Saying that I have a Ph.D elicits a fairly predictable reaction from most people. They will, in an attempt to appear interested, ask “What subject?” and then when informed that I did Astrophysics – one of the simpler branches of physics if you don’t tangle with cosmology or relativity but which appears to have a fearsome reputation in the eyes of the layman – their eyes glaze over and they either stop talking to me altogether, or else they desperately try to change the subject before I can get a chance to pounce on them, knock them to the ground and inject pure Science into their brains via their ear canal¹. There’s a second type of person out there, however; the freakish sort who are genuinely interested in science, and this second type will, after some circumspect small talk, eventually get around to asking me what my thesis was about. And this is a question to which I have gradually evolved a tried-and-tested one-sentence reply:

“I am trying to find out how much energy you need to blow up Pluto.”

As with all one-sentence descriptions it doesn’t even come close to summing up the totality of my work, but it is accurate and it does its job of seizing their interest in an unbreakable choke-hold so that they ask the follow-up question:“Why?” Today, you’re all going to find out. You lucky, lucky people.

What does it mean to destroy something? Gormless techno-fetishist Michael Crichton inadvertently touched on why this is a bit of a tricky question in one of his godawful dinosaur novels, in which the shameless author self-insert of Ian Malcolm tells another character that his statement that nuclear weapons could destroy the world is really, really goddamn stupid. The reasons for this should be fairly obvious given the nuclear weapons post – while nuclear weapons pose a significant threat to humans, they could do very, very little to imperil the Earth. They’d scorch some parts of the surface, irradiate others, screw up the atmosphere for years – things that would have dire consequences for the future survival of the human race — but all this would amount to nothing more than a mild skin rash as far as the Earth is concerned. It’d just keep on truckin’ quite happily while we killed ourselves off.

Clearly you need a different magnitude of threat altogether in order to stand a decent chance of destroying the Earth. The sort of exotic cosmic catastrophe so enamoured of the Hollywood disaster movie notwithstanding (solar flares, quasars, supernovae, mini-black holes etc.), stuff smashing into other stuff is a thing that happens fairly often in our Solar System². What happens if we hit the Earth with a really big space rock? Well, that’s actually happened. The Earth was hit by a Mars-sized object very early on in its lifetime. Mars-sized.  The impact was so destructive we have a constant reminder that it happened in the form of the Moon. The impact was so destructive it blew off a majority of the Earth’s surface material. Yet even after this colossal impact event which would have fit most people’s criteria for “destruction” the Earth got better.

Key to this is that while the physical structure of the Earth was shattered by the impact, with bits and pieces flying in all directions, the heavy iron core was left mostly intact which meant the gravitational centre of mass of the Earth remained largely unchanged. Unless the impact fragments had been boosted up to escape velocity they were gradually and inexorably pulled back towards that centre of mass, with the result that the Earth slowly reformed much like Robert Patrick in Terminator 2. The Mars-sized impactor also left a remnant that accumulated bits and pieces of ejected surface material from the Earth; this went on to form the Moon, and it’s why the Moon is mostly made up of elements we’d expect to find in the Earth’s crust and mantle.

So even if you hit a planet-sized object really, really hard you’re not guaranteed to “destroy” it in any real sense of the term; you will disrupt its physical structure temporarily, but it may eventually reform into a single homogenous body again over millions of years. This destruction thing is a tricky business when applied to planets, and even when dealing with smaller stuff it’s difficult to draw a line. How much of an object do you have to destroy in order to say that the object itself is destroyed? A third? Two thirds? Total destruction? This is the first fundamental question that faces scientists who want to model impact events, and the answer they’ve come up with may seem arbitrary but it does have logic behind it.

