Friday, February 15, 2013

Should we build a defense system against meteorites?

We were promised that today, the 2012 DA14 asteroid would pass just 27,700 km away from the surface of Earth today (watch live later tonight). That would be the closest distance recorded by humans for an object of this or larger size (diameter about 50 meters).

Also, we were told that no object would actually hit the surface of Earth on Friday 15th, 2013. Technically speaking, that was wrong. ;-) An unrelated meteor (Google News) was seen – and affected – the Chelyabinsk region in central Russia, 300 km South from our (Pilsen's) twin city of Yekaterinburg (formerly Sverdlovsk, named after a bloody communist murderer of the tzar family) where I spent July 1988. See a collection of amateur videos (plus YouTube) of this meteorite that is said to be the largest one since the 1908 Tunguska event (yes, Russia seems to have a monopoly in this field: Gagarin was just a minor example of this fact).

Despite the "uniqueness status" of both objects and their taking place on the very same day, these two events are almost certainly unrelated. The speed of DA14 relatively to the Earth was about 7.8 km/s while the speed of the Russian meteor relatively to the surface was about 15-30 km/s. It's remarkable that no one can provide us with more accurate numbers. It must be possible to extract the exact velocity vector from the amateur videos, right?

It's also being said that the direction of the Russian meteor was different (almost opposite) from that of the 2012 DA asteroid: DA14 went from South to North, the Russian rock went in the opposite direction.

What was the impact of the Russian meteor? People saw an impressive fireball in the sky, followed by a loud sound wave. The latter shattered lots of windows and broken windows and similar things injured about 1,000 people (mostly bruises), 50 of whom were injured somewhat more seriously.

The Russian officials reacted quickly and brought specialists to the scene. They also quickly offered a compensation for the broken windows. Russian citizens – who have been trained for 70 years how to maximally benefit from the socialist state's offers – were even faster. They immediately bought all the plastic temporary windows in the shop and as soon as they learned about their generous post-socialist government, they started to break their windows by their hands in order to get new ones and some money, too. ;-)

That's it. This is what meteorites do to us for one typical century. See how authentic Russian folks reacted.

Now, Anthony Watts believes that instead of global warming, people should spend lots of money for this threat. He kind of suggests that he considers the threat posed by similar cosmic objects to be as serious as global warming is serious according to the global warming alarmists.

Well, I surely agree that some folks should get millions and maybe even billions of dollars to develop technologies to monitor asteroids and/or destroy them by nuclear weapons sometime in the future. But to spend those global-warming-like trillions of dollars for asteroids? No way.

One should be reasonable about the costs-and-benefits analysis. If we were hypothetically able to prevent the damage caused by meteorites similar to the Russian one (by size as well as population density in the target), we could save millions or billions of dollars per century. No human lives so far. So we surely don't want to spend trillions per decade for avoiding this threat, especially because it's impossible.

I am more thinking about the larger – and less frequent – asteroids that sometimes hit the Earth. It would be good to have some plan in the case that those are seen – and most of the large ones may be seen. See NASA's Near Earth Object Program and its list of current threats. We could discuss the plans to break these objects into pieces by nuclear weapons etc. – I don't have too much original stuff to say that would go beyond the movies about these scenarios.

We're talking about objects that hit the Earth once per thousands or millions of years; I don't want to be too specific. Let me use the room in this paragraph to clarify some terminology. "Asteroids" used to be the name for small planet-like objects between Mars' and Jupiter's orbit but the word got abused so that it could represent vastly smaller objects, too. Therefore, when it comes to the size, the word "asteroid" is almost completely ill-defined these days. On the other hand, a meteoroid should be smaller than 10 meters or so. A meteoroid is the name for such an object while it's flying in the outer space; when it enters the atmosphere and shines, it becomes a meteor; and if and when it hits the surface of the Earth (some meteors are burned before they achieve this goal), it becomes a meteorite. Fine.

But let me return to the meteorites of the Russian size. Unlike Anthony, I think it's mostly preposterous to try to fight against similar threats. One may emit impressive numbers about the meteoroid's carrying the energy of 700 Hiroshima bombs but you know, it's not too much. The Russian H-bomb had somewhat higher energy still and it hasn't killed anyone. The same is true for most of such celestial objects because they don't try to hit the people.

