Sun's core "pinhead" illustration in error

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.

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.

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.

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.

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.

Apparently, whoever contrived this "pinhead" illustration merely
took 1 mm^3, 15 million C, and plugged those into the Stefan-Boltzman
equation:

P=epsilon*sigma*A(Tr^4 - Ts^4), where

P=radiated power
epsilon = emissivity (1 for ideal blackbody)
sigma = Stefan's constant (5.67E-8 watt/m^2 K^4)
A = radiating area
Tr = temp of radiator
Ts = temp of surroundings

Plug in those numbers and you get 1.7E16 watts. At 160km the flux is still
52 kilowatts/m^2, or 52x solar intensity, which is lethal.

However 1 mm^3 of core material doesn't have that much energy!!

That's like taking 1 mm^3 from the ITER fusion reactor which is 100
million C (7 times hot as the sun's core), plugging that into the
Boltzman equation and getting 3.4E19 watts. Behold! Each pinhead
of ITER plasma is 1000 times as deadly as the sun's core!

That's obviously absurd.

There are so many good illustrations that could have been used, and which
would have been accurate.

E.g. using the same illustration but saying "grapefruit size" instead of
pinhead might work. A grapefruit-sized chunk of solar core would
contain 4.7E14 joules, or the equivalent of 174 million kg of TNT,
if liberated in the same timeframe. That would probably kill someone
at 10 km. Something like that.

Or each square meter of the sun's core constantly produces 1.6 gigawatts,
the same as a large power plant.

Or each second the sun converts 4.4 billion metric tons of matter to energy,
and the largest H bomb only converted 2.7 kg.

It's very unfortunate when technically incorrect or scientifically
misleading illustrations are used, often in a misguided attempt to simplify
or impress.

"Joe D." wrote:

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.
(snip)
It's very unfortunate when technically incorrect or scientifically
misleading illustrations are used, often in a misguided attempt to simplify
or impress.

I agree that such descriptions are misleading, at best. How would
your opinion of the account change if it were changed to something
like:

A pinhead sized black body radiator, if it could maintain the
temperature of the core of the Sun, would eventually produce deadly
consequences for someone exposed to its radiation from 160 kM distance
with no absorbent or reflective material between them and the
radiator.

I think this is the sort of thing they are clumsily trying to express.

--
John Popelish

"John Popelish" wrote in message
...

I agree that such descriptions are misleading, at best. How would
your opinion of the account change if it were changed to something
like:

A pinhead sized black body radiator, if it could maintain the
temperature of the core of the Sun, would eventually produce deadly
consequences for someone exposed to its radiation from 160 kM distance
with no absorbent or reflective material between them and the
radiator.

I think this is the sort of thing they are clumsily trying to express.


John I agree your wording "patches up" the technical inaccuracies.

However the presumed goal was illustrate the sun's power in
a compelling and accurate way.

While it's true a 15 million C blackbody radiator would kill someone
160 kM away, it requires 1.7E16 watts to do that.

The ENTIRE SUN only produces 4E26 watts. The illustration requires
vast power perpetually funneled through that cubic millimeter -- power
that the sun doesn't have. Yet the goal was illustrate the sun's power.

The ITER fusion reactor's low density plasma is 100 million C.
If you blindly plug that into the Boltzman equation, you get
3.4E19 watts in EACH mm^3.

ITER's plasma volume is 837 m^3, or 837 billion cubic mm.

Based on that ITER should output 10,000 times the power of
the sun!!!

That's absurd beyond belief, yet that is EXACTLY what the
sun core "pinhead" illustration does.

There are many good illustrations of the sun's power. This
isn't one of them.

"Joe D." wrote:

"John Popelish" wrote in message
...

I agree that such descriptions are misleading, at best. How would
your opinion of the account change if it were changed to something
like:

A pinhead sized black body radiator, if it could maintain the
temperature of the core of the Sun, would eventually produce deadly
consequences for someone exposed to its radiation from 160 kM distance
with no absorbent or reflective material between them and the
radiator.

I think this is the sort of thing they are clumsily trying to express.


John I agree your wording "patches up" the technical inaccuracies.

However the presumed goal was illustrate the sun's power in
a compelling and accurate way.

