy to hold it in shape.

Strain Relief Mechanisms

One simple mechanism to consider is kinetic. A series of "tracks" could be mounted throughout the sphere, upon which high velocity chunks of matter (steel, for example) are moved around very rapidly. Niven's Ringworld actually spins fast enough to invert the equation and produce a gee outward, however we really only need a small fraction of that. A set of giant rings that exert outward pressure by spinning at over the natural orbital velocity could be imagined. However, it should be equally possible to use much smaller structures instead.

The total lateral force needed to make sure the structure doesn't collapse is not that much per square meter, the issue is that it needs to be enough to counteract the pressure of gravity upon each local area (which is slight). One possible way to do this would be to set up a series of circular loops, 1km or so in circumference, and induce momentum enough to produce a few gees on the weights contained inside (which could themselves be circular). They would impart constant pressure to the track, via magnetic levitation.

Another mechanism to consider is optical/electromagnetic. As with the solar collectors, 0.78 g/m gives the relationship between normal solar intensity and the sun's gravitational influence. Going to an average 42 kilograms is 5000 times as much. But as long as the light pressure is being used for pressure alone and not to alter velocity, it's not used up, so multiple reflections may be used.

We don't necessarily want to try to reflect too much light from the habitable area directly, but we could imagine a set of platforms comprising 0.1% of the inner surface area that reflect the sunlight 5 million times or so before exhausting it. At 1 AU, that's 5 gigawatts. A bit much, but maybe worth considering with a very efficient reflector.

A better way to do it might be to cover the whole surface with strain relief structures that reflect light laterally, instead of shooting it across the sphere. For example, every kilometer or so, there could be a series of lightweight fins sticking out the outside, designed to reflect light back and forth and transmit the pressure to the structure. Light could be slowly fed in from a laser, and allowed to escape after many reflections. The fins could be much larger than the area they protect, for example 10 km long for 1 km of separation. That reduces the radiation density they handle to 10% or 500 times that of the sun for our 42 kg model. The mass of such fins could be much lower than that of the shell, since they would be very thin.

There's another radiation mechanism to consider similar to the above, but it dovetails with a cooling mechanism, so see below.

A final strain relief source to consider would be magnets. This can be either diamagnetic materials sandwiched between permanent magnets, or permanent magnets oriented so as to repel from each other. This has the virtue of simplicity, and I can't really think of a down side.

Cooling Mechanisms

If we decide build at 1.0 AU, it's going to be too hot if we can't rapidly cool the outside of the shell. The physics imply that there's no way to cool faster in a vacuum, other than to increase the effective surface area. One way to do this without increasing the sphere size is to string out a long tether made of carbon nanofiber, or something else that has high thermal conductivity per unit mass, every so many kilometers. What ends up happening is that each tether radiates heat in infrared form along the way, then reabsorbs the same heat again from neighboring tethers. This puts considerable light pressure upon the tethers, causing them to "fall" in the opposite direction of the sun's gravity, sort of like a balloon.

So you can string lightweight tethers out quite some ways -- multiple AU, perhaps. There isn't really much of a limit, since the light pressure from the infrared is greater than the solar gravity, and the tether's own gravity isn't very substantial. If the pressure gets stronger than the tensile strength of the tethers, the tether can be made thicker or mass can be distributed along it.

Another way to deal with the thermal energy is to transfer it to matter, move the matter out to a distant point, then move it back again. Hydrogen has a good specific heat density, so we could imagine a system of balloons filled with hydrogen which venture to the outer solar system to radiate, then return after reaching cryogenic temperatures, and reinflate/rewarm upon contact.

Effects of Size

The OP suggests that 1.7 AU would not receive enough light for agriculture. I doubt that will be an issue. First, plant life could be adapted to need a little less light. Many plant species would survive fine (if growing more slowly) under 1/2 to 1/4 the light. Second, we could set up a gossamer bubble that reflects light half the time and transmits the other half, so as to produce a day/night cycle with twice as much light in the day. Third, we can use fluorescence to convert more of the radiation to visible spectrum. Finally, note that a large amount of visible spectrum light would naturally be reflected by the part of the sphere on the other side of the sun. So all things considered, a much larger sphere should be more reasonable than a 1.0 AU.

