atomic bomb question

[Loren Pechtel]

I didn't see Meteor but in the film, Armeggedon, I think they had a better plan in regards to the effectiveness of such a weapon: to drill into the body and plant the bomb inside. In the film, the scientific idea was to use the nuke to split the asteroid in two. While it appears this may not be possible on an object the size of the one in the film, I think the concept would yield a better result than exploding a nuke either nearby or even just at impact on the surface.

That said, I'm not sure how practical it would be to try to put a bomb plus drilling equipment up into space and then still have to have it bore into the object. I think the idea of sending astronauts up to do the drilling is even more ludicrous.

Splitting it is absolutely the wrong thing to do. The thing is a falling rock does an awful lot of overkill. Energy spent digging a crater doesn't kill anyone--they were already dead anyway. The damage radius goes up at the third root of the energy, since the area goes at the square of the radius the result is the damage area goes at the 2/3 root of the energy.

Lets take the simple case, you split the threatening object into 8 equal parts. Each part has half the damage radius (third root of 8) and one quarter the damage area. There are 8 parts, though--8 x 1/4 = twice the total damage area. (The math works regardless of the number of pieces, I just chose a number that wouldn't cause any irrational numbers.)

The only reason I can see to go for a split is if you are limited in blast energy rather than total mass. A carefully placed set of charges could perhaps blast it into two halves that are receding fast enough to generate a miss--this gives about 10x the efficiency of your bombs that nudging it aside would do. However, it requires landing and drilling to place the bombs while nudging can be done by a bomb that's coming in like a bat out of hell. (And note the geometry of an intercept against a rock that's going to hit soon--it's coming down our throat. No way to put enough delta-v to land on anything less than an Orion.) You had also be pretty darn sure of yourself if you're going for a split--if it doesn't split cleanly you'll have a bunch of rubble with no chance of stopping it.

I have a hard time picturing a situation where you are blast limited rather than mass limited. (NASA says a dinosaur killer is 3 months out, they'll have their pick of the world's nuclear arsenals for the asking. The limiting factor will be boosters.) If the rock is so big that we don't have enough megatonnage it's going to be so big I doubt we can drill it for splitting.

 

[fromderinside]

So bilby and Shadowy Man between them got it right while they didn't say it right.

In what way was what I said not right?

The ball at its core is heated heated several million degrees. That temperature decreases on an inverse square from the point at which the temperature is taken. So the idea of warming the ball to 6000 degrees is limited to what is radiated from the surface. that is not the temperature to which the entire ball is heated.

 

[Shadowy Man]

The ball at its core is heated heated several million degrees. That temperature decreases on an inverse square from the point at which the temperature is taken. So the idea of warming the ball to 6000 degrees is limited to what is radiated from the surface. that is not the temperature to which the entire ball is heated.

Yes, you are correct that the whole ball of gas is not heated to 6000 K. But what we see is radiation from the surface and that was the relevant part to the definition of "white".

 

[repoman]

The inverse square law only works for point sources (or approximations). It is not directly tied to temperature.

This makes me think of an interesting question though. Do the neutrinos (and their energy ranges) that come out of the sun help to pin down the temp at the core? Sort of like a neutrino "color"?

This looks interesting:

http://arxiv.org/pdf/hep-ph/0609030.pdf

 

[Shake]

Splitting the meteor in two sounds like a pretty dangerous strategy; The effect of multiple simultaneous small impacts is actually WORSE than the effect of a single large impact, so you would need to be very, very, confident that you are only going to end up with a manageable number of large pieces, and that the explosion that separates them will impart the right impulse to each fragment to ensure that they miss the planet - that's fairly easy to arrange if the meteor is many months away, but with days (or worse, hours) to go to impact, breaking the object up is far more likely to do harm than it is to do any good.

Lots of smaller impacts are worse, because in a large impact, the effects are localised, and you are just as dead at 100psi overpressure and 3,000K as you are at 1,000,000psi and 50,000K, so concentrating the impact energy in one spot actually reduces the number of immediate deaths. Of course, if the single impact can take out the whole human race, then making things 'worse' is irrelevant; but if you are talking about a fragment that's going to 'only' devastate New York City (and let's face it, it's a disaster movie, so you almost certainly are), breaking it up into a large number of fragments that will devastate the entire continental US, is not going to win any votes.

Even with a planet-killer, breaking it up shortly before impact likely just turns one existential problem into a larger number of equally existential problems.

Yes, but who's to say it'll only break up into 2 pieces? That was the premise of the movie, and I'm saying the result may be different. I don't know, of course, it's just speculation. I wasn't trying to say we should do exactly as in the film, nor to the same end. I just thought that perhaps drilling and detonating a device inside such an object may be more effective than what's already been suggested here: either hitting the object or detonating in front of it.

 

[bilby]

Splitting the meteor in two sounds like a pretty dangerous strategy; The effect of multiple simultaneous small impacts is actually WORSE than the effect of a single large impact, so you would need to be very, very, confident that you are only going to end up with a manageable number of large pieces, and that the explosion that separates them will impart the right impulse to each fragment to ensure that they miss the planet - that's fairly easy to arrange if the meteor is many months away, but with days (or worse, hours) to go to impact, breaking the object up is far more likely to do harm than it is to do any good.

