Large Structures in Space

[Jay-qu]

Science fiction has always played host to the idea of having large structures in space. From Dyson spheres to Death stars, these structures lay firmly in the realm of fiction, but will it always be this way? Human technology is growing at an alarming rate, now with the dawn of the space age behind us the sky is no longer a limit. If our technology continues to grow exponentially it seems logical that we will eventually be able to build such structures, but even logic must give way to physics in extreme cases. While it may follow logically, it will be physics that has the last say, whether it is physically possible to build these structures depends on a wide range of factors. Some of these factors include: size, material composition, availability of materials, stability etc.

 

One of the most famous of these large structures would have to be Dyson Spheres. They where first put forward by Freeman Dyson in 1959, in "Search for Artificial Stellar Sources of Infrared Radiation" in Science. Freeman Dyson was a Cambridge graduate where he did his bachelor degree of arts in mathematics; he then went on to become a Professor of Physics at Cornell University. Dyson himself admitted that the idea was not entirely his own, he was inspired by a book called ‘The Star Maker’ written in 1937 by Olaf Stapleton. It is even thought that Olaf may have got the idea from J. D. Bernal.

There is some confusion concerning what a Dyson Sphere is actually meant to be like. The original proposal was that by having many individual satellites orbiting about a star it would be possible to collect a large portion of the stars energy output. There are some other more fanciful theories that take a Dyson Sphere as a solid continuous sphere, which can even be lived in.

 

The idea of a Dyson Sphere comes from the constant need for more energy. It is theorised that as humanity continues to grow it will always be in need of more and more energy. To demonstrate the progression to using solar energy, these calculations have been included.

- The sun puts out 3.827*1026 Jules every second.

- The Earth has a radius of 6,378km this gives it a cross sectional area of:

 

Ae = 2*pi*(6,378x102)^2

Ae = 2.556*10^14 m^2

 

- The Earth orbits the sun at a radius of 1.496x10^11m, this makes the surface area of a sphere at that distance:

 

As = 4*pi*(1.496x1011)^2

As = 2.812*10^23 m^2

 

- Earth makes up a percentage of this sphere:

 

Ae/As * 100 = 9.088*10^-8%

 

- Hence Earth can only capture a small amount of the suns total energy output:

9.088*10^-10 * 3.827*10^26W = 3.478*10^17W

 

Albeit this is a tremendous amount of energy, but the entire Earths surface must be covered to get this energy. Even then there is looses from the atmosphere, clouds and our equipment.

One day in the future we may have the need to get more energy than this and a Dyson Sphere is one such solution.

 

For the purpose of energy collection a great many solar collectors surrounding a star would suffice as a solution. Though this solution is also going to be fraught with difficulty, imagine navigating swarms of satellites, thousands of them, each with their own individual paths. This would make maintenance and energy collection very difficult, though it remains the more physically plausible solution.

There are other uses for a Dyson Sphere that would require it to be solid, or at least continuous. For example if a civilisation wanted to hide themselves for security reasons or needed more space to live, a Solid Dyson would be required. The resources required to create a solid sphere would be truly enormous. If you wanted to live in the sphere and it was around a star that is like our sun, it would have to have a radius of one astronomical unit. For a sphere of radius 1Au and thickness y meters would have an approximate volume of:

 

V ≈ 2.812*10^23y m3

 

This means for a Sphere of just 1cm thick the volume of matter would be 2.812*10^21m3. This is twice the volume of the Earth. As you can imagine a 1cm think cube couldn’t be very strong, but if you increase this to even 10cm the volume quickly becomes more than that of all the matter in the terrestrial planets and asteroids in the solar system! This fact doesn’t make a solid Dyson Sphere impossible, just impractical. The impossibilities may lie in whether or not such a structure would be stable or not.

 

The effect of the spheres gravity on the sun is not a worry, since the net gravitational force of the sun due to the sphere will always equal zero. This can be thought out logically. If the sun was at the center of the sphere it would have equal amounts of mass distributed at the same distance from it in all directions, this all cancels to a net force of zero. While if the sun was off center then the side it is closest to would have a stronger field strength due to less distance, but at the same time it the opposing side now has more mass behind the sun and though it is further away these effects perfectly cancel each other out.

The suns gravity has no such cancelling effect and hence will have an effect on the stability of the structure. There have been theories that the gravitational force due to the sun on the sphere could be negated and the sphere essentially held up by radiation pressure and the solar wind. This is not to be confused with the solar wind, the solar wind is made up of high speed particles emitted from the sun. While it may have some effect and help hold up the Dyson Sphere, it is negligible, only 1% of what radiation pressure will do. It may sound absurd that light could hold up the sphere, but it may be possible for very low density materials. Radiation pressure is stronger the closer you get to the sun, this is a problem as gravity also gets stronger the closer you get, so this means it doesn’t matter how close or far away, no distance is at an advantage for this purpose.

