Dyson Sphere stability

[Jay-qu]

I have been doing some research into Dyson Spheres for an essay and have found heaps of info and even done some of my own calculations. I have surmised that to actually construct a type II (solid) sphere it would take a LOT of material, eg. For a sphere at radius 1Au and just 1cm thick would need the volume of the Earth to create it. This quickly gets beyond all the solid matter in the solar system for what I think would be needed for a stable sphere.

 

This is where I am a little hazy, what would make it stable (if it is at all possible)? 1m thick? or would it be better off staying really thin, but made of some funky strong material..

 

Discuss :doh:

[CraigD]

This is where I am a little hazy, what would make it stable (if it is at all possible)? 1m thick? or would it be better off staying really thin, but made of some funky strong material..

Unless it’s made of some exotic, negative-gravity matter (which there’s little reason to believe exists), a solid, star-enclosing sphere (or spheroid) can’t be made stable – it will at very least require some sort of active position sensing and maintaining system.

 

Analyzing the structural stresses on a solid Dyson sphere seems to me a complicated proposition, as such a large structure might flex and vibrate in complicated ways. However a rough calculation is possible.

 

Light (about 99%) and the solar wind (about 1%) produces an outward force depending roughly on the surface area, but varying considerable day-to-day and in many-year cycles. Gravity produces an inward force depending on the mass, and is nearly constant. It’s in principle possible to balance these forces by solving the equation

u*d*A*W / r^2 = p *A

where u is the standard gravitational parameter for the Sun (about 1.3*10^11 km^3/s^2)

d is the density of the sphere material (5500 kg/m^3 for average Earth-stuff)

A is an arbitrary surface area on the sphere (cancels)

W is the thickness of the sphere

r is the distance from the sun to the sphere (1 AU = about 1.5*10^11 m)

p is the radiation pressure (at 1 AU, about 4.6*10^-6 kg*m/s^2/m^2)

which gives

W = 145 m

Giving a volume of about 4*pi*r^2 *W = 4*10^26 m^3

A mass of about 2*10^30 kg

That’s about 1000 Jupiters, more mass than the solar system has.

 

So, using available material, you’d have to make the sphere either thin, and structurally able to hold itself together, or reduce the radius (since radiation pressure and gravity both vary as 1/r^2, the 145 m thickness remains constant). If you reduced the radius to about 0.05 AUs (about 7.5*10^9 m, or about 10 radius of the Sun), you could build the sphere with just 1 Earth (or Venus) worth of material.

 

PS: As always, be wary of my calculations, as I may have misplaced a decimal somewhere, and be off some factors of 10!

 

Also note I’ve ignored reflectivity, which has a considerable effect on light pressure.

[ronthepon]

Actually, If we do get to make something of that magnitude, we shall have to think beyond the puny constraints of limited material. After all, we have overcome the problem of large distances, proper and almost exact positioning, velocity control, etc.

 

There still remains the question of 'will it hold out against all the stresses?'

 

Some portions of the sphere will have to sustain different forces from the other (eg- one is in shadow of some big thing, thus no radiation pressure)

 

Such apparently small forces will be very signifaicant at the large distances involved.

 

Supposing be make it one centimeter thick, or one meter. Considering the huge surface area, it really won't make differences in basic behaviours of the sphere's reaction to the various stresses.

 

Instead, we could look at the possibilities of a number on concentric shells, with successive shells connected in manners so as to ensure maximum resistance to shearing and stretching forces, whie keeping the mass as less a possible.

This'll also help with the problem of limited available matter.

The cross-connections between the shells could consist of countless wires, having an infitessimally small radii. What makes their effect significant, is the extremely large number they are present in.

[CraigD]

Instead, we could look at the possibilities of a number on concentric shells, with successive shells connected in manners so as to ensure maximum resistance to shearing and stretching forces, whie keeping the mass as less a possible.

This'll also help with the problem of limited available matter.

The cross-connections between the shells could consist of countless wires, having an infitessimally small radii. What makes their effect significant, is the extremely large number they are present in.

Hey! No fair – I though Jay-qu’s starting post required us to limit ourselves to solid spheres!