Lots of smaller impacts are worse, because in a large impact, the effects are localised, and you are just as dead at 100psi overpressure and 3,000K as you are at 1,000,000psi and 50,000K, so concentrating the impact energy in one spot actually reduces the number of immediate deaths. Of course, if the single impact can take out the whole human race, then making things 'worse' is irrelevant; but if you are talking about a fragment that's going to 'only' devastate New York City (and let's face it, it's a disaster movie, so you almost certainly are), breaking it up into a large number of fragments that will devastate the entire continental US, is not going to win any votes.

Even with a planet-killer, breaking it up shortly before impact likely just turns one existential problem into a larger number of equally existential problems.

Yes, but who's to say it'll only break up into 2 pieces?

Nothing in my post suggests that it would.

Indeed, breaking objects into just two pieces is very difficult indeed, and is most unlikely to occur.

That was the premise of the movie, and I'm saying the result may be different. I don't know, of course, it's just speculation. I wasn't trying to say we should do exactly as in the film, nor to the same end. I just thought that perhaps drilling and detonating a device inside such an object may be more effective than what's already been suggested here: either hitting the object or detonating in front of it.

It could be. But it's a more risky strategy, and requires detailed knowledge of the structure of the object (which would be very hard to obtain), and even with that information, it would be massively more difficult to do than simply setting of an explosion near (or on the surface of) the object.

 

[Loren Pechtel]

Splitting the meteor in two sounds like a pretty dangerous strategy; The effect of multiple simultaneous small impacts is actually WORSE than the effect of a single large impact, so you would need to be very, very, confident that you are only going to end up with a manageable number of large pieces, and that the explosion that separates them will impart the right impulse to each fragment to ensure that they miss the planet - that's fairly easy to arrange if the meteor is many months away, but with days (or worse, hours) to go to impact, breaking the object up is far more likely to do harm than it is to do any good.

Lots of smaller impacts are worse, because in a large impact, the effects are localised, and you are just as dead at 100psi overpressure and 3,000K as you are at 1,000,000psi and 50,000K, so concentrating the impact energy in one spot actually reduces the number of immediate deaths. Of course, if the single impact can take out the whole human race, then making things 'worse' is irrelevant; but if you are talking about a fragment that's going to 'only' devastate New York City (and let's face it, it's a disaster movie, so you almost certainly are), breaking it up into a large number of fragments that will devastate the entire continental US, is not going to win any votes.

Even with a planet-killer, breaking it up shortly before impact likely just turns one existential problem into a larger number of equally existential problems.

Yes, but who's to say it'll only break up into 2 pieces? That was the premise of the movie, and I'm saying the result may be different. I don't know, of course, it's just speculation. I wasn't trying to say we should do exactly as in the film, nor to the same end. I just thought that perhaps drilling and detonating a device inside such an object may be more effective than what's already been suggested here: either hitting the object or detonating in front of it.

Lets throw some numbers at it.

The asteroid was the size of Texas. Assuming a sphere that gives us a body 518 miles across. I recall nothing about density or speed so I assumed minimal values for both: porous rock and an impact velocity of 8 miles/second.

For the atmosphere to shield us from that we need to break it into a few trillion pieces--that will reduce the blast to what happened to Chelyabinsk. (Note: I'm assuming it burns up just as high and I'm not at all sure of that assumption! It's coming slower, I suspect it penetrates deeper before it blows.)

Saved? Nope. The rock dumps 4.27E27 J of energy into the atmosphere--but the atmosphere only weighs 5.1E18 kg and only half of that is exposed to the rock, 2.5E18 kg. The specific heat of air assuming constant pressure (if it's heated the air will expand outward from the Earth) is about 1KJ/kg. That's going to heat the air to a couple million degrees.

Of course these are only back of the envelope calculations but when uncertain I'm taking the conservative choice--reality is probably worse.

 

[Bomb#20]

Yes, but who's to say it'll only break up into 2 pieces? That was the premise of the movie, and I'm saying the result may be different. I don't know, of course, it's just speculation. I wasn't trying to say we should do exactly as in the film, nor to the same end. I just thought that perhaps drilling and detonating a device inside such an object may be more effective than what's already been suggested here: either hitting the object or detonating in front of it.

Lets throw some numbers at it.

The asteroid was the size of Texas. Assuming a sphere that gives us a body 518 miles across. I recall nothing about density or speed so I assumed minimal values for both: porous rock and an impact velocity of 8 miles/second.

For the atmosphere to shield us from that we need to break it into a few trillion pieces--that will reduce the blast to what happened to Chelyabinsk. (Note: I'm assuming it burns up just as high and I'm not at all sure of that assumption! It's coming slower, I suspect it penetrates deeper before it blows.)

Saved? Nope. The rock dumps 4.27E27 J of energy into the atmosphere--but the atmosphere only weighs 5.1E18 kg and only half of that is exposed to the rock, 2.5E18 kg. The specific heat of air assuming constant pressure (if it's heated the air will expand outward from the Earth) is about 1KJ/kg. That's going to heat the air to a couple million degrees.

