David Dyer-Bennet <
dd...@dd-b.net> wrote:
> "Keith F. Lynch" <k...@KeithLynch.net> writes:
>> A sphere 20 light years in radius has a surface area of about 4E+35
>> square meters. An Earth-sized planet has a cross-sectional area of
>> about 1.3E14 square meters. So if a thousand rocks from Earth hit
>> it, there must have been about 3E+24 rocks from Earth.
> Neglecting gravity.
The rock would be approaching at solar-system escape velocity.
At such a speed, the destination planet's gravity would increase
its "capture cross-section" by at most only a few percent. The
destination star would have a similar, small, effect. When I get
a round tuit, I'll do the math. Unless someone beats me to it.
> But in fact the rocks don't travel through space purely at random.
They pretty much do. Any rock blasted off the Earth will be in an
Earth-crossing solar orbit. Many of them will eventually hit the
Earth or the Moon. Those that make close passes to the Earth will
have their eccentricity and orbital plane randomized. Some will make
close passes to other planets, or crash into them. Ones that pass
close to Jupiter may be boosted to solar system escape. (Or may lose
instead of gain velocity, and fall into the sun.) The ones that
escape are just as likely to have done so by passing over Jupiter's
pole as its equator, or somewhere in between. So there will be no
tendency for escaping rocks to travel in the ecliptic plane, or with
any other particular bias.
And even if there was a directional bias, since nearby stars are
scattered in random directions, it doesn't matter. (Very distant
stars are biased toward being in the galactic plane. But that's
tilted by about 60 degrees relative to the ecliptic plane anyway.)
>> For a rock to be able to shield life at its center from a million
>> years of cosmic radiation, it would have to have a volume of at
>> least a cubic meter. So 3E+24 cubic meters of rocks must have been
>> blasted out of Earth. But that's 3000 times the total volume of
>> our planet!
> Hmmm; that may be the problem. You're thinking of actual
> interstellar cosmic radiation, not just the local bits, right?
Both. Of course in the best case the rock would spend nearly all
its time in interstellar space rather than waiting millions of years
before passing close to Jupiter and being ejected from the solar
system. Not only does hanging out in the solar system increase the
total travel time, it subjects the rock to ionizing radiation from the
sun, and it subjects the rock to *heat*. Spores may last a million
years in cryogenic cold, but they certainly don't last that long at
anything close to room temperature. And something in an Earth-crossing
orbit is not going to be cryogenically cold.
> Lesser amounts of shielding don't instantly render it impossible,
> though, they just render survival less likely.
It gradually slides from very, very unlikely to absurdly unliekly.
It's about like walking a mile in a heavy thunderstorm and remaining
dry because all the raindrops just happen to miss you. That *could*
happen, but it's almost certainly never happened to anyone ever, and
it almost certainly never will.
Another problem with small rocks is the initial heating. The K-T
impact certainly produced a tremendous amount of heat, and it's hard
to see how anything nearby could escape being vaporized. If it could,
it would certainly at least get white-hot on the outside. So it had
better be thick and made of something that's a good thermal insulator
unless you want to deliver charcoal to the destination planet rather
than life.
>> And unless its entry angle was very shallow, like a reentering
>> space capsule, it would certainly burn up in the atmosphere.
As an aside, burning up in the atmosphere is not a problem on leaving
Earth. That's because of the weird dynamics of a K-T-sized impact.
The asteroid is traveling at escape velocity or faster, and would
lose almost no velocity in the atmosphere, which means that unless it
struck at a very shallow angle it would pass through most of Earth's
atmosphere in less than a second. And it's wide enough that when it
hits there wouldn't yet have been time for air to rush back into the
hole it left. So there would briefly be a tunnel of hard vacuum
extending right down to the surface of the Earth!
A direct rock-to-rock impact, like a baseball bat hitting a baseball,
would push the struck rocks *away* from this tunnel. But that's not
a useful process anyway, as it's hypersonic. When objects collide at
a speed greater than the speed of sound in the objects, the impulse
doesn't have time to propagate. So the objects would be destroyed,
not pushed. If a rock is successfully launched, it would be by
"surfing" a pressure wave, like a bullet in a gun barrel. And that's
likely to happen in all directions (except down), including right
into the tunnel of vacuum.
Indeed, the K-T catastrophe more than a thousand miles from the impact
probably consisted mostly of re-entering secondary meteors, the ones
that didn't reach Earth escape velocity. All those meteors burning
up at once would have heated the sky to incandescence everywhere,
and incinerated everything that wasn't deep underground or deep
underwater. The patterns of extinctions match this.
> Well, much of the mantle is permeated with life currently.
No. The mantle is red hot near the top, and even hotter lower down.
Any carbon compounds would be converted to charcoal. Or to graphite.
Or to diamond.