For an object that absorbs the incident radiation, which for a Dyson Sphere made for energy production it will presumably absorb most light, the force per m2 (or pressure) of the sphere due to radiation is:

 

Fr = L/(4*pi*r2*c) N/m^2

 

Where L equals the luminosity of the sun (3.827*1026W) c equals the speed of light (3x108ms-1) and r equals radius of the sphere.

The force per m2 of sphere due to gravity is:

 

Fg = (Msun*Ds*x*G)/r^2 N/m^2

 

Where Msun equals the mass of the sun (1.99x10^30Kg), Ds equals the density of the Dyson Sphere, x equals the thickness of the sphere, G equals the gravitation constant (6.67x10^-11m^3 kg^-1 s^-2) and as before r equals the radius of the sphere.

Hence the net force of the sphere would be:

 

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

= (1.02x10^17)/r2 – (1.33x10^20*Ds*x)/r^2 N/m^2

= (1.02x10^17 – 1.33x1020*Ds*x)/ r^2 N/m^2

 

For an Fnet of zero, ie forces balanced:

 

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

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

Ds*x = 7.65x10^-4

 

Hence if we where able to make a Dyson sphere out of aerogel - the least dense substance know to man at just 1.1kg/m^3, the sphere could only be 0.000695m thick, that’s less than a millimeter! Clearly a solid Dyson Sphere would not be able to support itself with radiation pressure alone! This means that it would have to rely on the materials own structural integrity. Whatever the material is it would have to be something with a very high tensile strength, relatively low density and also be very abundant in the solar system.

 

 

Another Large Structure is a Ring World or a Halo. It is a large ring that is habitable on the inner side. This idea is most famous from the recent video game series ‘Halo’ from which so far three books have sprung.

The main reason a civilisation would want to create one of these rings would be for habitation. For one reason or another, a civilisation may find that they are out of space on their home planet, or perhaps due to climate changes their world is becoming inhospitable to life. They will then need somewhere else to go. Some systems may have another planet to go to, while others may not. If travelling to another star system all together is out of the question – either due to not having the capabilities to travel the vast distances in between star systems, or not having enough ships to move a large part of the civilisation – a ring world may become an option in such a crisis.

The ring could be constructed in an orbit around the sun matching that of the planet, or even perhaps in orbit around the planet itself. The ring could be inclined to the sun at such a way as to have half in darkness and half in light, so that if it is set rotating at the right speed it would have a normal day/night cycle.

The concept of a ring world is much different from a Dyson Sphere, while inhabiting the inner side of a Dyson sphere was only a late addition to the theory; a ring world is solely intended for that purpose. This means that one way or another, the ring is going to have to supply its own gravity. Doing so by mass is out of the question, so we must look to more artificial means of creating gravity or at least simulated gravity. Since we have no means By far the easiest way of doing this would be to spin up the ring. The spin creates an centripetal force that makes objects stick to the inside of it, much the same way that a bucket of water spun around on Earth will not spill. The gravitational force can be calculated thus:

 

F = (mv^2)/r

ma = mv^2/r

a = v^2/r

Where r is the radius of the ring and v is the velocity at which it is spinning.

Hence to have Earth like gravity of 10ms^-2, a ring of radius r would have to be spun at:

 

V = √(10r)

If you want the ring to resemble Earth like conditions and have a 24 hour day, then:

 

Period of one rotation = 24*60*60 = 43200 seconds

Then:

V = (2*pi*r)/86400

From above:

√(10r) = (pi*r)/43200

10r = (pi2*r2)/(1.866x10^6)

re-arranging:

r = 1.890x10^9m

v = 1.374x10^5 m/s

 

This velocity may well prove to fast to implement in practice. It may be necessary to have longer days so the ring is allowed to spin at slower rate.

 

When building one of these rings for habitation, one of the main factors will be useable living space. Assuming that all of the operating parts can be stored within the ring, and that the inner surface is totally useable, then the habitable area would be:

 

A = 2*pi*r*w

 

Hence:

 

A = 11.88x10^6*w km2

 

Where w is the width of the ring in km. If the ring was just 10km wide it would have 80% of the land area that Earth does. This leaves plenty of space for farming and living space; water can be stored in the ring itself, with small lakes for aesthetic purposes.

 

Basically if you want more space to live in you have to increase the width.

