# Geology of a supermassive Dyson sphere

There was a question on here a while ago about lighting a massive Dyson sphere, that has gotten me to thinking.

Obviously, such an item needs some unobtainium to build, but ignore that. I'm figuring an inner shell of something like 1 AU across, that is totally empty, on top of this is a layer of rocky-planet type material sufficient to produce 1 g at the surface.

While such a world lacks a "core" and will not possess a magnetic field, the escape velocity is high enough that it should retain an atmosphere anyway (the problem will actually be the opposite of normal - its going to trap some of the wind of its illuminating suns, the hydrogen will react with local oxygen and you'll slowly convert atmospheric oxygen to water). It will have the radioactive materials to produce a heated layer outside the shell, though.

What I'm wondering about is plate tectonics. Do we have a geologically alive world that over time refreshes its surface, or will it simply erode down to flatland? And if the latter, is there any fix?

• I don't follow... the solar wind will be on the hollow inside. Or you mean there are additional non-enveloped suns illuminating the surface, too? May 9, 2016 at 7:39
• I believe the rimworld countered the erosion effects buy actively pumping silt from the river deltas to the tops of the (artificial) mountains and allowing it's weight to convert it to a type of sandstone. May 9, 2016 at 8:03
• @JDługosz No star inside, only outside. It's got plenty of mass to hold them. May 9, 2016 at 19:23
• But... that's the defining characteristic if a Dyson Sphere! You get all the solar power from the star. How about adding a diagram of the system you have in mind? May 9, 2016 at 22:58
• Btw, I wrote about a hollow shell with superdense plates to give normal surface gravity, on this site before. E.g. here May 9, 2016 at 23:03

Some classical physics. Using the equation f = Gm/r^2 for

radius r = 1 AU (1.5×10^11 m) and

f = 9.8 m/s2 -> earth's gravity

G = 6.67 × 10-11 m3 / kg s2

You get the mass of the system as m = 3.3 x 10^33 kg.

After some tinkering, the volume of a 10^7 m thick spherical shell of radius 1 AU is:

4/3 * pi * (r(outer)^3 - r(inner)^3)

Suppose r(outer) is (1.5 x 10^11 + 10^7) m and r(inner) is 1.5 x 10^11 m

Volume = around 6.8 x 10^29 m3

Earth's average density is 5500 kg/m3. Taking this as the average density for the sphere, you'd end up with a mass close to the required mass (3.7 x 10^33 kg). I'm not counting the shell weight itself but it will factor for something especially if it is strong enough to take all the problems coming at it, stay hollow and unliquefied with a molten mantle over it.

Theoretical rock shell without unobtanium shell factoring in: 10^7 meters = around 10000 km deep crust which is a pretty deep crust compared to earth's 5-70km and actually bigger than the earth's radius (6,371 km). With the shell: Depending on the unobtanium density.

If the shell allows a depth of atleast 3000km (depth to the earth's core): The Dyson sphere may just have plate tectonics of a new kind. If the radioactive material is hot enough to liquefy the underlying rock and the unobtanium is strong enough to withstand this. So we'd then have a crust floating on a basically slippery sphere. Given that only about half the earth's heat is from radioactive decay and the other half from primordial heat during formation, it may well be that who ever made the dyson sphere system just set it up with the right heat balance and didn't have to do any more.

The thing that will differ is the convection cells set up inside Earth's mantle can basically affect the crust and other convection cells planet-wide. For the Dyson's sphere, these cells would be local, changing the crust only close to that cell. Unless there are heating variations that set up mantle currents that can span larger areas of the sphere's surface, you might not find the continents moving as much as they do here. It may well lack the sheer dynamism of a complete-interior planet-wide tectonic system.

You could have igneous processes such as subduction (deep ocean trenches), uplifting (fold mountains), volcanism (islands and island chains) creating land features. You may have metamorphic processes depending on if the depth you choose for the rock shell is enough to generate the heat-pressure needed to compress rock into granite, diamond, etc. You'd still have sedimentary processes acting on the surface depending on whether you have water and how much of the water cycle happens here and/or wind (solar or atmospheric). Given that the sphere is so large, you may even have the effects of nearby planetary disturbances. So yes, theoretically you could have the crust renewing itself though someone would have to set up the system initially.

Given that there is no magnetic field to protect the atmosphere from getting stripped away, it is doubtful if oxygen will ever get generated in quantities enough to withstand getting blown away by super-sonic solar wind. Even if we posit the presence of maybe some super-resistant bacteria/algae/macro-plant-like organism that evolved/got put there.

