From: Jeff Davis (jdavis@socketscience.com)
Date: Fri Dec 01 2000 - 01:56:23 MST
Extropes,
The predicted instability of the solid version of the dyson sphere has been
a source of disappointment for moi ever since I heard about it. The idea
of the fully enclosed star was so delightful to me, and so elegant, that I
pondered long over the matter seeking some remedy, some bit of phenomenon
to rescue me from my despair. I considered the predicted instability, and
concluded that it was factually supported, but based on +considerations of
gravity and gravity alone. Gravity, to the exclusion of all other forces
in the universe, as if no other forces existed. Fortuitously, this is not
the case. Also fortuitously, the gravitational 'instability' is neutral.
That is, gravity does not actively drive the system to collapse, but rather
stands by, having no effect at all. This is in contrast to orbital
dynamics, where gravitational forces and inertial forces (centripetal
force) actively balance each other to create stability. At the risk of
repeating myself, the alleged instability (more precisely an absence of the
oh-so-familiar gravitationally-mediated stability of orbital systems) is
concluded to exist, because gravitational effect, by virtue of the
mass-within-a-spherical-shell configuration, is nullified. Ok. Fine.
With gravity, the 800 pound gorilla of the cosmic neighborhood, out of the
picture, I can look to other forces for the stability I seek. Second order
forces, as it were. To put it just a bit more strongly, in the absence of
gravitational effect, other forces, insofar as they come into play, MUST
determine the dynamics--and with it the stability or instability--of the
system.
Now that I have hand-recounted the ballots in this matter, I see that I
have two candidates available to undertake the task of stabilizing my Dyson
sphere. The first is clearly qualified. I've looked him/her over
carefully and s/he seems ready to deliver the goods. The second is either
a spoiler or a helper, I don't know which, perhaps you all can help me
figure out that part.
Radiation pressure, baby. It ain't big, but it's real.
Solar radiation on the interior of the sphere will tend to drive the sphere
so that the center of the sphere describes an 'orbit' around the star. To
see why this is so, consider what happens if the star is off-center. The
portion of the sphere nearest the star has the greater density of incident
photons to both absorb and reflect. It will reach a higher temperature and
thus a higher albedo, so it will reflect (rather than absorb) a higher
percentage of the incident photons than the more distant (and thus cooler)
interior surface. These two factors, photon density and correlated albedo
values, should be the determining factors in the net thrust derived from
radiation pressure. Higher albedo means higher reflection, and a reflected
photon delivers twice the thrust of an absorbed photon. This thrust should
act as a restoring force driving the sphere back towards the concentric
position. There being no particular reason for it to stop once it reaches
the concentric position, it would tend to overshoot, decelerate and then
reverse direction, oscillating in a back and forth manner. This
oscillation, in two dimensions, and out of phase, would stabilize to a
condition where the sphere center describes an 'orbit' around the star.
The exterior of the sphere will likewise have an asymmetric radiation
emission pattern resulting in a net thrust. A worst case scenario is that
the (waste) heat is transmitted through the shell locally and re-emitted
locally. Clearly, it would be re-emitted--dumped--at a lower wavelength
resulting in a lower net thrust (I think I got that right) than that caused
by the radiation forces on the interior. The interior and exterior
radiation reaction forces appear to work in opposite directions, but since
the radiation incident on the interior surface is a restoring force and the
greater of the two, the net effect is a restoring force.
One piece of this puzzle that goes beyond what I can handle is what is the
effect of the radiation in the interior of the sphere after it first
strikes the shell? If it's absorbed I have no problem, but if it's
reflected and then absorbed, or bounces around for several generations
before finally being absorbed, what is the net effect? I think first order
effects will dominate as described, but I'm prepared to hear other points
of view.
Someone may say that radiation forces are puny in the inertial arena. I
agree, but if they're the only forces in play, then they must dominate.
Response times are just very long.
Candidate number two is something of a mystery to me. I know it's there,
but I frankly don't know how it acts on the system or how it compares in
magnitude of effect to radiation pressure.
Magnetic field effects.
The star may have a magnetic field. The field lines may extend out into
space. How far out do they extend? They may interact with the dyson
sphere. They may be conducted through the dyson sphere. What is the
sphere made of? If it were made metallic and isotropic, would the star and
sphere be magnetically drawn together, or held stably concentric? Could a
non-isotropic or non-metallic sphere design take advantage of or circumvent
magnetic effects to passively achieve spherical concentricity?
Help me. I've fallen and I can't get up.
One last note. Though the 800 lb gorilla appears neutral in this matter,
that's only first order effects. Second order gravitational effects may
come into play. If the non-uniform heating of one side of the sphere
causes it to distort, or tidal forces cause it to distort, then
gravitational forces may again come into play. The devil's in the details.
Best, Jeff Davis
"Everything's hard till you know how to do it."
Ray Charles
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