And if we're unlucky, they will kill some people locally. But even in that sad case, you must see the damages in some proper context. A meteorite similar to the Russian one is as harmful as an earthquake of a certain moderate magnitude (try to insert the right number into this sentence). It has a similar local impact, too. Earthquakes of this equivalent magnitude are taking place much more frequently than the collisions with the Russian-size meteoroids. So the overall impact of the meteorites of this size is a small fraction of the impact of the earthquakes – and we don't really fight against the earthquakes too efficiently, either (even the arresting of innocent Italian seismologists fails to be an efficient way to fight earthquakes). Earthquakes don't exterminate the whole mankind.

Moreover, the collision with this particular Russian meteoroid couldn't have been mitigated. The object was invisible simply because it was coming from the Sun – not quite precisely but precisely enough so that it was overshadowed by the sunshine most of the time. Perhaps, we could see such a body 1,000 seconds or 15 minutes in advance. Multiply it by 20 km/s to get 20,000 kilometers – the distance from the Earth in which this object could become visible. But 15 minutes before the impact may already be too late.

I don't want to be too specific about these numbers because the technology is evolving and I am no expert in its current abilities, anyway. But what I really feel rather certain about is the other side: the expenses. We may compare the hypothetical anti-meteorite defense system with the world's best anti-missile defense system, Israel's Iron Dome which has made a real impact on the conflict with the terrorists in Gaza who try to shoot missiles to Israel all the time.

Iron Dome has deployed five batteries. Each of them costs $50 million and one anti-missile costs about$100,000. That's cheap, of course, but it's still expensive enough so that the managers of Iron Dome must ignore Hamas' missiles that are likely to land in unpopulated areas (fields). But if you want to protect the Earth against meteorites, you should count how many batteries you will need and how much more powerful, fast, and accurate they should be relatively to Iron Dome.

The problem you must realize is the speed of the meteoroids. Scuds and other Hamas' rockets move by the speed about 500-600 m/s. Only the intercontinental ballistic missiles are 13-14 times faster. At 7 km/s, they're getting closer to the meteoroid category of speeds. (The escape speed from the Earth is 11 km/s or so.) If you want to count the number of batteries you need, you must know which portion of the globe you want to protect, how much time in advance you learn about the meteoroids, and how does the speed of your anti-missiles compare with the speed of the meteoroids. And you must pray that the accuracy will be good enough.

I am convinced that even in the absence of any particular numbers, it's pretty clear that you will end up concluding that it's a waste of money to try to protect your land against the meteoroids of the Russian size. You know, it's harder to "shoot down" a very fast meteoroid than a Scud missile; they cause comparable damages; but the Scud missile arrives at least every week while the Russian-size meteoroid only hits Israel once per 2.5 million years (I multiplied 100 years for the whole Earth by 25,000, the ratio of the Earth's surface and Israel's territory). Now, 2.5 million years is about 100 million times larger than one week. It follows that the cost/benefit ratio is about 100 million times greater (less economic) for the anti-meteoroid defense system than it is for the anti-Hamas defense system. And even the latter is financially controversial! ;-)

So no, it's stupid to waste the money for these local threats. It seems to me that good folks like Anthony and others are driven by the utopia of a completely safe world where all the risks are zero. But such a world can't exist according to the laws of physics. In the real world, some risks always exist and it costs something to reduce them. You should be very rational about the costs and about the question which threats deserve to be wrestled with.

I think it only makes sense to discuss the defense against the nearly continental-in-size threats posed by the celestial objects on their collision course with Earth. And in that case, we're getting to the science-fiction realm whose typical time scale is counted in thousands or millions of years. Unless we are unlucky, we won't see such a continentally or globally devastating object hitting the Earth for centuries and probably much longer than that.

