[ExI] upon pondering your next million years

[spike]

> Subject: Re: [ExI] upon pondering your next million years
> 
> > ...On Behalf Of Damien Broderick
> > Cc: Robert Bradbury
> > Subject: Re: [ExI] upon pondering your next million years
> > 
> > At 09:46 PM 7/13/2008 -0700, Spike wrote:
> > 
> > >The Matrioshka terminology suggests solid shells within shells...
> > 
> > But you've left out the notion of consecutive optimized swarms 
> > *sucking up what's being radiated outward, the left-over solar 
> > goodness emitted in degraded form from the next shell/swarm inward, 
> > and so on until beyond, say, Neptunian orbital radius 
> they're down to 
> > shooing away dregs hardly above 3deg K... Damien Broderick
> 
> Ja, but I disagree with that aspect of the design, so the 
> omission was intentional...
> 
> In my version of an M-Brain the star would still emit a faint 
> glow in the higher frequencies normally associated with 
> stars, along with a more diffuse emission in the longer 
> wavelengths... spike

To elaborate on that comment, I did some BOTECs earlier this evening and
reminded myself of a conversation Robert B and I had a few years ago.
Assume no magic physics and the third law of thermodynamics continues to
hold, and envision a thin solid shell surrounding the sun with a radius of
one AU.  Regardless of what is going on inside that shell, particles
orbiting, collecting photons, re-emitting photons, completely regardless of
what they do, the first and third laws require that the 1AU shell would emit
blackbody radiation at a temperature of about 340 degK.  

How did I get that?  Assume the sun radiates energy at about 5000 degK and
we know that the sun subtends and angle of about half a degree, so its
radius is about a quarter of a degree and a radian is about 57 degrees, so
the earth's orbit radius is about 57 over a quarter or about 200 solar radii
and change.  Since blackbody radiation is constants times T^4 and the
radiating surface increases as the square of the radius, then the blackbody
temperature of the shell decreases as the inverse square root of the shell's
radius.  I know I didn't state that very clearly, apologies, but I am in a
hurry.  If the shell radius is one AU, then that's about 200 solar radii,
square root is about 14, so 5000/14 ~ 340 degK.  

If an M-Brain had a Neptunian orbital radius, then (if I recall correctly)
Neptune's orbit is about 30 AU, then that's about 6000 solar radii for
single digit precision BOTECs, square root is about 80, so a Neptune radius
M-Brain that big would still radiate photons at about 5000/80 or about 65
degrees Kelvin, 

***absolutely regardless of what the individual nodes are doing***

assuming the first and third laws apply in an M-brain universe.

Amara and other astronomy fans, do you follow my reasoning on why a
Neptune-orbit sized M-Brain would radiate photons at about 65 degK?

spike