So you believe we will spend trillions of dollars to send thousands of nukes to an imaginary asteroid whose path we can’t predict accurately but AGW is unsolvable so we shouldn’t even bother mitigating it.
Another thread won by your superior debating techniques!
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Let’s keep personal remarks out of GQ. There’s an active Pit thread available for your snarking needs. 
Colibri
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SamuelA is pointing out that, regardless of any deformation or internal changes, the same impulse always leads to the same change in velocity for an object of fixed mass. This is correct. At question is whether the text quoted in the OP suggests otherwise.
I’ll admit that I would have given editorial notes for the phrasing Stranger chose. “[T]he impulse … would likely be absorbed as deformation within the body” could be read as a claim that impulse-as-Delta(p) can somehow be dissipated through internal changes. That is not correct. But, because I know Stranger understands freshman mechanics, I assume that this is just a poorly worded statement that the impulse actually imparted depends on the mechanical properties of the material. That could certainly be true.
You are missing the fact that the springing back mass does detach itself from the asteroid and we do have multiple masses, so we are able to conserve momentum. That is the entire point. We are using the usual mechanism that creates craters and ejects the mass off the surface when a crater forms.
Craters are not simply formed by blasting a hole. There is a reaction to the initial deformation that rebounds and ejects the majority of mass out. Amongst other things this why you get the peak in the centre of craters.
Ultimately we can’t really answer the question without a detailed understanding of the asteroid’s composition and structure.
The best-case scenario is that you blast out a crater, with warm fragments flying off in one direction at relatively low speed. The rest of the asteroid stays in one piece. Here, most of the energy was not wasted by turning to heat or by sending fragments off at very high speed (high KE but relatively low momentum).
The worst-case scenario is that the asteroid absorbs its share of the energy but it’s not enough to vaporize or dislodge any matter. Here, all of the energy is converted to heat and the only momentum transfer is the photon pressure of the blast and a small amount from the bomb casing fragments. This is going to be many orders of magnitude below the best-case scenario.
Without knowing more, and without detailed simulations, you can’t know where on this spectrum you lie. Of course there are many intermediate points where some matter is vaporized, or some chunks fly off but at high speed (and low momentum), etc. So maybe it would be enough, maybe not. We know from basic physics that there must be some momentum transfer, but we don’t know how much simply by understanding the bomb alone.
All the ones I’ve seen photographs of look pretty solid. Where is the evidence of all these “gravel pile” asteroids if every one we’ve imaged at high resolution looks like a rock?
Vesta: 4 Vesta - Wikipedia
Eros, Steins, Gaspra, Ida: https://www.universetoday.com/wp-content/uploads/2014/08/Asteroid-shapes-craters.jpg
Mathilde: https://www.wired.com/images_blogs/wiredscience/2013/03/vestabehind_dawn_960-660x508.jpg
A bucket of sand looks solid–but it isn’t.
“Rubble pile” is an astrogeology term that simply means those bodies may not be solid monolithic rock. It does not mean they are anything like a floating pile of gravel, and certainly not in the context of collision behavior.
That is obvious from the Martian moon Phobos – also described as a “rubble pile”. Yet it was struck so violently by some object that (as described by NASA) it “likely came close to shattering” that moon: APOD: 2013 January 18 - Stickney Crater
If a “rubble pile” like Phobos can be struck so violently that it is nearly shattered yet it holds together, it would seem that anything puny humans could throw at it would not do worse.
In fact numerical studies indicate the reason Phobos survived the Stickney collision was because it not a monolithic rock but somewhat malleable and deformed to absorb the energy (Chapman et al., 1996a; Greenberg et al., 1996).
So the very nature of “rubble piles” like Phobos mean they are more capable of absorbing impact without flying apart than a solid rock. That is consistent with the imagery of that gigantic collision.
As the article you cited described described, a “rubble pile” in astrogeological terms means the object is like a partially melted shot and wax slug projectile commonly fired from a shotgun. It is cohesively bound together, just not brittle.
I’ll amend my previous analysis slightly having done a bit more reading. The dynamics of cratering and the ejecta are a bit different to my initial thoughts, but the core reasoning about momentum conservation remains the same. This page provides a nice overview of cratering from extreme energy events. Meteor impact are very close to nuclear weapons as in both cases the dominant energy transfer occurs due to vaporisation of the rock. (This was a significant cause of confusion in historical analysis of craters on the moon, as unless the impact angle is very low the crater will always be circular - which is because the energy comes from a symmetric vaporisation of the impactor and surface rock, and not from mechanical excavation by the impactor. The energy available in impactors was not understood, and the idea that so much energy was available hard to comprehend.)
The critical diagram on the page linked it Fig 7. Note the rock mass in orange. All of this mass is ejected from the surface. If the energy input is a nuke or a high velocity impactor it doesn’t make any difference. This ejected mass is the reaction mass that provides the momentum change for the asteroid. The trick is to get a mechanism to maximise the momentum in this ejected mass. It needs to have more than the escape velocity of the asteroid, which isn’t hard, but given a fixed energy input from the nuke, you actually want to minimise the velocity within this constraint and maximise the mass. e = mv[sup]2[/sup] whilst p = mv. As Dr. Strangelove notes, the worst outcome is very high velocities (in the extreme nothing more than photons) which provides the minimum possible momentum change.
