From: roberts@CMR.NCSL.NIST.GOV (John Roberts)
Newsgroups: sci.space
Subject: Re: Dyson sphere
Date: 16 Oct 92 05:05:49 GMT
Article-I.D.: cmr.9210160505.AA18523
Organization: National Institute of Standards and Technology
	formerly National Bureau of Standards


-From: asnd@msr.triumf.ca (Donald Arseneau)
-Subject: Dyson sphere
-Date: 15 Oct 92 04:48:00 GMT
-Organization: TRIUMF: Tri-University Meson Facility

-In article <1992Oct14.233332.4735@infodev.cam.ac.uk>, sl25@cus.cam.ac.uk (Steve Linton) writes...

-% I don't think you want a reflective Dyson sphere, for reasons discussed
-% much further back in the NewsGroup (you cook the inner planets). For a
-% loss of 50% of your lift you can make do with a black one which also
-% enables you to convert all the solar energy into something useful (Dyson's
-% original reason for proposing the sphere). 

-But the light bounces around to the other side and will still get absorbed 
-eventually.  If the sphere is 80% reflective, there will be 4 x 2 = 8
-times the pressure as for a black sphere.

-But what about the sun in the center?  I think the outer layers would heat 
-up a lot. Would that cause a huge solar wind?  Anyone want to speculate?

Christopher Neufeld and I worked part of that out some time ago. A completely
black sphere would receive twice the influx of energy per unit area as a
nonenclosed object the same distance from the sun, and net outward photon
pressure 1.5 times as great. Both these numbers would go up for a partially
reflective sphere. A perfectly reflecting sphere would eventually explode.

A black sphere surrounding the sun at 1AU would have an outer surface 
temperature of about 140 degrees Celsius (pretty hot - for a temperature
of 25 C you'd want the radius to be about 1.9AU), and would heat the surface
of the sun only a fraction a degree. A reflecting sphere would be *hotter*
and would heat the sun more. To make the calculations more interesting, try
a sphere that's reflective on the inside and black on the outside.

The net photon pressure on a partially reflective sphere might depend on
whether the reflectance of the inner surface is diffuse or specular.
Has anybody worked on that?

I'll try a few more calculations, based on the simplifying assumption that
a given substance is equally reflective at all wavelengths (generally not
true). Then if you assign each substance a reflectance rating of N (where
0 = black and 1 = perfectly reflective), and if you only consider diffuse
reflection, then for a sphere of a uniform substance, the incident radiation
on the inner surface is 2/(1-N) times the normal flux at that distance
from the star, the net photon pressure is 0.5 + 1/(1-N) times the normal
amount, and the temperature of the outer surface will be (1-N)^0.25 times
the temperature of a black sphere of the same dimensions, with the 
temperature measured in kelvins. For instance, with N of 0.9 (90% reflectance,
pretty good for a silver reflector, and probably not too far off for an
aluminum reflector), the incident flux on the inner surface would be 20
times the normal amount, the net photon pressure would be 10.5 times the
normal amount, and the temperature of the outer surface (1AU) would be about
470 degrees Celsius. To get back down to 25 C, you'd have to set the radius
to about 6AU.

John Roberts
roberts@cmr.ncsl.nist.gov
Xref: sparky sci.space:14170 sci.astro:10497