Natural planets capture a minute fraction of the life-giving energy of their stars. Earth’s cross-sectional area facing the Sun is 0.45 billionths of the total area at its orbital distance. What can be done to reduce the wastage? Freeman Dyson originally proposed civilized beings might build an immense spherical cloud of habitats to maximize the sunlight captured. Some presentations of his idea, perhaps incorrectly, represented him as proposing a solid shell surrounding the Sun.
Given nuclear strength materials a civilization can make such immense structures, immensely bigger than planets in area – Dyson Spheres, Niven Ringworlds, Alderson Disks and Banks Orbitals, all of which more efficiently capture the energy of the central star. I’ll discuss them all in turn, but let’s look at the Niven Ringworld, so named because Larry Niven’s novel “Ringworld” (1970) first presented the concept to a wide audience in fictional form.
The basic idea is that a continuous ring around a star is rotated to provide centrifugal gravity on its inside face. The speed of the Ringworld’s spinning has to be incredibly high – a Ringworld at Earth-like insolation from a Sun-like star would be spinning at 1,438 km/s to produce Earth-like gravity. Niven uses that to good effect in his tale, but the engineering practicalities boggle the mind.
First let’s look at the strength required. Assuming the outward centrifugal force on each unit area of the Ringworld is what is stressing the structure, we can compute the Hoop Stress, s, as…
s = P.r/t
…where P is the outward pressure, r the hoop radius and t the thickness of the material. The radius is somewhat larger than Earth’s orbital radius – a Ringworld experiences day/night cycles via “Shadow Squares” which shade the ring, but orbit closer in, thus allowing 24 hour night/dark cycles. This means the heat experienced is somewhat more, on average, so there needs to be an adjustment to compensate. I estimate a distance of about 1.4 AU is optimal, thus r = 2.11E+11 metres.
A method proposed to supply the mass needed, and extend the life of the Sun, is called “Star-lifting” which would provide 1E+30 kilograms of mass to play with. Thus a Ringworld 2.11E+11 metres in radius and 1E+9 metres ribbon-width would have an areal density of ~7.5E+8 kilograms/kg^2 and experience an outward pressure of about 7.4E+9 N. That means the Ringworld material needs to be strong enough to withstand a P.r stress of 1.56E+21 per metre of its thickness. Alexander Bolonkin estimates the strength of nuclear matter to be roughly ~1.6E+32 N/m^2, thus a thickness of 2E-11 metres is enough to provide the x2 safety factor for the mass loading implied above. The Ring will definitely be strong enough. In fact it can probably be made with significantly less nuclear strength material.
If we want 100 metre thicknesses of water or soil (50/50 split in area) then the total outward pressure of that would be about ~1.96E+6 N/m^2 and would require ~4.14E+17 N/m of stress to be supported by the nuclear matter. But we have to factor in the mass of the nuclear matter as well. After a bit of algebra we can compute the nuclear matter layer is just ~5 femtometres thick, with an areal density of ~2,500 kg/m^2 (assuming density of 5E+17 kg/m^3.) Thus the total mass of the Ringworld is just 2.6E+26 kg – about twice the mass of Neptune. A lot less than the half-a-Sun we had to play with.
How much energy is required to boost it up to speed? Lots. Roughly 23,000 years worth of the Sun’s output, which is a truly immense amount. But if we use rockets to do the job, powered by fusion, then we need only about 10% of the mass of the Ring (Vex ~0.05 c.) That’s surprisingly not a big burden on a project of this scale and relatively reasonable. Of course a mass of rockets boosting such a Ring up to speed would produce a brilliant display of energy that should be visible as a massive X-ray flare… which makes one wonder just how many Red-dwarf “flare-stars” are really undergoing massive natural flares and not fine-tuning bursts from their Ringworld motors?