First, impact scientists do not say impacts destroy something. We say they disrupt it, for the very good reason that disrupt is a term that can apply to any quantity of blown-off material, whereas saying something is destroyed runs into any number of problems up to and including the rather large one that matter cannot be created or destroyed, merely converted into energy. We define disruption by how much of the original body is left after we’ve whacked it with an impactor; in the case of my experiments I weighed my targets before they went into the gun, shot the crap out of them, and then weighed the biggest remaining chunk I could find afterwards. If that chunk was less than half the mass of the original body I’d rip open my shirt and beat my chest while let out an Arnie-in-Predator-esque roar of “DISRUPTION!”

The fifty-percent mark delineates disruption from cratering. If an impact removes less than fifty percent of an object’s mass it doesn’t count as disruption since the majority of the original object is still intact. Technically it’s a crater. It might be a really, really, really big crater – a crater that’s almost larger than the remaining mass of the body – but it’s a crater nonetheless. If the impact blows off more than fifty percent, though, it’s a catastrophic disruption outcome. This is as close to the word “destroyed” as you’ll ever get an impact scientist to go; personally I think the work in my thesis showed there’s a more granular range of impact outcomes than the simple binary choice of disruption and cratering described here, but my work was never published so eh.

So we’ve got a technical definition of “destroyed” now. In order to get there, we need to hit the object with enough kinetic energy to permanently disrupt more than 50% of its mass. Kinetic energy is worked out by the equation

where m is the mass of the impacting body and v is its velocity. Using kinetic energy allows us to make useful comparisons between an impact by a very small thing moving very quickly and an impact by a very big thing moving very slowly – i.e. it essentially makes the analysis independent of what the impactor actually is. We can further remove dependence on the size of the thing being hit by dividing the impacting kinetic energy value by the mass of the target; this gives the energy density of the impact, or Q, measured in joules per kilogram.

Q is, in theory, a very, very useful quantity. Say you have one target weighing 1 kilogram and another target weighing 1000 kilograms. By carrying out a series of impact experiments on 1 kilo targets in a lab environment you have determined that the energy density at which the 1 kilo target will lose more than 50% of its mass – the energy density at which it will suffer catastrophic disruption, or the critical energy density Q* — as 50 J kg^-1. In theory, it should then be possible to predict how much energy it’ll take to disrupt the 1000 kilogram target without having to manhandle any one-tonne weights around your laboratory; you just multiply by a thousand and bam, that’s how much energy you need to pump into it to remove 50% of its mass. In theory, we can predict how planet-scale masses will behave under impact using the same measurement we took from the 1 kilo target.

In practice, though, it doesn’t really work like this. You have a number of factors that alter Q* depending on the size of the target. At first, as you make a target larger, it actually becomes easier to disrupt, pound for pound, than a comparable smaller target. This is because cracks propagate far more easily through large objects than they do small ones, and it is crack propagation that breaks off the huge chunks of material required for disruption. So Q* will initially decrease as target size increases. Then, when you’ve increased the mass of the target to the point where its gravity starts to become a significant factor (as explained in the Earth impact example above), this trend reverses itself. From this point onwards the bigger – and therefore heavier – the target, the harder it is to disrupt, since you’ve not only got to blow the thing apart but you’ve also got to do it with enough force that you give the majority of the fragments escape velocity.

This is a graph from a paper published by Willi Benz and Eric Asphaug³ in 1999. Benz is a computer modeller while Asphaug does impact experiments in the laboratory; and they’ve combined their data in an attempt to put some numbers on how exactly Q* will change with target size. At first Q* decreases; the initial value of Q* and the rate at which it decreases will be heavily dependent on the material the target is made of – rock is harder to disrupt than ice, and so on – causing this to be referred to as the material regime. Then at target sizes of around 100 metres – 1 kilometre Q* starts to increase with target size; this is the gravitational regime. What’s really interesting about these graphs is that they’re for two wildly different materials – solid ice has a Q* of about 10 – 40 J kg^-1, while basalt is roughly twenty times that – and yet the shift to the gravitational regime occurs at exactly the same place and in exactly the same way for each. This means that once you hit a target size of 100-1000 m, the material strength of the target has entirely ceased to matter when calculating the result of an impact. It is instead the body’s self-gravity which must be overcome in order to disrupt it

