How often do small asteroids reach the Earth's solid surface?

[mersecske]

I have to model an asteroid collision to the surface of the Earth
In my model the infinite short stop is not sufficient
I have to suppose some time scale
which measure the time length of the stop in the surface
Could you help me?

 

[zhermes]

You could assume that the duration is roughly equal to the size of the asteroid divided by the velocity?

 

[DavidMcC]

Surely it's the depth of the crater that matters, not the diameter of the asteroid. The crater depth would produce a longer-duration deceleration. The crater depth is determined by the kinetic energy of the asteroid, and the kind of rock it's hitting, I guess.

 

[zhermes]

Surely it's the depth of the crater that matters, not the diameter of the asteroid. The crater depth would produce a longer-duration deceleration. The crater depth is determined by the kinetic energy of the asteroid, and the kind of rock it's hitting, I guess.

Craters generally aren't that deep. The majority of the deceleration happens in the first stages of the collision. Clearly, the penetration is something that would have an effect, but as an order-of-magnitude approximation, I think the asteroid diameter is adequate. Higher order effects would be difficult to include, and would require detailed knowledge of the materials and their responses to heat and pressure increases, etc etc.

 

[Drakkith]

I'd say find the average compressibility of the earth, and come up with one for the asteroid and go from there. I think you can just use that and the speed of the asteroid. More compressibility means longer impact times. Either that or just go with a close guess.

 

[DavidMcC]

Zhermes, I was thinking of meteor crater. Isn't it much deeper than the size of the impactor?

 

[DavidMcC]

I agree with Drakkith. It depends, of course, on the purpose of the exercise, but I doubt that hand-waving about the size of the impactor captures the esence of crater formation, which is about energy deposition, not how much space you need to accommodate the impactor.

 

[DavidMcC]

on second thoughts, I doubt that compressibility is really the issue. Craters are basically melt depths, as I understand it, so the thermal properties of the rock and the energy of the impactor should matter more than compressibility, shouldn't it?

 

[Drakkith]

on second thoughts, I doubt that compressibility is really the issue. Craters are basically melt depths, as I understand it, so the thermal properties of the rock and the energy of the impactor should matter more than compressibility, shouldn't it?

I'd venture a guess and say that a mixture of both would work. Even if the inital impact site is melting from the heat, the force of the impact is still being absorbed through the entirety of the asteroid and the Earth I believe.

 

[zhermes]

Here are the answers you want: www.lpi.usra.edu/publications/books/CB-954/chapter3.pdf
(Haven't read most of it).

Zhermes, I was thinking of meteor crater. Isn't it much deeper than the size of the impactor?

No. The depth is always within an order of magnitude the same size (generally about 1-3x the size of the impactor); while the breadth (diameter) can be 10-50 times larger.
See: http://www.lpi.usra.edu/expmoon/science/craterstructure.html"
http://en.wikipedia.org/wiki/Impact_crater"

I doubt that hand-waving about the size of the impactor captures the esence of crater formation

The size and energy (velocity) of the impactor is what establishes the characteristic scales of the problem. See following points:

on second thoughts, I doubt that compressibility is really the issue. Craters are basically melt depths

Compressibility is not the right way to look at it, because at the energies and velocities of interest the surface behaves more like a fluid. The surface isn't uniformly compressed, instead a shockwave is formed directly after impact.
Melting is also not the key feature (although it is important in determining the eventual shape). The timescale for heat-transfer is far longer than the impact itself.

I'd venture a guess and say that a mixture of both would work. Even if the inital impact site is melting from the heat, the force of the impact is still being absorbed through the entirety of the asteroid and the Earth I believe.

See above.

 

[DavidMcC]

Zhermes: "Melting is also not the key feature (although it is important in determining the eventual shape). The timescale for heat-transfer is far longer than the impact itself."

Can you give a reference for that, zhemes? The dominant mechanism creating the crater is melting. AFAIK, most of the ejected material is ejected in a molten state, which suggests that the impactor is still moving while the melting process is occurring IN THE CENTRAL REGION, under the impactor. Heat transfer to the outer region of a crater that is much larger than the impactor obviously takes longer, but still results in some ejection.

EDIT: I've just realized that we're all missing another major mechanism of crater formation: fracturing, leading to the shattering of the impacted rock. This would be faster than melting, but it is not compression.

 

[DavidMcC]

... Shattering the rock would enable the rapid transport of heat by friction between the particles, enabling the rapid spread of melting, IMO.

 

[DavidMcC]

Here's an article on crater formation:
http://www.weirdwarp.com/2010/03/how-impact-craters-are-formed/"

 

[zhermes]

Can you give a reference for that, zhemes?