Of course these are only back of the envelope calculations but when uncertain I'm taking the conservative choice--reality is probably worse.

Well, geez, if you want to throw numbers at it....

Let's generously assume the asteroid is only 294 miles across -- that means it's the area of Texas -- and has a density of 1.4, a low-end rubble pile. That's a volume of 5.7e16 cubic meters and a mass of 8e19 kg. The gravitational potential for half that mass at a radius of 235 km is GM/r = 11360 J/Kg. That comes out to 4.5e23 J -- 110 million megatons -- to break the asteroid in half and have the two pieces not promptly fall back onto each other from their own gravity. If the bomb scales up linearly from a W87 warhead, which delivers about two kilotons per kilogram, the bomb will need to weigh 55 billion kilos. For reference, the space shuttle's payload is about 23 thousand kilos.

 

[Loren Pechtel]

Lets throw some numbers at it.

The asteroid was the size of Texas. Assuming a sphere that gives us a body 518 miles across. I recall nothing about density or speed so I assumed minimal values for both: porous rock and an impact velocity of 8 miles/second.

For the atmosphere to shield us from that we need to break it into a few trillion pieces--that will reduce the blast to what happened to Chelyabinsk. (Note: I'm assuming it burns up just as high and I'm not at all sure of that assumption! It's coming slower, I suspect it penetrates deeper before it blows.)

Saved? Nope. The rock dumps 4.27E27 J of energy into the atmosphere--but the atmosphere only weighs 5.1E18 kg and only half of that is exposed to the rock, 2.5E18 kg. The specific heat of air assuming constant pressure (if it's heated the air will expand outward from the Earth) is about 1KJ/kg. That's going to heat the air to a couple million degrees.

Of course these are only back of the envelope calculations but when uncertain I'm taking the conservative choice--reality is probably worse.

Well, geez, if you want to throw numbers at it....

Let's generously assume the asteroid is only 294 miles across -- that means it's the area of Texas -- and has a density of 1.4, a low-end rubble pile. That's a volume of 5.7e16 cubic meters and a mass of 8e19 kg. The gravitational potential for half that mass at a radius of 235 km is GM/r = 11360 J/Kg. That comes out to 4.5e23 J -- 110 million megatons -- to break the asteroid in half and have the two pieces not promptly fall back onto each other from their own gravity. If the bomb scales up linearly from a W87 warhead, which delivers about two kilotons per kilogram, the bomb will need to weigh 55 billion kilos. For reference, the space shuttle's payload is about 23 thousand kilos.

Where are you getting the 294 miles? I went with a sphere that had a cross-sectional area the same as Texas.

And you're not blowing a rubble pile into two pieces no matter what charge you use!

 

[Bomb#20]

Well, geez, if you want to throw numbers at it....

Let's generously assume the asteroid is only 294 miles across -- that means it's the area of Texas -- and has a density of 1.4, a low-end rubble pile. That's a volume of 5.7e16 cubic meters and a mass of 8e19 kg. The gravitational potential for half that mass at a radius of 235 km is GM/r = 11360 J/Kg. That comes out to 4.5e23 J -- 110 million megatons -- to break the asteroid in half and have the two pieces not promptly fall back onto each other from their own gravity. If the bomb scales up linearly from a W87 warhead, which delivers about two kilotons per kilogram, the bomb will need to weigh 55 billion kilos. For reference, the space shuttle's payload is about 23 thousand kilos.

Where are you getting the 294 miles? I went with a sphere that had a cross-sectional area the same as Texas.

4 pi r² -- in the spirit of "so I assumed minimal values", I went with surface area instead of cross-sectional area as the interpretation of "the size of Texas" in order to give the "Armageddon" scenario the benefit of every possible doubt. But you're probably right about what Billy Bob Thornton meant...

And you're not blowing a rubble pile into two pieces no matter what charge you use!

True; but I did the calculation for the low end of known asteroid densities, which means rubble pile, and for only two pieces, in order to assume minimal values again -- blowing an asteroid into a trillion pieces will take a lot more energy than merely blowing it in half. The goal is to prove that the 55 billion kg bomb we'd have to lift is an underestimate.

 

[Loren Pechtel]

Where are you getting the 294 miles? I went with a sphere that had a cross-sectional area the same as Texas.

4 pi r² -- in the spirit of "so I assumed minimal values", I went with surface area instead of cross-sectional area as the interpretation of "the size of Texas" in order to give the "Armageddon" scenario the benefit of every possible doubt. But you're probably right about what Billy Bob Thornton meant...

That's really stretching "size of" but I'll concede.

And you're not blowing a rubble pile into two pieces no matter what charge you use!

True; but I did the calculation for the low end of known asteroid densities, which means rubble pile, and for only two pieces, in order to assume minimal values again -- blowing an asteroid into a trillion pieces will take a lot more energy than merely blowing it in half. The goal is to prove that the 55 billion kg bomb we'd have to lift is an underestimate.

Bigger bombs can have a better yield. Perfect is .7% conversion efficiency--3kt/kg. You're still not lifting that, though, even with Orion.