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Dyson sphere Edit



Dyson sphere
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Terra Prime is a Dysonsphere.
A Dyson Sphere is a colossal spherical structure constructed around a star, completely surrounding it. The interior of the sphere would absorb the entire energy output of that star, allowing for lifeforms to live on the interior surface almost indefinitely. Such a structure was theorized by 20th century physicist Freeman Dyson in the late 1950s.

For the interior of a Dyson Sphere to be habitable to most humanoid lifeforms, the radius of the sphere must be such that habitable temperatures (5 – 30 °C) are maintained. The radius would therefore depend on the size and the energy output of the star around which the sphere would be constructed; if a Dyson Sphere were to be constructed around the Terran sun, the radius would have to be approximately one astronomical unit. At such a radius, the interior surface area would be about 7 × 1016 km2, or 550 million times the entire surface area of the planet Earth. Such a surface area could easily support the lives of many quadrillions of beings.

Unsurprisingly, due to the almost immeasurable amounts of effort, resources and time required to construct such an immense structure, only one Dyson Sphere has ever been discovered. This particular sphere encased a G-type star and had a diameter of 200 million kilometers, giving it an internal surface area of approximately 250 million Terran class planets. As no radiant sunlight or solar wind escaped from the sphere, starships were not able to detect it until they were almost on top of it.As with the Dyson Sphere of Terra-Prime,the Nebula known as the Vault of Heavens,often masks outside detection.

A sphere of 1.33 AUs in diameter would be immens.The surface would appear to be perfectly flat for millions of miles. It is worth noting that the materials needed to enclose every single point in space that far away from a star would require the entire mass of many, many, many planets - probably all of the non-stellar matter in the system would have to be converted into sphere components.

Additionally, a Dyson Sphere would retain all energy produced by the star, and would somehow have to radiate much of this into space to maintain a habitable surface temperature. One possible way of conserving such vast quantities of energy without emitting any visible radiation (as seen on-screen) would be to convert all the energy to mass - essentially using a replicator-like technology to create the many, many, many planets' worth of matter necessary to construct the whole sphere.


A cut-away diagram of an idealized Dyson shell, a variant on Dyson's original concept, with a radius of 1 AU.
Look up Dyson sphere in
Wiktionary, the free dictionary.A Dyson sphere (or shell as it appeared in the original paper) is a hypothetical megastructure that was originally described by Freeman Dyson as a system of orbiting solar power satellites meant to completely encompass a star and capture its entire energy output. Dyson speculated that such structures would be the logical consequence of the long-term survival of technological civilizations, and proposed that searching for evidence of the existence of such structures might lead to the detection of advanced intelligent extraterrestrial life.

Since then, other variant designs involving building an artificial structure — or a series of structures — to encompass a star have been proposed in exploratory engineering or described in science fiction under the name Dyson sphere. These are not limited to solar power stations - many involve a habitation or industrial element. Most fictional depictions of a Dyson sphere describe a solid shell of matter enclosing a star (see diagram at right), which is the least plausible variant of the idea, due to the immense amount of solid matter required to form such a huge shell.

Contents
[hide]
1 Origin of concept
2 Variants
2.1 Dyson swarm
2.2 Dyson shell
2.3 Dyson bubble
2.4 Other types
3 Search for extra-terrestrial intelligence
4 Fiction
5 See also
6 References
7 External links



[edit] Origin of concept
See also: Future energy development
The concept of the Dyson sphere was the result of a thought experiment by physicist and mathematician Freeman Dyson, where he noted that every human technological civilization has constantly increased its demand for energy. He reasoned that if human civilization were to survive long enough, there would come a time when it required the total energy output of the sun. Thus, he proposed a system of orbiting structures designed to intercept and collect all energy produced by the sun.

Dyson is credited with being the first to formalize the concept of the Dyson sphere in his 1959 paper "Search for Artificial Stellar Sources of Infra-Red Radiation", published in the journal Science.[1] However, Dyson was inspired by the mention of the concept in the 1937 science fiction novel Star Maker, by Olaf Stapledon, and possibly by the works of J. D. Bernal and Raymond Z. Gallun who seem to have explored similar concepts in their work.[2]

