Re: Dyson shell redux

From: Michael Lorrey (mike@datamann.com)
Date: Wed Feb 21 2001 - 11:53:19 MST


Anders Sandberg wrote:
>
> You would need a gas pressure counteracting the weight of one square
> meter of the shell, or P=GmM/r^2. The ideal gas law (insert wild
> handwaving here) PV=nRT gives us VGmM/(Rr^2)=nT or 4*pi*GmMr/(3R)=nT
> when we factor in the volume.
>
> Putting in numbers,
> R=8.31451 m^2 kg/s^2 K mol
> G=6.673e-11 m^3/kg s^2
> M=1.989e30 kg
> m=42 kg/m^2 (from my own FAQ, http://www.nada.kth.se/~asa/dysonFAQ.html#ENOUGH)
> r=1.50e11 m
> gives us nT=4.2e32.
>
> Assuming we spread out all of the sun as hydrogen gas, we get
> n=1.989e30/2.016e-3 =9.8e32 mols. Wow, same order of magnitude! So in
> this case you could manage with a mere T=0.42 K gas. However, this is
> of course unrealistic as the gas itself will start contracting if it
> is cold.
>
> If we accept T=1000 K as the maximum temperature our system can stand,
> then we just need a thousandth of this mass and things look a little
> better - but not much, since now we will have an active fusing star in
> the middle heating the gas up! A more likely gas temperature would be
> the sun's surface temperature 6000 K or solar wind temperature
> 150,000K - ouch! And in this case the gas will not be as thin as the
> solar wind is now, it will really transfer heat to the
> construction. You better have good cooling.

Actually, remember that since the sun will be larger diameter, its
surface area will be greater. The solar wind is high temp because it is
like an evaporation vapor. Assuming the sun's fusion rate remains the
same when it expands, you are dealing with an inverse cube reduction in
surface temperature, I think, as the radius increases. Thus the temp at
the core can remain high enough for fusion while the surface would be
cool enough to contact the sphere wall. With a radius somewhere around
the distance of Saturn (is this right), the shell may easily radiate the
light converted to heat into the low IR range. Coating the inside wall
with a variable reflectivity dielectric layer, it could automatically
increase its transparency as temperature differential increases.



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