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Suppose you were a society with the means to construct a Dyson's sphere (shell), roughly how many earth-sized planets would you need to mine in order to obtain enough minerals to build such a megastructure?

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  • $\begingroup$ Does this assume that the minerals required to build the mining installations and tools are freebies? Also, does the material constituents of the worlds being mined actually matter? Could the planet be entirely iron ore, for instance? Also: What class is the star contained in the sphere? That will make a difference with regards to the size of the sphere... $\endgroup$ – Ayelis May 21 '15 at 22:25
  • $\begingroup$ Which would be the radius of the sphere? 1 AU? That said, the question is "tricky" because, as we currently do not have any material up to the task, we would be "inventing" it (and its characteristics), given too many options (would it be plancks 1 meter thick of "supertitanium", or carbon nano-threads of 1 cm thick, or a 1 mm sheet of unobtanium? And how much supertitanium or unobtanium can we mine from a standard earth-sized planet?) $\endgroup$ – SJuan76 May 21 '15 at 22:36
  • $\begingroup$ Use only materials and dimensions that we're familiar with, so Sun-sized star, and mostly iron and magnesium, so the shell would probably have to be pretty thick, or re-enforced using some kind of special structural design. I'm also considering making the sphere modular, as in constructed out of millions or barge, or arc-like segments that can detach from each other if a star becomes unstable and make an exodus to a new star. $\endgroup$ – ShemSeger May 22 '15 at 16:31
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About 31.

However, it all depends on the thickness of the shell. This is typically given as mass per cubic meter though, because the material density is difficult to know.

We'd probably need more than what we have in our solar system for a one AU Dyson shell. From the wiki article:

Anders Sandberg estimates that there is $1.82×10^{26}$ kg of easily usable building material in the Solar System, enough for a 1-AU shell with a mass of $600 kg/m^2$—about 8–20 cm thick on average, depending on the density of the material. This includes the hard-to-access cores of the gas giants; the inner planets alone provide only $11.79×10^{24}$ kg, enough for a 1-AU shell with a mass of just $42 kg/m^2$.

For the former estimate of a $600kg/m^2$ wall density, with $1.82×10^{26}$ of required mass, we'd need 31 Earth sized planets (by mass). It's actually closer to 30.48, but I'm assuming we are working with an integer number of planets.

To make that actually work though we should assume we have perfect control of fission and fusion to create whatever elements we need to build our sphere. This is called nuclear transmutation, a call back to alchemy. Then all we require is mass, without needing to worry about which elements will work in construction or not.

Why build at one AU? If we build it in our solar system then we're either going to use the Earth in the process or kill the Earth by blocking the Sun. By building it at one AU and setting it spinning, an inside ring (on the plane of rotation) will be habitable and maintain Earth-like gravity. The gravity would reduce to zero moving away from the ring, this would provide a lot of area for advanced manufacturing plants requiring low gravity as well as recreational areas (though the atmosphere would reduce in kind).

If no one is going to live there and you just want to block out the star then significantly less mass would be required. A tightly packed dyson-bubble would approximate a shell and could be constructed using just the mass from a small moon. However, keeping such a fragile structure in place would likely require removing a majority of the rest of the mass in the solar system to keep it from disturbing the shell.

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    $\begingroup$ Why build it at 1 AU? At .1 AU you could build a 4200kg/m^2 shell out of just the inner planets, or part of the core of one of the gas giants. $\endgroup$ – ckersch May 21 '15 at 23:00
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    $\begingroup$ @ckersch If no one is going to live on the inside that could work. The one AU is obviously so the inside would be habitable. $\endgroup$ – Samuel May 21 '15 at 23:06
  • $\begingroup$ Using rotation instead of gravity wouldn't work without unobtainium, and who says someone would live there? $\endgroup$ – Mithoron May 21 '15 at 23:16
  • $\begingroup$ @Mithoron There are no stipulations saying unobtanium, or Scrith, would not be available. I addressed why people would live there in the answer. $\endgroup$ – Samuel May 21 '15 at 23:23
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It depends upon the size of Dyson Sphere you are making.

My other answer about Dyson Spheres indicates that spheres with a 10 M shell thickness around white dwarf stars only require materials massing about 1 Earth sized planet's mass.

Such Dyson Spheres have the added benefit of putting the materials under much lower stresses.

enter image description here

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  • $\begingroup$ According to the paper you seem to be citing, the construction materials would actually be under impossibly high stresses. I'm trying to figure out if this can be rectified by making the sphere larger, but my physics-fu isn't what it used to be. $\endgroup$ – Blazemonger Mar 26 '16 at 23:31
  • $\begingroup$ It's been a while since I did a calculation of the stresses involved. But most of the time that I see articles like this, they ignore the required strength of materials. They do the analysis as a mind game and not intending it to represent a real-world structure. I'll have to play with the numbers later and see if they look right. The engineering is pretty simple. Just treat it like a pressure vessel. $\endgroup$ – Jim2B Mar 27 '16 at 20:00
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Dyson actually was talking about a shell of independently orbiting solar collectors and habitats, which is dynamically stable and much easier to build. The solar collectors can be quite thin, and habitats can be as large or small as you want (a habitat with a zero g interior can be essentially a small bubble).

Another possibility is to use "Statites" to suspend your habitats from large solar sails at a set distance from the Sun. This would be a gossamer construct which would be far lighter than either a solid shell or a swarm of orbiting objects, and could possibly be built using just an asteroid:

http://en.wikipedia.org/wiki/Dyson_sphere#Dyson_bubble

"The practicality of this approach is questionable with modern material science, but cannot yet be ruled out. A statite deployed around the Sun would have to have an overall density of 0.78 grams per square meter of sail.[9] To illustrate the low mass of the required materials, consider that the total mass of a bubble of such material 1 AU in radius would be about 2.17×1020 kg, which is about the same mass as the asteroid Pallas.[10] Another illustration: Regular printing paper has a density of around 80 g/m2."

I like the Dyson bubble using just an asteroid myself.

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