A spherical shell Dyson sphere in our solar system with a radius of one astronomical unit would have a surface area of at least 2.72x1017 km2, or around 600 million times the surface area of the Earth. This would intercept the full 4x1026 watts of the Sun's output; other variant designs would intercept less, but the shell variant represents the maximum possible energy captured for our solar system at this point of the Sun's evolution.[3] To put this figure in perspective, it is approximately 33x1012 times the total energy consumption of humanity in 1998 which was 12x1012 W.[4] Dyson's proposal did not detail how such a system would be constructed, but focused only on issues of energy collection.[1]

While it is believed that some of these design variants are impractical, if not physically impossible, some designs do not require any major breakthroughs in our basic scientific understanding for their construction. Spacecraft and satellites using photovoltaics can be seen as a first small step in this direction.[5] In general, however, such power sources are not economically competitive with current Earth based ones (see Solar power satellite).[6]


[edit] Variants
In many fictional accounts, the Dyson sphere concept is most often interpreted as an artificial hollow sphere of matter around a star (see diagram at top of page). This perception is a misinterpretation of Dyson's original concept. In response to letters prompted by his original paper, Dyson replied, "A solid shell or ring surrounding a star is mechanically impossible. The form of 'biosphere' which I envisaged consists of a loose collection or swarm of objects traveling on independent orbits around the star."[7]

There are several variants on Dyson's original concept that have been proposed over the years, which differ based on their composition and method of construction. While the most often depicted variant — the Dyson shell — is considered by many to be impractical or even impossible, other proposed design variants of the sphere based on orbiting satellites or solar sails do not require any major theoretical breakthroughs in our scientific understanding.[5] However, such constructs, on the scale of the solar system, are well beyond our present-day industrial needs or capabilities. It is also likely that there are unforeseen industrial scaling difficulties in such a construction project, and that our current understanding of industrial automation is insufficient to build the self-maintaining systems needed for the sphere's upkeep.


[edit] Dyson swarm

A Dyson Ring — the simplest form of the Dyson Swarm — to scale. Orbit is 1 AU in radius, collectors are 1.0×107 km in diameter (~25× the Earth-Moon distance), spaced 3 degrees from center to center around the orbital circle.

A relatively simple arrangement of multiple Dyson Rings of the type pictured above, to form a more complex Dyson Swarm. Rings' orbital radii are spaced 1.5×107 km with regards to one another, but average orbital radius is still 1 AU. Rings are rotated 15 degrees relative to one another, around a common axis of rotation.
The variant closest to Dyson's original conception is the "Dyson swarm". It consists of a large number of independent constructs (usually solar power satellites and space habitats) orbiting in a dense formation around the star. This approach to the construction of a Dyson sphere has several advantages: the components making it up could range widely in individual size and design, and such a sphere could be constructed incrementally over a long period of time.[5] Various forms of wireless energy transfer could be used in order to transfer energy between constructs.

Such a swarm is not without drawbacks. The nature of orbital mechanics would make the arrangement of the orbits of the swarm extremely complex. The simplest such arrangement is the Dyson ring in which all such structures share the same orbit. More complex patterns with more rings would intercept more of the star's output, but would result in some constructs eclipsing others periodically when their orbits overlap.[8] Another potential problem is the increasing loss of orbital stability as adding more orbiting constructs increases the probability of orbital perturbations of other constructs.

As noted below, such a cloud of collectors would alter the light emitted by the star system, but as can be seen here, it is unlikely that such an alteration would be complete, and that some of the star's natural light would still be present in the system's emitted spectrum.[1]


[edit] Dyson shell
The variant of the Dyson sphere most often depicted in fiction is the "Dyson shell": a uniform solid shell of matter around the star (see diagram at top of page).[3] Unlike the Dyson swarm, such a structure would completely alter the emissions of the central star, and would intercept 100% of the star's energy output. Such a structure would also provide an immense surface which many envision being used for habitation, if the surface could be made habitable. There are several serious theoretical difficulties with the solid shell variant of the Dyson sphere:

Such a shell would have no net gravitational interaction with its englobed sun (see the divergence theorem applied to gravity), and could drift in relation to the central star. If such movements went uncorrected, they could eventually result in a collision between the sphere and the star — most likely with disastrous results. Such structures would need either some form of propulsion to counteract any drift, or some way to repel the surface of the sphere away from the star.[9]