I think the point of the exercise is to illustrate what the fourth
power of temperature and the tremendous temperature at the center of
the Sun means for energy exchange through small areas.

While it's true a 15 million C blackbody radiator would kill someone
160 kM away, it requires 1.7E16 watts to do that.

Yes. isn't it amazing what can pass through a pinhead size area when
such temperatures are involved.

The ENTIRE SUN only produces 4E26 watts. The illustration requires
vast power perpetually funneled through that cubic millimeter -- power
that the sun doesn't have. Yet the goal was illustrate the sun's power.

We disagree, there.

The ITER fusion reactor's low density plasma is 100 million C.
If you blindly plug that into the Boltzman equation, you get
3.4E19 watts in EACH mm^3.

ITER's plasma volume is 837 m^3, or 837 billion cubic mm.

Based on that ITER should output 10,000 times the power of
the sun!!!

That's absurd beyond belief, yet that is EXACTLY what the
sun core "pinhead" illustration does.

There are many good illustrations of the sun's power. This
isn't one of them.

I don't think the exercise is about the Sun's power at all.

--
John Popelish

"John Popelish" wrote in message
...

I don't think the exercise is about the Sun's power at all.

I assume you mean it's intended only as an illustration of
the sun's core temperature, not its power?

-- Joe D.

"Joe D." wrote:

"John Popelish" wrote in message
...

I don't think the exercise is about the Sun's power at all.

I assume you mean it's intended only as an illustration of
the sun's core temperature, not its power?

Exactly. It is an attempt to give a feel for the physical effects of
that kind of temperature.

--
John Popelish

"John Popelish" wrote in message
...
"Joe D." wrote:

"John Popelish" wrote in message
...

I don't think the exercise is about the Sun's power at all.

I assume you mean it's intended only as an illustration of
the sun's core temperature, not its power?

Exactly. It is an attempt to give a feel for the physical effects of
that kind of temperature.


I understand what you're saying and I accept what the
originator of that illustration was attempting.

My problem is he apparently just blindly plugged 15 million C into
the Stefan-Boltzman equation. That produces a POWER
output which in turn determines lethal range. The impact of
the illustration centers on power, regardless of whether
temperature was the goal. Without power you have no
lethal range. Yet that power doesn't exist in the stated
volume.

The Voyager space probe detected temperatures
of ONE BILLION degrees in the Uranus magnetosphere.
Plug that into the Boltzman equation and it spits out
3.4E23 watts!!!

By the exact same illustration, using the exact same
technique, a pinhead of material from the Uranus magnetosphere
would kill someone 100,000 km away (I just did the math).

Obviously you can't just convert temperature to radiant
power with that equation and have it mean something.
Yet that's what the original illustration does.

The only reason it slips by is the sun is viscerally hot, so
everybody figures that's accurate.

If I'm in error, let me know.

BTW there's a nice on-line calculator for the Stefan-Boltzman
equation at http://hyperphysics.phy-astr.gsu.edu...stefan.html#c2

Joe D. wrote:

The Voyager space probe detected temperatures
of ONE BILLION degrees in the Uranus magnetosphere.

Reference please.

"Sam Wormley" wrote in message
news:Z5IGd.10908$OF5.9106@attbi_s52...
Joe D. wrote:

The Voyager space probe detected temperatures
of ONE BILLION degrees in the Uranus magnetosphere.

Reference please.

http://www.madsci.org/posts/archives...2372.As.r.html

Joe D. wrote:
"Sam Wormley" wrote in message
news:Z5IGd.10908$OF5.9106@attbi_s52...

Joe D. wrote:


The Voyager space probe detected temperatures
of ONE BILLION degrees in the Uranus magnetosphere.

Reference please.


http://www.madsci.org/posts/archives...2372.As.r.html



Thank you.
http://www.madsci.org/posts/archives...2372.As.r.html

"I bring this up because there can be ridiculously high temperatures in
the Universe, but they don't mean much! For example, the Voyager probe
measured a temperature of over one billion degrees in the magnetosphere
of Uranus. Imagine! But really what it was measuring were particles
moving extremely quickly. If you stood (well, floated) in Uranus'
magnetosphere, you wouldn't suddenly vaporize. On the contrary, you'd
freeze! The particles may be very very hot, but there simply aren't
enough of them for them to heat you up."