And it seems reasonable that such large objects would actually be visible years or decades in advance. They should have some quasi-elliptical orbits and we should be able to see them many periods ahead of the collision, just like in the NASA's Near Earth Object Program. If we have decades for the preparations, we should be able to invent something. In some sense, I think that decades of time is a lot of time for thinking and it is useless to do the preparations before we (or our descendants) actually face the threat. Even after 3 seconds of thinking, one may invent the idea of simply sending some thermonuclear weapons against the celestial object and try to tear it apart. I guess that with a year (or years) of discussions among true experts and best engineers, one could get better or more reliable solutions.

It seems to me – although, strictly speaking, I don't have a proof – that dinosaurs and other ancestors of ours didn't have the required know-how and weapons. Apologies if my reasons look racist to you but I just find these lizards rather stupid! ;-) We have a much better chance to protect ourselves against certain continental types of destruction – perhaps with the help of evacuation, too.

What about even larger events similar to the Cretaceous-Tertiary extinction event 66 million years ago? I am not sure whether we have a chance. I think that we would know about the threat many, many years in advance, too. It's just unlikely that something sufficiently large enters the Solar System along a hyperbolic (or parabolic) trajectory because the surrounding space is rather empty and boring.

I am sure that people will try their best if they learn about the looming extinction. And if they decide that the Earth is doomed, I am sure that they will try to create Noah's arc to protect some species in outer space or on the Moon or other planets (so that they may return to the Earth once it's safe again). If it were a top priority, I am confident we could store some species and humans etc. on the Moon, too. Just multiply the funding for NASA by a factor of 100 and you will see some improvements.

Of course that humans shouldn't close their eyes and ignore all conceivable threats. And if they see a threat, of course that humans shouldn't be – and won't be, whether we think that they should or shouldn't be – waiting for the Armageddon to devour us. However, I don't think we should be preparing for totally unspecified, abstract dangers of this sort long before we see any of them and long before we see what they exactly are. These premature preparations wouldn't improve our (or our descendants') situation too much but they could be way too costly (and grow into an irrational self-supporting hysteria similar to AGW, anyway). That's why I am probably not going to join Anthony's club of asteroid alarmists anytime soon.

And that's the memo.

1. it would be absolutely stupid if they don't develop systems to stop objects that could destroy cities and countries. and first they have to practise.

2. No need to go the Moon, some people could choose to live in some deep underground cavities or purpose built bunkers... I'm not sure it'd be enough to survive Armageddon time though...

3. CNN has got a suggestion as to why it happened:
http://www.dailymail.co.uk/news/article-2277529/CNN-anchor-suggests-meteor-hurtling-Earth-result-global-warming.html
Isn't it incredible?!

4. The probability of another Chixulub event is on the order of 10^-8 per year which, clearly, should be ignored given the current state of technology.
In order to destroy such a 10-km, 10^12 ton object with a nuclear bomb, the bomb would have to be detonated deep within the object: a surface explosion would not work. If discovered early enough, It might be possible to dig a 1 to 2 km deep well and detonate a high yield device 1 to 2 km below the surface. If the cohesive strength of the object were not too great the resulting blowout could deflect the remaining 99 to 99.9% of the object enough to miss the earth. A rough calculation shows that this would have to be done several months before impact if the object’s trajectory happened to be exactly centered on our planet. In order to optimize the chances of success a small diameter exploratory boring could be used to characterize the object’s mechanical properties and do real engineering. Guesswork would likely fail. At any rate we would need several year’s warning for such a task.

If the object were an Oort cloud object (comet) it would be relatively easy, however. Dirty snowballs, we could manage.

If the object happened to to consist of strong rock or, heaven forbid, metal, this would not be feasible at all. Even if we were to marshall every available resource the chances of success would be essentially zero. Any human survivors on earth would have to go to an underground bunker with a couple of decade’s food supply.

Of course I’m not going to lose sleep over this completely negligible threat.

5. according to a documentary from BBC called Space and Hyperspace with Sam Neill, the time that there should be an impact has already passed. i am not saying that what the documentary says is necessarily right but if this is true the chances are much more since such events happen during certain periods.

i am not saying that it has many chances of happening but if it happens once is enough. much more money is spent on much less important things. such collisions are very frequent in the Solar System but we are protected by some of the bigger planets.

hoping for something not to happen although it could wipe out life on the planet is stupid, especially if the technology would cost some hundred millions which is peanuts compared to its importance.

