[meteorite-list] Re: Crackpot Theory Redux

From: Sterling K. Webb <kelly_at_meteoritecentral.com>
Date: Mon Oct 31 03:04:24 2005
Message-ID: <4365CFDA.FC43FC51_at_bhil.com>

Hi, G?ran, Axel, List!

    Right you are, G?ran. I screwed up the
calculation. It was too late for me too :-}
It's probably always too late for me...

    The surface area of the Earth is
500,000,000 square KILOMETERS,
not square meters, and half is
2.5 x 10^14 m^2! You're using the
cross-sectional area, which is more
reasonable.

    We don't even need to consider
the total for the Earth at all, really.
We're interested in the energy per
unit area. The rain of iron particles
might not impact the whole Earth.

(1 kg x (4 x10^5)^2)/2 => 8 x 10^10 joules
for each square meter. The thermophysical
calorie is about 4 - 1/8 joule, so the
1,941,340,000 calories is the same
value as the 8 x 10^10 joules.

    Yes, the solar flux figure is per second.
or 1400 W/m^2 per second. So, the
8 x 10^10 joules is equal to 57,142,857
times the Sun's flux! Man, that's hot!

Of course that's for 1 kilogram of iron
(entering at 400,000 meters per second)
per m^2 per second. For 1 gram per
m^2 per second, it would be
57,143 times the solar flux. For
1 milligram, it would be 57
times the Sun's flux IF that
mass were evenly distributed
over the square meter.

    A Type Ia supernova ejects about
one solar mass of iron into the interstellar
medium over a roughly 100 day period

    That would be 2 ? 10^33 grams of
iron from a surface of 1.2 x 10^13 m^2.
That's a density of 1.7 x 10^20 g per m^2
expelled over 10^7 seconds, or 1.7 x 10^13
g per m^2 per second expelled at 10^7 m/sec,
or a per second density of 1.7 x 10^6 g per m^2.

    At an expanded 10 light year radius out
from the star, that density is reduced to
about 60 milligrams per square meter
per second in-fall flux of iron particles.

    At 100 light years out, the flux is 6 milligrams
per square meter per second. That is still enough
to produce 320 times the solar flux on impact
with the atmosphere at 400 km/second. But
at 40 km/sec, it's only 3.2 times the solar flux.

    HOWEVER (and that's a big "however"),
I don't believe that the iron particles would be
moving at these velocities. While they are
expelled at very high speeds, nobody
repealed the law of gravity.

    As an escaping particle leaves a large
body at high speed, the gravity of that
body continually reduces its velocity as
it travels away. The escape velocity of
such a heavy star is several thousand
km per second. (The Sun's escape
velocity is 617,000 m/sec!)

    Moreover, the iron grains' interaction
with the gas that envelopes it will further
slow its velocity. Interstellar dust clouds
have velocities of 10's of km/sec, not
hundreds.

    I don't know, and I'm not sure anybody
knows the actual velocities of iron grains
expelled from a supernova. They have
never been observed in motion, fast or
slow. All we know about them is that
they exist. So all of this is problematic.
We are at a primitive stage in our under-
standing of the post-implosion dynamics
of a supernova.

    However, I have to hand it to you,
Axel. Your intuition was correct. The
impact of even small amounts of matter
at high speeds into the upper atmosphere
seems to be capable of producing a
Big Flash, always assuming I didn't
screw up the math again... The real
question is, are there such high-speed
particles in the real world?

    I also ran across this reference to
atmospheric impact generated heat:
<http://www.lpl.arizona.edu/SIC/impact_cratering/Enviropages/wildfiresweb.html>

    Speaking of the Chicxulub impact:
    "Jay Melosh at the University of Arizona
and several of his colleagues realized that the
post-impact fires were produced when impact
ejecta superheated the atmosphere. Some of
the debris ejected from the Chicxulub crater
rose above the Earth's atmosphere before it
rained back down to Earth. The particles of
material in the ejecta plume, just like falling
meteors, heated the atmosphere. There was
so much debris falling through the atmosphere
at the same time, that it heated the atmosphere
to far higher temperatures than individual meteors
. A large fraction of this heat was radiated to the
ground, raising surface temperatures to several
hundreds of degrees and causing vegetation to
burst into flames."