The Problem of Gravity

This is the biggest issue with the whole idea. Solving it with a centrifuge is inelegant, as you don't get to use the inside of the sphere as a landmass that way. Moving to a white dwarf has the issue of not being the problem we are trying to solve. Moreover, gravity as we know it just doesn't work for the inside of a sphere. So we need more of a "clarketech" solution to make sure people fall to the floor and sustain a breathable atmosphere.

Fortunately, an idea that works for this purpose has been thought of that breaks no known laws of physics: Utility fog.

Utility fog is a system of microscale robots, which connect to each other using an octet truss configuration, with extensible arms and graspers, all too small to see. With careful programming, you can use them to simulate liquid, gas, solid, and weirder things still, i.e. gas that you can fly through, liquid that you can breathe. What we are interested in is something like the buoyancy effect of water, but made to run in reverse, so instead of floating, it pushes you "down".

Now, that effect alone might not be enough to fool your body. But the inside of your bones and even the matrix between your cells can be threaded with appropriately programmed foglets or comparable micro/nano systems. Thus, the effects could be very close to natural gravity as far as biology can tell, including the prevention of weakening of muscles and bones and the maintenance of normal appetite. As an added bonus, such foglets could be programmed to turn gravity "off" whenever you decide to do so.

Utility fog is a good setting for stories about "magic", since it's pretty flexible. But if you use it this way, remember that it has limitations: For example, you can disintegrate it with heat, and it has finite strength. (Aluminum oxide is preferred over carbon, since we don't want it to be flammable. However, it still obeys the physics that say very small things can be heated up very quickly.)

Another idea for pseudo-gravitation would be to imbue all life with magnetic particles (hematite, say, or maybe some rare earth nanocrystal that works better) and use a magnetized sphere. Since we're considering magnetic strain relief mechanisms anyway, it could make sense. Maybe both systems could be used by different factions on the same sphere -- the magnet people could be those who evolved in an area where the utility foglets broke down, or something like that.

The kinetic strain relief mechanism above might be adapted to become a series of ring-style habitats (actually, you could do away with the shell and make it a set of conjoined rings, each containing a magnetically coupled, spinning habitat that balances out the gravitational pressure). This would give you far less surface area to play with, but some authors might find it more plausible or interesting than programmable nanobots.

Scientific Advancement Rate

The kind of advanced nanotech (nanorobotics) needed to produce utility foglets is, well, not here yet. Perhaps we need hundreds of years to break through using the current set of laboratories and scientific instruments.

However, if we had trillions of physics laboratories working in parallel, trillions of computers crunching the necessary math, and so on, it becomes harder to rule out rapid breakthroughs. We could also run new kinds of experiment with tougher materials, higher pressure conditions, exotic matter, and so on. So the assumption that we wouldn't make various advancements within years of the first DS is grossly conservative.

Nonetheless, mostly, we just need to intelligently apply what we already know. For the issues mentioned here, as far as I can see, you don't need new science to work around them.

Conclusion

There's a lot of story potential in the Solar Dyson Shell Habitat idea, and it at least can fall under the auspices of hard sci-fi, though smaller habitats have more actual likelihood of happening. The prerequisites are thinkable, and not as far in the future as is generally assumed -- it is primarily a matter of having a self-replicating industrial infrastructure, properly organized, which makes use of space based resources. But it also takes some creativity and understanding of the obstacles.

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  • $\begingroup$ Very healthy view on the task, few places where you missed the scale of the thing and energy flow(heat moving with hydrogen), but overall very good. $\endgroup$ – MolbOrg Feb 11 '17 at 1:27
  • $\begingroup$ could you not spin a dyson sphere for gravity and only inhabit the equator? Use the rest for collectors and factories. $\endgroup$ – John Jun 19 at 20:27
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There are two assumptions that you make which doom the habitability of the Dyson sphere. They aren't inherently wrong, but I don't think they make much sense if such a thing were to actually be built.

