According to some rough calculations I just did, the sun is actually capable of supporting a biosphere contained in a Dyson Sphere equivalent to 8,861,225,912 earths comfortably for several billion years.
That represents a human population of 6.2*10^19 human beings, plus all the plant and animal life to have a stable biosphere, and with a living standard far greater than our own here on earth today.
These numbers were obtained by finding the surface area of a sphere with radius 1 astronomical unit in kilometers. Then I divided by the surface area of the earth's disk(a circle, because this represents the percentage of the sun's light we recieve.)
This gave the number of "earths" the sun can support. Since the disk is equal to 1/4 of the earth's actual surface area, this just means the dyson spere can be constructed "thick enough," perhaps a couple kilometers thick, to support human population and the biosphere of an entire planet on 1/4 the surface area. Imagine America stacked on top of itself several times. Or essentially just a solid sphere of arcology.
After I had found the 8861225912 earths number, I then assumed a population of 7 billion for earth.
With the degree of forward planning I would suggest, things are planned so perfectly that there is almost never energy waste in any fashion whatsoever. The Sphere is designed with the maximum human population in mind from the beginning, and is done modularly anyway, so that if there is any oversight, it can simply be worked around (build from the inside out, for example.)
This means constructing transport mechanisms to handle future loads. Since all of the energy comes from the sun's radiation and ejecta (plus possibly fusion and/or anti-matter annihilation of those materials collected from this radiation and ejecta,) transportation of materials is primarily for the basis of supporting life, maintaining the dyson sphere, and maintaining the transport mechanisms.
Long before the Dyson Sphere is actually completed, 99.99% of all manual labor and materials transport will be done by specialized autonomous robots (non-self aware) and ROVs, as well as other transport mechanisms I have previously described in other posts.
The materials for construction of this come primarily from the asteriods, planets, dwarf planets, moons, and comets in the solar system. Once a framework of 3 interlocking Dyson Rings is constructed, these can be used to collect materials from the Sun which are then used to fill in the intervening spaces, working from the inner layers outward.
Of course, we would still want to expand to other stars relatively quickly to minimize the chance of death to civilization through catastrophism. By the time a Dyson Sphere (or the closest possible thing, such as Dyson Swarm;) by the time its actually completed, humans would already have populations on several other star-systems, and possibly even be starting several other Dyson Megastructures.
G'day Quantum
Nice thinking mate
"What will they think of next"
Nice thinking mate
"What will they think of next"
Just build a Death Star i say 
On a serious note, very interesting.
On a serious note, very interesting.
This post is to deal with a mistake made by Dr. Michio Kaku in this video.
http://www.youtube.com/watch?v=QI6vANpHhOA&feature=related
Here, the Dr. is attempting to explain the concept f the Kardashev scale of civilizations, but he explaination actually falls quite short.
When he gets to the Type 2 civilization:
He describes the Star Trek's Federation as being Type 2, but this is simply not the case. The Federation only inhabits a few hundred planets, and does not have Dyson Mega-structures on any of those planets. Thus the Federation only uses a few hundreds Earths worth of total energy output. As stated above, a true Type 2 Civilization has the population and energy equivalent of over 8.8 billion earths. That is almost 10 orders of magnitude larger than a type 1.00 civilization. The Federation is at most 2.5 orders of magnitude larger than a Type 1.0 civilization. Thus the Federation is BARELY more than a Type 1 civilization, and certainly far closer to Type 1.0 than they are to type 2.0.
When he gets to type 3 civilization, he makes a similar mistake in claiming that the Galactic Empire is a type 3 civilization.
I will show that this is clearly a mistake. As it turns out, the Galactic Empire may not even have the energy equivalent of even one true Type 2.0 civilization.
The definition of a true Type 3 civilization basicly requires a Dyson Sphere constructed around every object in the host galaxy, or enough equivalent number of Dyson Rings and Swarms in enough galaxies to equal that equivalent amount of energy. Check the wiki article on the Kardashev scale. Though it is not directly stated that way, this is the only reasonable way of obtaining Type 3 status.
