[ExI] upon pondering your next million years
spike
spike66 at att.net
Tue Jul 15 05:22:38 UTC 2008
> 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
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