My, that all got a little bit technical. If you didn’t understand the fine detail don’t worry; I didn’t explain it that well and it’s not necessary to grasp all of it to understand what I was doing with Pluto. All you need to take away from it is this:

• We can do impact experiments in the laboratory to get a value for the amount of energy we need to hit a target with to blow it up.
• We can then take that energy value and, allowing for variations in Q* with target size as per the above graphs, scale it up to larger bodies to predict how much energy we’d need to hit them with to blow them up.

So that’s how I was trying to find out how much energy we’d need to blow up Pluto. But why Pluto? And why is it important? Unfortunately I’ve already rambled on a little more than I really intended to, and thinking about it I probably need to explain some additional background before I get on to that. So it will have to wait a week or two. Sorry!

1. Presumably.
2. Over a timescale of hundreds of millions of years, that is.
3. Fun fact: I met Eric Asphaug at a conference in Spain and stole all his water.

The post I Am Become Q*, Destroyer Of Worlds. appeared first on The Scientific Gamer.

This is not what the interior of a light gas gun looks like.

 Time for something a little more hands-on. There’s all sorts of crap hurtling around the solar system — satellites, asteroids, comets and so on – and most of it is travelling at velocities that are, to put it mildly, completely insane. Supersonic jets and rifle bullets travel at about 1 km/s. Ramjets go at around 3 km/s. The average Earth-crossing asteroid, on the other hand, is hurtling through space at 20 km/s. This is Very Fast, and the reason Earth-crossing asteroids (so called because they cross the Earth’s orbit) worry people so much is because the kinetic energy of an object is proportional to the square of its velocity as per the equation

It doesn’t help that asteroids also tend to be rather heavy, and so they tend to possess a rather staggering amount of kinetic energy. Kinetic energy that would, if released on Earth somehow – say, by the asteroid hitting it – just ruin everyone’s day.

 So, that shit be fast and potentially very destructive. This makes studying asteroid and comet impacts an area of interest to scientists, since not only would we quite like to know what would happen if the Earth ever were hit by an asteroid, but it turns out stuff hitting other stuff is actually fairly intrinsic to the way the Solar System has developed and will continue to develop over time. Unfortunately there’s one small problem with this particular avenue of research: the human race has, in the entirety of its history, directly observed and recorded exactly one naturally-occuring impact in the Solar System. This was the Shoemaker-Levy 9 comet impact on Jupiter in 1994, which was funny because despite the fact that comets are sodding huge a lot of people didn’t think the impact would be that big. I’d have paid a fair amount of of money to see their faces when this happened.

 Why have we only observed one impact? Well, it’s actually very, very tricky to predict when and where a particular comet or asteroid’s orbit will intersect with that of a planet. You may notice every so often the news will report on an asteroid that astronomers think has a small chance of hitting the Earth, but they’re not really sure and need some time to figure out exactly where it’s going — and remember, those are the ones you’d think we’d particularly care about, what with them having the potential to wipe out vast swathes of the human race. Instead of spotting asteroids before they hit us (or something else) we normally only find out about the impact after it’s happened. For example, another asteroid/comet hit Jupiter in 2009 and the first we knew of it was when somebody spotted a dark patch on the surface that wasn’t there before. Even big impacts on Earth tend to go unnoticed; the famous one is the Tunguska event*, which exploded with the force of a 15 megaton bomb but which was only observed by the few Siberian natives unlucky enough to be standing nearby at the time.

The point I’m trying to make here is that gathering the data we need from actual impacts in the Solar System is practically impossible because we barely ever see one. If we want to study how impacts work, we have to create them ourselves. We’ve done this a couple of times by crashing probes into various astronomical bodies of interest (see Deep Impact) and learned a lot from it, but that sort of thing is prohibitively expensive since space probes don’t grow on trees. What we really want is a method of carrying out impacts in a laboratory setting – but here we run into the problem I mentioned at the start of this piece, which is that these things move really goddamn fast and even the fastest conventional manmade objects don’t even come close to their velocities.

