Starpower?
william mook
collectors onto the solar surface. The sun puts out 3.86x10^26 watts
of power. Distributed over a sphere whose radius is equal to the
radius of Earth's orbit this falls to a little less than 1,400 watts
per square meter. But on the solar surface this energy density
exceeds 60 megawatts per square meter! Clearly, if we could figure
out how to build useful devices that operate under the extreme
conditions of the solar surface, we could collect solar energy 40,000x
more efficiently than we can on Earth!
Any ideas?
The business model would be as follows;
(1) build a factory that makes the equipment that operates on the
solar surface.
(2) Launch the equipment in a rocket to Jupiter.
(3) Execute a gravity assist from Jupiter to cancel all orbital
motion, allowing the equipment to fall toward the sun.
(4) Somehow slow the equipment to survive its 'landing' on the solar
surface - perhaps using solar sails.
(5) Unfold the equipment on the solar surface, and beam 60 megawatts
per square meter to anyplace in the solar system (or beyond) you need
it.
Interesting things to keep in mind;
About the sun;
http://blueox.uoregon.edu/~jimbrau/astr122/Notes/Chapter16.html#facts
About optics;
http://www.licha.de/AstroWeb/articles_fullsize.php3?iHowTo=16
http://www.astro.ufl.edu/~oliver/ast3722/lectures/Scope%20Optics/scopeoptics.htm
About astrodynamics;
http://www.go.ednet.ns.ca/~larry/orbits/gravasst/gravasst.html
(you can cancel orbital speed as well as add to it!)
A thin film system capable of operating on the solar surface could
process quite a bit of power. A square kilometer for instance has a
million square meters and could process over 60 trillion watts of
power. At a few grams per meter a 'sheet' this size could weigh only
a few tons. Something people could build today.
Using conjugate optics
http://www.futureworld.dk/tech/ether/phasecon/phasecon.htm
It is possible to energize a thin film laser medium and then
interrogate that system with another laser, extracting a large portion
of the energy contained in that medium and delivering it to where its
required.
The accuracy which things can be delivered large distances are limited
by Rayleigh's limit;
Theta = 1.22 Lambda / Diameter
GREEN LANTERN OPTICS:
So, if lambda is 500 nm and diameter is 1 km then theta is;
Theta = 1.22 * 500e-9 / 1e3 = 5e-10 radians
Multiply this angle by 150 million km (1.5e9 m) and we can see that a
1 km diameter optically active film producing laser beams efficiently
on the surface of the sun could create a spot that's 0.75 meters
across on the surface of the Earth (capable of putting over 60
trillion watts into that space too - depending on laser and optical
efficiencies! But even an overall efficiency of 1% yeilds 600 billion
watts per square kilometer)
This is more energy than humanity currently uses. With the ability to
produce multiple beams we can deliver this energy to billions of users
simultaneously and power any manner of industrial or transportation
processes. Including space transportation systems.
A quadrillion watts - 1e15 watts - enough to power a starship
-requires 16 square kilometers. A circle 4.5 kilometers across on the
solar surface processes this much power.
Stretching our beam out to 1,000 AU from 1 AU, and noting the increase
in diameter, we can see that we can deliver this beam to a 'spot' 250
meters across 1000 AU from the sun. At this point, we can reflect the
beam around the sun and use the sun's own gravity to focus it reliably
any distance we like from the sun, to be used by owners of laser light
sails anywhere in the galaxy.
But of course, we need to figure out how to make something work
reliably on the solar surface. Which I haven't done.
Again, any suggestions?
Hermit
news:407c5321.04040...@posting.google.com...
Keep taking the pills.
Ian Stirling
> The ultimate in solar collectors must be the deposition of solar
> collectors onto the solar surface. The sun puts out 3.86x10^26 watts
> of power. Distributed over a sphere whose radius is equal to the
> radius of Earth's orbit this falls to a little less than 1,400 watts
> per square meter. But on the solar surface this energy density
> exceeds 60 megawatts per square meter! Clearly, if we could figure
> But of course, we need to figure out how to make something work
> reliably on the solar surface. Which I haven't done.
Trivial matter of engineering...
60Mw/m^2 is not a big problem.
A millimeter of copper will only have about 140C across it at 60Mw/m^2.
The problem is the cooling.
You can only radiate to the sky, no convection is possible.
It may be possible to get a hair under solar temperatures by using
coatings that are more efficiant radiators than the solar atmosphere
(no absorbtion bands) but you'r still looking at well over 5000K.
This is a problem, as everything melts at this temperature.
It's probably easier to move out a bit, as you'r not charged by
the square meter for solar surface.
william mook
Well, following up on this idea.
The melting point of Copper is 1,357K the melting point of W is 3695K.
This translates to;
Solar Surface: 5770K 64 MW/m2 - Surface (400,000 km from center)
MP Carbon: 3800K 12 MW/m2 - 522,000 km (922,000 km from
center)
MP Tungsten: 3695K 10 MW/m2 - 610,000 km (1,010,000km from
center)
MP Copper: 1357K 195 KW/m2 - 6,830,000 km (7,230,000)
Still 50 million miles inside of Mercury's orbit..
Peak radiation color is;
Solar Surface: 5770K 502 nm Blue/Green
MP Carbon: 3800K 763 nm Dark Red
MP Tungsten: 3695K 785 nm Deep Red
MP Copper: 1357K 2,137 nm Infrared
A carbon film 1,000,000 km in radius and 1 micron thick would have a
volume of 12,566,370,614,359,172,953 cubic meters and weigh
28,487,962,182,752,245,086 metric tons.
A solid ball of carbon this size would have a diameter of 145 km.
A fancy carbon nanotube structure composed of lots of empty space
encompassing the sun might mass 1 quintillion tons which would be 48
km in diameter before deployment. Think of a wire mesh reduced to the
scale of carbon tubes.
Could we concievably process a ball of carbon 50 km across, and unfold
it to embrace the entire output of the sun?
Why not?
There is sufficient resources in the asteroid belt to do this -
carbonaceous chondrites would do nicely.
GaAs lasers would radiate at this wavelength. Carbon nanotubes could
be structured to emit laser light at any wavelength when energized.
Combined with conjugate optical techniques the bulk of this energy
could be made to radiate at any color or mix of colors anywhere.
And we could make use of the entire output of the sun!
Of course, we'd have to take care to keep the Earth and other planets
illuminated as they are now.
This is also a technique that could manage the increasing brightness
of the sun over the aeons - by controlling the output falling on Earth
and the other planets - its possible to maintain present conditions
for astronomical time periods.
Mike Miller
> A carbon film 1,000,000 km in radius and 1 micron thick would have a
> volume of 12,566,370,614,359,172,953 cubic meters and weigh
> 28,487,962,182,752,245,086 metric tons.
