Prove: Earth has enough materiel to create a dyson sphere.
Let the radius of the sphere be 8000 million km. That's 8*10^3*10^6^10^3 m, or 8*10^12 m.
Let the thickness of the dyson sphere be 1 km.
Volume of the dyson sphere: ((8*10^12m)^3 - (8*10^12m + 1)^3)*4/3pi. Or, 2*10^20 m^3 * 4/3pi. Yes that's an approximation, and it's rounded up.
The earth is 6.3*10^3km thick, or 6.3*10^3*10^3m thick, or 6.3*10^6m in radius. The volume of the earth, then, is 2.16*10^20 m^3 * 4/3 pi.
(more really, I rounded down to 6.)
Now that's assuming a dyson sphere that's uniformly thick. My room growing up was 10ft^3 and the walls were about .5ft thick. Probably less but shhhh we're going for easy math. That's a ratio to (much, much less than) (10.5ft^3)/(10ft^3) or about 16% of the volume being taken up by materiels. So the real volume of required material for the dyson sphere is less than 10% of the earth's volume.
Energy to get the @#(! to the point in space:
Thank god for basic newtonian mechanics, eh? P = GH, and H = well, we'll call it the average. Because the amount of material being moved is proportionate to the cubed distance it travels, the average is somwhere lower than what we need, which is an overestimate (sorry, drunk, and therefore disinterested in going too deep on this). Let's assume that all the material needs to be moved up to H where H = 8000 million km. Or 8*10^12m. We can also assume that the average position of Earth is 0. If you need me to walk through the logic of the Earth's average position being where the sun is, then shut the $#@! up and kiss my pissflaps.
(if we were clever monkeys, like we seem to think we are, it'd actually be possible to make the delta H in this equation simply equal to the difference of 8000 million km and the earth's orbit, but I like it this way because it's easier on me)
(yes I know Earth's orbit is elliptical, but if you haven't figured out the game of my overestimate-underestimate here, you should consider jumping in a lake)
(well I mean if you're not jumping in a lake right now I don't know what you're doing with your life but it must suck because swimming is one of life's joys. But I meant drowning earlier.)
Anyways the equation gets a little complicated here, but nothing we can't deal with thanks to Sir Isaac Newton. Basically what we need is the sum of the amount of energy needed to move the mass from H = 0 to H = 8000 million km. I don't have a numpad on this so sorry.
The integral of: m * G * H with respect to H, except that G is actually F/m. Which means that it's the integral of F*m*H/m, or FH from 0-8000 million km. F = G (m1)(m2)/(h^2) so our actual equation ends up being the integral from 0-8000m km of G(m1)(m2)(h)/(h^2)dh. This means we need the mass of the materials we're moving. Basically I'm going to argue that the mass is close to 1. Steel, etc, has a mass of 8 or so (in the units we're using), but most people talk about carbon nanotubes and carbon has a density of about .93. Being the nice person I am, let's move our assumed density to 10 because we're an idiot and trying to build our dyson sphere out of more dense steel.
Oh fun fact, there's a helluvalot of constants here, so our integral is really G(m1)(m2) * integral from 0-8000 million km of 1/h dh. Long story short, this is insolvable as written. Oddly, it's NOT insolvable if we just assume it's from 1 m to 8000 million km. Incidentally, this introduces almost 0 error. (ln of 0 is undefined, ln of 1 is 0). So let's move that to 1m - 8000 million km. Virtually no error but we also don't have to deal with some serious bull@#(!. So now we have g(m1)(m2)*ln(8*10^18), or g(m1)(m2)*44. m1 is, according to our guestimation, 2*10^20 m^3 * 4/3 * 1000 kg/m^3 * pi. Or, 2*10^23 * 4/3 * pi. m2 is 2*10^30. Yes, the sun is big. Really big. I mean like, ginormously insanely colossally big. It's pretty much six orders of magnitude larger than our 1km thick dyson sphere that's been carefully constructed outside of Pluto's orbit... at least in terms of mass.
