How does blast size scale with energy required? In other words to increase distance of vaporization from an epicenter of a blast at what rate does the energy of the blast have to go up? Is it linear, logarithmic, or what? I guess that kilotons of TNT is a common measure of source energy. Example: to double a blast radius of vaporization from 500 miles to 1000 mile how much additional energy is required.

This is so outside my field of study, so please keep it simple. Thank you.

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"Quaerendo inventis"

The volume of material vaporized (and the energy required to vaporize it) goes up as the cube of the radius of the crater...

However, with craters, there will be other lower-order effects having to do with the materials and environments, such as how well the atmosphere contains the blast. As the size of the blast increases, it is easier to pop the atmosphere above the blast, and so some energy is lost.

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As the cube...WOW!

Can vaporization occur outside the radius of the crater and what if it was an airburst?

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"Quaerendo inventis"

If the crater is in basalt, but there is a big thin sheet of dry ice a few crater radii away from ground zero, you can expect there will be some vaporization outside the crater... it all depends on how much energy is required to vaporize any given material.

Air bursts still transfer energy, but the formula for crater radius and depth becomes more complicated. It is still basically based on the volume to be vaporized, but also includes factors having to do with lost energy in other directions.

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That's the part that I knew there was no way I was going to figure it out. To vaporize organic material (plants and animals) on the surface out to a radius of a 1000 miles, or 500, with an airburst would take what?

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(By the way, I hate it that so many papers in the areas of planetary science and geology are not easily available to the dreaded "non-subscribers". It is like they are screaming at me: "YOU CAN'T HANDLE THE TRUTH". Good, I feel better now.)

"Quaerendo inventis"

It depends on the material, but it is easy enough to calculate what it would take for something where you know the specific energy required to vaporize something.

Let's say that you have a cubic centimeter of ice at 0 C sitting 1000 km from a big bomb explosion. That ice will vaporize at 100 C, and that will take a little over 400 Joules to accomplish (standard Earth Science). So the question is How big does the explosion have to be for a square centimeter to absorb 400 Joules when it is a million meters from the source?

Four Pi R-squared is the surface area of that sphere, so 4 trillion square meters, and one square centimeter is a ten thousandth of that, so the energy of the blast would have to be 40 quadrillion times the energy required to melt the cube, which is 16 quintillion Joules.

You probably are thinking about this in terms of megatons. Google found me a nice Joule to megaton converter... 4 quadrillion Joules per megaton... That means that a 4 gigaton bomb would be about what it would take to vaporize that block of ice.

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Is something of that magnitude even possible by an impactor without destroying the planet?

And thank you for your time and patience.

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"Quaerendo inventis"

It would be devastating to the surface of the planet, but not to the planet as a whole. See if you can find how much energy was released 65 million years ago at Chicxulub.

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Good idea, I think I have that here somewhere. Obviously it would be a bad day to be standing half the distance from the epicenter!

Again thank you.

edit to add: most sources are around 100,000 gigatons for the K/T event.

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"Quaerendo inventis"

The physics of an airburst can be very difficult to determine for an object hurling 10's of thousand of miles an hour into the atmosphere, as can be expected by an asteroid or cometary fragment.

A year ago, Sandia Labs did supercomputer simulations (see the article and movie links here). The study was based on observed effects at Tungusta.

As you hinted, an atmospheric burst from an asteroid or comet is totally different than that from a nuclear weapon. For the former, the total energy released is equivalent to 1/2*m*v². For the latter, it's in terms of kt-equivalents of TNT.

Furthermore, the rate at which the energy is released will determine the nature and the extent of the damage. Nuclear weapons release their energy far more rapidly than do meteors or comets.

If Tunguska was a comet, the effect probably involved the breakup of loosely aggregated ice and dust. The effect would be similar to tossing a bucket of water onto a beach ball, although the scales are somewhat different... The point is that the energy released probably occurred over many seconds, and all booms, bangs, and shattered windows were merely the result of the initial atmospheric entry shockwaves.

By contrast, had the same mass hit the planet, intact, we'd probably have had another event similar to the K/T extinction event.

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If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

Not likely. The K/T event was caused by an asteroid on the order of 6 miles across. Tunguska was a few tens of meters across.

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Ok, let's call it 70 m. Compare that to the roughly 300 m chunk which formed the mile-wide Meteor Crater in Arizona, and the 2000 m chunk behind K/T.