Are you sure of that mass?
I get the following volume for a 1-micron thick, 2 million kilometer
diameter disk:
Volume = (1,000,000,000 meters) x (1,000,000,000 meters) x Pi x
(.000001 meters)
Volume = 3,140,000,000,000 cubic meters.
With a density of 2000 kilograms per cubic meter (2 metric tons per
cubic meter), the mass is
Mass = 6,282,000,000,000 metric tons.
In a spherical form, that volume of carbon would have a diameter of
about 18km.
A micron is 1 millionth of a meter, right?
Mike Miller, Materials Engineer
Karl Hallowell
Rather than a single large structure, this is likely to be achieved by
a host of small structures. It makes it easier to pass light through
since one could orient the structures edgewise to the Sun whenever
they pass through the plane of the Solar system.
Care needs to be taken with Earth since the radiating structure would
still have the heat output of the Sun. That coupled with the
illumination that would be required means that the Earth gets heated
in two ways.
Power transportation is also a problem. Visible (or UV) light lasers
should be able to illuminate efficiently throughout the inner Solar
system, but it'll take significant surface area or higher frequencies
to beam power out to say Uranus (IMHO). Still dissipation appears to
be a problem to me particularly outside the Solar system. You will
need to find a better way to transport power there.
Karl Hallowell
kha...@hotmail.com
Alex Terrell
fusion, which would heat up the sun, which could go Nova.
william mook
Well, lessee, we all make mistakes...
Okay, I'm talking about a hollow sphere totally encompassing the sun
with a 1 million km (1e9m) radius. The area of a sphere that big is;
A = 4 * pi * r^2
= 12.566 * (1e9 m )^2
= 1.2566e19 m2
and 1 micron thick, (1e-6 m)
V = A * t = 1.2566e19 * 1e-6 = 1.2566e13 m3
That's 12 trillion cubic meters.
http://hypertextbook.com/physics/matter/density/
2,250 kg/m3 so, total mass is;
2.8274e16 kg or 2.8274e13 tonnes
which is what I think I calculated earlier. The diameter of a solid
sphere equal to 1.2566e13 m3 is;
V = 4/3 * pi * r^3 --> r = ( 0.75 * V / pi )^(1/3)
r = (0.75 * 1.2566e13 m3 / 3.14159)^.33333
= 14,422 m
Diameter of 30 km. Which is not what I got before, so that's
troubling. I think I slipped a digit last time.
Cameron Dorrough
>
> Well, lessee, we all make mistakes...
>
> Okay, I'm talking about a hollow sphere totally encompassing the sun
> with a 1 million km (1e9m) radius. The area of a sphere that big is;
>
Just a sec... If your sphere contained solar cells of some kind that
absorbed even a tiny fraction of the stellar radiation, wouldn't it get kind
of *dark* back here on Earth?
.Perhaps even "life as we know it would cease to exist" kind of dark??
Cameron:-)
william mook
A 'structure' composed of trillions of mass produced 'cells' does have
an advantage, as long as all the 'cells' operate together optically.
Discrete structures separated by millions of meters can operate
together optically via conjugate optics, as described here;
http://ol.osa.org/abstract.cfm?id=7073
Not only can light be reflected from an array of discrete components
as if the entire array of components were operating as a single
optical element, but the reflected light can be amplified via laser
action;
http://ol.osa.org/abstract.cfm?id=8347
So, for these reasons I have assumed that the entire 'structure' -
regardless of how its assembled, acts as a single optical element 2
million kilometers - or 2 billion meters - in diameter.
So, the limits of resolution of a 2 billion meter diameter optical
element is easily computed.
http://www.mellesgriot.com/products/optics/gb_2_3.htm
The diameter of the airy disk is;
sin(theta-r) = 2.44 * lambda / r
and
r = 1e9 m
lambda = 1e-6 m
so
sin(theta-r) = 2.44e-15 ~ 2.44e-15 radians ~1.4e-13 degrees
This implies at various distances most of the energy (86.5%) will fall
within a disk of a particular diameter.
A light year is the distance light travels in one year. So, this is;
3e8 * 3600 * 24 * 365.25 = 9.467e15 meters
A spot that is
2.44e-15*9.467e15 = 23.1 meters in diameter
can be reliably illuminated by an optical element 2e9 meters in
diameter at this distance by 1 micron wavelength light. Tighter
resolutions can be achieved at higher wavelengths. Green light for
example would have an airy spot half this size.
Of course, illuminating smaller portions of the sphere reduces the
effective size of the optical element you're dealing with. Anyone in
the solar system requiring power would only need interrogate a small
portion of this 2 million kilometer diameter optical element.
A kilometer diameter sized spot could be formed to power a laser light
sail or laser sustained rocket up to 40 light years from sol at 1
micron and up to 80 light years from sol in green light. Up to 160
light years in UV. Response times could be a problem. Because you
must wait round trip times in one spot for the power to respond to
your request for it. In these instances it may be preferable to set
up automated equipment to deliver 'waves' of power - like a surf on
the beach - that repeat in well defined spaces and patterns. That way
to make use of the energy, all ships must do is communicate with the
automated equipment as to the times dates and places of the next
series of light surf.
Radio telescopes could communicate information great distances
allowing the coordination of deep space travel from star to star.
They could also allow the collection of electronic payment for use of
energy. So, fees could be collected from great distances
automatically over long periods of times. The size, scope and length
of time such economic entities could exist would be unprecedented in
human history. Against these vast economic powerhouses even present
day governments pale by comparison.
Of course, controlling the output of entire stars and reliably
delivering that output anywhere in a volume up to 100 light years from
that star is also unprecedented in human history. Such capacity would
give our species immediate access to the galaxy and would likely end
poverty as we know it. Although I would suspect poverty as we don't
know it now would likely continue.
kha...@hotmail.com (Karl Hallowell) wrote in message news:<c582c1e3.04042...@posting.google.com>...
Mike Miller
> Okay, I'm talking about a hollow sphere totally encompassing the sun
> with a 1 million km (1e9m) radius. The area of a sphere that big is;
Ah, I thought I read 2-million km diameter *disk,* not a sphere. I see
what you're getting at now.
Mike Miller, MatE
william mook
Light pressure can be used to support stationary cellular elements
above the solar surface at any distance. Since the light pressure and
gravitational attraction both scale as the inverse square of distance
from the sun's center, they the acceleration exerted by sunlight will
be the same at any distance.
