Dyson Statite!
Welcome to lets build a dyson sphere! In this episode we'll be using solar sails and counterweights.
As usual we build at 1AU away from the sun.
The counterweight masses 1000 metric tons. Newton's law of gravitation tells me that it will fall toward the star at 0.006m/s/s (6000N of force toward the star)[1]. Wikipedia tells me that a sail would require 700kg/N [2] so to get those 6000N requires 4.2million kg sail. Also from wikipedia I find that the material weighs 7g/m^2 and thus the sail has an area of 600million square meters.
A sphere with a radius of 1AU has an area of 2.8e23 square meters [3]. There is room for 460 trillion segments. In practice not all of these can be put in place because of the danger that they might interfere with each other or crash. Let's assume 300 trillion can be put in place.
Each segment has a mass of 5200 metric tons. The whole dyson masses 1.56e18 metric tons.
1-http://www.wolframalpha.com/input/?i=gravitation+constant+%28%282e30kg*1e6kg%29%2F%281.5e11m%29^2%29
2-http://en.wikipedia.org/wiki/Magnetic_sail
3-http://www.wolframalpha.com/input/?i=sphere+with+150000000000m+radius
Now here's my problem: I've always had the impression that to burealistic dyson swarms says that you would need to disassemble multiple planets to make it work. However this let's me block about 65% of the star's light and requires less than the mass of the moon to build.
Are my assumptions or math wrong somewhere?