Here is a copy of the Dyson sphere discussion from 1960.
Freeman Dyson -
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. The size and shape of the individual objects would be chosen to suit the inhabitants. I did not indulge in speculations concerning the constructional details of the biosphere, since the expected emission of infrared radiation is independent of such details.
Here is the Dyson sphere FAQ
Update: There is a follow up article on Dyson bubbles, statites, molecular nanotechnology and submerged dyson spheres
Passive, sun-pointing, millimeter-scale solar sails could be used for the heliocentric orbits.
Update: Welcome instapundit readers
Taking inspiration from the orbital dynamics of dust, we find that spacecraft length scaling is a means of enabling infinite-impulse orbits that require no feedback control. Our candidate spacecraft is a 25 μm thick, 1 cm square silicon chip equipped with signal transmitting circuitry. This design reduces the total mass to less than 7.5 mg and enables the spacecraft bus itself to serve as a solar sail with characteristic acceleration on the order of 0.1 mm/s2. It is passive in that it maneuvers with no closed-loop actuation of orbital or attitude states. The unforced dynamics that result from an insertion orbit and a launch-vehicle separation determine its subsequent state evolution. We have developed a system architecture that uses solar radiation torques to maintain a sun-pointing heading and can be fabricated with standard microfabrication processes. This architecture has potential applications in heliocentric, geocentric, and three-body orbits.
A Passive Microscale Solar Sail
A type I Dyson sphere can be built gradually, without any supertechnology or supermaterials, just the long-term deployment of more solar collectors and habitats. This work could start today (and one might argue that our satellites are the first step). Using self-replicating machinery the asteroid belt and minor moons could be converted into habitats in a few years, while disassembly of larger planets would take 10-1000 times longer (depending on how much energy and violence was used).
The inner system contains enough usable material for a dyson sphere. If one assumes a 1 AU radius, there will be around 42 kg/m^2 of the sphere. This is probably far too little to build a massive type II dyson sphere, but probably enough to build a type I dyson sphere where mass is concentrated into habitats and most of the surface is solar sails and receivers, which can presumably be made quite thin.
With the extra material from the outer system, we get around 600 kg/m^2, which is enough for a quite heavy sphere (if it was all iron, it would be around 8 centimeters thick, and if it was all diamond around 20 centimeters).
Devon Crowe - Large Bubbles in Space
Large bubble structures in space could accelerate our ability to build large collectors for Dyson swarms.
Nasa Institute for Advanced Concepts in March 2007 meeting had Devon Crowe of PSI Corporation making large space structures from bubbles that are made rigid using metals or UV curing.
A single bubble can be 1 meter in earth gravity, 100 kilometer in low earth orbit or 1000 kilometers in deep space. Foams made of many bubbles could be far larger in size. The size of a 1000 kilometer bubble is nearly the size of Charon, the moon of Pluto. Charon is 1200 kilometers in diameter. Saturn's moon Tethys is 1050-1080 kilometers in diameter Ceres the largest object in the asteroid belt is 970 kilometers in diameter. A single tesselation foam (like in the picture) of 1000 kilometer bubbles would be about the size of Earth's moon. A Penrose tesselation like the one in the picture of 1000 kilometer bubbles would be in between the size of Neptune or Saturn. A Tesselation foam of 100 kilometer bubbles in earth orbit could form an object the size our existing moon or larger.
This page has a lot of imagined types of dyson swarms.
This page has applet animation of objects in a dyson swarm.
Kardavshev Two - Capturing 100% of the Solar Energy is 386 Yottawatts
1% of the solar energy is 3.86 Yottawatts or 3.86 X 10^24 watts
Using all of the deuterium in the Earth's Ocean would last a 1% of Kardashev Two civilization just over one year. Using all of the deuterium in the Gas giants (Jupiter, Saturn, Neptune and Uranus) would last a full Kardashev Two civilization 100,000 years.
10^12 W TW terawatt (The total power used by humans worldwide (about 16 TW in 2006) is commonly measured in this unit.)
10^15 W PW petawatt (the total energy flow of sunlight striking Earth's atmosphere is estimated at 174 PW)
Brett Bellmore Comment
Brett, a reader of this site, added a good comment and here it is. I would just mention that the shadowing problem could be mitigated with some level of energy efficient heliocentric orbit modification ability by the solar collectors. Also, up to a few percentage points of coverage (which is still trillions of times our current energy level) there is minimal shadowing problems.
The basic problem of the Dyson swarm is shadowing between the individual components. As you approach 100% coverage of the star, this becomes quite severe, meaning that you won't capture much of the star's energy, AND the individual units capturing the energy will be doing so in thermodynamically unfavorable circumstances, shadowed and exposed to the waste heat of other units.
The 'solid' sphere allows for 100% coverage, while providing better circumstances for thermodynamic efficiency, since both the absorbing and emitting surfaces are subject to steady state conditions, the spherical surface neither shadows itself on the inside, nor sees itself on the outside.
The classic problems of the 'solid' Dyson sphere are that, 1, it must be made of some absurdly strong material, 2, it is not self centering on the star, and 3, it is radically unstable while partially complete. All of these problems are a result of not analyzing the sphere as a real engineering proposal.
Problem 1 is solved by building the sphere as a dynamic structure: The absorbing and emitting surfaces would be stationary with respect to the star, but magnetically coupled to rotating bands of material traveling at well above orbital velocity. The greater this excess, the less of the structure has to be devoted to it, of course. This allows the structure to be self-supporting with all forces locally neutralized, it does not require materials stronger than we currently have access to. Elements not suited to structural purposes could be used as ballast in the support rings.
Problem 2 is almost trivially solved by the use of stabilizing algorithms, rather than reliance on natural stability. It does require some fraction of the weight and energy budget to be devoted to station keeping, but this could be very small, assuming the sphere were kept close to where it was supposed to be.
Problem 3; You don't build half a Dyson sphere. You build a band around the star, in a natural orbit. You then bring the bulk of it to a halt, while accelerating it's support ring to full speed. Build another such band, at an angle, repeat, attach to the first. The sphere can be assembled gradually as material is mined, and is stable at all stages in it's construction. The first ring requires no more material than would be found in a moderate sized asteroid.
Finally, you don't live on the Dyson sphere, this is inefficient. You beam the power to habitats distant from the enclosed star, where the background temperatures allow you to utilize the beamed energy with much higher efficiency. Dyson spheres are power sources for clouds of habitats in the cometary zone, not places where people will live.
A real-world Dyson sphere would not be some massive affair with people standing on it's inner surface, looking up at the sun. It would be a fairly thin structure devoted only to energy capture and transmission, probably amounting only to grams per square meter. It would be so light that a significant fraction of it's support might come from the star's radiation pressure. (Actually, the radiation pressure of the light reflecting about inside the sphere; The radiation pressure from the star's *net* emission would have to cancel out with that of the waste heat and transmitted power, or the sphere would continually rise in temperature.)