## Sunday, December 26, 2004 ... /////

### Friday 13th: Asteroid won't hit Earth

In the morning, 25 years before the asteroid was supposed to land, I had to ask: which bike is mine and which of the bins is for 1 PETE containers? :-) Incidentally, this story is dead because the impact probability dropped to 10^-5 in the afternoon of December 27th, 2004 - as was expected - but nevertheless it may still be fun to read how the story looked before it disappeared. The text below is obsolete, but have fun:

The probability than an asteroid named 2004 MN4 of around 390 meters (previously reported as 440 and then 380 meters) will hit Earth is estimated to be around 2.7 percent right now. It carries the number 4 on the Torino scale - clearly the highest rating of all such objects ever observed because no previous object has ever been above 1! However, there is still a 97% likelihood that the estimated probability will start to decrease soon, as the observations become more accurate; in fact, the probability has already reached 2.4 percent, then dropped to 2.2 percent, before jumping to 2.7 percent. However, it may also continue to grow...

I hope that you're not superstitious because the possible colission will take place on Friday, April 13th, 2029. According to my calculations, it could occur at 9:07 pm (Universal Time), and this is enough for you to figure out which place on Earth will it roughly land at.

We may want to produce some more nukes and make them ready for the unexpected application - splitting such an asteroid into pieces. Actually in the case that the probability won't decrease below 1 percent in 4 months, or if the Torino classification jumps above 4 (to the orange or red zone), I would endorse an immediate action - just send a couple of H-bombs to that asteroid and break it in two halves - even if it were just a training. If it does not work, we must send a better mission that will drill a hole in it and put H-bombs in the hole. The earlier you deflect such a thing, the cheaper it is. According to an Australian "astronomy educator", if an asteroid is made of stone, it will mostly evaporate in the atmosphere. Most of the commentators on this blog however agreed that the atmosphere is clearly unable to destroy an asteroid as large as 2004 MN4. So the impact won't be too different as the impact of an iron type asteroid whose colission would be equivalent to 100 Hydrogen bombs - over one thousand of megatons of TNT.

It's not a big deal on the global scale. The previous large asteroid that collided with Earth 20,000 years ago was 100 meters in diameter - which is just by a factor of 60 smaller volume than the expected one - and it only created a 1 kilometer large crater in Arizona. Moreover, there are only 38 potentially hazardous close encouters between now and 2079. ;-)

But sure, I know. The most serious threat are not earthquakes or asteroids, but a temperature rising by half a degree that could make some sissy liberals whose parents and grandparents were already liberals feel a little bit too warm!

Once again a summary of the asteroid: the public should not worry about such things. The impact probability in this case has been rising, but it may also start to decline, and moreoever, the impact would only be like one hundred thousands of Hiroshimas.

Happy rest of holidays!

#### snail feedback (27) :

Lubos - You know, if it's made of stone, it will mostly evaporate in the atmosphere...Perhaps you were joking, but I don't think so. The intervening atmosphere has a mass per unit area of about 10^4 kg/m^2, so only about 10^10 kg of air stands between us and a 440 m diameter asteroid. If you guess that the asteroid has a rock like density of say, 2.5*10^3 kg/m^3, it has a mass of about 10^11 kg. That's not enough air to very much slow down or disrupt the asteroid before it hits. So the effect will be for the 10^8 ton asteroid to drive another 10^7 tons of air into the earth's surface at 9 or 10 km/sec.

Cheers!

Pig

Hi pig,
I also found it counterintuitive, but this is what they say at

http://www.heraldsun.news.com.au/common/story_page/0,5478,11787338%255E401,00.html

More precisely, the astronomy educator Paul Floyd said it. ;-) I don't know how much should we trust astronomy educators, but he says that most of a stony type asteroid would vaporise.

Best
Lubos

Does it matter whether it vaporizes or not? The asteroid will deposit its huge kintetic energy into the atmosphere almost instantly and that's dangerous to humans. OK, If it vaporizes quickly, there will be less of a crater and more energy will remain high up in the atmosphere. But surely a portion of such a huge rock would make it to the ground -- hopefully it's not Cetral Park. :))

Regarding the previous post and your question, Lubos: The short answer is that I do not know how reliable the simulation is. But it was prepared by scientists who I would think have nothing to do with those alarmist morons who lie to the public about global warming. Notice also that it is meant to depict a real event, so they could use real data in tuning the computer program.