Take Venus for example (I said Mars earlier but Mars has a lower gravity so it won't serve as an example). Venus doesn't have a magnetic field and does suffer atmospheric loss due to solar wind despite the presence of oxygen ions at that height: https://en.wikipedia.org/wiki/Atmosphere_of_Venus and http://www.scientificamerican.com/article/solar-wind-transforms-venus-into-shape-of-comet/. What happens is the water molecule simply gets carried off into space. There has to be a constant oxygen generating something. Given that some process will have to physically convert something to oxygen and then have it lost out of the system, how long will this oxygen supply source last?

Plus the Dyson sphere will still have an induced magnetosphere if there is an atmosphere, just like Venus, no helping physics. But even this is not a guarantee to mop up cosmic radiation. Any reaching the surface is still harmful to life. Some horror stories: http://futurism.com/6-horrible-consequences-earth-losing-magnetic-field/

Umm, also the reaction 2 H2 + 02 => 2 H20 doesn't just generate water, it generates massive amounts of heat. Where does all that heat go?

I'd just say, the planet itself is okay, the atmosphere may need help.

• I must have really blown the math on the shell thickness, I thought it was upwards of a thousand miles. If it's as thin as you say my whole idea doesn't work. May 9, 2016 at 14:18
• You've got some math problems here! Using two different calculators I find online and a 1 AU radius I'm getting a surface area in the 10^24 m^2 range, a difference of around 10^10 fold. May 9, 2016 at 23:47
• Hi Loren, you're right, my math was wrong and I almost took your dream from you (really sorry for that). I changed the answer. Hope you like it - it's just as you want it! May 10, 2016 at 3:11
• More investigation into the math shows that if the support has zero mass (I was figuring they did something to the fabric of spacetime as opposed to a material object) the thickness of the layer should be the same as the thickness of the Earth (surface to center, not clear through.) I would also expect more primordial heat--the easiest way to build it would be to simply toss whatever mass was available at it--and it hits at half a percent of lightspeed by the end of the process. Heat galore! May 10, 2016 at 3:41
• Given it's high escape velocity the atmosphere isn't going to be lost. The H + O reaction won't produce enough heat to heat the planet appreciably. What is the relevance of the magnetic field and radiation at the surface, though? Magnetic fields don't stop UV, the atmosphere stops stray particles. With no magnetic deflection you'll have a tremendous aurora but that's not dangerous. May 10, 2016 at 3:44

The landforms will not be generated and maintained by tectonics. Rather, it will be more like the way a park or zoo is maintained: send a work crew and materials to put feature X at location Y. Mountain habitat a bit warn down with the original watershed all messed up? Tear it out and put the new arctic lagoon there instead.

The idea of a superdense shell is exactly what I describe here except for the overall shape.

There are access hatches and maintainance corridors beneith that some residents may find... In the rock below the topsoil but above the [hyperdense material] would be machines. It "gardens" from time to time to undo erosion and just to randomly rework the habitat. Stores of normal matter and a moon's worth of minerals are stored in the hollow, so it can throw up mountains and add bedrock.

Note that the hollow interrior can be used to store raw bulk material, for sculpting mountains or whatnot. Think of it like the cabinet under the terrarium, storing decorations, bags of gravel, etc. for use when you feel like changing around the habitat.

Depends on how this world is built.

Nothing can stop you from adding thick surface layer 3000-10000km with heater beneath it.
The 6000km thick layer will have 2g on the surface. 3000km thick layer and it will be 1g on surface (counted for 3500kg/m3 density) 1000 will be enough to have magma flows if you have a heater. Heat surface of your sphere not evenly, to get desired flows and surface look.

Probably you may also(or instead) utilize same construction to make gravitational gradients just by bending surface, not necessary sphere itself, place some bags between the upper layer and sphere - pump water or something. Bags are also not necessary, just pump some stuff between sphere and layer - will be enough. Heat, in that case, is also not necessary, it will be slippery enough, and make gradients of force.

If heat is main management power here, then the upper crust will be like here on earth if magma temperature is same, but you may adjust that actually, by turning the heater up and down - so you may have more or less volcanic activity, thickness etc.

There is no reason to think that something is absent in that structure, this or another way everything can be done, and this is the Point, it will be as it desired by the Constructor of it.