If you increase the width then the mass is going to go up. With increasing mass means an increasing amount of energy will be needed to make it spin. The rotational kinetic energy for a hoop is:

 

Kr = ½mrv

 

With the values found previously that is an energy of:

 

Kr = 1.30x10^14m J

 

This is a tremendous amount of energy and it may or may not be available to the race at that time, but the function of the ring depends on it, or else no gravity, no day night cycle. This amount of energy could be achievable through the use of antimatter. It could be set up to have many thousands of boosters around the outside of ring where antimatter is annihilated with normal matter. During an antimatter/matter annihilation all mass is turned into energy in the ratio of E=mc^2, since c^2 is such a large number (9x10^16), these reactions allow a high energy yield from a small amount of mass. That said for the purposes of spinning up the ring, you would require 0.72g of antimatter per kilogram of the mass of the ring. To produce such a large amount of antimatter the civilisation would have to have quite an efficient means of creating it. Recently released data by CERN stated that when their facilities are fully operational, they will theoretically be able to produce 10^7 antiprotons per second. So to produce that 0.72 grams of antimatter it would take us approximately 1.44 billion years! And that’s not even considering how the antimatter would be stored until use, that in itself could prove quite a feat.

There are yet still even more problems that need working out, problems that conceivable solutions are yet to be found. For example I have not addressed how the atmosphere of such a ring would be maintained. Earth has an atmospheric pressure of 101kPa at sea level, but we can survive in much less – astronauts only have 30% of that when they go EVA but then the oxygen level is increased to compensate. This would become a problem for metals that are susceptible to corrosion. Even then, trying to maintain the atmosphere at 30% of Earths could still prove difficult, if not impossible. As one possible solution to overcome the problem of leaking atmosphere, some designs have the ring enclosed and like a giant tube, this is plausible but would require a lot more materials.

 

In order for a ring world to be constructed many engineering feats would have to overcome. The stresses on such a structure would be enormous. It may be necessary to have supporting spokes like that on a bicycle wheel. Just like a Dyson sphere, to provide the strength needed it would probably have to be constructed out of some exotic form of matter that we are yet to discover.

 

A fictional large structure that is also worth mentioning is the Death Star for the famous Star Wars saga. The death star has a much different function than that of the previous two I discussed; the death star is a weapon. It is a weapon of far greater power than any ‘weapon of mass destruction’ that we know of. The death star is able to destroy a whole planet, reducing it all to a floating mess of asteroids. The first death star constructed was 160km in diameter, large enough to be mistaken for a small moon. It was constructed to enforce the Imperial’s totalitarian rule over the galaxy. There is not much insight into how the weapon and manoeuvring systems, only that they are powered by a hypermatter reactor. Since there is no such thing (as yet) called hyper matter, the death star remains firmly in science fiction. However the concept that one day a weapon of this magnitude could be constructed remains evident.

 

Isaac Newton once wrote “to myself I seem to have been only alike a boy playing of a seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.” Newton had only scratched the surface of what science would one day be able to do. These days we may have lifted our head slightly and started uncovering small parts of this vast truth, but there will always be more to learn. Taken with what we know right now, these ideas of large structures may seem impossible, but with what we may know one hundred or even a thousand years in the future, these structures may become a commonplace. The sky is no longer a limit.

 

By Jayden Newstead

[ronthepon]

Great Job of compiling it all, Jay-Qu, It's a beauty of an article!

 

Wonder how much time it would have taken...

[Tormod]

Great post...I'll read it as soon as I can sort out all the letters. :)

[cwes99_03]

A bit long good buddy. But all the same interesting.

[Jay-qu]

Well it is an article, so not that long for an article - not even 3k words..

 

Thanks guys :)

[hummingbird]

:unsure: I'm slow so maybe hours later I'll completely understand what I'm reading.

[Eclipse Now]

:) I'm slow so maybe hours later I'll completely understand what I'm reading.

 

Yeah, unless I'm really interested in the bottom line I tend to like things a bit shorter and less technical. But I appreciate the work that went into it! (And the training that enabled the calcs... out of my league).

 

So here's some images that I've added to various "terraforming Mars" threads that ended up discussing torus stations / halo's.

 

This is the mother of them all, a "Dyson Sphere" without a north and south pole, the RINGWORLD! (With a surface area of about a million earth's).

 

 

I have a proposal. Maybe we should cut this "Terraforming other planets" thread off at post 81 and insert here? Because we had about 3 or 4 pages of 'Halo' discussion, complete with pictures. ;)

 

Then one of my favourite subjects could continue in a valid location.

 

(And maybe we need a 'Stickie' or 'pinned' official thread for "Terraforming Mars" as it keeps coming up? How do you guys handle subjects that keep reappearing?)