As to the friction aspect, I am a theoretical high-energy physicist by training and don't have any expert knowledge about fluid dynamics. But if you just examine a naive hydrodynamic wave equation (for a viscous fluid), it seems to be an almost trivial fact that solutions become solitonic in the limit of large wavelength to amplitude ratios. If you do estimates, keep in mind that your number of 10 meters for the amplitude is only realistic for the moment when it hits the coast. Out there on the open ocean, I think, it should be a factor 100 or so less than that. By contrast, the wave lengths can be tens of kilometers.

Again, I am just speculating, so everyone can do the same or correct me if they can.

Best, John

Thanks for illuminating remarks, John, we see all these things almost equally and have comparable (lack of) training for these issues. Which is one of the reason I must ask why do you exactly think that a vaporized asteroid would still be harmful to the humans?

There are many smaller stones that are burned in the atmosphere, and so far I thought that all these processes are much more healthy than a stone landing on your head ;-). Are you suggesting that the energy of the evaporated asteroid could contribute to global warming?! :-) Wow. That would be serious! :-)

I have been an astronomy educator (a term that can encompass high school teachers to full professors at Harvard) and a lot of us/them don't know shit. Your source is overgeneralizing from much smaller meteorites. A small meteorite (less than 10 m in diameter, say) is rapidly slowed down and ablated in the atmosphere. This doesn't work for big ones, where the mass is much greater than the mass of the intervening atmosphere. A big 400 m asteroid plunges thru the bottom 90% of the atmosphere in 1 or 2 seconds - there is no time for significant ablation.

It's simpler than that though, just think about the momentum. At 30 to 200 times the speed of sound, there is no way for any of the air in its path to get out of the way and the whole mass, air, asteroid, and ablated material crashes into the earth at 10 to 70 km/sec.

Also, my sources estimate the Arizona crater meteoroid as more like 40 m. in diameter. So scale up your impact by a thousand or two.

It looks like the projected possible impact is a low speed one - about 11 km/sec - compared to the plausible comet impacts at up to 70 km/sec - the Jupiter impacts a few years back were at 300 km/s plus, but we don't have that kind of gravitational potential.

Such an impact would cause total destruction over ten's of thousands of square miles and major devastation over a continent sized region - probably comparable to a worst case 10-12 C global warming.

Hey guys, yes, OK, I personally believe that you're right and it is impossible for the atmosphere to destroy such an animal. Let me correct the weird sentence in the article. ;-)

My thought was very simple. A bullet flying at 3000 m/s has a kinetic energy roughly equal to the chemical energy stored in as much TNT as the bullet weighs. An asteroid moving at that speed having a diameter of about 400m would make for a pretty good bomb, no? However, typically an asteroid might move ten times that fast, making it 100 times more energetic. That puts you in the ball park of huge hydrogen bombs, and I am not sure whether it matters exactly what material the asteroid is made of. The kinetic energy is there in any case.

OK, now the kidding aside: I *am* worried about the global warming due to asteroids. ;) It's getting hotter in Massachusetts by the day!

-John

Hey John! I am not asking you about the kinetic energy. I know exactly what the kinetic energy of the asteroid will be. But if it evaporates, then it's just converted into the heat in the atmosphere, does not it? And the pressure from the "momentum" will be just divided to tens of squared kilometers of Earth's surface, which is a negligible pressure wave, is not it?

There's a lot of new snow here. It was a good idea to make the bike trip yesterday. ;-)

...And the pressure from the "momentum" will be just divided to tens of squared kilometers of Earth's surface, which is a negligible pressure wave, is not it?Negative Lumo. For the reasons I gave above their is no plausible way the momentum can be defocussed for such a large fast moving object. Sound waves just don't move fast enough. Do the arithmetic (or look it up).

For what it's worth I followed your link to the page giving a 2.2% probability of impact, and it now shows 100% probability of impact, with ground zero in Central Park - I think somebody is messing with us.

The correct link is:

http://neo.jpl.nasa.gov/risk/

It currently shows an impact possibility of 2.7%

Recent comment of Lubos regarding basic facts of large meteror impact and ocean wave progation speed shows how poor his physics training is.

OK, I know he is specialized in high energy physics, not tsunami waves. But you've got to first receive gerenal physics training before you study your Ph.D. Trivial questions like ocean wave propagation speed are high school physics problems!

I knew how to estimate progagation speed of waves in a tank of water when I was only 14 years old! It's roughly the square root of (density * earth gravity / water depth), and has nothing to do with amplitude or wavelength!!!