    And this:
    "New model calculations of these processes
by David Kring (Univ. Arizona) and Daniel D.
Durda (Southwest Research Institute) show
how the fires were ignited, initially around the
impact site and, soon afterwards, at a spot on
the opposite side of the Earth where a
concentrated stream of debris rained back
down on Earth."

    These debris would not be high-speed
impacts, like the iron grains are supposed
to be, but sub-orbital re-entries of massive
amounts of material. But small quantities
of much faster material could produce
the same result.

    Perhaps only a tiny fraction of the iron
grains achieve high velocity in the initial
explosion of the supernova and the rest
are expelled at lesser velocities. The truth
is we just don't know.

    A lengthy Google search demonstrates
that no one has actually recovered a single
supernova pure iron grain, from meteorites or
from cosmic dust. We know they exist because
of the purely theoretical knowledge of the
nuclear transformations that take place in
the stars that go supernova. The vast cosmic
abundance of iron is due to its production
in supernovae. We know that 60-Fe is
produced only in supernovae or rarely
by cosmic ray impact, so finding an atom
of 60-Fe is proof of a recent supernova,
since 60-Fe has a half-life of only
1,500,000 years.

    Having a sky flux as great as the Sun's
light flux is not that rare. I once saw a
daytime bolide that produced secondary
shadows almost as dark as the primary
shadows from the Sun, so it had a light
flux almost as great as the Sun's. I certainly
didn't feel any heat from it!

    Certainly, if there is a rain of fast iron
particles from a supernova, they won't hit
the ground (or mammoth tusks) as Firestone
thinks they will, but if they exist, they could
well produce a devastating thermal event.
Since there are claims of finding carbon
(soot) layers from the 65-million year old
impact, surely there would be plenty of
evidence of an atmosphere flash heating
event only a few thousand years ago?
But there isn't such evidence, so...


Sterling K. Webb
------------------------------------------
G?ran Axelsson wrote:

> Hi!
>
> It's too late for me to do all the math, but I think you got some
> numbers wrong. It breaks the physics law of common sense.
>
> One kg iron hitting the earth at 4x10^5m/s gives 0.5 joule per square
> meter...
> (mv^2)/2=8x10^10 joule => 320J/m^2... wait a minute. The earth radius is
> approximative 6370 km which gives a cross section of R^2*pi=1.25*10^14,
> a lot more than your 250*10^6 m^2. This gives 0.6 mJ energy per square
> meter.
>
> 250.000.000 square meters sounds big at first, but that would have us
> standing 24 persons on each square meter. A teenyy weeny more crowded
> than the earth of today.
>
> The solar flux is missing a dimension. 1400J/m^2, is it per second? per
> hour? year?
> I think it is per second which gives 1400 W/m^2.
> If your calculations were correct with 2.8 tons of iron hitting the
> atmosphere per square meter (per second) to give the same effect as the
> solar flux, then the opposite reasoning would also be valid. The sun
> would dump enough energy onto the earth that it would be enough to give
> 2.8 tons of matter escape velocity (every second). This is the
> unrealistic part, the sun would boil the surface of the earth at that
> intensity.
> You forgot to divide the mass with the area.
>
> This is not saying that this theory is valid, only that your
> calculations are out of this world.
>
> :-)
>
> Regards, G?ran
>
> > Every kilogram of material striking the
> >atmosphere at 40,000 m/sec (average for a
> >meteoroid) generates a specific heat
> >(proportional to temperature) of 194,134
> >calories. That's 8.12256656 ? 10^12 ergs.
> >At 400,000 m/sec, it's 100 times greater, or
> >8.12256656 ? 10^14 ergs. The surface area of
> >ONE SIDE of the Earth is 250,000,000 m^2.
> >So the average energy delivered is
> >3,000,000 ergs per m^2 per kg, at this
> >velocity, or about 1/2 of a joule.
> >
> > The Sun's flux is about 1400 joules
> >per m^2, so to equal the heat of Sun,
> >the event would require 2800 kilos
> >PER SQUARE METER impacting the atmosphere,
> >or more than a ton of iron particles per
> >square meter. This is unlikely many light
> >years from a supernova. (If you were closer,
> >you'd have other, bigger problems!)
> >
> > Big sigh of relief... On the other hand,
> >this calculation raises an interesting point
> >for meteoritics. The impact of a really big
> >object (100's of meters) would involve the
> >atmospheric impact (first) of billions of
> >kilos in a few thousand square meter area.
> >
> >
Received on Mon 31 Oct 2005 03:03:39 AM PST