[meteorite-list] Average size of craters across the solarsystem?

From: Sterling K. Webb <sterling_k_webb_at_meteoritecentral.com>
Date: Mon, 29 Jan 2007 15:47:35 -0600
Message-ID: <003201c743ef$1688b050$7ce68c46_at_ATARIENGINE>

Hi, List,

    The "head-on" collision is a real rarity because of its
improbability. But all things happen given time enough.
A comet rounding the Sun on a highly eccentric orbit
could have its perihelion at the orbit of your planet and
be traveling in the opposite direction. If the comet was
hyperbolic (like SWAN M4), it would be moving at just
above the local escape velocity from the Sun at that orbital
distance. The combined collision velocities would be
2.414 times the orbital velocity of the planet. (Escape
velocity is 1.414 times orbital velocity.)

    For Mercury, that would be 115.64 km/sec. For the
Earth, 72.94 km/sec. But the "head-on" is unlikely. A bit
more likely is "crossing paths," when a body in a highly
eccentric orbit smacks us upside the planet, a right-angle
collision. The velocity there is that of the comet plus
the acceleration of the Earth's gravity on it, a complicated
sum that depends on the precise details, but likely an impact
velocity of ~ 54 km/sec for the Earth.

    For smaller random bodies, the minimum impact velocity
is the velocity gained by falling down the larger body's
gravity well, the escape velocity of the planet, if the falling
body started "at rest" at a distance from the planet. But few
things are "at rest" in the solar system. "Common" objects
(like most meteoroids) have terminal velocities of 15 to
25 km/sec, 11.2 km/sec gained from falling to the Earth and
the rest is what they approached with.

    At Mercury, things are likely to be approaching much
faster, so velocities, as a statistical matter, are likely higher.
The energy of the collision goes up by the square of the
velocity, so, yeah, speed counts more than mass.

    [This is an excursion.]
    A standard "BB" weighs 0.12 gram. If it fell in through
the Earth's gravitation field, its energy would be 15,053 Joules,
or 0.00178 pounds of TNT: the explosion of about a gram
of TNT. Hmmm. Let's shoot that BB out a rail gun at 500
km/sec (quite achievable); now it has the impact energy of
14.33 pounds of TNT. Heck, let's boost it up 1% of the
speed of light. Impact energy? 2400 TONS of TNT. Just
stand off a few billion miles and fire three pound iron balls
at a planet at 1% of light speed. 25 Megaton impacts. Call
it the Tunguska Cannon.

    Luckily, gravity wells are natural limiters of speed; go
too fast and you're out of here.

    The other end of the speed problem comes up a lot in
modeling "giant" collisions, like the formation of the Moon
by the "impact" of a Mars-size body on the Earth. It just
doesn't work if the two big bodies are moving very fast relative
to each other when they smack or even just graze. Escape
velocity is way too fast. They have to "kiss" at only 1 or 2
km/sec or even less. How the heck does that happen?

    The only way is if the two bodies are in very similar
orbits with similar velocities and are perturbed gently into
each other. How do you get a Proto-Earth and a Mars Mass
(or two) into the same orbit? I would propose that the
Proto-Moon was a big Earth-orbit Trojan that was perturbed
out of its Lagrangian resonance and drifted along the orbit
until we met up with each other.

> would a 10 cm object hitting Mercury at top velocity
> not make a larger crater with Mercury's larger velocity?

    Yes, on average, but there's so much variation in mass
and speed circumstances that averages don't mean much.
Callisto is not massive nor does it have a high orbital velocity,
yet the Valhalla Basin is 4000 km. The impactor was probably
pretty good sized! The fact that little Mars has so many big
basins suggests multiple big impactors.

    I listed the biggest hits because impactors follow a statistical
distribution of sizes and energies, a power law with a variable
coefficient. The size and number of the biggest ones is a good
indicator of the size of the impactor population. I would propose
that Mars had a bigger impactor population than other planets.
(I told you this was a bad neighborhood.) And the "saturation"
(means new craters just destroy old craters) of most cratered
surfaces wipes out the fine details of the cratering population,
so that all cratering populations look alike after a while. All the
airless rocky bodies have more or less the same statistical
distributuon of craters. There's always enough rocks to go
around. The big basins are the only clues left.

    As for the three meteorites spotted on Mars, well, any object
that makes it safely to the surface of any planet is a lucky bird,
a one in 100,000, one in a million, and that phenomenon is
really unrelated to the "big picture." Meteorites are improbabilities.
They most likely have a) low approach velocities, b) low angles
of incidence to the atmosphere, c) an initial or intermediate
aerodynamic shape, and d) luck (again). That the rovers have
now spotted three meteorites on Mars in such a tiny land area
of the planet as they survey suggests there may be a lot of
meteorites on Mars. Why?

    Using our terrestrial minds, our first thought is that lots
of meteorites must fall. But it ain't necessarily so. The surface
could just be very old, quite undisturbed. Frankly, I'm beginning
to get suspicious about Mars. Dating the surface is "entangled;"
so much human expectation is involved.

    Thanks to the wonderful rovers and orbiters, we've had the
opportunity to watch Mars for these past years. (By we, I mean
us poor schlubs with computers going to the websites.) OK,
we've got THREE new sub-striations in gullies in five years, and...
Anything else? Mars is a big place. Something must be happening,
says our Earthly expectation. Mars is as big as the Earth!

    Before somebody dashes to correct me, here's what I mean:
the land area of Earth is 148,939,100 km? and the land area of Mars
is 144,798,465 km? because ALL of Mars is land area. Anyway,
as I watch the surface, I'm starting to get the impression that
most of the surfaces we see are old, really OLD. Has that iron
meteorite been sitting there for a thousand years? A million years?
A billion years?

    Our terrestrially trained minds want to say, "A billion years?
That's silly!" But is it? A mud flat, a dune field, pebbles on the
ground. On Earth, they are transient phenomena; take your eyes
off them, something happens to them. But on Mars? Maybe
the Red Planet is really the Dead Planet. (So depressing; give
me back those canals!)

    We are SO invested; we find a new scratch in the side of
a gully where there are thousands of scratches in one gully
among the ten thousand gullies and we want to party all night!
Doesn't mean the gullies haven't looked pretty much the same
for the last 1.4 billion years.


Sterling K. Webb
---------------------------------------------------------------------------
----- Original Message -----
From: "Darren Garrison" <cynapse at charter.net>
To: <meteorite-list at meteoritecentral.com>
Sent: Sunday, January 28, 2007 11:25 PM
Subject: Re: [meteorite-list] Average size of craters across the
solarsystem?


On Sun, 28 Jan 2007 22:41:40 -0600, you wrote:

>Hi,
>
> The biggest craters are multi-ringed; they are
>big enough that they are called "multi-ringed basins"
>or just "basins." Properly, I suppose we should
>call them "impact features" rather than craters.

Not so much the biggest craters, but I'm wondering if all craters tend to be
larger-- for example (no attempt at accurate figures here) if a 10 cm object
hitting the moon at the top valocity for an object hitting the moon (a "head
on"
collision" made a crater 5 meters across, would a 10 cm object hitting
Mercury
at top velocity not make a larger crater with Mercury's larger velocity?
And
wouldn't Mars' slower speed mean for "lighter" hits than for the moon (or
Earth)? Which could factor into how iron meteorites are surviving to be
found
on the surface of Mars by the rovers, even though Mars' thinner atmosphere
means
less loss of speed?

http://www.sjsu.edu/faculty/watkins/orbital.htm
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Received on Mon 29 Jan 2007 04:47:35 PM PST