 

A Dyson swarm such as ron describes is, IMHO, more likely for future advanced engineers to build than a solid sphere, mostly because it can be done incrementally. One can reasonably argue that the orbiting bodies of the solar system, including Earth and the sprinkling of artificial satellites and spacecraft we’ve put up, already are a very sparse Dyson swarm. As new spacecraft are launched, a swarm can “thicken” over centuries, possibly never requiring any sort of physical connection between the individual crafts.

 

A swarm is particularly attractive when one considers that it can be a “smart swarm”, where managing the potentially unmanageably complicated orbital mechanics of the whole can be displaced among the individual parts. For example, a thin, flat spacecraft – essentially a light sail – can move to or maintain position at effectively any useful location in the solar system, by turning edge-toward the sun to fall inward, flat-toward it to be pushed outward, or an angle in between to be pushed tangentially.

[Janus]

I have been doing some research into Dyson Spheres for an essay and have found heaps of info and even done some of my own calculations. I have surmised that to actually construct a type II (solid) sphere it would take a LOT of material, eg. For a sphere at radius 1Au and just 1cm thick would need the volume of the Earth to create it. This quickly gets beyond all the solid matter in the solar system for what I think would be needed for a stable sphere.

 

This is where I am a little hazy, what would make it stable (if it is at all possible)? 1m thick? or would it be better off staying really thin, but made of some funky strong material..

 

Discuss :D

 

A couple of things to consider:

 

Assuming that you are planning to live on the inside surface of this sphere, how do you keep everything, atmosphere included, from drifting away and falling into the Sun.

 

Would you necessarily want to build it with an 1AU radius?

1AU keeps the Earth comfortably warm, but the Sun doesn't shine directly down on all points of the lit side, You essentially have a cross section of sun light 127796483 Km² (the area of a circle with the radius of the Earth.) spread out over a surface of 255592966 or twice the area.

 

Having the Sun beat down directly on every surface of the interior might mean that we will have to increase the radius of the sphere or build air conditioning devices to pump heat from the interior to the exterior, where it will radiate away. Otherwise, we might not be able to maintain a temperate climate.

(If the substance we build the sphere out of is heat conductive enough, we might get away with just mounting radiator fins on the exterior of the sphere)

[Tormod]

(If the substance we build the sphere out of is heat conductive enough, we might get away with just mounting radiator fins on the exterior of the sphere)

 

Brilliant thought. :D

[CraigD]

Non-real estate Dyson spheres / "Ringworld" as a definitive reference book

 

Assuming that you are planning to live on the inside surface of this sphere…

That’s a major – though common – assumption.

 

Another possible use of a Dyson sphere/swarm/whatever is a source of power. Such a structure might be designed only to collect as much of a star’s energy as possible. People might live elsewhere – with a star worth of energy at their disposal, practical environment engineering problems could be much simplified. It’s also not beyond the realm of the possible that biological people won’t figure significantly into the priorities of furure engineers. We may all, or nearly all, be “machine intelligences.”

 

A Dyson swarm used by a machine intelligence/machine intelligence civilization is known as a Matrioshka brain.

… how do you keep everything, atmosphere included, from drifting away and falling into the Sun.

 

Would you necessarily want to build it with an 1AU radius?

1AU keeps the Earth comfortably warm, but the Sun doesn't shine directly down on all points of the lit side, …

Good questions.

 

Larry Niven’s novel “Ringworld” (which is about a ring, not a full sphere, though still a colossal (3 million earths) expanse of real estate) answer them as follows:

• 1AU so that light intensity is about what its original planetary inhabitants were accustom to.
  
• Day and night is created by an inner ring of “shadow squares”
  

Given the speculative, far-future nature of Dyson spheroid engineering, works of science fiction like Ringworld can almost be considered “definitive”.

[Janus]

Larry Niven’s novel “Ringworld” (which is about a ring, not a full sphere, though still a colossal (3 million earths) expanse of real estate) answer them as follows:

• 1AU so that light intensity is about what its original planetary inhabitants were accustom to.
  