6. thanks for share...

7. LOL. Bill Nye's measured IQ jumped about 10 points here.

8. blonde girl knows what she says :)
http://www.ecoenquirer.com/global-warming-asteroid.htm

From the magnificent warmlist:
http://www.numberwatch.co.uk/warmlist.htm

9. " the bomb would have to be detonated deep within the object: a surface explosion would not work."

Gene, that's the argument in a movie. To have astronauts, emotion and Bruce Willis making holes.

10. "If the object happened to to consist of strong rock or, heaven forbid, metal, this would not be feasible at all. Even if we were to marshall every available resource the chances of success would be essentially zero."

Nuclear bombs are cheap and unlimited power.
Able to deflect any hard asteoride by evaporation of part of its surface.

11. Detection of objects of about that size would be good. (FWIW: I saw a TV news report where they compared the meteorite to the size of a small car -- with a picture of a Trabant for illustration :-) which totally distracted me from whatever was said next.) Even 15 minutes is sufficient warning for many populated areas. It gives people enough time to put their heads between their knees and kiss their @rse goodbye.

Seriously though; the risks of flying glass from atmospheric "explosions" can be reduced by having people keep away from windows and preferably indoors. Warning messages need to be clear and give SIMPLE instructions to the populations that are at risk.

Such events are rare. Very rare. So there's no point in "drills" for the wider population.

Warnings to areas also serve to "prime" emergency response teams in a region so that they can deal with actual damage more rapidly; and NOT produce a really bad response such as a nuclear counter-strike to an imagined terrestial threat.

The probability of large meteor strikes is small. The probability of people over-reacting is close to 1.0

12. Wow, it looks like you've been working on these Armageddon savior projects for decades, Gene! ;-)

13. The Soviet Tsar Bomba, which Khrushchev ordered detonated over Novaya Zemlya, released 50+ megatons of energy but did very little surface damage. It was the largest explosion in history and the cleanest (per megaton) due to the fact that it was mostly a fusion device. They could easily have exceeded 100 megatons with an optimized uranium tamper but it would have been very dirty. A Tsar Bomba detonation in a vacuum would just produce a sub-microsecond blast of gamma rays. Any human living within a kilometer or so would be completely (and explosively) evaporated by this radiation but the shock wave would be minor.
Explosions have to be backed up by a substantial mass to be effective and air works pretty well up to a few megatons. For Tsar Bomba, most of the mechanical blast energy was launched into outer space.

I recall a picture of Edward Teller with his arms wrapped around a Tsar Bomba replica. He loved it!

14. Nuclear bombs are powerful but huge ones are very heavy; there is a practical limit simply due to the mass that has to be delivered to an incoming body in deep space. Even the Tsar Bomba would require a launch vehicle far larger than anything ever built.
Surface vaporization by a nuclear device will produce a recoil but the effect is useless for a Chixulub-size impactor. If you do the numbers you will see that the detonation would have to take place many millennia prior to earth impact for a nuclear device of deliverable mass.
Look, If you don’t have the knowledge to do the calculations, fer XYZ, you are just guessing and that is a waste of your time and ours. Give it up and, for heavens sake, learn how to write complete sentences and how to spell “asteroid”.

15. George, have you even heard of the concept of quantitative thinking?

16. Your first sentence is a bit pessimistic,
Gordon. If you could turn the asteroid into an expanding debris cloud and that cloud had time enough to expand to many earth diameters only a small fraction of the mass would impact our planet. Of course there is a pretty severe size limit for this strategy to work. I would put this limit at 10^8 to 10^9 tons depending on the asteroid’s mechanical properties. If there are large metallic bodies coming at us our goose is cooked but this is very unlikely.

17. You’re right but you wouldn’t need to be very deep underground. The big factor would be food supply until things could get green again. It would be best to not eat all of the seeds you had stored.

Of course if you happened to be near ground zero you would be finished. It is interesting that most of the Yucatan Peninsula has no rivers or streams. The Chixulub impact broke up all of the geological formations creating a huge sponge. Even in this tropical land, water makes its way to the sea underground.