For the same reason, such a shell would have no net gravitational interaction with anything else inside it. The contents of any biosphere placed on the inner surface of a Dyson shell would not be attracted to the sphere's surface and would simply fall into the star. It has been proposed that a biosphere could be contained between two concentric spheres, placed on the interior of a rotating sphere (in which case, the force of artificial "gravity" is perpendicular to the axis of rotation, causing all matter placed on the interior of the sphere to pool around the equator, effectively rendering the sphere a Niven ring for purposes of habitation, but still fully effective as a radiant energy collector) or placed on the outside of the sphere where it would be held in place by the star's gravity.[10][11] In such cases, some form of illumination would have to be devised, or the sphere made at least partly transparent, as the star's light would otherwise be completely hidden.[12]

The compressive strength of the material forming the sphere would have to be immense. Any arbitrarily selected point on the surface of the sphere can be viewed as being under the pressure of the base of a dome 1 AU in height under the Sun's gravity at that distance. Indeed it can be viewed as being at the base of an infinite number of arbitrarily selected domes, but as much of the force from any one arbitrary dome is counteracted by those of another, the net force on that point is immense, but finite. No known or theorized material is strong enough to withstand this pressure, and form a rigid, static sphere around a star.[13] It has been proposed by Paul Birch (in relation to smaller "Supra-Jupiter" constructions around a large planet rather than a star) that it may be possible to support a Dyson shell by dynamic means similar to those used in a space fountain.[14] Masses traveling in circular tracks on the inside of the sphere, at velocities significantly greater than orbital velocity, would press outwards due to centrifugal force. For a Dyson shell of 1AU radius around a star with the same mass as the Sun, mass traveling ten times orbital velocity (300 km/s) would support 99 (a=v2/r) times its own mass in additional shell structure. The arrangement of such tracks suffers from the same difficulties as arranging the orbits of a Dyson swarm, and it is unclear how much energy would be consumed ensuring the velocity of the masses was maintained.

There may not be sufficient building material in the Solar system to construct a Dyson shell. Dyson's original estimate was that there was enough material in the Solar system for a 1 AU shell 3 meters thick, but this included hydrogen and helium which are unlikely to be much use as building material. Anders Sandberg estimates that there is 1.82×1026 kg of usable building material in the Solar system, enough for a 1 AU shell with a surface density of 600 kg/m²—about 8–20 cm thick depending on the density of the material. This includes the cores of the gas giants, which may be hard to access; the inner planets alone provide only 11.79×1024 kg, enough for a 1 AU shell with a surface density of just 42 kg/m².[15]


[edit] Dyson bubble

A Dyson Bubble: an arrangement of statites around a star, in a non-orbital pattern. Note: so long as a statite has an unobstructed line-of-sight to its star, it can hover at any point in space near its star. This relatively simple arrangement is only one of an infinite number of possible statite configurations, and is meant as a contrast for a Dyson Swarm only. Statites are pictured as the same size as the collectors pictured above, and arranged at a uniform 1 AU distance from the star.
A third type of Dyson sphere is the "Dyson bubble". It would be similar to a Dyson swarm, composed of many independent constructs (usually solar power satellites and space habitats) and likewise could be constructed incrementally.

Unlike the Dyson swarm, the constructs making it up are not in orbit around the star, but would be statites—satellites suspended by use of enormous light sails using radiation pressure to counteract the star's pull of gravity. Such constructs would not be in danger of collision or of eclipsing one another; they would be totally stationary with regard to the star, and independent of one another. As the ratio of radiation pressure and the force of gravity from a star are constant regardless of the distance (provided the statite has an unobstructed line-of-sight to the surface of its star[16]), such statites could also vary their distance from their central star.

The practicality of this approach is questionable with modern material science, but cannot yet be ruled out. A statite deployed around our own 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.[15]

Such a material is currently beyond our ability to produce; the lightest carbon-fiber light sail material currently produced has a density — without payload — of 3 g/m², or about five times heavier than would be needed to construct a solar statite.[17]

However, there has been some speculation about the creation of ultra light carbon nanotube meshes through molecular manufacturing techniques whose density would be below 0.1 g/m².[18] If production of such materials on an industrial scale is feasible, and such materials could be used in light sails, the average sail density with rigging might be kept to 0.3 g/m² (a "spin stabilized" light sail requires minimal additional mass in rigging). If such a sail could be constructed at this areal density, a space habitat the size of the L5 Society's proposed O'Neill cylinder–500 km², with room for over 1 million inhabitants, massing 3×106 tons–could be supported by a circular light sail 3,000 km in diameter, with a combined sail/habitat mass of 5.4×109 kg[19]. For comparison, this is just slightly smaller than the diameter of Jupiter's moon Europa (although the sail is a flat disc, not a sphere), or the distance between San Francisco and Kansas City. Such a structure would, however, have a mass quite a lot less than many asteroids. While the construction of such a massive inhabitable statite would be a gigantic undertaking, and the required material science behind it is as yet uncertain, its technical challenges are slight compared to other engineering feats and required materials proposed in other Dyson sphere variants.

