If you follow UK news at all you’ll know that recently there was a bit of a brouhaha over the Royal Navy’s failed Trident II missile test just off the coast of Florida. Some of the more hysterical accounts of the incident have the missile veering towards the US mainland before self-destructing; these sound a little dubious, but there’s at least a sense of irony to the idea as Trident is a US-developed weapons system. The UK abandoned its own nuclear weapons development program back in 1958 in favour of simply buying the technology from the Americans, and there are some very good reasons why this is so. One of them is Violet Club.

The UK’s first serious attempts to develop a nuclear weapon actually predate the Manhattan Project, but after it became apparent just how much industrial capacity the US was willing to devote to producing a working fission bomb the British sensibly dropped their parallel development and instead swung their resources behind the American program. The British contribution consisted of both materials and scientists and significantly accelerated the completion of the bomb, but unfortunately one of the scientists in question was the spy Klaus Fuchs, who handed over a vast quantity of atomic data to the Soviet Union. Once this came out it really turned the Americans off of the idea of post-war collaboration on nukes, and after Roosevelt died and the only American copy of the agreement detailing post-war cooperation between the UK and US was lost (the British copy was sent to them, but certain suspicious figures in the US government weren’t convinced it was authentic) the US unilaterally broke off all collaboration, forcing the British to resume independent development of nuclear weapons.

British efforts culminated in the shipborne Operation Hurricane test detonation in 1952 and the first operational nuclear bomb — Blue Danube, which was essentially a copy of the Manhattan Project Fat Man — being tested in 1953. Unfortunately by this point both the US and the Soviets had tested their first thermonuclear weapons – if you want an explanation of the difference between nuclear and thermonuclear weapons you can read either the Wikipedia article or my own blog post on the subject, but a quick primer would be that a thermonuclear weapon uses a regular fission bomb as a first stage to kick-start nuclear fusion in hydrogen isotopes, which releases several times more energy than nuclear fission and creates a commensurately bigger bang.  Thermonuclear weapons effectively rendered pure fission bombs obsolete, as there were hard limits on the amount of fissile fuel that could be converted to energy by the chain reaction in the tiny fraction of a second before that energy was released and the bomb destroyed itself – much of the nuclear material inside a fission bomb therefore ends up being wasted, and cramming more uranium or plutonium into your weapon results in diminishing returns in terms of yield because it ends up being scattered into the shockwave as fallout material rather than being released as explosive power.

This was something of a problem for the British military establishment, as it was additionally becoming very clear that the delivery system of choice for a nuclear weapon was going to be a missile rather than a bomber. A missile has a far smaller payload capability than a bomber, which made the small, efficient thermonuclear devices ideal in comparison to large wasteful fission bombs. Unfortunately for them they’d expected fission bombs to have a longer lifespan and were stockpiling large amounts of highly-enriched uranium to build them. Not only would there be a gap in capability while they developed their own thermonuclear weapons, but said weapons would only require small amounts of this fissile material to trigger the second stage. As they were unwilling to see this expensive nuclear material go to waste, and using a smaller (yet saner) amount of plutonium would have been even more expensive, it was eventually proposed that an “Interim Megaton Device” be constructed using uranium to fill the perceived need for a megaton-grade weapon until the UK could build its own hydrogen bombs. Hence Violet Club.

Even on paper Violet Club sounds like a tremendously stupid idea. It’s a classic implosion design: a sphere of highly-enriched uranium surrounded by a set of high explosive lenses. When triggered the lenses explode inwards, compressing the uranium core so that it achieves critical mass; the uncompressed uranium core on its own is sub-critical and can’t go nuclear unless the explosive lenses trigger, and the explosive lenses are very difficult to trigger accidentally, making this a relatively safe design for fission weapons up until this point. The problem with Violet Club was that the target yield of one megaton was so much larger than a typical fission yield (which at this point was on the order of a hundred kilotons or so) that they had to cram in a truly ridiculous amount of uranium to achieve it. So much uranium, in fact, that the uncompressed mass of the uranium sphere was actually greater than one critical mass. The reason it wasn’t instantly going nuclear was because the Violet Club core was spread out into a thin, hollow uranium shell – critical mass is a bit of a misleading term and should be thought of as more like critical density as it relies on having a lot of fissile atoms in very close proximity so that they can bounce neutrons off one another — and the big gap in the middle was enough to stop the chain reaction from running out of control.

Now, a key feature of nuclear weapons, even back then, was that they should be fail-safe. If the weapon is not armed then it should be impossible for it to go off, even if e.g. the bomber it’s being carried on gets shot down and crashes, or if there’s a fire on-base and the building that it’s being stored in collapses. Violet Club was very emphatically not fail-safe, however; if the uranium core was crushed or damaged in any way that led to that hollow gap in the middle being squeezed out of the sphere, the chain reaction would start and the bomb would detonate. It wouldn’t be as destructive as if it were triggered intentionally as without the explosive lenses to compress the core the reaction would be even more inefficient than it already was, but it would certainly have been enough to ruin the day of anyone caught within a mile or two of the epicentre. This is why the bomb designers included a rather dubious safety feature: a small hole was bored through the uranium shell through to the hollow gap inside through which 133,000 steel ball-bearings were inserted. The ball-bearings were then sealed inside with a plastic bung. The theory went that as long as the ball-bearings were present inside the weapon, that hollow gap that prevented it from going nuclear couldn’t be crushed out of the core and the bomb would remain safe.

