The planet Mercury is a pretty good source of material:
Mass: 3.29×1023 kg (which is about 70% iron)
Radius: 2.44×106 m
Volume: 6.08×1019 m^3
Density: 5411 kg/m^3
Orbital radius: 0.39AU=5.79×1010 m
A spherical shell around the sun at roughly same radius as Mercury’s orbit would have a surface area of 4.21×1022 m^2, and spreading out Mercury’s volume over this area gives a thickness of about 1.4 mm. This means Mercury alone provides ample material for collecting all of the Sun’s energy via reflecting light – very thin spinning sheets could act as a swarm of orbiting reflectors that focus sunlight onto large power plants or mirrors that direct it to elsewhere in the solar system. Spinning sheets could be made somewhere between 1-100 μm thick, with thicker cables or supports for additional strength, perhaps 1-10 km wide, and navigate using radiation pressure (using cables that bend the sheet, perhaps). Something like 1015 or 1016 mirrors would be enough to intercept and redirect all of the sun’s light.
The gravitational binding energy of Mercury is on the order of 1030 J, or on the order of an hour of the Sun’s output. This means in theory the time it takes for a new mirror to pay it’s own manufacturing energy cost is in principle quite small; if each kg of material from Mercury is enough to make on the order of 1-100 square meters of mirror, then it will pay for itself in somewhere between minutes and hours (there are roughly 10,000 w/m^2 of solar energy at Mercury’s orbit, and each kg of material on average requires on the order of 107 J to remove). Only 40-80 doublings are required to consume the whole planet depending on how thick the mirrors are and how much material is used to start the process. Even with many orders of magnitude of overhead to account for inefficiency and heat dissipation, I believe Mercury could be disassembled to cover the entire sun with reflectors on the order of years and perhaps as quickly as months; certainly within decades.
The planet Mercury is a pretty good source of material:
Mass: 3.29×1023 kg (which is about 70% iron)
Radius: 2.44×106 m
Volume: 6.08×1019 m^3
Density: 5411 kg/m^3
Orbital radius: 0.39AU=5.79×1010 m
A spherical shell around the sun at roughly same radius as Mercury’s orbit would have a surface area of 4.21×1022 m^2, and spreading out Mercury’s volume over this area gives a thickness of about 1.4 mm. This means Mercury alone provides ample material for collecting all of the Sun’s energy via reflecting light – very thin spinning sheets could act as a swarm of orbiting reflectors that focus sunlight onto large power plants or mirrors that direct it to elsewhere in the solar system. Spinning sheets could be made somewhere between 1-100 μm thick, with thicker cables or supports for additional strength, perhaps 1-10 km wide, and navigate using radiation pressure (using cables that bend the sheet, perhaps). Something like 1015 or 1016 mirrors would be enough to intercept and redirect all of the sun’s light.
The gravitational binding energy of Mercury is on the order of 1030 J, or on the order of an hour of the Sun’s output. This means in theory the time it takes for a new mirror to pay it’s own manufacturing energy cost is in principle quite small; if each kg of material from Mercury is enough to make on the order of 1-100 square meters of mirror, then it will pay for itself in somewhere between minutes and hours (there are roughly 10,000 w/m^2 of solar energy at Mercury’s orbit, and each kg of material on average requires on the order of 107 J to remove). Only 40-80 doublings are required to consume the whole planet depending on how thick the mirrors are and how much material is used to start the process. Even with many orders of magnitude of overhead to account for inefficiency and heat dissipation, I believe Mercury could be disassembled to cover the entire sun with reflectors on the order of years and perhaps as quickly as months; certainly within decades.