A particle that absorbs perfectly all light falling on it from the Sun
will feel a force equal to;
f = pA = 3.56e-18 N
At 1 AU.
where, p = 4.53e-6 newtons/m2 at 1 AU
and where, for a 1 micrometer diameter particle projected area is;
A = 7.85e-13 m2
Now, the mass of a 1 micrometer diameter spherical particle with a
density of 1 gram/cc is its volume times its density;
m = 5.24e-16 kg
So, acceleration is equal to;
a= 6.79e-3 m/sec2
at 1 AU.
Now the gravitational acceleration is equal to;
a = f/m = GM/r^2
and at 1 AU this is equal to;
a = 5.92e-3 m/sec2
And the ratio (which is independent of R from the solar center) is;
1.15
Which explains why comet tails point away from the sun. The ice
particles of which they are composed are smaller than 1 um in
diameter.
Particles that are denser than ice, such as carbon particles, must be
smaller than 1 um to be supported by light pressure alone.
Structured carbon particles that interact with light to project
powerful laser energy in response to being illuminated with weaker
laser energy must be smaller than 386 nm in diameter in at least 1
dimension to be supported by light pressure.
A 'laser flake' of structured carbon that absorbs sunlight and
projects powerful laser beams in response to being illuminated by weak
laser beams that is 350 nm thick and perhaps a millimeter in diameter,
would have the capacity to navigate throughout the solar system if it
could control its transparency and reflectiveness.
With the ability to circulate a current around its edge, the 'laser
flake' would have added control by affecting the passage of solar
wind.
These cells would make a mass at 1 million km radius that is about
1/3rd the total mass computed earlier which assumed a shell 1 um in
thickness.
http://www.pcimag.com/CDA/ArticleInformation/coverstory/BNPCoverStoryItem/0,1848,76195,00.html
http://ol.osa.org/abstract.cfm?id=7877
Ceramic, rather than carbon, microspheres or micro flakes would likely
make better lasers that operate more efficiently at high temperatures
using less mass overall to encompass the sun.
In this scenario several asteroids of the appropriate composition
would be processed into microspheres and those spheres ejected from
the surface of the asteorid. Once free of the asteroid's gravity, the
microspheres would navigate to their operational radius and begin
operation. As the 'cloud' of 'flakes' accumulated, output of the
system would increase. One of the first uses of the systems output
would be to beam energy to the chosen asteroids so as to increase
their output by increasing the energy available to the automated
manufacturing processes.
Karl Hallowell
No. This is a real sweet setup that William is talking about here. The
Earth intercepts a very small fraction of that energy. It would be
possible to both continue to bath Earth in the sunlight to which it is
accustomed and beam vast amounts of power (in the form of reflected,
focused sunlight) to those extraordinary distances at the same time.
Incidentally, if you pardon the cliche, this is the mother of all
control problems. You have effectively a relativistic fluid made of
intelligent objects. You wish to avoid certain nasty effects: flash
frying or deep freezing the Earth and other targets, collisions
between the solar sail components and with debris. You want to deliver
power efficiently. How much control should be delegated to the
components? How to deliver the energy?
Karl Hallowell
kha...@hotmail.com
william mook
Yes. But, you could set up a system that transmits 5770K temperature
white light at the appropriate intensity to all the planets on a
continuous basis. Compared to building the sphere in the first place,
it would be simple to achieve.
I even mentioned that the light of the sun changes over time. We
could keep it constant and extend the term of life on Earth as a
result.
I also mentioned that we could change the illumination levels of the
other planets. Cooling of Mercury and Venus for example, heating up
Mars and Europa or Ceres. Making them all quasi-habitable with simple
gear.
I also mentioned the ability to power very capable spacecraft that
zipped from planet to planet across the interplanetary deeps.
In short, we would recreate the solar system as a 1950s retro sci-fi
movie complete with simple bases on other worlds and silvery
spaceships safely propelled by powerful energies.
william mook
> You would also heat up the sun, which would increase the rate of the
> fusion, which would heat up the sun, which could go Nova.
Really?
Consider, two spherical surfaces one nested inside the other sharing a
common center. One is 800,000 kilometers across (the surface of the
sun) another 2,000,000 kilometers across (the surface of the power
shell).
Now, if the temperatures of each of the surfaces are such that the
amount of energy radiated from a sphere 2 million kilometers across is
equal to the amount of energy radiated from a sphere 800,000
kilometers across - there is no opportunity for energy to accumulate
in the sun, increasing rate of fusion presumably.
But this begs an interesting question. Could one increase the rate of
fusion? (Nova's are something quite different see
http://observe.arc.nasa.gov/nasa/space/stellardeath/stellardeath_4a.html
)
This would brighten the star and increase total output of the sun.
Which could be interesting if more energy is needed. Could this be
done? I don't know. It does seem that if we have a sphere made of
reflectors that return energy to the sun, then the sun would heat up.
This is likely to result in an increase in the solar wind. Which
could be interesting. The solar wind might be harvested for raw
materials like hydrogen, helium, and other elements it contains.
But since it takes on the order of 10,000 years for energy to move
from deep inside the sun to the surface, it is likely to take equally
long for surface changes to affect deep processes like rate of fusion
(if it affects it at all!)
But it would be cool to be able to control illumination levels on each
of the planets while independently controlling stellar output over
some range. But, I'm not smart enough to figure out right now if this
will indeed happen. Maybe a solar astronomer can give us a clue.
One thing is for certain. Theconditions are not right for a nova.
It would shorten the life of the sun, but that life span is
fantastically long to start out with.
william mook
500,000 metric tons of thrust requires 780 TW. Call it one
quadrillion watts. The sun produces 386 billion Q-Watts. So, by
capturing all of the sun's output and delivering 12% of it reliably
anywhere across 100 ly would be sufficient to accelerate 40 billion
ships each 500,000 tons in mass per year.
This is sufficient to power self-propelled space colonies near light
speed for every family or individual on the planet.
Alex Terrell
> > You would also heat up the sun, which would increase the rate of the
> > fusion, which would heat up the sun, which could go Nova.
>
> Really?
>
> Consider, two spherical surfaces one nested inside the other sharing a
> common center. One is 800,000 kilometers across (the surface of the
> sun) another 2,000,000 kilometers across (the surface of the power
> shell).
>
> Now, if the temperatures of each of the surfaces are such that the
> amount of energy radiated from a sphere 2 million kilometers across is
> equal to the amount of energy radiated from a sphere 800,000
> kilometers across - there is no opportunity for energy to accumulate
> in the sun, increasing rate of fusion presumably.
>
increasing the insulation of the sun. Therefore, to emit the same
amount of radiation, it needs to be hotter. However, if it's hotter,
it will emit more radiation. This will either stabilise at a hotter
sun, or be unstable and go nova.