If the statites which form the Dyson bubble are propagated until they completely surround the star, then the Dyson bubble becomes a form of Dyson shell. Unlike the standard notion of a Dyson shell, however, such a structure would be non-rigid.


[edit] Other types
Another possibility is the "Dyson net", a web of cables strung about the star which could have power or heat collection units strung between the cables. The Dyson net reduces to a special case of Dyson shell or bubble, however, depending on how the cables are supported against the sun's gravity.

The Ringworld, or Niven ring, could be considered a particular kind of Dyson sphere. Larry Niven, who first developed the concept, described it as "an intermediate step between Dyson Spheres and planets".[20] The ringworld could perhaps be described as a slice of a Dyson Sphere (taken through its equator), spun for artificial gravity, and used mainly for habitation as opposed to energy collection. Like the Dyson Shell, the Niven ring is inherently unstable without active measures keeping it in position with regards to its central star — a fact recognized by Larry Niven and addressed in the sequels to his novel on the concept, Ringworld.[21]

Stellar engines are a class of hypothetical megastructures, whose purpose is to extract useful energy from a star, sometimes for specific purposes. For example, Matrioshka brains extract energy for purposes of computation; Shkadov thrusters extract energy for purposes of propulsion. Some of the proposed stellar engine designs are based on the Dyson sphere.[22]


[edit] Search for extra-terrestrial intelligence
In Dyson's original paper, he speculated that sufficiently advanced extraterrestrial civilizations would likely follow a similar power consumption pattern as humans, and would eventually build their own sphere of collectors. Constructing such a system would make such a civilization a Type II Kardashev civilization.[23]

The existence of such a system of collectors would alter the light emitted from the star system. Collectors would absorb, and re-radiate, energy from the star.[1] The wavelength(s) of radiation emitted by the collectors would be determined by the emission spectra of the substances making them up, and the temperature of the collectors. Since it seems most likely that these collectors would be made up of heavy elements not normally found in the emission spectra of their central star — or at least not radiating light at such relatively "low" energies as compared to that which they would be emitting as energetic free nuclei in the stellar atmosphere — there would be atypical wavelengths of light for the star's spectral type in the light spectrum emitted by the star system. If the percentage of the star's output thus filtered or transformed by this absorption and re-radiation was significant, it could be detected at interstellar distances.[1]

Given the amount of energy available per square meter at a distance of 1 AU from the Sun, it is possible to calculate that most known substances would be re-radiating energy in the infrared part of the electromagnetic spectrum. Thus, a Dyson Sphere, constructed by life forms not dissimilar to humans, who dwelled in proximity to a Sun like star, made with materials similar to those available to humans, would most likely cause an increase in the amount of infrared radiation in the star system's emitted spectrum. Hence, Dyson selected the title "Search for Artificial Stellar Sources of Infrared Radiation" for his published paper.[1]

SETI has adopted these assumptions in their search, looking for such "infrared heavy" spectra from solar analogs. As of 2005 Fermilab has an ongoing survey for such spectra by analyzing data from the Infrared Astronomical Satellite (IRAS).[24]


[edit] Fiction
Main article: Dyson spheres in fiction
As noted above, the Dyson sphere originated in fiction,[25][26] and it is a concept that has appeared often in science fiction since then (see Dyson spheres in fiction for listed examples). In fictional accounts, Dyson spheres are most often depicted as a Dyson shell with the gravitational and engineering difficulties noted above with this variant, largely ignored.[3]

for losers, asteroids are where the action will be at. A civilization with space travel and nanotech would have no problem detecting asteroids. Anyone have numbers on the resolution of a telescope array spanning our asteroid belt?


Gas giants can be harvested only with the greatest of difficulty. They would be a secondary stage in the dismantling of a solar system since you need lots of startup material. You start by building a giant space station in orbit. Then you lower a SkyHook? several kilometers into the atmosphere. Then you collect, solidify and move the carbon up to orbit through the SkyHook?. This is an extremely time-consuming and resource intensive process. By comparison, a probe that landed on Earth could immediately build solar collectors, take over the biosphere within a a few days, then start stripping the planet by shooting it into orbit using railguns. This is only possible because you can be where the carbon is abundant and still receive light.