Your assumptions are:

  1. All energy captured will be used inside the sphere.
  2. The external surface of the sphere will be perfectly smooth.

Energy Use

One of the main reasons to build a Dyson sphere for collecting the entire output of a star is because you've got a lot of things to do with the energy. If, for instance, we were generating antimatter to fuel our interstellar starships then that is a whole lot of energy which we're collecting and using outside the sphere. If we keep up our current efficiency for making antimatter we're going to need to grab a whole lot of energy to make usable amounts. For regular trips to other stars, a Dyson sphere will be an excellent source of extra energy.

The Surface

Extra surface area with the same radius is simple to achieve. Just look at golf balls. The dimples on golf balls add about 35% to the surface area of the sphere. That's a simple macro structure to add, if on top of that you add microscopic features you can easily increase the surface area required to radiate all additional energy from the Dyson sphere. Evidence for increased emissive cooling by macro features is here and increased micro features here for non-ideal black bodies.


Increasing surface area via texture for an ideal black body sphere will likely not increase its radiating power. The Stefan–Boltzmann law applies, but will not change the amount of power radiated away (further detail available here). The solution then is a more active release of energy, rather than the completely passive one described.

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    $\begingroup$ I'm pretty sure the surface area argument doesn't work. As the surface becomes convoluted, some parts begin to illuminate other parts, and I'm pretty sure the end effect is to reduce the effective surface to that of a smooth sphere. This doesn't apply to convection, of course, but convection is not a mechanism which applies in this case. $\endgroup$ – WhatRoughBeast May 22 '15 at 9:37
  • $\begingroup$ @WhatRoughBeast It does, actually. You can easily visualize this on a golf ball surface with dimples slightly less half a sphere, vectors normal to the surface won't collide with with the surface. But, if intuition fails, I've added two links demonstrating increased emissive cooling from both macro features and micro features. $\endgroup$ – Samuel May 22 '15 at 14:52
  • $\begingroup$ @WhatRoughBeast Besides, either one of the things I listed is enough to fix the issue you're seeing with Dyson spheres on their own. You could even vent antimatter or fire powerful lasers into space, if you needed to. I just gave options which will fix the problem indirectly or passively. $\endgroup$ – Samuel May 22 '15 at 15:01
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    $\begingroup$ Sorry, but no go. The first deals with the wall behind a radiator. Increasing roughness increases both wall temperature (by increasing emissivity/absorption) and convective coupling, but neither is a radiative coupling to the environment, since the wall is then cooled by convection. The second deals with chip cooling, and while increasing emissivity does improve radiation losses, in no case is it asserted that the emissivity will increase to greater than unity. Since a black body (as used in the OP) has emissivity of 1, changes in texture cannot provide an increase in emissivity. $\endgroup$ – WhatRoughBeast May 22 '15 at 17:31
  • $\begingroup$ @WhatRoughBeast Ok, if you've already assumed an ideal black body then fine, it may not improve. Though I'm not completely convinced that the additional surface area in the way I describe won't work at all. You're conveniently ignoring my other point, that there are many other ways to dispose of energy outside of the sphere. $\endgroup$ – Samuel May 22 '15 at 17:59
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The arguments against using a Dyson Sphere design are many:

  • Zero gravity. Unless you have a gravity field generator, you're going to have serious problems using the sphere for anything productive except the collection of the star's emitted energy. You can't alleviate this by spinning the sphere. That might make certain sections livable, but others would become much much worse.

  • Because of the Zero gravity, you have no atmosphere, no soil, no water, etc, etc. We can assume that, because they've built a Dyson sphere, they've alleviated a lot of these problems, but it's just doesn't seem very efficient to have to rely on artificially creating everything you need.

  • Mass requirements. We can assume the mass requirements for a Dyson Sphere are high. Depending on the required parameters (very high tensile strength if you're attempting to spin it to almost nothing if you're not.) You'd need to devour each and every object from the inner planets to the Oort cloud to make sure nothing punches a hole in your new toy. And even then, I'm not sure that'd be enough mass to create it; even if you had a near 100% efficient conversion rate.