Another way of looking at it: The spehere will reflect / reemit a
proportion (>50%) of the energy it receives in the direction of the
sun. That has the effect of increasing the heat generated by the sun
by more than 50%.
william mook
By structuring materials on the nanometer scale it is possible to make
highly reflective films as described here;
http://www.3m.com/about3M/technologies/lightmgmt/products_solutions/product_solutions.jhtml
http://www.photonics.com/spectra/tech/XQ/ASP/techid.877/QX/read.htm
These films are 99.9% reflective and are made of plastic. Films made
of ceramics, carbon layers, or vapor deposited layers of metal like
tungsten, can be equally reflective and thin and withstand high
temperatures.
A square meter of film that absorbs 0.1% of the light that falls on it
will need to dissapate heat at 1/1000th the rate of a film that
absorbs all the light that falls on it.
The materials of the shell that I described earlier in this thread
could absorb and re-radiate energy at about 10 MW per square meter.
Multiply this by 2,000 - which involves radiation from both sides of a
hot film and a factor of 1,000 because 99.9% of the energy is
reflected, and you end up with 20 GW per square meter of reflected
radiation to sustain this level of radiation into the vacuum. At
these power levels 'thrust films' would produce around 10 kgf per
square meter. At 10 grams per square meter a film by itself if
illuminated at 20 GW per square meter would undergo accelerations of
1,000 gees! This is sufficient to accelerate to nearly light speed in
8 hours.
Of course as speeds increase doppler shifts reduce thrust levels.
Practical speed limits are about 1/3rd light speed. So, at 1,000 gees
a film by itself would take less than 3 hours to accelerate to light
speed.
Of course, a structured film could be fired at another structured film
for a new sort of accelerator. One involving significant mass as well
as significant energy.
Back to the more mundane uses of such a high powered film, consider a
500,000 ton spacecraft would require 50 square kilometers of laser
light sail to accelerate at 1 gee. This is a sail about 8 km in
diameter. A 100 ton spacecraft - something the size of the space
shuttle - would require only 10,000 square meters of film to
accelerate at 1 gee. A disk 120 meters across.
It takes about a year at 1 gee to get to light speed. About 4 months
to get to 1/3rd light speed at 1 gee.
It is the nature of dichroic film to become more reflective the more
layers one uses. This has diminishing returns though as things get
thicker. Even so, it may be feasible to make films that are 1,000
times more reflective than considered here. If such super reflective
films become possible this increases the energy one may handle with a
film by 1,000 times. That's 10 tons per square meter, and 20 TW per
square meter. At these super illumination levels it would take a film
only 50,000 square meters to lift a super tanker and only 10 square
meters to lift the space shuttle.
What this means is that the films can pretty much be the outer skin of
the spacecraft - avoiding the need to handle sails of the stuff to
produce thrust. A disk shaped craft with super reflective skin, with
perhaps deployable super reflective fins for guidance and boosted
acceleration.
The super-tanker sized vehicles would enjoy constant acceleration
during boost phases of flight and might be spun to produce gravity
forces during coast phases of flight.
william mook
> willia...@mokindustries.com (william mook) wrote in message news:<407c5321.04042...@posting.google.com>...
> > alext...@yahoo.com (Alex Terrell) wrote in message news:<d81e59c9.04042...@posting.google.com>...
> > > You would also heat up the sun, which would increase the rate of the
> > > fusion, which would heat up the sun, which could go Nova.
> >
> > Really?
> >
> > Consider, two spherical surfaces one nested inside the other sharing a
> > common center. One is 800,000 kilometers across (the surface of the
> > sun) another 2,000,000 kilometers across (the surface of the power
> > shell).
> >
> > Now, if the temperatures of each of the surfaces are such that the
> > amount of energy radiated from a sphere 2 million kilometers across is
> > equal to the amount of energy radiated from a sphere 800,000
> > kilometers across - there is no opportunity for energy to accumulate
> > in the sun, increasing rate of fusion presumably.
> >
> You are correct in the steady state.
Yes.
> However, you are effectively
> increasing the insulation of the sun.
Not if the same amount of energy is dumped into space.
> Therefore, to emit the same
> amount of radiation, it needs to be hotter.
I agree to the extent the shell acts as an insulator the temperature
of the sun must go up. Yes. According to solar astronomers I've
spoken with this will most likely result in an increase in the solar
wind - as the fusion rate is determined by density not temperature.
Further, any temperature increase will take thousands of years to
communicate to the center, and such an increase would be slight
compared to the tens of millions of degrees maintained at the center
of the sun.
> However, if it's hotter,
> it will emit more radiation.
Yes.
> This will either stabilise at a hotter
> sun,
Hotter surface if the shell insulates, yes. Preciesly right.
> or be unstable and go nova.
No. Instabilities and novas operate by totally different processes
involving massive changes in density and composition. Recall the sun
is increasing in brightness anyway because as hydrogen fuses to helium
it leaves helium as a sort of ash at the center. Helium then fuses to
form heavier materials - and this occurs at a higher temperature. So,
as the helium accumulates in the sun the rate of helium burning goes
up, and with it solar temperature and solar brightness. This results
in a path along the Hertzsprung Russell diagram.
http://instruct1.cit.cornell.edu/courses/astro101/java/evolve/evolve.htm
Solar mass not insulating properties of the solar surface determine
the sun's path along the HR diagram.
It is interesting to note that the sun has doubled in brightness since
the Earth was formed. This process if it continues will make Earth
uninhabitable in about 900 million years. The sun has not gone nova
in that time because nova's occur under specific conditions having
nothing to do with insulating properties of solar surfaces.
The rate of fusion is a function of density more than temperature and
that has to do with mass. So, even if a blanket operated as you
suggest - the rate of fusion would not change appreciably. That's
because a blanket doesn't change the density or composition of the
solar interior. Compared to the tens of millions of degrees at the
center, a blanket wouldn't change the core temperature by much - once
surface changes were communicated to the sun's interior. Which takes
tens of thousands of years.
A blanket changes the surface temperature of the sun if it has some
insulating properties. This may change the amount of solar wind
slighlty. It will not cause any changes in the internal operation of
the core of the sun.
This solar wind could be captured and used by humanity though - ending
our mining of the planets.
> Another way of looking at it: The spehere will reflect / reemit a
> proportion (>50%) of the energy it receives in the direction of the
> sun.
Not quite. A point on a shell operating as a black body radiator will
emit energy in all directions. It is true that slightly more than
half its energy outward and slightly less than half its energy inward.
The half that is emitted outward will not heat the sun. The half that
is emitted inward will be radiated in all directions from that point.
Only a small range of angles will intercept the solar surface and send
energy back to the sun.