Anyways, let's run the numbers. It takes 4*10^53 * 4/3 pi * 6.6*10^-11, or 6*10^41 J, to get this stuff from point A to point B. The current luminosity of the sun is only about 4*10^26 watts (joules per second). In order to grab the amount of energy we're looking for, it'll take 1.5 quadrillion seconds or only about 50 million years.
Let's get started boys!
Some $#@!er let P1 buy whiskey
Don't find fault, find a remedy; anybody can complain.
Cookie Monster wrote:QUOTE (Cookie Monster @ Apr 1 2009, 09:35 PM) But I don't read the forums I only post.
Yes I probably $#@!ed up the arithmetic a million ways to hell on this, but c'mon we're half a bottle of whiskey down and also the other stuff I drank tonight.
Don't find fault, find a remedy; anybody can complain.
Cookie Monster wrote:QUOTE (Cookie Monster @ Apr 1 2009, 09:35 PM) But I don't read the forums I only post.
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Duckwarrior
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Someone asked me if there was even enough stuff on Earth to make it happen. The answer was "yes." Besides, in 50 million years I figure we'll find a solution to that heat exchange problemRaveen wrote:QUOTE (Raveen @ Jul 24 2015, 04:30 AM) Your problem once the sphere is built is how do you stop it melting? You'll likely need some substantial heat exchangers to pass energy throguh the structure.
EDIT: I $#@!ing punted that integral. It's 1/h^2 not 1/h. 0 still is not a valid number (lol) but the good news is we cut about 17 orders of magnitude off the original estimate. Hazy back-of-the-envelope calculations (yes I'm lazy when I'm hung over) make it 3*10^24J, meaning we can get that much power out of the sun in about a second. More since our solar panels are on the planet earth, of course.
Last edited by zombywoof on Fri Jul 24, 2015 5:52 pm, edited 1 time in total.
Don't find fault, find a remedy; anybody can complain.
Cookie Monster wrote:QUOTE (Cookie Monster @ Apr 1 2009, 09:35 PM) But I don't read the forums I only post.
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Globemaster_III
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There are several serious theoretical difficulties with the solid shell variant of the Dyson sphere:
Such a shell would have no net gravitational interaction with its englobed star (see shell theorem), and could drift in relation to the central star. If such movements went uncorrected, they could eventually result in a collision between the sphere and the star—most likely with disastrous results. Such structures would need either some form of propulsion to counteract any drift, or some way to repel the surface of the sphere away from the star.[11]
For the same reason, such a shell would have no net gravitational interaction with anything else inside it. The contents of any biosphere placed on the inner surface of a Dyson shell would not be attracted to the sphere's surface and would simply fall into the star. It has been proposed that a biosphere could be contained between two concentric spheres, placed on the interior of a rotating sphere (in which case, the force of artificial "gravity" is perpendicular to the axis of rotation, causing all matter placed on the interior of the sphere to pool around the equator, effectively rendering the sphere a Niven ring for purposes of habitation, but still fully effective as a radiant-energy collector) or placed on the outside of the sphere where it would be held in place by the star's gravity.[21][22] In such cases, some form of illumination would have to be devised, or the sphere made at least partly transparent, because the star's light would otherwise be completely hidden.[23]
If assuming a radius of one AU, then the compressive strength of the material forming the sphere would have to be immense to prevent implosion due to the star's gravity. Any arbitrarily selected point on the surface of the sphere can be viewed as being under the pressure of the base of a dome 1 AU in height under the Sun's gravity at that distance. Indeed it can be viewed as being at the base of an infinite number of arbitrarily selected domes, but because much of the force from any one arbitrary dome is counteracted by those of another, the net force on that point is immense, but finite. No known or theorized material is strong enough to withstand this pressure, and form a rigid, static sphere around a star.[24] It has been proposed by Paul Birch (in relation to smaller "Supra-Jupiter" constructions around a large planet rather than a star) that it may be possible to support a Dyson shell by dynamic means similar to those used in a space fountain.[25] Masses travelling in circular tracks on the inside of the sphere, at velocities significantly greater than orbital velocity, would press outwards on magnetic bearings due to centrifugal force. For a Dyson shell of 1-AU radius around a star with the same mass as the Sun, a mass travelling ten times the orbital velocity (297.9 km/s) would support 99 (a=v2/r) times its own mass in additional shell structure.