Even if you don't know how to derive that relationship. Common sense should tell you if you ever observed how waves propagate in a water tank when you take a bath.

The pig is here again to take another whack at our poor old asteroid.

Lumo saith: I know exactly what the kinetic energy of the asteroid will be. But if it evaporates, then it's just converted into the heat in the atmosphere, does not it? About 100,000 Hiroshimas of heat in fact. If we assume the evaporation takes place at say 100,000 m (and it sure as hell won't) the resulting fire ball will convert about 10000 km^2 of earth to glass, and a much larger area will be incinerated. A large plug of the atmosphere would then eject into space, producing several hundred mile/hr winds into the area vacated.

And the pressure from the "momentum" will be just divided to tens of squared kilometers of Earth's surface, which is a negligible pressure wave, is not it?Let's assume the momemtum could be spread over say 100 km^2 (and I/ve already explained how it will be much more tightly focussed than that. Since the total momemtum transferred is about 10^17 kg m/s, the pressure pulse will be on the order of 10^9 N/m^2 (assuming a pulse wavelength of the same size as the asteroid diameter - very conservative, since this is really a shock wave). That's about 10^4 atmospheres and more than sufficient to completely crush any structure.

Don't they teach physicists to calculate anymore?

Hey pig,

you're essentially right although a few orders of magnitude obviously don't mean too much for you - much like they don't usually mean much for the particle physicists, which I appreciate. ;-)

The mass of that object is 8e10 kilograms, the velocity with respect to Earth will be 1.3e4 m/s. The momentum is therefore 1e15 kg.m/s. Here you've added two orders of magnitude.

100 squared kilometers is 1e8 squared meters. The momentum divided by the area is 1e7 kg/(m.s). Finally we must divide it by the time in which the pressure will be felt, and in my opinion it will be closer to the order of one second - or a bit less - which is the time it takes for the object to penetrate through the atmosphere.

OK, I did not grab any other orders of magnitude, just the two mentioned at the beginning, and it gives 100 atmospheres or more. How can one visualize the pressure of 1e7 Pascals? Note that the pressure of a column of liquid is h.rho.g. For water, rho=1000 kg/m3, g=10, so h.g=1e4. So the 1e7 Pa pressure is like from a kilometer of water, which I agree is probably enough :-) to crash most buildings.

Best
Lubos

Of course, I forgot to say "most building except for those designed by the Czech architects", like

http://en.wikipedia.org/wiki/Hiroshima_Peace_Memorial

Incidentally, what size of tsunami do you get if you calculate the effect of such an asteroid in the ocean? I am getting pretty good tsunami. ;-) I tend to believe that this asteroid would have to be stopped even if it planned to land in the middle of Pacific.

Lubos - You are right about the two extra orders of magnitude :-( in momentum. My bad.

Rather than argue about the width of the pressure pulse, it's probably better to think about the momentum transfer - still about 8*10^6 kg/(m*s) - like colliding with a ton of bricks/m^2, moving at 4000 m/s. Not sure even Czech architecture can stand up to that.

PS - Shock wave are about 1 mean free path thick. Even after decay to sound waves, the pressure pulse should be very narrow, much thinner than my initial estimate.

The Czech architecture can certainly stand up to that! The only question is whether everyone will have the money to rebuild their houses with a Czech architect. ;-)

You know, one cannot be too sissy. Someone was hit by a stone and cried the whole night. A friend of my friend was so tough that when he collided with a ton of bricks, he did not even make a beep. :-)

I don't know if your bricks are correctly calculated - the bricks deliver the momentum very quickly.

Sure, if you sort of preserve the "solidity" of the material, you will still obtain horrible results. The asteroid itself has 13 km/s, which is too fast. Even if you expand the area of its impact from 400 meters to 40 kilometers (100 times linearly, 10,000 quadratically), the momentum will still be like from a 400 meters thick asteroid with 1 m/s velocity, or 1 meter thick asteroid with 400 m/s velocity. It's still horrible.

I am kind of confused why they think that such colissions would be just at the level of a small country. I even agree with you that you can get at least these 2 orders of magnitude back from the "time" if you consider something like that shockwave.

Imagine it lands in the ocean, and creates a big wave in the ocean - consider a ring between 5 and 10 kilometer radii. How tall the initial water column in that ring will be? Is it enough to compare the potential energy of water with the kinetic energy of the asteroid? If it propagates for thousands of kilometers in the ocean, how big tsunami will you get at the end?