A point at a radius of 1 million kilometers from the center of the sun
will see the solar surface subtend about 43.6 degrees. This is about
4% of the sky that the point at 1 million kilometers sees. So, about
4% of the isotropic radiation radiated from each point will find its
way back to the sun. Assuming of course that the radiators are not
engineered to shadow the sun.
> That has the effect of increasing the heat generated by the sun
> by more than 50%.
The surface temperature of the sun inside such a shell may rise in
temperature sufficient to dump this extra 4% of energy into space -
assuming each point radiates in all directions. This temperature to
achieve this may be computed by Stephan's Law;
P = sigma * T^4 = 5.67e-8 W/m2/K4 * T^4
where T is in kelvins. The sun's surface temperature is 5,770 K. An
increase of 4% of power output from the sun would require the surface
temperature rise by
1.04^(1/4) = 1.00985
or a little less than 1%.
That is, the surface temperature of the sun worst case would increase
by less than 58 C - from 5,770 K to 5,828 K. The core temperature
which operates in the tens of millions of degrees would, once steady
state was achieved in 10,000 years - would rise by the same 58 C -
from say twenty million to twenty million and 58. Kinetic energy
scales as the square of temperature so this one part in a million rise
would cause a one part in a trillion rise in kinetic energy and result
in one part in a trillion rise in reaction rates - worst case. This
is not sufficient energy to maintain the higher temperature so it is
not sufficient to cause a runaway heating effect as you suggest.
Therefore there is no runaway rise.
william mook
7th - and my comments have yet to see the light of day. Which is
unacceptable in my book.
alext...@yahoo.com (Alex Terrell) wrote in message news:<d81e59c9.04050...@posting.google.com>...
> willia...@mokindustries.com (william mook) wrote in message news:<407c5321.04042...@posting.google.com>...
> > alext...@yahoo.com (Alex Terrell) wrote in message news:<d81e59c9.04042...@posting.google.com>...
> > > You would also heat up the sun, which would increase the rate of the
> > > fusion, which would heat up the sun, which could go Nova.
> >
> > Really?
> >
> > Consider, two spherical surfaces one nested inside the other sharing a
> > common center. One is 800,000 kilometers across (the surface of the
> > sun) another 2,000,000 kilometers across (the surface of the power
> > shell).
> >
> > Now, if the temperatures of each of the surfaces are such that the
> > amount of energy radiated from a sphere 2 million kilometers across is
> > equal to the amount of energy radiated from a sphere 800,000
> > kilometers across - there is no opportunity for energy to accumulate
> > in the sun, increasing rate of fusion presumably.
> >
> You are correct in the steady state. However, you are effectively
> increasing the insulation of the sun. Therefore, to emit the same
> amount of radiation, it needs to be hotter.
How much hotter?
This is easy to compute. First figure out how much energy gets back
to the solar surface. Then figure what the new stable temperature of
the solar surface must be in order to handle this increased heat load.
The first is a simple matter of geometry. Examine a point on the
surface of the larger shell and sum over all points on the shell.
Find that about 4% of the energy in the outer shell will indeed find
its way back to the smaller sphere of the sun - worst case. Clever
engineering can get around this. But let's not argue that point.
Lets look at worst case and see if your concerns are valid.
The second is a simple application of Stephan's law. Since energy
radiated from a black body grows at a rate equal to the fourth power
of the temperature, we merely take the quartic root of 1.04 to see
that the temperature of a jacketed solar surface is less than 1%
higher than the unjacketed solar surface. So, the temperature would
rise from 5,770K to 5,827.7K
> However, if it's hotter,
> it will emit more radiation.
It will rise to a temperature that allows it to shed the extra 4% of
energy the jacket is radiating back to it. There is a feedback. It
will actually be the infinite sum;
1 + (1.04 - 1) + (1.04^2 - 1) * (1.04^3 - 1) + ... + (1.04^n - 1)
Which is pretty darn close to 1.04
So, let's say the new temperature of the solar surface is stabilized
at 5,828K
> This will either stabilise at a hotter
> sun, or be unstable and go nova.
Well, temperature and pressure determine the reaction rate deep within
the core of the sun. This is absolutely true. It is also true that
increased temperature will result in increased reaction rate by
increasing the kinetic energy of the hydrogen atoms flying around
inside the sun. The Lawson relations give us reaction rate
temperature and pressure curves for fusion of hydrogen.
Please note that the sun's brightness is already increasing because of
increasing levels of helium at the solar core. Helium fuses hotter
than hydrogen. Hydrogen fusion makes helium. So, the sun is about
twice as bright today as it was when the Earth first formed. In about
900 million years the sun will be too bright to sustain life as we
know it on Earth. These changes are slow, and this is not the cause
of the recent rise in Earth temperatures during the rise of industry
on Earth. That's due to increased levels of CO2.
Changes in temperature on the sun's surface on the order of tens of
degrees may increase solar wind or increase convection rate - both
very slightly - and not be communicated deep within the sun. If so,
reaction rate won't change.
Any changes that do communicate deeply to the core of the sun will
take a long time to occur. It takes thousands of years for energy to
pour out of the sun from the center. It will likely take at least as
long for any effects of a poorly designed jacket to communicate
temperature changes deep to the core of the sun.
But, for fun, lets look at worst case. Within 1 million years of
applying a poorly designed jacket -one that radiates energy back to
the solar surface- the core temperature of the sun will indeed rise by
58C because of this.
The core temperature is measured in tens of millions of degrees. So,
this increase in temperature will be around 1 part per million
increase. Given the relation of temperature to fusion rates this
worst case would cause a 1 part per trillion increase in fusion rates.
A one part per trillion increase in reaction rate would cause a
brightening of the sun equal to 1 part per trillion, increasing energy
flow by the same amount.
Application of Stephan's law again says that the quartic root of
1.000000000001 times the original energy flow is equal to one quarter
part per trillion increase in temperature. Summing all these very low
numbers over time yeilds less than one quarter part per trillion
increased brightness of the sun.
>
> Another way of looking at it: The spehere will reflect / reemit a
> proportion (>50%) of the energy it receives in the direction of the
> sun. That has the effect of increasing the heat generated by the sun
> by more than 50%.
Your geometry is wrong. Only 8% of the inward moving radiation will
actually make it back to the sun. 92% of the inward moving radiation
will miss the sun and hit other parts of the shell that surrounds the
sun. This is 4% of the total energy since half the energy is radiated
outward and has no chance of hitting the sun at all.
Getting the geometry right makes it simple. Points on the surface of
a shell that emits as a black body will radiate in all directions
equally. All points at a radius of 1,000,000 km will see a 400,000 km
radius sphere subtend 41 degrees of the entire sky. A ball that
subtends 41 degrees covers about 4% of the entire sky viewed from that
point.