The Galactic Empire is composed of mostly a hodge-podge of planetary civilizations that, individually, almost none of them are even anywhere near being Type 1.0 civilizations. The Death Stars 1 and 2 are the largest artificial structures constructed in the history of the galaxy, this can be shown from Han, Luke, and Obi Wan's reactions when they first see the Death Star 1 in Episode 4. At first, they cannot believe it and think it is a "small moon". Then Obi Wan suggests it is a battle station, and Han Still can't believe it at first.
In all of the episodes of the movies, we never see even one Dyson Megastructure, and as stated, the closest things we see in any of the movies are the planet Coruscant and the Death Stars. We see stars everywhere in the background in all of the movies, indicating nobody has Dyson Spheres on any of the stars. Additionaly, There are few, if any, such megastructures in any of the expanded universe either.
The Galactic Empire only consists of "habitable planets" orbiting "some star systems" in the galaxy. The only two planets we saw in any of the movies that were Type 1 civilizations in their own right were Alderaan and Coruscant, and I'm not even convinced on Alderaan.
Most of the planets and moons we saw in the movies had sentient populations of less than 1 million beings, and almost all of them had sentient populations of less than 1 billion, again, the only exceptions being Alderaan and Coruscant. Even in the expanded universe, almost none of the planets have Billionaire populations.
Even if the Galactic Empire had a Type 1 equivalent member civilization on every star in the Galaxy, and if the "galaxy" is an average one, then that only represents a maximum energy equivalent of about 400-600 million Type 1 civilizations. Well, as I showed above, a True type 2 civilization in a Dyson Sphere on a main sequence star is the energy equivalent of over 8.8 billion Type 1 civilizations, which is in and of itself more than an entire order of magnitude larger than the maximum energy equivalent of the Galactic Empire.
Therefore, the Galactic Empire of Star Wars is actually ONLY at most, a Type ~1.9x Civilization, and is not even remotely close to being a true Type 3 Civilization.
http://www.youtube.com/watch?v=QI6vANpHhOA&feature=related
Here, the Dr. is attempting to explain the concept f the Kardashev scale of civilizations, but he explaination actually falls quite short.
When he gets to the Type 2 civilization:
He describes the Star Trek's Federation as being Type 2, but this is simply not the case. The Federation only inhabits a few hundred planets, and does not have Dyson Mega-structures on any of those planets. Thus the Federation only uses a few hundreds Earths worth of total energy output. As stated above, a true Type 2 Civilization has the population and energy equivalent of over 8.8 billion earths. That is almost 10 orders of magnitude larger than a type 1.00 civilization. The Federation is at most 2.5 orders of magnitude larger than a Type 1.0 civilization. Thus the Federation is BARELY more than a Type 1 civilization, and certainly far closer to Type 1.0 than they are to type 2.0.
When he gets to type 3 civilization, he makes a similar mistake in claiming that the Galactic Empire is a type 3 civilization.
I will show that this is clearly a mistake. As it turns out, the Galactic Empire may not even have the energy equivalent of even one true Type 2.0 civilization.
The definition of a true Type 3 civilization basicly requires a Dyson Sphere constructed around every object in the host galaxy, or enough equivalent number of Dyson Rings and Swarms in enough galaxies to equal that equivalent amount of energy. Check the wiki article on the Kardashev scale. Though it is not directly stated that way, this is the only reasonable way of obtaining Type 3 status.
The Galactic Empire is composed of mostly a hodge-podge of planetary civilizations that, individually, almost none of them are even anywhere near being Type 1.0 civilizations. The Death Stars 1 and 2 are the largest artificial structures constructed in the history of the galaxy, this can be shown from Han, Luke, and Obi Wan's reactions when they first see the Death Star 1 in Episode 4. At first, they cannot believe it and think it is a "small moon". Then Obi Wan suggests it is a battle station, and Han Still can't believe it at first.
In all of the episodes of the movies, we never see even one Dyson Megastructure, and as stated, the closest things we see in any of the movies are the planet Coruscant and the Death Stars. We see stars everywhere in the background in all of the movies, indicating nobody has Dyson Spheres on any of the stars. Additionaly, There are few, if any, such megastructures in any of the expanded universe either.