The difficulties Strange noted are touched upon later in the page I link to. They discuss the differences in shockwave propagation and dynamics of excavation in different material. If you have nice solid material the sock wave travels nicely, the excavation proceeds with good transfer of kinetic energy. If the material is dispersive you lose energy and the amount of excavation falls.
An interesting point about the choice of nuke for asteroid interception is that you want the maximum amount of energy to be available as gamma rays. You can tune the nuke with different tampers and other surrounding materials. We want more gamma rays and fewer fast neutrons. I suspect the use of tungsten tamper is intended to augment gamma production.
Ugh, missed the edit window to fix a place-marker - where I wrote “The difficulties Strange noted” please read “The difficulties Dr Strangelove noted” :o
Some of the medium-to-smaller asteroids do look quite loosely packed. Here’s Itokawa asteroid, which is probably best described as a contact binary; it seems to consist of two fairly solid lumps joined together by a ‘neck’ of dusty material and boulders. I would expect this to change shape considerably if exposed to any propulsive blast from a nuke - maybe even split into two or more pieces.
https://upload.wikimedia.org/wikipedia/en/d/d1/Hayabausa_Image_of_the_asteroid_Itokawa.jpg
Having just now heard of it, you are of course now qualified to correct the established consensus reached by the real scientists on the matter.
[URL=“Are Asteroids Rubble Piles?”]Another link.](APOD: 2013 January 18 - Stickney Crater)
Let’s assume - and this is unlikely, as LSLGuy has suggested - that we can identify a collision-course asteroid ten years out with sufficient accuracy to compel a national or international response. Let us further suppose that the chosen response is to launch a series of nukes to try to divert the asteroid with a sideways nudge.
If you want to make it happen, you have to deliver your nukes to the asteroid while it’s still a long ways out. That means your missiles need a LOT of speed, on top of an escape velocity of about 25,000 MPH. These are going to be BIG rockets. The Saturn V could take 107,000 pounds to trans-lunar injection. A nuke weighs a lot less than that, but you’re not stopping at the moon; you need to be hustling past the moon about as fast as you can go, if you want to get to the asteroid in time. Plus, if you want to consistently detonate your nukes on one side of the asteroid, you’re going to need some amazing targeting hardware and software, and/or some maneuvering thrusters. Maybe even some braking thrusters so you don’t require amazingly precise detonation timing. So your payload isn’t just a simple 1,000-pound nuke. Bottom line, you’re stuck with big rockets, which take a while to design and build.
So…ten years’ warning? Even assuming sufficient motivation, it’ll be at least two years before your first nuke leaves the earth, and it’ll be several more years before it gets to the asteroid. At which point the asteroid is no longer ten years out, it’s more like four years out, and now needs a pretty big nudge to assure a miss. But the rest of your nukes are going to arrive later, when the asteroid is even closer. I think it’s pretty optimistic to believe that we could build/launch rockets the size of the Saturn V at intervals shorter than six months, so you’re only going to get a handful of nukes up to the asteroid before it lands in your front yard.
Well, a near-Earth asteroid is likely to have an orbital period fairly close to the Earth’s, and make many near misses before it makes a hit. For instance, Apophis has a period of 0.89 years. So in theory if you wanted to nudge Apophis out of a potential hit, you could send whatever to it during one of the scheduled near-misses, such as in 2029, when it will come within around 20,000 miles of the surface. You are therefore probably a tiny bit less screwed seeing a Near-Earth asteroid 10 years out than you are seeing a comet 10 years out.
Actually I had heard of them for years, I just thought it was a different object category from the recently imaged asteroids and Martian moon Phobos.
The term “rubble pile” can be confusing and the comments on this thread illustrate that. People tend to picture it this way: https://photos.smugmug.com/photos/i-pWWDz5W/0/8f2a1ca7/S/i-pWWDz5W-S.jpg
Such a loose pile of rocks would fly apart like cosmic billiards if struck by an object. Yet that clearly did not happen to Phobos (also described as a “rubble pile”) during the massive Stickney impact:
The reason for the cohesive strength of these “rubble piles” is still being researched by scientists, but a key 2013 paper determined it’s because the fine material acts as a “cement”, making a cohesive matrix that binds the aggregate into a body (Sanchez et al., 2013):
http://inspirehep.net/record/1237623/files/arXiv%3A1306.1622.pdf
So the first article you quoted which described these as “partially melted shot and wax” was correct from the standpoint of this paper.
While some of these objects do not look like nor behave like literal “rubble piles” (at least from a collision standpoint), they also don’t behave like monolithic rock.
Regarding the thread topic of asteroid momentum transfer, the imagery of the Stickney crater on Phobos shows what happened when a huge impact caused momentum transfer to that object.