This 4% increase if allowed to occur will cause a 1% rise in suface
temperature. This 1% rise in temperature if not disposed of by the
sun in any other way (convection and solar wind changes) will increase
the core temperature by 1 part per million. This rise in core
temperature will increase the reaction rate by 1 part per trillion.
This rise in reaction rate is trivially small compared to the original
increase in temperature. The periods of time involved and the changes
in brightness involved - worst case - are swamped by natural increases
in brightness that are occuring right now due to accumulating helium
at the solar core.
>
> > But this begs an interesting question. Could one increase the rate of
> > fusion? (Nova's are something quite different see
> > http://observe.arc.nasa.gov/nasa/space/stellardeath/stellardeath_4a.html
> > )
> >
> > This would brighten the star and increase total output of the sun.
> > Which could be interesting if more energy is needed. Could this be
> > done? I don't know. It does seem that if we have a sphere made of
> > reflectors that return energy to the sun, then the sun would heat up.
> > This is likely to result in an increase in the solar wind. Which
> > could be interesting. The solar wind might be harvested for raw
> > materials like hydrogen, helium, and other elements it contains.
> >
> > But since it takes on the order of 10,000 years for energy to move
> > from deep inside the sun to the surface, it is likely to take equally
> > long for surface changes to affect deep processes like rate of fusion
> > (if it affects it at all!)
> >
> > But it would be cool to be able to control illumination levels on each
> > of the planets while independently controlling stellar output over
> > some range. But, I'm not smart enough to figure out right now if this
> > will indeed happen. Maybe a solar astronomer can give us a clue.
> >
> > One thing is for certain. Theconditions are not right for a nova.
> >
> > It would shorten the life of the sun, but that life span is
> > fantastically long to start out with.
Novas occur because of compositional changes that occur in the core of
stars over very long times. They do not occur because of changes in
opacity of shells that surround a star. Stars entering dusty regions
of the galaxy for example do not suddenly go nova. Their solar winds
change to process the change in surface condition. This suggests that
there may be a very small change in the nature of the solar wind worst
case. But, stars caught in very opaque clouds don't have much of a
change. The sun encased in a power shell is likely to have no
observable changes in its physical condition - since natural changes
will overwhelm any man made changes.
Gordon D. Pusch
I'm sorry, but stars don't work that way. Gravitationally bound bodies such
as stars exhibit the rather peculiar property of "negative heat capacity"
--- see <http://www.arxiv.org/abs/cond-mat/9812172>. Slow down the rate at
which heat escapes from a star (effectively increasing the opacity of its
atmosphere), and it _EXPANDS AND GETS BRIGHTER AND REDDER_. (The same thing
happens if one compares high-metallicity stars to low-metallicity stars
of the same mass: The higher opacity resulting from the higher fraction
of "metals" causes the high-metallicity star to be larger, redder, and more
luminous. The same thing is happening to the Sun: As it gets older and more
hydrogen gets converted to helium, it gets brighter, fatter, and redder.)
What you need to compute is instead how much more _area_ the Sun will need
to dispose of the increased heat flux at the lower equilibrium temperature
induced by the increase in the effective opacity of its atmosphere.
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
Alex Terrell
You appear to be broadly correct, though I think I see one small error
willia...@mokindustries.com (william mook) wrote in message news:<407c5321.04050...@posting.google.com>...
> > Another way of looking at it: The spehere will reflect / reemit a
> > proportion (>50%) of the energy it receives in the direction of the
> > sun.
>
> Not quite. A point on a shell operating as a black body radiator will
> emit energy in all directions. It is true that slightly more than
> half its energy outward and slightly less than half its energy inward.
>
> The half that is emitted outward will not heat the sun. The half that
> is emitted inward will be radiated in all directions from that point.
> Only a small range of angles will intercept the solar surface and send
> energy back to the sun.
Yes, but the rest will go the shell, > 50% to be emitted again towards
the inside.
>
> A point at a radius of 1 million kilometers from the center of the sun
> will see the solar surface subtend about 43.6 degrees. This is about
> 4% of the sky that the point at 1 million kilometers sees. So, about
> 4% of the isotropic radiation radiated from each point will find its
> way back to the sun. Assuming of course that the radiators are not
> engineered to shadow the sun.
>
But 96% goes to the shell, and >48% is reemitted. Assuming your 4% is
correct, the radiation back to sun would be 4% / (1-i) where i is the
proportion reflected/reemitted back inwards. For a black body shell,
i=50%, so 8% ends up on the sun's surface. (A perfect, mirror would
give i=1, and would give some interesting effects).
> > That has the effect of increasing the heat generated by the sun
> > by more than 50%.
>
> The surface temperature of the sun inside such a shell may rise in
> temperature sufficient to dump this extra 4% of energy into space -
> assuming each point radiates in all directions. This temperature to
> achieve this may be computed by Stephan's Law;
>
> P = sigma * T^4 = 5.67e-8 W/m2/K4 * T^4
>
> where T is in kelvins. The sun's surface temperature is 5,770 K. An
> increase of 4% of power output from the sun would require the surface
> temperature rise by
>
> 1.04^(1/4) = 1.00985
>
> or a little less than 1%.
>
1.08^(1/4) = a little less than 2%
> That is, the surface temperature of the sun worst case would increase
> by less than 58 C - from 5,770 K to 5,828 K. The core temperature
> which operates in the tens of millions of degrees would, once steady
> state was achieved in 10,000 years - would rise by the same 58 C -
> from say twenty million to twenty million and 58. Kinetic energy
> scales as the square of temperature so this one part in a million rise
> would cause a one part in a trillion rise in kinetic energy and result
> in one part in a trillion rise in reaction rates - worst case. This
> is not sufficient energy to maintain the higher temperature so it is
> not sufficient to cause a runaway heating effect as you suggest.
> Therefore there is no runaway rise.
>
seems the sun is pretty stable.
>
>
> >
> > > But this begs an interesting question. Could one increase the rate of
> > > fusion? (Nova's are something quite different see
> > > http://observe.arc.nasa.gov/nasa/space/stellardeath/stellardeath_4a.html
> > > )
> > >
> > > This would brighten the star and increase total output of the sun.
> > > Which could be interesting if more energy is needed. Could this be
> > > done? I don't know. It does seem that if we have a sphere made of
> > > reflectors that return energy to the sun, then the sun would heat up.
> > > This is likely to result in an increase in the solar wind. Which
> > > could be interesting. The solar wind might be harvested for raw
> > > materials like hydrogen, helium, and other elements it contains.
> > >
> > > But since it takes on the order of 10,000 years for energy to move
> > > from deep inside the sun to the surface, it is likely to take equally
> > > long for surface changes to affect deep processes like rate of fusion
> > > (if it affects it at all!)
