Re: Sun's core "pinhead" illustration in error
From: Everett Hickey (everett_at_ev1.net)
Date: 01/18/05
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Date: Tue, 18 Jan 2005 14:34:52 -0600
"Joe D." <joe@nospam.invalid> wrote in message
news:hAyGd.53356$zy6.10555@bignews5.bellsouth.net...
> There's a common illustration of the sun's power which is in error.
> This is notable since it's widely used in many books, science web
> sites, etc. Any comments welcome.
>
> The illustration is a 15 million degree C pinhead of the Sun's core if
taken
> to earth would kill someone 160km away. If you search on "sun", "core" and
> "pinhead", you'll see it repeated everywhere. I can't tell where this
first
> started.
>
> I questioned this when I first heard it, and finally did some research and
> it seems drastically wrong.
>
> Consider the Russian "Tsar Bomba" 57 megaton H bomb. It converted 2.7 kg
of
> matter to energy at 100 million C, released 2.4 x 10E17 Joules, yet it
> wouldn't kill someone 160 km away. In fact the manned aircraft dropping it
> was only 45km away at detonation.
>
> If 2.7kg of matter converted 100% to energy won't kill someone at 160km,
how
> could a pinhead of the sun's core? You can't get more energy from matter
> than E=mc^2. The solar core density about 150 times water.
> 1 mm^3 of hydrogen at that pressure is about 0.15 grams.
Nuclear bombs don't convert anywhere remotely close to 100% of their matter
to energy. Not even antimatter can accomplish that feat, and antimatter
weapons would be orders of magnitude more powerful. All a nuke does is
reduce the resulting matter by a small fraction, and the process of
unbinding the particles is what releases the energy, not the conversion
process. E=mC2 is the raw conversion of mass to energy, but the actual
calculation for a nuclear bomb is considerably more complicated, as you have
to take into account the expected efficiency, and the nature of the
reaction. Hydrogen bombs are more efficient than simple atomic bombs, and
are thus incredibly powerful in comparison. And that's just converting a
slightly higher miniscule fraction of mass to energy. Then again, the sun
does the same thing - ie it's not very efficient in conversion.
> In actuality the core's fusion power density is not uniform but increases
> toward the center. If we take the absolute highest power density at the
very
> center, that's 276.5 watts per m^3, or 2.76 x 10E-7 watts per cubic
> millimeter, or .28 microwatts per cubic millimeter. It's actually
remarkably
> low.
There is no fusion at the center of the sun. The core is primarily helium,
with traces of other elements (including some unprocessed hydrogen that
escaped fusion, though a very very low figure). The actual fusion process
occurs in a slowly expanding shell around the core, at the boundry point
between helium and hydrogen. As the hydrogen is slowly fused into helium
(releasing energy as a tiny tiny bit of mass is lost in the fusion process),
the helium collects in the center. It doesn't fuse because the temperature
is not remotely close to what's required to fuse helium.
The density does increase, because of the pressure. But there is no power
density involves as it's merely exceptionally hot helium plasma, and the
center is not very close at all to the area where fusion is actually
occuring (thousands upon thousands, (or even millions?), or kilometers away
from center.
> A cubic mm pinhead of solar core material producing 0.28 microwatts isn't
> going to hurt anyone standing adjacent, much less someone 160km away.
>
> However what about the stored energy based on specific heat?
>
> We must assume it's kept confined to 1 mm^3, else it's
> not a pinhead. Also the illustration is about radiant energy, not blast.
If
> de-confined there would be significant blast effects as the hydrogen is
> under 250 billion atmospheres.
I'd think that alone would do the job. It would cool as it expanded, but
the intense heat combined with ravaging blast would kill for a great radius.
How big a radius I have no clue or care.
> The specific density of hydrogen at sun's core is 150. The specific heat
of
> hydrogen is 14304 Joules per kg per degree K. Core temp is 15 million C.
I won't argue the figures as that's my weak suit, but what is hydrogen doing
in any great quantity in the central core? Isn't the core defined more or
less as the fusion shell, inside of which there is negligible hydrogen
content?
> So 1 mm^3 hydrogen at that pressure is 0.15 grams, and specific heat is
> 14.304 Joules per g per degree K.
>
> 14.304 J/g/K * 15e6 K * 0.15 g = 32 megajoules.
>
> By comparison gasoline contains 45 megajoules per kg.
>
> So the pinhead of core material contains about the energy of 1 liter of
> gasoline. That's not fatal at 160km, nor even 1 km.
Somehow that doesn't add up. I've played with Astrolite (chemical
explosive), which has a considerable expansion rate. That rate is still
nothing compared to the equivilant of 250 billion atm expanding almost
instantly. And one cubil milimeter of astrolite (at normal density) has
destructive power that I'd rate as higher than a liter of gasoline (which
would be difficult to ignite in one instant reaction anyway except as an
aerosol).
I won't support the destruction radius mentioned, but regardless of the
figures quotes, a cubic milimeter of solar core material would carry some
absolutely devastating effects.
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