See the first reference in my previous post, 'chapter3'.

The dominant mechanism creating the crater is melting.

That is not accurate.

AFAIK, most of the ejected material is ejected in a molten state, which suggests that the impactor is still moving while the melting process is occurring IN THE CENTRAL REGION, under the impactor.

I don't think most of the ejected material is molten (while some surely is), nor do I see why---if that were the case---it would imply what you think it does.

EDIT: I've just realized that we're all missing another major mechanism of crater formation: fracturing, leading to the shattering of the impacted rock. This would be faster than melting, but it is not compression.

Yes, fracturing is extremely important. On first order you can include this in a fluid-shock treatment.

... Shattering the rock would enable the rapid transport of heat by friction between the particles, enabling the rapid spread of melting, IMO.

I don't think that makes sense.

 

[DavidMcC]

Zhermes: "I don't think that makes sense."
Then I suggest that you think a bit more. It's friction between separate lumps of fractured rock, causing local heating at greater distances than would be possible by thermal diffusion in unshattered rock.

 

[DavidMcC]

More detail: the shock wave that causes cracking also sets up intense acoustic waves. These would constitute oscillations that would not usually be normal to crack surfaces. Thus, you have surfaces rubbing over one another, causing frictional heat generation remote from the impact site.
It's just an extension of basic materials science.

 

[DavidMcC]

Thinking about moon craters, I have noticed that there seems to be evidence of the dramatic differences between rock strata. I am thinking of images such as those shown here:
http://cseligman.com/text/moons/earthmoonpix.htm

Larger craters are flat-bottomed and vary greatly in width, but not much in depth. Thus, there must be a few crack-stopping interfaces at specific depths, causing the impactor energy to be diverted from vertical propagation to horizontal (a well-known characteristic of layered materials).

 

[zhermes]

Then I suggest that you think a bit more.

Alright buddy, great idea. This coming from the guy who can't bother to read the references I've already provided, and has been wrong on just about every account so far.

More detail: the shock wave that causes cracking also sets up intense acoustic waves. These would constitute oscillations that would not usually be normal to crack surfaces. Thus, you have surfaces rubbing over one another, causing frictional heat generation remote from the impact site. It's just an extension of basic materials science.

Once again, you clearly haven't even ready the few pages I already pointed you too. The shock itself caries the majority of the energy with it. Thus by the time the rocks are fractured... the energy has been dissipated and deposited.

The question from the original post has been answered. Further conjectures should be placed in a new thread.

 

[DavidMcC]

I apologise to mesekske for bringing in moon craters that are very likely caused by comets, not asteroids. (The reason being that they show signs of a poor inertial match between the impactor and the lower rock stratum that forms the base of the large, flat-bottomed craters.)

EDIT: However, they do illustrate that crater depths in general do not have to be determined by the size of the impactor. In the case of these moon craters, it is instead, the thickness of the overlying rock. The reason I butted into this thread (and obviously irritated zhemes) is that it is not good physics to just look at a crater and assume that its depth is the same as the impactor size, especially if you do not know anything about the impactor.

 

[DavidMcC]

Zhermes, I think you are missing the point about the relationship between cracking and melting. Of course the cracking extends beyond the melt zone, but that does not mean that rapid cracking didn't help the shockwave cause melting in the first place. It simply doesn't cause the entire cracked region to melt.

 

[DavidMcC]

...but sorry for the reference to acoustic waves. It is indeed the initial shock wave that is responsible for the cracking and melting that ejects material. I rend to think of a shock wave as an extreme case of an acoustic wave.

 

[DavidMcC]

Before you snap again zhermes, I appreciate that a shock wave is not an oscillation, whereas an acoustic wave is. However, both cause cracking that causes remote melting, so it is the same issue of "short-circuiting" of thermal diffusion.

 

[mersecske]

Another question.
How frequent is that an asteroid (maybe very small but) reach the Earth solid surface.

 

[zhermes]

Another question.
How frequent is that an asteroid (maybe very small but) reach the Earth solid surface.

From a google search (which would be your best bet), I found this set of http://www.agu.org/pubs/sample_articles/sp/2000JE001343/figures.shtml#fig01" .
And it looks like the minimum size to have some remnant actually hit the surface is about 50m (much bigger than I would have guessed). You should look for more references for that number though.
This translates to roughly an impact every 100 years or so (smaller than I would have guessed).

Try searching http://scholar.google.com/schhp?hl=en&tab=ws" for articles on the subject. Meteor impacts / craters / etc, is generally included in the 'geophysics' or 'earth science' discipline.