If one went to the effort then Uranus would be useful to harvest, quite unlike Jupiter which is made up of > 99% non-metals (hydrogen and helium).


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Is this >99% mass or >99% volume we're talking about here? In any case I think that a 99% atmosphere to core ratio is too high of an estimate.


That's 99% of the entire planet's bulk mass. Jupiter has a liquid hydrogen core. If Jupiter actually had a solid core made of metal then believing it to make up as much as 1% of its bulk mass would be crazily overoptimistic. Jupiter is basically a proto-sun.


Can anyone expand a little on spectral analysis in this context? Is it any easier to detect the presence of hydrogen than it is to detect say, carbon or iron?


Say a nanoprobe already has enough hydrogen (collected from solar winds via a "sail" during its travels, or whatever). Could the gas of a Gas Giant be converted into a more useful state through oxidation? How long would it take to burn Jupiter's atmosphere, using powerful lasers or orbital nuclear bombardment to ignite the atmosphere?


Jupiter has little or no oxygen and any oxygen it has is already be bound in H2O so there is no free oxygen to oxidize anything.


I remember some kind of speculation that a GG's core might be a very dense material like diamond, this would be useful building material. I'll try to find more info on this. -- CarstenKlapp


The emphasis is on like diamond. I bet they're talking about metallic hydrogen.


No, the speculation is that there might be some sort of solid core, made of heavier elements, lower down than the metallic hydrogen. But it would only be about terrestrial-sized, isn't that easy to get to, and would undoubtedly undergo phase changes if you tried to take it out.


I found a page that said something to that effect except it didn't have any details (not even the hypothetical size). Are there any useful references on the web about planetary composition? I never took the astrophysics class and I didn't even recall that Jupiter and Uranus had very different composition.


Only thing I care to find at the moment is http://seds.lpl.arizona.edu/nineplanets/nineplanets/nineplanets.html


I don't know who started it, but I first read about a possible diamond core for Jupiter in ArthurCeeClarke's 2010: Oddesey Two. As I recall, he hypothesized that over the millennia all the carbon that used to be in the atmosphere worked its way downwards to the core (through gravitation) and were compacted into a big diamond of around the size of the Earth. -- GavinLambert


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How would oxidation help you? There isn't much oxygen available. Remember, it's almost all hydrogen.


I was thinking about burning off the atmosphere as an easier way to get at the core, and burning it would also convert the gas into something else hopefully more useful. -- Carsten


Now, if your nanoprobe can utilize fusion to transform hydrogen into other elements, you can get away with this. Presumably, this is what Clarke's TMA2 (I can't remember the Russian name he gave to it later) did to Jupiter. -- RobertWatkins


Wasn't that the Monolith? -- GavinLambert


Assuming you're talking about using hydrogen in fusion reactors then it's too slow and inefficient. Using tons of material in order to create (micro?)grams of metal (anything heavier than helium) per year is a losing proposition. If you're just talking about igniting Jupiter (eg, using a black hole) then why not fling it into the sun and be done with it? See also MegaStructures


"Fling it into the sun and be done with it." (An AI with a sense of humour, I love it! THIS PLANET IS IRRELEVANT. LOL. BEGIN DISPOSAL PROCEDURE. LOL.) -- Carsten

The main point of stellifying Jupiter is getting more energy out of it. Flinging it into the sun won't work; that is, it won't get you a lot more energy than the sun is already producing; considering that you will have to deal with its kinetic energy, Mv*v/2, I dare say that it's not what you'd want to do. -- MihaiCiumeica


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Getting back to the title topic for a moment - why would you want a Dyson sphere? Put a big magnetic bottle around the sun and drain it into a few thousand Jupiters and you can mine them for hydrogen as you need it to run your streetlights and space heaters for trillions of years (or even higher powers of 1000, depending on your population). StripMineTheSun?!


Obviously you've missed the fact that the sun is a thermonuclear fusion reactor. An eminently safe, cheap and utterly practical one that ALREADY EXISTS. We don't have to deal with containment, radiation, fuel, waste, radioactivity, nor even construction. All we have to do is gather the generated power. So why would we want to demolish a WORKING giant nuclear fusion reactor in order to create lots of hypothetical useless itty bitty ones?


