Jupiter has a gravity of 2.506 g. A supermundane sphere around Jupiter would be pretty heavy if at 1 Jupiter radius and supported by Jupiter's atmosphere. To get it down to 1g, we'd have to increase the radius to 1.583 times what it is now, without increasing its mass. I have just thought of another way to do this. What if we built a number of fusion reactors into the supermundane shell, and used it to heat Jupiter itself. If we could heat Jupiter enough, then just like a balloon, it would expand to 1.583 its normal size, we would also have to make Jupiter hot enough to build enough pressure to support the shell.
In the mantle, temperatures range between 500 to 900 °C (932 to 1,652 °F) at the upper boundary with the crust; to over 4,000 °C (7,230 °F) at the boundary with the core.
What if we heated Jupiter so that the level that is at sea level pressure is at 500 to 900 °C? Basically by turning Jupiter into an artificial sun, using Fusion reactors to replace the core of the sun as a heating element. we can then exploit the temperature difference between the atmosphere underneath the shell and that above it to generate the energy to provide artificial illumination for the outside as this diagram shows:
Alternatively, We could place a G2 V star in orbit around the black hole and shell at a radius of 176,000,000 km which would place star at 1 AU from the surface of the shell. Thus we would have a Geocentric Star System. A solar mass G2 V star would take 65.2559 days to orbit around this black hole and shell. I suppose we could make the shell rotate in the opposite direction. if the sphere rotates in the opposite direction once every 180 hours the surface gravity experienced would be 0.750734 g at the equator and around 1 g at the poles.
]]>Antius, that would only be the case (retaining an atmosphere) if the black hole is an appreciable fraction of the mass of Terra. If it's the mass of Luna, then it will have the same escape velocity (for the same distance from the centre). If you made it the mass of Ceres, whilst you'd have a (small) world with a 1g surface, the escape velocity only a few hundred kilometres from the surface would be too low to hold on to an atmosphere.
Of course, given that you have copious amounts of energy and a very high tech level, it would be trivial to hold it in with foglets, or plasma windows, or by ionising it and forcing it back down...
The quantities of interest are the kinetic energy needed for escape at the precise point of departure of the molecules, the energy distribution of the molecules at that height and their density. That would allow calculation of leak rate.
The required kinetic energy for escape would be equal to the integral of force w.r.t distance from the centre. You are correct that there are limitations to the minimum size of such a world, as the steep gradient of the gravity field would limit the local escape velocity. It is not immiediately clear what the limiting parameters would be. One of us could work it out I guess...
]]>Of course, given that you have copious amounts of energy and a very high tech level, it would be trivial to hold it in with foglets, or plasma windows, or by ionising it and forcing it back down...
]]>At a certain point, construct a spherical compressive shell around it. The surface of the shell would have 1g gravity levels, sufficient to hold an atmosphere. That way you can build a planet using very little valuable metal and silicate materials. Most of the mass can be extracted from the outer planets. Just don't fall through any gaps in the shell - it would be a short drop and a sudden stop.
]]>Excuse me and thank you - you're absolutely right ... it is Birch Supra-habitat in the way it provides it's surface gravity and it is Dyson sphere the way it collects all the underbody's radiation!
]]>Just for the record.:
The described "dyson sphere" around a white dwarf is NOT dyson sphere but
PAUL BIRCH's SUPRAMUNDANE HABITAT,
using a white dwarf as an underbody.
The material of these Turkish guys clearly states that it shall be inhabited on the outside.
The authors noticed that the 1G surface coincides with the 1 Sol surface around a big class of white dwarfs.
Paul Birch Archive: http://www.orionsarm.com/fm_store/Paul% … 20Page.htm , enjoy.
Well actually its both, while the habitat is clearly on the outside, it also collects the excess energy from the white dwarf.
You see this diagram? Light radiates outward from the white dwarf, most of it hits the underside of the Sphere, which is both a Supramundane habitat and a Dyson Sphere. You see the window in this diagram lets light through and a convex parabolic mirror suspended above the window then reflects spreads the light back towards the Surface. For a white dwarf such as Sirius b, the habitable zone coincides with the 0.22 g sphere, this is almost 8 million km in diameter. A normal supermundane sphere around a planet doesn't collect much energy, because a planet doesn't radiate much. Sirius b is however self luminescent, and at any rate it is too far away from Sirius a to receive enough light from that star, so most of the light it needs comes from Sirius b inside the shell. There are shutters in the windows that when shut turn day into night. Probably their are lenses inside the shell to concentrate light to fit through the window, the window itself is a lens which defocuses the light to make the rays roughly parallel, and the convex mirror above then reflects and spreads that light back upon the outer surface. When the shutters are closed, the light gets reflected back towards the stars or absorbed by the inner surface of the shell. I think there needs to be some radiating surfaces on the outside of the shell so some of the energy can be converted to electricity. There would be a lot of surfaces rising above the atmosphere to radiate the excess heat into space. A 0.22 g environment would be interesting, but to make something more suitable for humans, one would have to reduce the radius of the sphere. Lets call the gravity 1/5th of Earth's gravity to simplify the math, we don't know the exact mass of Sirius b anyway, I've seen some estimates that it is just above the mass of Sol to just below it. Lets use 8 million as the radius of the sphere at 1/5th Earth's gravity. So we need 5 times that gravity, the square root of 5 is 2.2360679774997896964091736687313, divide 8 million km by this number to get 3.577,709 million km as the new radius, but as we quintuple the gravity, we also quintuple the radiation received by the undersurface of the sphere, we need larger radiators to dump all that excess heat into space, while at the same time we shield the environment on top of the sphere from all that excess heat. So lets say the average surface temperature is supposed to be 15 C this is 288.15 K, 5 times that temperature is 1440.75 K which converts to 1167.6 C. Fortunately the melting point of steel is 1371 degrees C. the steel heat shield would need to be cooled by a circulating fluid, which is then pumped up through some very tall radiator fins. Walls would have to surround the fins as they rise into space to shield the habitat from radiated excess heat such that most of it goes into space. Of course the whole framework or magnetically suspended rings would also have to be shielded as well as the superconductors.
