Re: Nova bomblet - a question about KE weapons used against stars
- From: Michael Ash <mike@xxxxxxxxxxx>
- Date: Thu, 01 Jan 2009 10:45:39 -0600
chornedsnorkack@xxxxxxx wrote:
On 1 jaan, 07:18, Michael Ash <m...@xxxxxxxxxxx> wrote:
Luke Campbell <lwc...@xxxxxxxxx> wrote:Yes, but the Sun is very much colder to begin with
On Dec 31, 2:04?pm, Michael Ash <m...@xxxxxxxxxxx> wrote:
According to Wikipedia, the Sun converts 4.3 million tonnes per second of
matter to energy every second. Google says the total mass of the sun is
about 2e30kg. Putting these two figures together and you have around
2.2e-21 of the Sun converted to matter each second. That's not really a
lot! To put it in non-scientific numbers, 0.00000000000007% of the Sun's
mass is converted to energy in each year.
To put it another way - the interior of the sun is non-convective.
All the hydrogen in the fusioning core stays in the core. ?The sun's
lifetime is about 10 billion years. ?This means that at the
temperature and pressure of the core of the sun, it takes on average 5
billion years for a proton to fuse. ?That is a very slow rate!
This is a really smart, intuitive, and elegant way to express it. Very
nice! Wish I'd thought of it.
Compare that number with a fusion bomb, where the much nicer
deuterium/tritium reactants are all used up in a matter of microseconds,
and it should be fairly clear why the bomb/explosion analogy doesn't apply
to a star.
The temperature in the core of the Sun is mere 15 million kelvins. The
Boltzmann energy of a particle is just 1400 eV. This means that a
hydrogen atom has 2800 eV energy between proton and electron, and
there is some extra (how much?) for photons.
Helium has lower heat capacity. Just 3 particles, and this for 4
nucleons rather than 1.
Fusing 4 proton into an alpha produces 28 MeV, about 7 MeV per
nucleon. Which is something like 4000 times the thermal energy of
solar core. 99,9 % of the heat generated in Sun?s core over the last 5
milliards of years has been radiated away, and less than 0,1 % is
still there.
If you heated the core of the Sun to 1000 times its current
temperature,would protium fusion get any faster?
Certainly. Consider that the largest stars live only a few million years,
so in them a proton "only" has a half-life of a few million years. It's
still not going to give you a chain reaction or self-sustaining explosion
or even a noticeable temporary rise in output. What happens when you raise
the temperature of a small patch of stellar surface to 1000 times the
temperature of the core? Well, you get a few fusion events and then it all
stops as the material involved flies away at high speed and radiates the
energy out into space. Even if you create a shockwave in the star which
somehow involves stellar core temperatures and pressures, even Eta Carinae
core temps and pressures, you still have near-zero energy output being
produced.
To put it another way, you'd get orders of magnitude more effect by
dumping gasoline and liquid oxygen onto the thing.
The mental model seems to be that of a fusion bomb. But the difference in
reaction rates is about twenty orders of magnitude, even when examining a
really enormous and hot star which is on the verge of blowing itself to
pieces.
And even a fusion-bomb is not a self-sustaining reaction. You can't get a
bigger bang by simply piling more fusion fuel next to the bomb. A fusion
weapon is a race against time to get most of your fuel fused before the
reaction forcibly disassembles your reactor, and it takes very careful
design to make this happen. It is possible to scale fusion bombs up
without limit, but this is done by building up stages, each one triggering
the next, larger one and getting it to explode quickly before it, too,
disassembles.
--
Mike Ash
Radio Free Earth
Broadcasting from our climate-controlled studios deep inside the Moon
.
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