Best
Lubos

Quantoken said:
" I knew how to estimate propagation of water waves in a tank of water when 14 years old. It is roughly the square root of (density*g)/h and has nothing to do with amplitude or wavelength"

Tsanumi have nothing to do with ordinary waves you see in a tank or pond or bath. They are "shallow water" waves meaning they have very long wavelengths (typically 100km and over) and long periods. They are essentially solitions--solutions of nonlinear wave equations like the Kortweg-de Vries equation in the "shallow water" approximation given when the ratio (h/wavelength) is very small.
Their velocity is given by
v= sqrt(g * h) where h is the water depth, and the rate at which they lose energy is proportional to the inverse of the wavelength. These solutions are verified in the lab.

Since the wavelength is very large they don't dissipate efficiently (are solitonic) with very negligible energy loses and can travel 100s or even 1000s of km...with devastating results as we have just seen unfortunately.
Steve M

Lubos, Steve, et. al., The answers to your tsunami questions can mostly be found in this paper by Ward.

Within a hundred km of impact, a 200 m asteroid would produce a tsunami several hundreds of meters high, but would have relatively short wavelength and hence decay relatively rapidly, resulting in a garden variety 2-3 m. tsunami a few thousand km away. Bigger asteroids would produce longer wavelenths and greater amplitudes, so might be considerably more dangerous.

I don't think it's correct to describe tsunami as solitons. They are roughly 10km in wavelength, and hence in contact with the ocean bottom so they are shallow water waves, but the medium is still quite dispersive. See Ward cited above.

Gravity waves, section 15.2, chapter 15
http://www.pma.caltech.edu/Courses/ph136/yr2004/

I've seen articles desribing the Tsunumi mostly as solitons, although I am much more familiar with solitons in physics as solutions of the sine-gordon equation, nonlinear schrodinger equation and the KdV equation. Oceanic hydrodynamics and wave propagation is invariably a much harder application. Surely the Tsunami would pass through a solitonic phase though? The destructive power is certainly not in question however, with over 22,000 dead nows let not forget plus colossal damage. Normally I would consider this math interesting but the word tragic is a more appropriate description right now under the circumstances. Nature simply does'nt care if we get caught in the way.
Steve M

Mr anonymous was right I remembered the formula wrong. The correct one is sqrt(g*h). What I remembered is the wave go slower in shallower water (what a tongue twister:-). You can get that formula by simple classical mechanical considerations. Or you can use dimentional analysis, a method often used when you study fluid dynamics. You figure to give the correct unit, sqrt(g*h) is about the only correct combination.

Tsunami waves are just like regular water waves created by a splash in a bathtub. The two are different only in scale. Actually scientists do use bath tub like water containers to do physics simulations of the actual thing. Since the wave slow down when it reaches the shallow water of the coast, the later arriving faster waves would push the early arriving slower waves. They pile up and so create high tides on the coast. You actually see the same thing when you spill water out of bathtubs.

Quantoken

Professor Motl, even though you said that the public should not worry about such things, I believe that there is a chance that another asteroid besides 2004 MN4 could be approaching the earth. Especially, if it were the case, I believe the chance that the U.S government doesn't disclose its information to the public is 99.9%, cause they don't want the public to panic. Of course, there aren't many things the public can do, when an asteroid is approaching the earth. So, even though an asteroid might be approaching us, it still remains to be true that it is best to public's interest that the public doesn't worry about such things. So, you are right, in a sense, I agree, the public should not worry about such things. But, personally, I have some other reasons to believe that an asteroid hits the earth soon. In that sense, I don't agree with you for 100% either.

Dear contributor,

I think that the MN4 example shows that NASA *is* publishing information about it because it's their job. Your conspiratory theories about the US government are particularly confusing especially because George W. Bush and his cabinet themselves are probably far from being able to calculate the paths of the asteroids. You know, I admit his inability to calculate the asteroids even though I am his supporter. ;-)

It must be done by the real scientists (well, it's mostly automatized today), and not just one, and be sure that the information would leak.

Best
Lubos

Dear Professor Motl
I believe that the information would not leak, because they fear punishments. B/C It should be a state secret.
Would you mind betting 1000 dollar on this issue with me? If an asteroid doesn't hit the earth by December 31st, 2023, I will give you 1000 dollar by January 1st, 2024. If an asteroid hits the earth anytime from now to between December 31st, 2023, you give me 1000 dollar in a month from the day the asteroid hits the earth.(if both of us are alive) Does it sound reasonable?