> > >
> > > But it would be cool to be able to control illumination levels on each
> > > of the planets while independently controlling stellar output over
> > > some range. But, I'm not smart enough to figure out right now if this
> > > will indeed happen. Maybe a solar astronomer can give us a clue.
> > >
> > > One thing is for certain. Theconditions are not right for a nova.
> > >
What proportion would you need to reflect back to do so?
william mook
> An impressive use of numbers. Thank you for your time and brain.
>
> You appear to be broadly correct, though I think I see one small error
It wouldn't be the first time.
> willia...@mokindustries.com (william mook) wrote in message news:<407c5321.04050...@posting.google.com>...
> > > Another way of looking at it: The spehere will reflect / reemit a
> > > proportion (>50%) of the energy it receives in the direction of the
> > > sun.
> >
> > Not quite. A point on a shell operating as a black body radiator will
> > emit energy in all directions. It is true that slightly more than
> > half its energy outward and slightly less than half its energy inward.
> >
> > The half that is emitted outward will not heat the sun. The half that
> > is emitted inward will be radiated in all directions from that point.
> > Only a small range of angles will intercept the solar surface and send
> > energy back to the sun.
>
> Yes, but the rest will go the shell, > 50% to be emitted again towards
> the inside.
Yep.
> >
> > A point at a radius of 1 million kilometers from the center of the sun
> > will see the solar surface subtend about 43.6 degrees. This is about
> > 4% of the sky that the point at 1 million kilometers sees. So, about
> > 4% of the isotropic radiation radiated from each point will find its
> > way back to the sun. Assuming of course that the radiators are not
> > engineered to shadow the sun.
> >
> But 96% goes to the shell, and >48% is reemitted. Assuming your 4% is
> correct,
Yep. Imagine a spherical cap atop a spherical surface. The radius of
the spherical cap is r1, the height of the cap is h, and the radius of
the sphere is r - so;
Sc = 2 * pi * r * h
The area of a sphere is
S = 4 * pi * r^2
So, we know r = 1,000,000 and r1 = 400,000 - so; h = 83,485 then;
S = 4 * pi * 1e12 = 12,566.4e9
Sc = 2 * pi * 1e6 * 83,485 = 524.55e9
Ratio = Sc/S = 4.174%
http://mathworld.wolfram.com/SphericalCap.html
> the radiation back to sun would be 4% / (1-i) where i is the
> proportion reflected/reemitted back inwards. For a black body shell,
> i=50%, so 8% ends up on the sun's surface. (A perfect, mirror would
> give i=1, and would give some interesting effects).
Your formula suggests that a perfect reflector would deliver an
infinite amount of power to the solar surface. This is not the case.
There are time effects that become dominant as you approach perfect
reflectivity. Although I will concede a perfectly reflective mirror
encompassing the sun will deliver a sharp rise in power at the solar
surface for as long as the reflective coat lasts.
> > > That has the effect of increasing the heat generated by the sun
> > > by more than 50%.
> >
> > The surface temperature of the sun inside such a shell may rise in
> > temperature sufficient to dump this extra 4% of energy into space -
> > assuming each point radiates in all directions. This temperature to
> > achieve this may be computed by Stephan's Law;
> >
> > P = sigma * T^4 = 5.67e-8 W/m2/K4 * T^4
> >
> > where T is in kelvins. The sun's surface temperature is 5,770 K. An
> > increase of 4% of power output from the sun would require the surface
> > temperature rise by
> >
> > 1.04^(1/4) = 1.00985
> >
> > or a little less than 1%.
> >
> 1.08^(1/4) = a little less than 2%
If your formula given above is correct, yes.
> > That is, the surface temperature of the sun worst case would increase
> > by less than 58 C - from 5,770 K to 5,828 K. The core temperature
> > which operates in the tens of millions of degrees would, once steady
> > state was achieved in 10,000 years - would rise by the same 58 C -
> > from say twenty million to twenty million and 58. Kinetic energy
> > scales as the square of temperature so this one part in a million rise
> > would cause a one part in a trillion rise in kinetic energy and result
> > in one part in a trillion rise in reaction rates - worst case. This
> > is not sufficient energy to maintain the higher temperature so it is
> > not sufficient to cause a runaway heating effect as you suggest.
> > Therefore there is no runaway rise.
> >
> seems the sun is pretty stable.
Yes. Despite it doubling its brightness since the Earth was formed,
and despite the fact it continues to increase in brightness as helium
accumulates at its center - its far far removed from becoming a nova.
> >
> >
> > >
> > > > But this begs an interesting question. Could one increase the rate of
> > > > fusion? (Nova's are something quite different see
> > > > http://observe.arc.nasa.gov/nasa/space/stellardeath/stellardeath_4a.html
> > > > )
> > > >
> > > > This would brighten the star and increase total output of the sun.
> > > > Which could be interesting if more energy is needed. Could this be
> > > > done? I don't know. It does seem that if we have a sphere made of
> > > > reflectors that return energy to the sun, then the sun would heat up.
> > > > This is likely to result in an increase in the solar wind. Which
> > > > could be interesting. The solar wind might be harvested for raw
> > > > materials like hydrogen, helium, and other elements it contains.
> > > >
> > > > But since it takes on the order of 10,000 years for energy to move
> > > > from deep inside the sun to the surface, it is likely to take equally
> > > > long for surface changes to affect deep processes like rate of fusion
> > > > (if it affects it at all!)
> > > >
> > > > But it would be cool to be able to control illumination levels on each
> > > > of the planets while independently controlling stellar output over
> > > > some range. But, I'm not smart enough to figure out right now if this
> > > > will indeed happen. Maybe a solar astronomer can give us a clue.
> > > >
> > > > One thing is for certain. Theconditions are not right for a nova.
> > > >
> What proportion would you need to reflect back to do so?
Dunno. See the other response to my comments below and note 'Stars
don't work that way.' That is, recall I said at the outset this is a
worst case scenario and the most likely outcome is no change at all in
the core reaction rate of the sun.
Since stars are balls of plasma held together by gravitational forces
and heat applied to the stellar surface changes the gravitational
balance of things at the surface adding heat to the surface of a star
does vanishingly little to the interior.
The most likely outcome as I have already noted is an increase in
solar wind a change in convection currents which absorb the heat.
I don't know what a perfect reflector would achieve in any sense. My
guess is that a perfect reflector would would cause a blast of heat
high in the solar atmosphere which would result in a counter balancing
stream of ionized particles to blast out of the sun as the heat
diffused inward from the surface.