18. I was just remembering an exchange with a friend, which took place some 20 years ago. Our motivation was pure curiosity, nothing more.

19. suits you much better. there are more dangerous and less dangerous areas in the galaxy, the knowledge and technology from such a use would be very useful for this and other purposes, it would not cost that much compared to money spent on less important things. it did come pretty close didn't it? there were collisions before weren't there?

because you, Lubos and others connect this with global warming does not mean it is the same.

20. 'Asteroide' is spanish, no inane. A small mistake (A small mistake of Armada Invencible http://en.wikipedia.org/wiki/Spanish_Armada, why not speak spanish everybody:)

-Designs of the 60's have up to 10 Megatons per tonne. " The US claimed in 1963 that it could produce a 35 Mt fusion bomb, and put it on a Titan II (3,700 kg payload)," http://en.wikipedia.org/wiki/B41_nuclear_bomb

- For example Cassini has 2-3 tons. To save the Earth we can send a few more.

-An asteroid with speed of 20 km / s, and diameter 1Km. Suppose 3000Kg/m3 density. Kinetic energy Ec=1/2*(4/3*pi*500^3*3000)*20000^2 = 3.14E20 J.
Each megaton are 4E15 J. To deflect the asteroid 1 Earth radius ( About 200 seconds at that speed) we need about 6 months in advance if the energy transferred by a megaton explosion 100% efficiency. Or 10 megatons in 10% efficiency. Etc.

21. fer XYZ: “Asteroide” is, indeed, the Spanish word for “asteroid” but it is not what you wrote, which was “asteoride” and that is just inane or, if you prefer, stupid. You owe it to your readers to avoid such inexcusable laziness.

And as I told you, guessing never works for someone who does not get the basics of physics. Assuming that 100% or 10% (or 0.01%) of the energy a nuclear explosion at the surface of an large asteroid might be converted into kinetic energy of that asteroid is just wrong, by orders of magnitude. The laws of physics limit nuclear yield to about 6 kT/kg so arbitrarily large bombs are infeasible. Give it up.

First, my friend, you need to learn about momentum conservation. Failing that you are just flailing around and wasting our time. Please also consider conserving energy, yours, and ours. Your silence would be appropriate here.

22. Small asteroids, such as the 10,000 ton Chelyabinsk meteorite, can be destroyed/deflected by a nuclear device but they pose no significant threat; we are well protected by the earth’s atmosphere. This meteorite was around a 50 to100 year event. The sonic boom from such events can be detected around the world and there have been none of this size during the last five decades or so. It was a coincidence that Chelyabinsk struck in a populated area; the chance of that is less than 10% on a global basis. There is no record of any humans being killed by a meteorite although I understand a cow was once bonked by one.

The Tunguska meteorite was not much larger and very little of it reached the surface either. Siberian trees are generally easy to knock down. They have shallow roots and are often so close together that they fall like dominoes. This accounts for the wide area of downed trees. Nickel-iron meteorites can be deadly but they are rare. The metallic meteorite that created Meteor Crater in Arizona was about the same size as Chelyabinsk but several times more massive. About half of it survived to strike the surface with a kinetic energy of about 10 MT, creating the huge crater.
The Chixulub meteorite was 200,000,000 times more massive than Chelyabinsk and vastly too large to be affected by nuclear devices detonated near its surface. As a general rule, anything that can be deflected by a surface nuclear detonation poses no threat.

23. The huge asteroids have been found now. So a KT extinction event isn't going to happen for a long long time.

Trying to deflect these asteroids might be a waste of money but just surveying them is a relatively cheap thing to do.

The Large Synotpic Survey Telescope will be quite good at detecting moving things in the sky and it costs almost nothing (compared to other telescopes or government programs).

The 1km+ asteroid is almost never going to hit us, but the 10-100m one is much more likely, and its not so expensive to look for it. Also that size can be destroyed by nukes.

Having a broad coverage of the night sky is great science as well as common sense. A couple of million dollars per country would give us an almost perfect model of important asteroids.