Much is unknown about the geology of these objects, but current information indicates they differ in internal composition. Some like Itokawa are more clearly in the “rubble pile” category. 25143 Itokawa - Wikipedia
Others like Lutetia are probably not “rubble piles”: 21 Lutetia - Wikipedia
I think this is a reasonable analysis. Obviously this is a bad case scenario. My main point was really that each nuke you set off is getting you more push per kilogram of payload mass. Also, I had implicitly assumed you were going to spend the propellant to brake, but your idea is better - just fly by and set off the nuclear shaped charge at the right nanosecond. And yeah, you would have to pick the patch you set it off next to carefully, apparently the material type matters.
Apollo 10 and 11 were launched just two months apart, and if Apollo 11 had failed, there were additional Saturn Vs in the pipeline for two more missions that year. So even when global survival was not at stake, the capability existed (at least then) to launch them every two months.
But the entire Saturn V production pipeline from the subcomponent level to the Vehicle Assembly Building and test facilities were designed from the outset to support that launch rate. Achieving that infrastructure took about seven years.
The SpaceX Falcon Heavy can lift about half the Saturn V payload, and in theory given enough time SpaceX’s production rate might be increased but it would take years. OTOH presumably the NEO deflection scenario would be an issue of global survival so funding might dwarf Apollo. This implies the effort would be nationalized or a consortium of nations.
Considering a NEO deflection mission would be unmanned, the time-consuming aspect of man-rating the vehicle would not apply, so that would help some. The fastest spacecraft ever flown - New Horizons - was launched by an Atlas V to a solar escape velocity of 36,000 mph: New Horizons - Wikipedia
The Atlas V 551 has about 1/8th the payload capacity of a Saturn V and about 1/4 the capacity of Falcon Heavy.
Despite the relatively limited payload, it launched New Horizon to such a high velocity it passed earth’s moon in eight hours, vs three days for Saturn/Apollo. It reached Jupiter in about one year, vs about two years for Voyager 2 (which was launched on a Titan III).
However to achieve that velocity on a relatively small booster, New Horizon only weighed about 1,000 lbs.
The actual real-world yield to weight ratio for a nuclear warhead is about 400 kg per megaton. So for a booster the approx. size of the Atlas V 551 that launched New Horizon, the warhead payload might be less than 200 kg (440 lbs) to allow mass for the spacecraft structure, power, communications, guidance, thrusters, etc. If it were only 100 kg that would equate to an approx. 250 kiloton warhead that could reach Jupiter’s orbit in a year if launched from an Atlas V 551 or equivalent.
Probably the first thing you would launch is a tracking/guidance and imaging probe. Dual use, get pictures of the asteroid and land a guidance transmitter on its surface. Once you have the guidance transmitter in place getting the nukes into the right position and timing their detonation is going to be vastly easier. Without reasonably detailed imaging you probably have little chance of having any clue when and where to use the nuke(s).
I suspect a mass budget of 50:50 is a bit optimistic. It is a bit depressing just how much of any interplanetary probe is still mostly fuel and support infrastructure. In a crash build programme one would expect just about everything possible would be repurposed from existing designs, and possibly even existing hardware.
If you need an Armada of craft and nukes it is possible the pacing factor would be the tooling to make launch vehicles. Some things you can throw money and people at, some things can’t go any faster no matter what you do.
Personally I suspect a huge issue would still be politics. You can guarantee that there will be a huge body of asteroid-deniers convinced that the entire thing is a fabrication/conspiracy. The notion of having a number of nukes in space with targeting and delivery systems capable of dropping them anywhere would not be a an easy thing to stomach for any nation. Even after the asteroid is deflected - have all the nukes been used? What assurances do we have about this? If an international programme was used (and we would assume it was) has every nation (ie US, Russia, maybe China) ensures in a verifiable manner that there are no nukes left? Etc, etc. Nothing is insuperable, but the technical difficulties might only be the beginning.
There is no question a guidance and imaging probe would make things easier, and that would probably be done. However I don’t think it’s absolutely necessary. The Rosetta probe landed on a comet despite not having any prior close-up imagery or emplaced navigation aids, the NEAR spacecraft landed on Eros, same situation. The OSIRIS-Rex probe will land on an asteroid and return a sample, also without prior imaging or emplaced nav aids.
Yes, you always need more vehicle mass which hurts payload fraction. However in this case (using New Horizon as a guide) the payload was 1,054 lbs (478 kg). If we use 200 kg for the warhead, that is a fraction of 42%. I also mentioned 100 kg which would be 21%. But if it were only 50 kg (10.4% payload mass fraction) that still equates to 125 kilotons.
Actually they could not be dropped anywhere – that would require a reentry vehicle with the associated heavy aeroshell and frictional thermal protection. When the vehicle is headed directly away from earth at 36,000 mph, every gram counts, so you’d never waste so much mass accelerating a useless atmospheric heat shield to the outer solar system.
Get Liam Payne to swallow it.