• Day and night is created by an inner ring of “shadow squares”
  

Given the speculative, far-future nature of Dyson spheroid engineering, works of science fiction like Ringworld can almost be considered “definitive”.

 

In Ringworld Engineers Niven corrected an omission he made in the first novel, the fact that the ringworld would need attitude jets to hold it into position with respect to its Sun, (For the same reason as why it is impossible for Saturn's Rings to be solid)

 

Also, in Niven's anthology A Hole In Space,(1974), he included the article, Bigger than Worlds, in which he discusses everthing from Heinlein's generation ship from Universe, to Blish's "Okie cities", to Dyson spheres, to "traveling" Ringworlds.

[Jay-qu]

Hey! No fair – I though Jay-qu’s starting post required us to limit ourselves to solid spheres!

 

Yes you are right, I have already considered the non-solid type but wanted to discuss in particular the possibilities of having a stable solid one. Impracticalities should be stated, but what im looking for is impossibilities of a solid DS.

 

A couple of things to consider:

 

Assuming that you are planning to live on the inside surface of this sphere, how do you keep everything, atmosphere included, from drifting away and falling into the Sun.

 

1AU keeps the Earth comfortably warm, but the Sun doesn't shine directly down on all points of the lit side, You essentially have a cross section of sun light 127796483 Km² (the area of a circle with the radius of the Earth.) spread out over a surface of 255592966 or twice the area.

 

Yes this is something to consider, but we have a lot of incoming energy, which can be used to cool and some of the heat through. Living on the inside means we either have to spin it up for gravity (which will only work around the equator) - which gives up further stability problems, or keep ourselves confined to little rooms affixed to the sphere.

 

Great responses guys, cheers :( J

[Jay-qu]

ok I have some calculations that I am just going to put out there, tell me if you think I am in error anywhere.

 

Fnet = L/(4*pi*r^2*c) – (Msun*Ds*x*G)/r^2 N/m2

= 1.02x10^17/r^2 – 1.33x10^20*Ds*x/r^2 N/m2

= (1.02x10^17 – 1.33x10^20*Ds*x)/ r^2 N/m2

 

Where L equals Luminosity of the sun, Msun equals the mass of the sun (1.99x1030Kg), Ds equals the density of the Dyson Sphere, x equals the thickness of the sphere, G equals the gravitation constant (6.67x10-11m3 kg-1 s-2) and as before r equals the radius of the sphere.

hence if you want these forces to balance:

 

0 = (1.02x10^17 – 1.33x10^20*Ds*x)/ r^2

now this step im not sure is entirely correct..

1.02x10^17 = 1.33x10^20*Ds*x

Ds*x = 7.65x10^-4

 

hence using aerogel at a density of 1.1mg/cm^3 or 1.1kg/m^3 the sphere could only be of thickness 0.000695m

 

Is that right? because that would mean hard mathematical proof that it cant be supported by the radiation pressure alone.

[CraigD]

ok I have some calculations that I am just going to put out there, tell me if you think I am in error anywhere. ...

After correcting my calculations for the half-expected units error (the standard gravitational parameter for the Sun is 1.3*10^11 km^3/s^2 - I used 1.3*10^11 m^3/s^2, rather than 1.3*10^20 m^3/s^2), my results agree with Jay-qu's

 

Note that radiation pressure can be increased by a factor approaching 2 if the surface can be made reflective.

[ronthepon]

Basic moral of the story seems that the sphere must be stabilised by other forces. What about the raw tensile strength of the material of the sphere? Will it have any chance of supporting the mass?

 

Now seriously guys... did you really think you could do wonders with solar power?:silly:

[Jay-qu]

yes the factor can be increased by 2 with a reflective surface, but the reasoning I took was that if we planned on using this energy it would need to be absorbed - not reflected.

 

And Ron, our solar arrays are not all that flash, but they have come a long way and have great potential. For the sake of this discussion assume if a civilisation was advanced enough to bother creating a sphere around the sun that they would have sufficient power capturing capabilities also.

 

So now radiation pressure is out of it, like ron said - would the structural strength of any material be able to withstand such forces?