But what about this? Let's suppose, for a moment, we don't really want a Dyson Sphere - we just want to collect as much energy as possible. We could keep a strip of the Dyson Sphere open at the 1 AU mark and on the ecliptic plane. In that strip, we could build and orbit small spinning HALO rings. These rings are redundant - we'd fill the orbit with them - maybe put them in each others Trojan orbits, so they're not prone to wander. Next, we fill the 1AU orbit above and below the ecliptic with a gossamer thin material that collected nearly 100% of the star's radiation and beam it at collector stations inside. These... Dyson Hemispheres aren't being lived on, so there's no need to worry about making gravity or whatever and at the same time, we're capturing a very large part of the stars output as energy.

Our population? They're on the spinning rings. Plenty of room and we can make more as we gain more mass.

If anything comes into our solar system, we can fry them with the exo-joule lasers we can power with our Dyson Hemispheres. Put one laser on each 'pole' of the Hemispheres and you have more than enough coverage to safely protect your star system for the foreseeable future.

Just my 2 copper mate.

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This answer provides an alternative to the one you propose.

As an alternative to a Dyson Sphere around a Main Sequence Star, Turkish scientists argue that it makes more sense to build a Dyson Sphere around a White Dwarf Star.

Statistics
The Sphere:

  • diameter - about $ 1 \times 10^6 km $
  • surface gravity - about $ 1 g $
  • mass of sphere $ 10 m $ thick ~ $ 6 \times 10^{24} kg $ (roughly Earth massed)
  • stellar luminosity at this distance is roughly terrestrial normal
  • temperature - the sphere size is tailored to the White Dwarf to yield the correct gravity and temperature - so habitable
  • living area ~ Earth's area $ \times 10^{5} $

enter image description here

Safety
A sphere around a white dwarf is much safer than around a Main Sequence star since you don't need to worry about the upcoming giant stage engulfing your construct.

Instability
The sphere still suffers from dynamic gravitational instability. I assume a civilization capable of building such a thing is capable of both figuring this out and fixing the issue.

Engine
If you leave a hole in the sphere, you now have an engine to push your construct around too (using radiation & solar wind). You'll need some sort of restorative force (electromagnetic? gravity?) keeping star and sphere co-centered. The acceleration of this engine would be absolutely miniscule.

Living Area
Everyone would live on the outside of the sphere under open skies. The atmosphere would remain gravitationally bound to the sphere on its own with no extraordinary measures. If you cut the hole for propulsion in, you'd need to rim it with 1000 mile high mountains (or equivalent) to keep the atmosphere from falling into the hole.

Lighting
Light the place by including transparent slices in the sphere and mounting mirrors high above the slices to reflect the light back onto the surface.

Power
Power can be generated by many methods. The most direct of these would be to line the inside of the sphere with high efficiency PV cells.

Alternatively, harness the temperature gradient across the sphere's shell (inner surface to external heat exchangers) to drive indirect (e.g. turbine) or direct power generation.

You will probably require heat exchangers to get maximum power efficiency out of your equipment. However, you might be able to utilize passive devices such as heat pipes.

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  • $\begingroup$ Must be my browser acting up. I'll shut it down and retry. Thanks for fixing that for me :) $\endgroup$ – Jim2B May 22 '15 at 4:18
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To add a third point to what @Samuel said:

Why are we living on the surface?

Why would you be living on the inner surface of the sphere anyway ? After all the inner surface is where you are collecting the energy - living quarters would get in the way of that. Living quarters would make much more sense if they were in the ring.

How many people are you accommodating anyway?

The surface area of the earth is 510.1 million km^2 and presently supports 7 billion humans plus every other living thing that currently exists (that we know of). The inner surface of your sphere is 5.3x10^8 times bigger than this. This of course largely makes my first point irrelevant, even if you set aside an area 10 times the size of earth in the habitable ring part of the sphere as a "Spherical Park" (National Park being inappropriate in the context) this would make bugger all difference to the energy collection capacity of the sphere.