Assuming roughly equivalent velocities, and since KE is proportional to mass, which is proportional to the cube of the diameter, letting a 70 m chunk equal a factor of 1, we have the following:

70 m: 1 (if Tunguska had not broken up, but had struck the Earth)
300 m: 79 (meteor crater)
2000 m: 23,324 (K/T)

However, the factor for the 70 m assumes it struck Earth. Tunguska did NOT. Rather, it broke up high altitude, and in the process accelerated a large air mass to mach velocities. It's this accelerated air mass which struck the Earth, and toppled the trees for miles around. Nothing of the original mass remained at that point except chunks ranging from dust through bb's, to bullets, and a few sizes as large as shotgun slugs. The rest was probably aggregated but small chunks of ice which broke up before turning to water, and perhaps steam.

Comparing the actual Tunguska event to the above scale, since it didn't impact with the Earth itself, the Energy it imparted to the ground was considerably less than it would have been with a direct impact, at least by one order of magnitude, giving Tunguska a high .1 on that scale.

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If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

This seems logical and explains why the Tunguska crater was not found until recently. However, it seems the blast radius and destructive force of the airburst is greater because the energy is not absorbed by the ground upon impact. Wasn't one of the reasons, the military detonated their nukes at altitude was to maximize their effectiveness?

Except the rock behind K/T was more like 10,000m (6 miles), making your number low by a factor of 25.

Oh, and Veeger, you're right about that one. An airburst nuke delivers all the energy from a hemisphere (the bottom half of the explosion) to the target, while a groundburst only delivers the energy from a narrow ring - the rest goes into the air or into the ground, and is completely wasted.

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Oops. I saw the 6 and thought, "6,000 ft."

Er... No. There are airbursts, then there are airbursts. Furthermore, shock waves do funny things while travelling horizontally over the surface of the Earth.

Essentially, there are three components to an airburst: initial wave, reflected wave, and mach wave. The mach wave always travels at the speed of sound. The initial and reflected, however, do not. They begin at many mach, then slow down below mach. The point where they meet is called the "triple point," and that point is the product of many factors.

Suffice to say that it can be calculated so that the yield and altitude of the burst can be set to maximize desired effects.

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

Listening casually to a tv science show, it was stated that the meteor cuts a hole through the atmosphere that allows ejecta a pathway out of our atmosphere, given enough initial velocity. I had not heard that before, but it seems plausible. No doubt, size is critical to this.

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Yes, but in general, an airburst will do more damage than a groundburst for the reason I stated. The exact height required for the airburst to be optimized will vary though.

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Well...

It's your comment about "An airburst nuke delivers all the energy from a hemisphere (the bottom half of the explosion) to the target..." that doesn't fit the facts.

The target, ground zero, receives very little of the blast. If it's a circle with a radius equal to the length of a football field (300'), and the air burst is at 3,000 feet, and 80% of the bottom half of a 1 MT explosion is delivered within a 10,000 ft radius of ground zero, then...

1. 1 MT * .5 * 0.80 = 400 kt

2. Total area = pi * r² = 113,097,335 ft²

3. Target area = pi * r² = 282,743

4. Ratio of total area to the target area: 400.

Thus, the target area would receive 1/400th of the 400 kt blast, or just 1 kt. It would be as if a 1 kt (2,000 tons of TNT) were surface-detonated at the target.

Therefore, an airburst does NOT deliver "all" the energy from a hemisphere (the bottom half of the explosion) to the target. It only delivers a tiny portion.

Rather, an airburst distributes it's power over a wide area, and the altitude is calculated such that the triple point occurs around the distance where the initial and or reflected waves cease to cause the desired damage. In that way, an airburst extends the radius of destruction.

But if you want decimation of a smaller target, a ground burst works better.

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

By "target," I was referring to the general area surrounding the detonation, assuming you would want to decimate a large area (like a city).

If you want to completely obliterate a small target, then yes, a ground burst works better.

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If we consider an ET object (meteor, comet) and we assume a normal incoming velocity, what ground effects evidence (distance from epicenter versus destruction) should we look for, i.e. differential rate of destruction, to back track and determine type of impactor? Putting it another way, at distance x a tree is vaporized, at distance y a tree is knocked down, at distance z a tree is singed, how can these pieces of evidence be quantified to make an estimate of what hit?

edit to add: in the case of airburst.

edit to add #2: at Meteor crater the sand was changed by the blast from yellow to white powder sand. Energy required?

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"Quaerendo inventis"

The effects depend on three four main factors: mass, density, velocity, impact area characteristics.

Surprisingly, the impact angle can vary quite a good amount without much difference in the effects or the ultimate outcome.

Generally, you start with the diameter and depth of the crater. Then you include peripheral information, such as crater ejecta (type, composition, effects), as well as similar characteristics of the crater and it's walls. Third, you search for pieces of the meteor itself, as that will give you clues as to it's density, as well as to it's potential size (ratio of meteor found vs other matter). Then you crunch the numbers and can determine it's mass and velocity.

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.