 Enter the light gas gun (or “space laser”, as certain friends of mine have taken to calling it against my strenuous objections). This is a custom-built piece of laboratory apparatus specifically designed to accelerate very small millimetre-scale projectiles up to the lower bound of the velocities we might expect a typical asteroid to have**. It works more-or-less the same way as a regular gun – the projectiles are encased in a sabot, the barrel is rifled, and it relies on a rapidly expanding gas to drive the projectile – but with one crucial difference which you can probably guess from the name.

 To ram this home I’m going to have to explain how normal guns work. Or to be more precise, normal bullets, since it’s the bullet cartridge which contains all the stuff which makes the bullet go. The cartridge contains gunpowder and a primer; when the trigger of the gun is pulled a firing pin comes down which strikes the primer, igniting the gunpowder. The gunpowder burns and turns into an expanding gas which is confined by the gun barrel; since every other component of the gun is fixed in place the only way it has to expand is by pushing the bullet ahead of it, which is then propelled out of the gun at what is to us a reasonably high speed. So the gun basically fires the bullet by way of a precisely directed explosion; the problem here, though, is that gunpowder has what is called a low brisance. This means it doesn’t explode very fast in comparison to a high explosive like nitroglycerin.

 Now, from the gun manufacturer’s point of view this is a desirable attribute for gunpowder to have, since packing a gun with an explosive that has a higher brisance would rupture the barrel and injure the person shooting it, not to mention creating enough recoil to shatter the shooter’s arm. From the impact scientist’s point of view, though, this is rubbish. Not only does gunpowder expand slowly but it also burns unevenly, producing a sizeable pressure gradient in the column of gas propelling the projectile – in other words the front of the gas column that’s pushing the projectile is expanding faster than the rear of the gas column, meaning all the kinetic energy in the rear of the gas column never gets to the bullet and ends up being wasted. As it turns out, gunpowder is woefully inefficient for the purposes of carrying out impact experiments.

 This is why light gas guns don’t use gunpowder as their primary propellant. Instead they use a light gas such as hydrogen or helium, which have the lowest molecular weights possible. Further, they separate the propellant gas and the projectile into two distinct stages separated by a small metal burst disc. In the first stage, a shotgun shell detonates driving a piston down the gun which compresses the light gas very, very quickly. Once the light gas has been compressed enough it’ll have enough pressure to rupture the burst disc separating it from the projectile. This allows the light gas to expand again, and since there’s no burning of gunpowder going on it expands evenly and transfers all of its kinetic energy to the projectile.

But why use a light gas at all? It’s because gases with a low molecular weight will compress to a greater degree than heavier gases, giving them a higher expansion velocity once the burst disc bursts. Every aspect of the gun’s firing process is designed to wring the maximum possible amount of kinetic energy out of it, allowing the tiny projectiles it fires to reach velocities of up to 7 km/s! This is perfect for simulating impacts that might take place out in the Kuiper belt, with the caveat that you’re unlikely to find that many impactors out there which are perfect spheres composed of pure stainless steel. But hey, the gun only gets you so far. Scaling your lab results which use millimetre-diameter projectiles up to the sort of object sizes you’re likely to encounter out in the Solar System is a whole different bag of cats. But that, again, is a post for another day.

*Technically not an impact since the Tunguska meteorite exploded in the atmosphere before hitting the ground, but it proves the point.

 **It helps that things in the Solar System move slower the further out they are from the Sun’s gravity well. The icy stuff beyond the orbit of Pluto in the Kuiper belt ambles along at a relaxed 3 km/s, so the light gas gun works well for simulating that kind of impact speed.

The post Light Gas Guns And You. appeared first on The Scientific Gamer.