[extropy-chat] sjbrain calcs

[Spike]

> ...  I might speculate that a JBrain would somehow 
> figure a way to use that dust by making it into computronium?  
> Perhaps a JBrain might have little or no solid core, having 
> dissembled itself into dust in order to maximize its surface 
> area, so that its actual size is enormous, perhaps much larger 
> in volume than the star that it orbits...spherical...SBrain?
> 
> If a light-minute diameter spherical cloud of computronium
> particles each a picogram (about 30-50 billion Si-C atoms, or a 
> sphere about a micron diameter if I calculate it in my head) 
> were to orbit a sunlike star, with a total mass of the cloud 
> about one Jupiter...
> 
> Hold on, this is going to take some calculations and thinking.
> More later.  spike...

I did some first order calcs and found my mental figures were not
half bad.  If we assume picogram carbon/silicon particles with 
density about 2 g/cm^2 and a Jupiter mass of them (2E27kg) or about
2e42 particles of computronium orbitting about a light hour from 
a sunlike star in a loosely spherical swarm of about a light 
minute diameter, I get an average density of about 6E11 particles 
per cubic meter, these particles being about a micron diameter.
The average spacing about 100 microns, so that from the point
of view of each particle, an average neighboring particle would 
appear about the size the full moon appears to us on this 
particularly large dust particle we call home.

Clearly this cloud would be completely opaque to all frequencies
emitted from the star, so that all the energy that falls on that
light-minute diameter sphere would be absorbed.  This can allow
us to estimate its temperature while waving our hands furiously
and chanting "to first order."  But before I calculate anything,
I realize that these nodes could turn a dark or light face in or
out, so that the SBrain could adjust its temperature to almost 
anything it wanted.

So look at Jupiter: average surface temperature 130 Kelvin and realize
that the heat loss and heat gain mechanisms are both proportional to
the surface area.  If the SBrain does nothing and has the same albedo
as Jupiter and is about a Jupiter distance from a sunlike star, it
too would be emitting at about 130K.  Right?  So now the question 
becomes how far away can an object be seen which is 130K and diameter 
2E10 meters by Lockheeed produced SIRTF?

The surface temp of a G star like our sun is about 5800 K and its
diameter is about 5 light seconds, so to estimate the amount of 
energy across the entire spectrum reaching us from the SBrain, 
Boltzmann's constant cancels and the rough calculation is 
E = (60/5)^2(130/5800)^4 = 4E-5 times the amount of energy reaching 
us from the star.  So the problem for SIRTF isn't really the *amount* 
of energy reaching us from the star, which is more than adequate, 
but rather *resolving* it from the nearby star which is over 25,000 
times brighter.  

I don't have the specs from the Lockheeed SIRTF, but my intuition 
tells me any instrument of the 1 meter class would not have anywhere 
near the resolution needed to distinguish a Jupiter-like SBrain 
(SJBrain?) from its star, even if the SJBrain-star pair is in the 
immediate neighborhood.  Damn.  {8-[

spike