Also if assuming a radius of one AU, then there may not be sufficient building material in the Solar System to construct a Dyson shell. Anders Sandberg estimates that there is 1.82×1026 kg of easily usable building material in the Solar System, enough for a 1-AU shell with a mass of 600 kg/m2—about 8–20 cm thick on average, depending on the density of the material. This includes the hard-to-access cores of the gas giants; the inner planets alone provide only 11.79×1024 kg, enough for a 1-AU shell with a mass of just 42 kg/m2.[12]
The shell would be vulnerable to impacts from interstellar bodies, such as comets, meteoroids, and material in interstellar space that is currently being deflected by the Sun's bow shock. The heliosphere, and any protection it theoretically provides, would cease to exist.
Such a shell would have no net gravitational interaction with its englobed star (see shell theorem), and could drift in relation to the central star. If such movements went uncorrected, they could eventually result in a collision between the sphere and the star—most likely with disastrous results. Such structures would need either some form of propulsion to counteract any drift, or some way to repel the surface of the sphere away from the star.[11]
For the same reason, such a shell would have no net gravitational interaction with anything else inside it. The contents of any biosphere placed on the inner surface of a Dyson shell would not be attracted to the sphere's surface and would simply fall into the star. It has been proposed that a biosphere could be contained between two concentric spheres, placed on the interior of a rotating sphere (in which case, the force of artificial "gravity" is perpendicular to the axis of rotation, causing all matter placed on the interior of the sphere to pool around the equator, effectively rendering the sphere a Niven ring for purposes of habitation, but still fully effective as a radiant-energy collector) or placed on the outside of the sphere where it would be held in place by the star's gravity.[21][22] In such cases, some form of illumination would have to be devised, or the sphere made at least partly transparent, because the star's light would otherwise be completely hidden.[23]
If assuming a radius of one AU, then the compressive strength of the material forming the sphere would have to be immense to prevent implosion due to the star's gravity. Any arbitrarily selected point on the surface of the sphere can be viewed as being under the pressure of the base of a dome 1 AU in height under the Sun's gravity at that distance. Indeed it can be viewed as being at the base of an infinite number of arbitrarily selected domes, but because much of the force from any one arbitrary dome is counteracted by those of another, the net force on that point is immense, but finite. No known or theorized material is strong enough to withstand this pressure, and form a rigid, static sphere around a star.[24] It has been proposed by Paul Birch (in relation to smaller "Supra-Jupiter" constructions around a large planet rather than a star) that it may be possible to support a Dyson shell by dynamic means similar to those used in a space fountain.[25] Masses travelling in circular tracks on the inside of the sphere, at velocities significantly greater than orbital velocity, would press outwards on magnetic bearings due to centrifugal force. For a Dyson shell of 1-AU radius around a star with the same mass as the Sun, a mass travelling ten times the orbital velocity (297.9 km/s) would support 99 (a=v2/r) times its own mass in additional shell structure.
Also if assuming a radius of one AU, then there may not be sufficient building material in the Solar System to construct a Dyson shell. Anders Sandberg estimates that there is 1.82×1026 kg of easily usable building material in the Solar System, enough for a 1-AU shell with a mass of 600 kg/m2—about 8–20 cm thick on average, depending on the density of the material. This includes the hard-to-access cores of the gas giants; the inner planets alone provide only 11.79×1024 kg, enough for a 1-AU shell with a mass of just 42 kg/m2.[12]
The shell would be vulnerable to impacts from interstellar bodies, such as comets, meteoroids, and material in interstellar space that is currently being deflected by the Sun's bow shock. The heliosphere, and any protection it theoretically provides, would cease to exist.
Last edited by Globemaster_III on Fri Jul 24, 2015 7:06 pm, edited 1 time in total.
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Globemaster_III
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what about all the trashed and junk out there ?
Nix1 need another bottle
sorry, I am lazy
Nix1 need another bottle
sorry, I am lazy
Last edited by Globemaster_III on Fri Jul 24, 2015 7:14 pm, edited 1 time in total.