But comets are always a wild card :)

The swift–tuttle comet would have wiped out most life on earth. They come in so fast and without notice that it would be hard to prevent it. In 100-500 years (if we dont kill ourselves) its probably not going to be such a big deal. We just have to hope one doesnt hit us between now and then (which is a pretty good bet).

24. Nuclear bombs in space would have to detonate very close to the target.

For a 10-100m sized asteroid the photon work could disperse it enough to neutralize its danger.

Bombs in space are far less dangerous than in an atmosphere. But stars are held in place by photo pressure, so while its not easy , its not impossible.

The biggest problem is the total energy, huge asteroids will cook the surface of the earth, it doesn't matter if they are in one piece or 1million. Smaller asteroids can be absorbed by the earths atmosphere without boiling us.

25. Nuclear bombs couldnt "deflect" a Chixulub size asteroid.

We would have to use gravity probes or implant thrusters on to it (or other ideas such as making one side more white so it will be pushed by the sun) (which would be effective as a product of its rotation).

If a 15km wide asteroid was heading for earth, we would be for a lack of a better word, fucked :)

26. The cost of a warning system and drills would far outweigh the damage of these once in a century events.

Its hard to see how you can prepare for such an unlikely event anyhow. It could hit anywhere, on the water, in moscow, or in the middle of siberia.

Its worth studying the sky more, I dont think its worth doing much else without a serious threat though.

27. Oort cloud objects are easy?

Comets mostly come in as one time objects and at enormous speeds.

It doesn't matter if its ice or metal, its just the total energy. A smaller comet can be vaporized and the total added heat to the earth isnt much.

But a huge ice ball or a huge chunk of metal is going to be the same. That energy is going to heat up the atmosphere the same.

If we were going to nuke an object this big, it would take a huge lead time. Bombs aren't so effective in space, without the atmosphere they dont do so much damage.

Drilling a few km is hard enough on earth, let alone on an asteroid, unless you are Bruce Willis.

28. If 90% of the life on the surface of earth was wiped out, its going to take a huge amount of baked beans to survive it :)

29. This also depends on the composition of the asteroid. Which will determine how the energy is dispersed.

Huge asteroids like the Chixulub one are better avoid by nudging. Almost no asteroid this big is going to be a rigid body required to split it apart as we would want. Even if just 1km wide hit us, it would be a really bad day. The last day for most people.

Explosions in space are not anywhere as effective as in an atmosphere like earth. Nuclear bombs in space just have photos and the few kg of material that makes them to push.

30. I did say: Such events are rare. Very rare. So there's no point in "drills" for the wider population.

I also alluded to the real threat of such events; not the direct damage, but the over-reactions of (fearful) people.

Say e.g. if international tensions are high and a feral régime is thought to be testing/amassing medium-range, nuclear-capable missiles. It's neighbours will be on a hair-trigger. A sudden bright burst of light; brighter than the sun, followed by a shock wave that knocks down walls and shatters windows may be confused with an air-burst of a low-yield nuke.

31. Maybe I said something to you to show that aggressiveness and lack of education?
If permute two letters is "stupid" (asteROide-> asteORide). How would you rate your physics or historical errors?
I do not know what kind of rational debate are your assertions "Your silence would be Appropriate here."
I have no problem recognizing that the correct and complete calculation is with momentum conservation (*)
You're right about that point. But you are probably wrong on his calculation (the momentum from vaporization is greater what you seem "calculate"), and in many other aspects, as I will show below. Will you be able to recognize it?

"..The laws of physics limit nuclear yield to about 6 kT/kg so arbitrarily large bombs are infeasible. Give it up."

False. The physics limit, assuming a 0.7% mass loss, would 150 kt / kg .
25 times higher than your figure, no permutation of two letters,
0.007 * c^2 / 4.2E12 J/kt = 148.3 kt/kg Do you agree?

Anyway I was saying that the ratio kt / kg of Tsar Bomb (50Mt/27t) was widely surpassed by the 1963 USA design (about 10 kt / kg), and actually deployed B41 bomb (> 5 kt / kg ), as shown the wikipedia link from b41.