The Galactic Empire only consists of "habitable planets" orbiting "some star systems" in the galaxy. The only two planets we saw in any of the movies that were Type 1 civilizations in their own right were Alderaan and Coruscant, and I'm not even convinced on Alderaan.
Most of the planets and moons we saw in the movies had sentient populations of less than 1 million beings, and almost all of them had sentient populations of less than 1 billion, again, the only exceptions being Alderaan and Coruscant. Even in the expanded universe, almost none of the planets have Billionaire populations.
Even if the Galactic Empire had a Type 1 equivalent member civilization on every star in the Galaxy, and if the "galaxy" is an average one, then that only represents a maximum energy equivalent of about 400-600 million Type 1 civilizations. Well, as I showed above, a True type 2 civilization in a Dyson Sphere on a main sequence star is the energy equivalent of over 8.8 billion Type 1 civilizations, which is in and of itself more than an entire order of magnitude larger than the maximum energy equivalent of the Galactic Empire.
Therefore, the Galactic Empire of Star Wars is actually ONLY at most, a Type ~1.9x Civilization, and is not even remotely close to being a true Type 3 Civilization.
Let us consider the figure of 8,861,225,912 earth populations per Dyson Sphere.
This number looks like a giant number, because it is. However, if we consider a human population growth rate of only 1.2 percent per decade, then a Type 1 human Civilization transitioning to a type 2 human civilization and maintaining this average growth rate, would exceed that number in "only" 19, 210 years.
That isn't very long at all in the greater scheme of things.
During that time, humans could easily send out hundreds of world ships to colonize stars up to about 2,000 to 4,000 light years distant even at speeds ranging in the quite manageable 0.1c to 0.2c.
Even at 0.2c, every star in the galaxy could have a Dyson Swarm consisting of at least one World Ship within another 600,000 years. Stars in the galaxy only average a light years to a few dozen lightyears distance from their closest neighbour in any given direction, so moving from one star to a close neighbour is relatively easy for a civilization that is on the high end of 1.x or low end of 2.x.
===
So literally, in order to become a True Type 3 civilization would basically be obtained within about 620,000years, and this limit only exists because of the distances involved. If "near light speed" travel became practical (anti-matter pulse engines or something similar,) This number is cut to about 1/4 the time.
If you had 0.8c travel with anti-matter pulse engines, then all stars in the Milky Way could have fully populated Dyson Spheres as soon as 170,000 years. This represents about 150,000 years travel time to most distant star, and then another 20,000 years for colonists to make and populate the Dyson Sphere there.
To facilitate communicate between all of these Dyson Spheres, interstellar relays are used.
This number looks like a giant number, because it is. However, if we consider a human population growth rate of only 1.2 percent per decade, then a Type 1 human Civilization transitioning to a type 2 human civilization and maintaining this average growth rate, would exceed that number in "only" 19, 210 years.
That isn't very long at all in the greater scheme of things.
During that time, humans could easily send out hundreds of world ships to colonize stars up to about 2,000 to 4,000 light years distant even at speeds ranging in the quite manageable 0.1c to 0.2c.
Even at 0.2c, every star in the galaxy could have a Dyson Swarm consisting of at least one World Ship within another 600,000 years. Stars in the galaxy only average a light years to a few dozen lightyears distance from their closest neighbour in any given direction, so moving from one star to a close neighbour is relatively easy for a civilization that is on the high end of 1.x or low end of 2.x.
===
So literally, in order to become a True Type 3 civilization would basically be obtained within about 620,000years, and this limit only exists because of the distances involved. If "near light speed" travel became practical (anti-matter pulse engines or something similar,) This number is cut to about 1/4 the time.
If you had 0.8c travel with anti-matter pulse engines, then all stars in the Milky Way could have fully populated Dyson Spheres as soon as 170,000 years. This represents about 150,000 years travel time to most distant star, and then another 20,000 years for colonists to make and populate the Dyson Sphere there.
To facilitate communicate between all of these Dyson Spheres, interstellar relays are used.