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  • $\begingroup$ Well, there's the gravity thing. Remember that a hollow sphere exerts no gravitational force on things inside it, so the only gravity is from the sun. Which isn't much, and means sunlight is coming from under your feet. Of course you could rotate it to get artificial gravity near the equator, but that'd give you something like a Ringworld... $\endgroup$ – jamesqf May 22 '15 at 5:51
  • $\begingroup$ Gravity is not a problem - what you say is only true if the sphere is uniform. Put more mass under the Spherical Park. $\endgroup$ – Dale M May 22 '15 at 6:02
  • $\begingroup$ I don't think living quarters need to get in the way of collection. After all, a significant portion of solar collection done today is on top of living quarters. To approach Earth gravity by adding mass would require a staggering amount of material. That, combined with not having direct sunlight, seem like good reasons not to live on the outside surface. $\endgroup$ – Samuel May 22 '15 at 7:00
  • $\begingroup$ @Samuel - see point 2 of edit. $\endgroup$ – WhatRoughBeast May 22 '15 at 17:34
  • $\begingroup$ @Samuel actually it would only require about 1 earth mass, when building a ring that uses all the matter in the solar system this amounts to a note on the blueprint. And the plan was to live on the inside of the sphere. $\endgroup$ – Dale M May 22 '15 at 21:05
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I am not a big fan of the spheres and I have no solution for the gravity issue, but I'll make a fake answer to make some points about the energy issues that are really bit too long to be comments.

Outer shell temperature

Can be anything you want within upper and lower bounds set by engineering and the total energy of the star. There are lots more variables than trivial models assume since the structure of the sphere is realistically more complex. There is no one-to-one connection to the temperature of the inner shell. You can use insulation to make the outer shell cooler than the inner shell. You can use heat pumps powered by photoelectrics to make it hotter. Or more robustly simply connect it to hot areas of the inner shell.

Inner shell is not isothermal

Yes, I said hot areas, there is no reason why areas of the inner shell must all have the same temperature. You can give different areas different albedo. Or simply link different areas on the inner surface to areas of variable size on the outer surface. If areas A and B on the inner surface have the same area but the outer shell radiator A is connected to has ten times the area of the radiator B is connected to, A will be cooler. The sphere is not, cannot be, made from homogeneous mass, it has structure.

Radius is not that big a deal

Since the temperatures of inner and outer shell are not directly linked, you can use insulation to make the sphere habitable at a distance higher than usual or cooling to make it habitable closer. So you do not need to worry about what the insolation or habitability of a planet at that radius would be. For example if the sphere is larger, you can replace parts of the inner surface with mirrors reflecting light to the inhabited parts. If smaller you might give the inhabited parts higher albedo, so that radiation is reflected to the uninhabited parts.

Dyson sphere is NOT a habitat

There is no known way to get a comfortable gravity to the inner (or outer) surface. Nor should there be. a Dyson sphere is not a habitat, it is an energy collector. You should build your spin gravity habitats separately and just use the power collected by the sphere to power them. Or just use planets. Technology needed for a Dyson sphere should allow building planets. And the mass needed would allow building lots of them. Just because having six planets on the same orbit is not stable, doesn't mean you can't make it so. It would be easier than building a Dyson sphere. And making the planets habitable would be much easier.

Like I said in the beginning this was not really an attempt to give an answer. Just some comments too long to fit into actual comments. You should not expect any of what I said to be true or accurate. Just some food for thought.

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    $\begingroup$ "Outer shell temperature Can be anything you want that the energy of the star can support." Sorry, no. There is a lower limit due to energy conservation / black body considerations. It's true that you can increase temperature by decreasing emissivity. $\endgroup$ – WhatRoughBeast May 26 '15 at 2:20
  • $\begingroup$ @WhatRoughBeast Yes, but that lower limit depends on the radius and few other variables you can control. For example you can simply have holes in the shell. There isn't actually any rule that says you must cover the star fully if you don't need all of its energy. Or that all areas of the outer shell must have the same temperature. But still there is probably an absolute practical lower limit in any case, it is just more complex than is usually assumed since the structure of a sphere is more complex than trivial models assume. I'll edit in a mention that such limit exists, thanks. $\endgroup$ – Ville Niemi May 26 '15 at 8:49

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