Actually, light that is reflected is not absorbed, thus saving the problem of radiating the heat. Reflecting the light through the windows and around the edges of the mirror and into space.
The described "dyson sphere" around a white dwarf is NOT dyson sphere but
PAUL BIRCH's SUPRAMUNDANE HABITAT,
using a white dwarf as an underbody.
The material of these Turkish guys clearly states that it shall be inhabited on the outside.
The authors noticed that the 1G surface coincides with the 1 Sol surface around a big class of white dwarfs.
Paul Birch Archive: http://www.orionsarm.com/fm_store/Paul% … 20Page.htm , enjoy.
]]>If a society goes to that extent, would they dismantle all planets? Replace them with O'Neill colonies, Bernal spheres, Stanford torus, etc? That would provide access to all metals in planetary cores.
]]>Scientists have never given up on Dyson spheres—we've even conducted a few legitimate searches for their infrared heat signatures. Now, physicists Ibrahim Semiz and Salim Ogur may have an explanation for why we can't seem to find the megastructures. If Dyson spheres exist, they're probably a lot smaller than we thought.
Since Dyson first proposed his massive space habitats, scientists have tried to imagine how such structures could physically work. By and large, researchers have focused on Dyson spheres encircling Sun-like stars. But this scenario poses a few major, and perhaps insurmountable, problems. For starters, such a sphere would have to be built at a distance of roughly 1 AU, the same distance between the Earth and the Sun. That means the structure would be utterly massive, requiring huge volumes of material to construct. What's more, the surface of the sphere would experience only minuscule levels of gravity. To live on it, humans would either need substantial genetic modification, or some sort of advanced artificial gravity system, the likes of which we haven't been able to piece together, even theoretically.
From "Relics," the Star Trek episode that introduced millions to Dyson spheres.
A white dwarf star—the dimmer stellar remnant left over after a Sun-like star swells up and explodes—might be a better option for Dyson spheres. A white dwarf's habitable zone is much closer, so the sphere would end up being significantly smaller. The researchers calculate that a one meter-thick sphere built in the habitable zone of a white dwarf would require 10^23 kilograms of matter, slightly less than the mass of our moon. A Dyson sphere encircling a white dwarf would also have almost Earth-like gravity, according to the researchers' calculations.
There's just one catch: Because white dwarfs are less luminous than Sun-like stars, the infrared heat signatures emitted by a white dwarf Dyson sphere would be much smaller and harder to detect. If intelligent aliens are out there, it may be a while yet before our scopes are powerful enough that we're able spot them from Earth. [arXiv via MIT Technology Review]
Top image via Slawek Wojtowicz
A small footnote: The researchers estimate that a Dyson sphere surrounding a white dwarf would be roughly 10 ^6 kilometers in radius. As pointed out by an astute commentator, this puts the newly proposed Dyson sphere within an order of magnitude of the one featured in Star Trek: The Next Generation. It may be new to science, but it seems Star Trek figured this all out loooong ago.
Contact the author at maddie.stone@gizmodo.com or follow her on Twitter.
As an exercise, how big would the Dyson sphere around this star be, and what would be its surface gravity?
Sirius B
With a mass nearly equal to the Sun's, Sirius B is one of the more massive white dwarfs known (0.98 M☉[102]); it is almost double the 0.5–0.6 M☉ average. Yet that same mass is packed into a volume roughly equal to the Earth's.[102] The current surface temperature is 25,200 K.[7] However, because there is no internal heat source, Sirius B will steadily cool as the remaining heat is radiated into space over a period of more than two billion years.[103]
A white dwarf forms only after the star has evolved from the main sequence and then passed through a red-giant stage. This occurred when Sirius B was less than half its current age, around 120 million years ago. The original star had an estimated 5 M☉[7] and was a B-type star (roughly B4–5)[104][105] when it still was on the main sequence. While it passed through the red giant stage, Sirius B may have enriched the metallicity of its companion.
This star is primarily composed of a carbon–oxygen mixture that was generated by helium fusion in the progenitor star.[7] This is overlaid by an envelope of lighter elements, with the materials segregated by mass because of the high surface gravity.[106] Hence the outer atmosphere of Sirius B is now almost pure hydrogen—the element with the lowest mass—and no other elements are seen in its spectrum.[107]
Here is a larger version of this image.
http://imageshack.com/a/img822/6954/9o4s9.jpg
This is the scaffolding under the surface of the Dyson Sphere, as you can see it consists of a number of overlapping rings, inside are the centrifuges that hold the Dyson Sphere up against the White Dwarf's gravity. In order for this to work centrifugal force needs to balance out the attactive force of gravity on the Dyson Shell above this superstructure.