A Dyson Sphere is a massive solar power collector that entirely encloses. I used the concept in my series Alien Civilizations as a means to capture all the outpouring energy from all the stars in the universe.
The concept I used is likely the most feasible: a swarm of independently orbiting collectors, each with its own orbit, all controlled by computer system to keep them from crashing into each other. This doesn’t require any undiscovered materials or technology, and we could probably begin building such a structure today. The only problem is the sheer amount of mass that would have to be transformed and transported, required enormous space-based infrastructure and manufacturing capabilities.
But there’s another design that is far less feasible, but more interesting: a single solid shell, 2 AU in diameter, used as a huge space habitat. This has a number of problems, not the least of which is that it is unstable.
Newton’s Shell Theorem states that in any hollow uniform sphere, the net gravitational force in any location is zero. Simply put, if you were inside a hollow sphere, you would not “fall” in any particular direction due to gravity. At all points, the gravitational force from all parts of sphere cancel each other out. The problem is: how you keep such a thing centered on the Sun?
One obvious answer is attitude thrusters, but that seems a bit drastic, and energy intensive. My idea is, well, what if it isn’t a uniform sphere? What if we specifically constructed the Dyson Sphere so that it was more massive on one side? Could we set up some sort of psuedo-orbital situation from that?
Second is how you go about constructing it. Half a sphere is also very unstable, but is an inevitable stage in construction. Or it is? Instead, what if we were to first build the equator-region in inertial orbit? What if we start by building a giant ring that it orbiting the Sun? Then, we start building towards the poles, keeping the center of mass within the equatorial plane at all times?
Last is the fact that the Dyson Sphere will heat up. Now because the Dyson Sphere is so huge, it actually won’t get as hot as the Sun. In fact, we can calculate where, at thermal equilibrium, the Dyson Sphere will be a comfortable 72 degrees F. In order for it to be that way, a Dyson Sphere should be around 265 million km in radius, or about 1.77 AUs. This is quite a bit larger than the orbit of Earth, but that it because all parts of the Sphere are in full daylight constantly, whereas half the Earth is always in shadow. Also, the spherical shape of the Earth spreads out the incoming heat from the Sun onto a larger area (specifically twice as large).
Of course, the main challenge is finding a material that could withstand such enormous structural stresses, and finding enough matter to actually build it. For those, I have no idea. The amount of usable material in the solar system is probably not enough.
Well, but if we do overcome those obstacles, maybe we could build one. It would certainly be a sight to see. Or not. Considering the sphere would completely cover the Sun, it would only appear as a giant black disk from outside. How boring.