This ionized particle blast would scrub any mirror with ionizing
particles reducing its reflectivity, and perhaps destroying it -
leaving the sun with a slowly expanding shell of material surrounding
it - part of that material which used to be a perfect reflector.
This might be a way to mine the sun if the slowly expanding shell of
material can be mined of stuff the reflector is made of and the stuff
returned to reflective status so as to deliver another pulse of
material. Or if the ion blast can be dealt with by the shell somehow.
Given the operation of Fick's law it may even be possible to be rather
selective about the ions one retrieves from the sun in this way. Iron
could be preferentially heated in the upper atmosphere with a
selective laser for example, increasing iron's pressure while leaving
the bulk of the solar atmosphere unaffected. In the limit this gives
rise to a pulse of ionized iron blasting out of and otherwise
quiescent sun.
>
>
> > > > It would shorten the life of the sun, but that life span is
> > > > fantastically long to start out with.
Hmm... if carried to the extreme I must reluctantly admit that you
could 'ping' a star like the sun and turn it into a variable star.
The blast of ions would compress the remaining sun slightly. The
compression wave if perfectly shaped would increase the pressure of
the core dramatically giving rise to a blast of increased nuclear
fusion. If timed right - as well as shaped right - this could
initiate a continuous oscillation in brightness - which could be added
to over time - like pushing a swing to increase its height of swing.
Which could result in significant amounts of solar material evolving
from the sun.
This slowly evolving oscillation could conceivably over time be
managed to tear the entire sun apart leaving a cloud of expanding gas
in place of the sun.
This is not a nova since the heavier materials wouldn't be formed as
in a nova, and the conditions under which the sun comes apart would be
far gentler. Even so, I doubt that would matter to non-technical
people living on Earth.
On the other hand, you could mine a star in this way. And since the
mass of stars outweigh their planets by a factor of billions - this
might be a very useful trick to have.
william mook
You are precisely correct! Additional heat dumped into the Solar
atmosphere will cause an increase in the diameter of the affected
region. Increasing the solar wind.
http://www.uni-hamburg.de/~stcd101/PAPERS/AMES_DUST/node3.html
http://www-star.st-and.ac.uk/~kw25/teaching/stars/new1.ps.prn.pdf
If the shell radiated selected colors into the solar atmosphere it
could energize specific species of atoms - the same ones that cause
absorption lines of those species - and increase the flux of those
atoms from the solar surface.
Please recall, I mentioned at the outset that the Sun doesn't work
that way - but if it did - even if it did, worst case - the Sun would
still not go nova.
Although after more careful analysis I have determined that the Sun
*could* be torn apart by the careful management of an all encompassing
shell over an extended period of time. By reflecting a considerable
amount of energy back to the sun in a way to create a spherically
symmetric pressure pulse - one might introduce an artificial
variability that pumps material out of the sun at an accelerated rate,
resulting ultimately in the destruction of the Sun.
This could be applied to any number of stars as well.
That way a technical species control as much resources in one star as
a species who controls the planetary systems of a billion stars. A
handful of stars mined this way across the local group would give
humanity access to as many resources as another species might have who
controls an entire galaxy of planetary systems.
This suggests that planetary sized space stations are the preferred
mode of existence among such species.
So, there are two modes of operation possible;
(1) Power generators beaming energy to anywhere within 100 ly of a
star
(2) Mines - tearing a star apart and using its material to build
stuff
We could literally rebuild the galaxy with this technology.
With this power we could add a third nuance;
(3) Super collider - make black holes by colliding massive
quantities
of materials at high speeds and use collections of black holes
in
a variety of super machines
(a) time machine
(b) superluminal travel
In this venue the civilized portions of the universe would be dark -
the power from the stars would either be captured and used or shut off
as they're torn apart.
This might explain the missing mass problem - and the spherical
structure of dark regions of the universe.
g_d_pusch_remo...@xnet.com (Gordon D. Pusch) wrote in message news:<gi65b0i...@pusch.xnet.com>...
william mook
alext...@yahoo.com (Alex Terrell) wrote in message news:<d81e59c9.04051...@posting.google.com>...
> An impressive use of numbers. Thank you for your time and brain.
>
> You appear to be broadly correct, though I think I see one small error
>
> willia...@mokindustries.com (william mook) wrote in message news:<407c5321.04050...@posting.google.com>...
> > > Another way of looking at it: The spehere will reflect / reemit a
> > > proportion (>50%) of the energy it receives in the direction of the
> > > sun.
> >
> > Not quite. A point on a shell operating as a black body radiator will
> > emit energy in all directions. It is true that slightly more than
> > half its energy outward and slightly less than half its energy inward.
> >
> > The half that is emitted outward will not heat the sun. The half that
> > is emitted inward will be radiated in all directions from that point.
> > Only a small range of angles will intercept the solar surface and send
> > energy back to the sun.
>
> Yes, but the rest will go the shell, > 50% to be emitted again towards
> the inside.
> >
> > A point at a radius of 1 million kilometers from the center of the sun
> > will see the solar surface subtend about 43.6 degrees. This is about
> > 4% of the sky that the point at 1 million kilometers sees. So, about
> > 4% of the isotropic radiation radiated from each point will find its
> > way back to the sun. Assuming of course that the radiators are not
> > engineered to shadow the sun.
> >
> But 96% goes to the shell, and >48% is reemitted.
Wrong. 4% makes its way back to the Sun and 46% goes to the shell -
and 50% goes to space. The energy is scattered perfectly in a black
body radiator again, so 4% of that 46% or 1.84% finds its way back to
the Sun, while 50% of that 46% or 23% is emitted to space, and 46% of
the 46% or 21.16% finds its way back to the shell in the second
round... adding all rounds together we have;
4%*(.46^0 + .46^1 + .46^2 + .46^3 + .46^4 +...
4% + 1.84% + 0.8464 + ...
~ 7.4%
> Assuming your 4% is
> correct,
Take a sphere 1 million km in radius and figure out the area. Then,
take a cap 400,000 km in radius and figure its area. Divide the
smaller area by the larger one and you'll find you'll get a little
more than 4%
> the radiation back to sun would be 4% / (1-i) where i is the
> proportion reflected/reemitted back inwards. For a black body shell,
> i=50%, so 8% ends up on the sun's surface. (A perfect, mirror would
> give i=1, and would give some interesting effects).
A perfectly spherical mirror 1 million kilometers in radius would have
a characteristic reflection time of about 4.6 seconds. So, each stage
in the infinite sum would take 4.6 seconds on average.
4.6 4.6 4.6 4.6
.04 --> .0784 --> .115264 --> .15065344 -->
1st 2nd 3rd 4th etc.
Its NOT .04, .08, .12, .16 - as you have assumed... So, the results
are not as interesting as you have imagined.
[snip]