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[edit] See also
Megascale engineering
Star lifting
Stellar engineering
Technological singularity
Alderson disk
Klemperer rosette
Globus Cassus
Hollow Earth



[edit] References
^ a b c d e f Freemann J. Dyson (1960). "Search for Artificial Stellar Sources of Infra-Red Radiation". Science 131: 1667–1668. doi:10.1126/science.131.3414.1667.
^ Dyson FAQ: Was Dyson First?. Retrieved on 2006-09-01.
^ a b c Dyson FAQ: What is a Dyson Sphere?. Retrieved on 2007-07-26.
^ Order of Magnitude Morality. Retrieved on 2007-10-06.
^ a b c Dyson FAQ: Can a Dyson sphere be built using realistic technology?. Retrieved on 2006-09-01.
^ Landis, Geoffrey A.. "Reinventing the Solar Power Satellite". NASA TM-2004-212743, February 2004.
^ F. J. Dyson, J. Maddox, P. Anderson, E. A. Sloane (1960). "Letters and Response, Search for Artificial Stellar Sources of Infrared Radiation". Science 132: 250–253. doi:10.1126/science.132.3421.252-a.
^ Some Sketches of Dyson Spheres. Retrieved on 2007-10-06.
^ a b Dyson Sphere FAQ: Is a Dyson sphere stable?. Retrieved on 2007-10-06.
^ Drashner, Todd; Steve Bowers, Mike Parisi, M. Alan Kazlev. Dyson Sphere. Orion's Arm. Retrieved on 2007-10-07.
^ Badescu, Viorel; Richard B. Cathcart. Space travel with solar power and a dyson sphere. Astronomy Today. Retrieved on 2007-10-07.
^ Fermi Conclusions. Retrieved on 2007-10-06.
^ Dyson FAQ: How strong does a rigid Dyson shell need to be?. Retrieved on 2006-03-08.
^ Supramundane Planets (ZIP). Retrieved on 2006-03-02.
^ a b Sandberg, Anders. Is there enough matter in the solar system to build a Dyson shell?. Dyson Sphere FAQ. Retrieved on 2006-08-13.
^ Sunlight Exerts Pressure. Retrieved on 2006-03-02.
^ Clark, Greg (2000). SPACE.com Exclusive: Breakthrough In Solar Sail Technology. Space.com. Retrieved on 2006-03-02.
^ Researchers produce strong, transparent carbon nanotube sheets. PhysOrg.com (2005). Retrieved on 2006-03-02.
^ Dinkin, Sam (2006). The Space Review: The high risk frontier. Thespacereview.com. Retrieved on 2006-03-18.
^ Larry Niven. "Bigger than Worlds", Analog, March 1974.
^ Dyson Sphere FAQ: Other Dyson Sphere-Like Concepts. Retrieved on 2007-10-06.
^ Stellar engine. The Internet Encyclopedia of Science. Retrieved on 2007-10-08.
^ Kardashev, Nikolai. "On the Inevitability and the Possible Structures of Supercivilizations", The search for extraterrestrial life: Recent developments; Proceedings of the Symposium, Boston, MA, June 18-21, 1984 (A86-38126 17-88). Dordrecht, D. Reidel Publishing Co., 1985, p. 497-504.
^ Carrigan, D. (2006). Fermilab Dyson Sphere search program. Retrieved on 2006-03-02.
^ Olaf Stapledon. Star Maker
^ J. D. Bernal, "The World, the Flesh, and the Devil"

[edit] External links
Dyson Sphere FAQ
Dyson Sphere
Search for Artificial Stellar Sources of Infra-Red Radiation
Matrioshka Brains
Dyson Shell Supercomputers as the Dominant "Life Form" in Galaxies
Toroidal Dyson Swarms simulations using Java applets
Outside Dyson shells
Dyson Sphere article at Memory Alpha, a Star Trek wiki

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Case Study: The Dyson Sphere



Case Study: The Dyson Sphere
"That's all well and good", you might say, "but this is a sci-fi website, not an ancient history website." True enough, so let's leave the dreary Egyptian desert and boldly go where no man has gone before. First stop: the Dyson Sphere. The Dyson Sphere was a spectacularly massive structure. In fact, it is the most massive structure I can recall seeing in sci-fi, even bigger than Unicron or any of the mighty worldships of Galactus. It was featured in the TNG episode "Relics", and no one knows who built it, or how old it is. The only thing we do know is that its builders must have wielded forces and engineering skills far beyond any of their counterparts in the Star Trek universe. Contrary to certain popular (albeit painfully simple minded) beliefs, the difficulty of constructing such a vast structure does not end with the procurement of the necessary raw materials.