"..As a general rule, anything that can be deflected by a surface nuclear detonation poses no threat."

Fortunately deflect asteroids not depends on your calculations, would be lost without hope :)
No need to drill hundreds meters deep. Subsurface blasts are suitable according to numerous papers http://scholar.google.es/scholar?q=asteroid+nuclear+subsurface

(*)My quick approximate calculation comparing energies happens to be quite correct. One of those curious coincidences of life. A megaton blast just 5 meters deep deflects a 1Km asteroid about 1 terrestrial radio in a few months.

But even you can see this example at 150 m above the surface:

"Numerous studies have been conducted in the past to understand the effect of a standoff nuclear explosion and its ?V capability. One particular study simulated the effect of a nuclear standoff detonation on homogeneous 1 km-diameter NEOs with densities between 1.91 and 1.31 g/cm m. Approximately 40 seconds after the standoff burst, at 150 m above the NEO’s surface, the NEO’s speed change ranged from 2.2 to 2.4 cm/s. It was estimated that 97.5% of each NEO from all simulations remained intact, while about 2.5% of its mass was ejected at greater than escape speed by the rebound to the shock wave that passes through the body in reaction to the ejection of heated material."

2.3 cm/s are 1 Earth radius in 10 month, similar to my approach.

"..There is no record of any humans being killed by a meteorite "

Obviously, mortality is concentrated in very rare and destructive events without historical memory but with a statistic of deaths / year higher than what we might think. (questionable calculations from docens/year to thousand/year)

32. defeatist :)

33. Maybe I said something to you to show that aggressiveness and lack of education?
If permute 2 letters is "stupid" (asteROide--asteORide). How would you rate your physics or historical errors?
I do not know what kind of rational debate are your assertions "Your silence would be Appropriate here."
I have no problem recognizing that the correct and complete calculation is with momentum conservation (*)
You're right about that point. But you are probably wrong on his calculation (the momentum from vaporization and rebound material from shock wave is greater what you seem "calculate"), and in many other aspects, as I will show below. Will you be able to recognize it?

"..The laws of physics limit nuclear yield to about 6 kT/kg so arbitrarily large bombs are infeasible. Give it up."

False. The physics limit, assuming a 0.7% mass loss, would 150 kt / kg .
25 times higher than your figure, no permutation of two letters,
0.007 * c^2 / 4.2E12 J/kt = 148.3 kt/kg Do you agree?

Anyway I was saying that the ratio kt / kg of Tsar Bomb (50Mt/27t) was widely surpassed by the 1963 USA design (about 10 kt / kg), and actually deployed B41 bomb (> 5 kt / kg ), as shown the wikipedia link from b41.

"..As a general rule, anything that can be deflected by a surface nuclear detonation poses no threat."

Fortunately deflect asteroids not depends on your calculations, would be lost without hope :)
No need to drill hundreds meters deep. Subsurface blasts are suitable according to numerous papers http://scholar.google.es/scholar?q=asteroid+nuclear+subsurface

(*)My quick approximate calculation comparing energies happens to be quite correct. One of those curious coincidences of life. A megaton blast just 5 meters deep deflects a 1Km asteroid about 1 terrestrial radio in a few months.

But even you can see this example at 150 m above the surface:

"Numerous studies have been conducted in the past to understand the effect of a standoff nuclear explosion and its ?V capability. One particular study simulated the effect of a nuclear standoff detonation on homogeneous 1 km-diameter NEOs with densities between 1.91 and 1.31 g/cm m. Approximately 40 seconds after the standoff burst, at 150 m above the NEO’s surface, the NEO’s speed change ranged from 2.2 to 2.4 cm/s. It was estimated that 97.5% of each NEO from all simulations remained intact, while about 2.5% of its mass was ejected at greater than escape speed by the rebound to the shock wave that passes through the body in reaction to the ejection of heated material."

2.3 cm/s are 1 Earth radius in 10 month, similar to my approach.

"..There is no record of any humans being killed by a meteorite "

Obviously, mortality is concentrated in very rare and destructive events without historical memory but with a statistic of deaths / year higher than what we might think. (questionable calculations from docens/year to thousand/year)