This is a spherical shell with 100 million km radius. Let's imagine that its wall thickness is 2 km, and its shell has the same density as iron (yeah, I know, it's suposed to be "carbon neutronium", as if it makes sense to combine a lightweight element with superdense degenerate matter). Anyway, the mass of an iron shell would be roughly 2E30 kg, or one solar mass! Not only is this an absolutely staggering amount of resources to call into action (it suggests they'd be able to build stars at will, in places of their choosing, since they can summon up solar masses of engineering materials), but it would require staggering material strength.

It is tempting to imagine that it is rotating about its axis to generate artificial gravity, but if that were so, the resulting centripetal force would be unsuitable for the creation of a uniform M-class environment on the sphere's interior. The problem is that if we visualize the axis of rotation as vertical, then the centripetal force will be horizontal. At the equator, this will work perfectly. But if we move away from the equator toward the poles, we will see that direction of the centripetal force vector diverges farther and farther away from the "surface normal" of the sphere. In other words, as your latitude increases, the proportion of the centripetal force that acts like gravity will decrease, and the proportion of the centripetal force that slides you sideways along the surface (toward the equator) will increase, as shown below:



One look at the diagram and the problem should be obvious: all of the atmosphere, oceans, and other surface material will eventually end up in a thin band around the equator of the sphere. This is obviously unacceptable; there's no point building such a huge structure if 99.9% of it will be uninhabitable. Unlike Niven's far more realistic Ringworld, the Dyson Sphere cannot possibly generate its surface gravity through rotation. Therefore, the Dyson Sphere must have near-zero angular velocity in order to keep from pushing all of its material toward its equator, and it must use something other than the centrifuge principle to generate its artificial gravity.

So if there is no centrifuge stress, would there be any stress? The answer is yes, because an object of such stupendous size will generate significant gravity, which will add to the existing gravity of the star at its centre. Since the sphere's radius is only 2/3 of an A.U., its sun would have less than half of our Sun's luminosity (or the oceans on the sphere's inner surface would have evapourated), so it would probably have less than half our Sun's mass as well. This means that its mass is roughly 1E30 kg.

From an engineering standpoint, the Dyson Sphere can be thought of as a thin-walled spherical pressure vessel, and the gravitational force can be thought of as the "pressure" (once it's divided by the internal surface area, of course). The mass of the sphere is 2E30 kg, the mass of the star is 1E30 kg, and the radius is 1E11 m, so Newton's law of gravitation gives us 1.33E28 N. The internal surface area of the sphere is 1.26E23 m², so the equivalent "pressure" would be roughly 106 kPa.

Now, that's not a lot of pressure (it's roughly 1 bar), but it's acting over an enormous surface, and that comes into play when you try to calculate the resulting stress in the sphere wall. The equation for in-plane stress in a thin-walled spherical pressure vessel is pr/2t where p = pressure, r = radius and t = shell thickness, so the tensile stress on the shell would be roughly 2.65 TPa! To put this in perspective, it's roughly ten thousand times the yield strength of structural steel. Not bad, eh? It's also insensitive to the exact wall thickness of the sphere, because a thicker wall will increase the load-bearing area but it will also increase the mass of the sphere and hence the load (a full derivation would show the wall thickness term cancelling out).

As if it isn't enough to need steel which is ten thousand times stronger than normal, we still have to consider the construction problem: how would you build such a beast? A full sphere would have at least twice the mass of the star but the effect of its gravity on the star would be symmetrical and therefore nullified, so that the star isn't disrupted. However, what if they've got only one quarter of the sphere done? That would pull the star to one side, severely disrupting it in the process. They would have to carefully balance the construction of countless trillions of balanced segments around the star as they build the sphere so that symmetry is preserved at all times, and they would have to use huge engines to hold these pieces in place until they can be joined together into the finished sphere.

We can build a ping-pong ball today, but that doesn't mean we'll ever be able to build a Dyson Sphere (although, to be honest, Ringworld is a much better idea anyway).



Editors Note;

Not for the dysonsphere known as Terra-Prime.a Ringworld would not be big enough to fit all the worlds I wish place upon this artificial world.

Doc Thompson.


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