That was the theory, anyway. In practice the ball-bearings were even dumber than the bomb itself:

• Having to remove 133,000 pieces of steel from the interior of your weapon before it can be considered armed turned out to take some time – a minimum of half an hour, in fact (and up to 90 minutes during bad weather), which was far too slow considering the increasingly truncated warning time that was expected to precede any hostile nuclear action.

• The ball-bearings increased the weight of the Violet Club bomb assembly by half a tonne. The V-bomber force of the time (so-called as the UK’s nuclear deterrent consisted of Valiant, Vulcan and Victor bombers) could not carry a bomb that heavy, so the ball-bearings had to be removed from the bomb before takeoff. This ensured that Violet Club would always be armed while it was in the air, and this made it far too dangerous to be flown on exercises or even sent to a dispersal base to mitigate the effects of an expected nuclear strike.

• The bombs had to be stored inverted when not in use, as otherwise there was a risk that the plastic bung would fall out and the ball-bearings would exit the core, arming the bomb.

• By their nature nuclear bombers spent a lot of time sitting around on exposed airstrips waiting for an alert, and so did the bombs they carried. If it was a particularly cold day the ball-bearings would freeze solid inside the bomb, rendering it useless.

And so on. The Violet Club bombs were quite possibly the most dangerous and impractical nuclear weapons ever made, and the RAF knew it: 12 were ordered, but only 5 were delivered, and the ground crew who had to handle them were absolutely terrified of them. To add insult to injury, it was estimated (we’ll never know for sure as Violet Club was deemed too dangerous to even test) that thanks to the inherent inefficiency of pure fission bombs Violet Club would have a yield of around 400 kilotons – far short of the one megaton target yield.  In short, it was not an ideal outcome for the UK’s homegrown nuclear weapons development program, and god knows what else we might have come up with if we’d been allowed to continue bodging together the safety features that kept our nuclear deterrent from prematurely exploding.

Fortunately for us the Operation Grapple tests of 1958 proved to the US that we had the capability to build thermonuclear warheads of our own, and at that point the Americans figured that if we were going to get them anyway, they might as well make a few bucks by giving us their warhead blueprints and then selling us the delivery systems to go with them. The 1958 Mutual Defense Agreement swiftly followed and ensured Violet Club was the last purely British nuclear weapon ever deployed; Red Beard (the more prevalent — and conventional — successor to Blue Danube) remained in service until the switch to a primarily submarine-based deterrent force and the first Polaris patrol in 1968. And whatever else you can say about the American designs, at least they aren’t armed by physically yanking out a plastic bung from the warhead casing.

The post Violet Club appeared first on The Scientific Gamer.

While I was on holiday I decided to watch Interstellar. This was a terrible, terrible mistake, but at least you’re getting what is hopefully a reasonably entertaining blog post out of it. Needless to say, though, this post is going to spoil the hell out of the film, so don’t read if you haven’t seen it yet.

Interstellar is the worst science fiction film I’ve seen since Prometheus.

To understand my particular problems with Interstellar you have to know about the difference between hard science fiction and soft science fiction. Soft science fiction is mainly concerned with telling a story, and using “science” to enable that story. It doesn’t particularly care how its science works — hence the quotation marks — and if it knows what’s good for it it won’t even bother with an explanation unless it’s directly relevant to the plot, instead presenting objects and concepts that outright break the known laws of physics as a fait accompli. This is an approach that works, and works well; it’s the story that matters to soft science fiction, and nobody is going to care about the precise physics behind lightsabers or artificial gravity unless you make the very poor decision to point it out to your audience. Soft science fiction requires lots of imagination and very little actual scientific nous to write, and so it’s not particularly surprising that soft sci-fi encompasses the vast, vast majority of science fiction. Pretty much every single sci-fi film, television show, and 95% of sci-fi books released in the last fifty years are soft science fiction.

I say this because I want to make it clear I’m not about to brutally suplex Interstellar through a table just because I like nitpicking. I’m very capable of enjoying sci-fi stories that screw established science up into a little ball and throw it into the dustbin, because if they’re written well enough and don’t go out of their way to draw attention to it I can suspend my disbelief and just accept it as something that’s necessary to the story. Prometheus was soft sci-fi, and my issues with that largely stemmed from the fact that it involved the most imbecilic group of movie scientists I’ve ever seen rather than any of its actual “science”. Soft science fiction is fine, in principle. If Interstellar was soft sci-fi it would still have problems, but those problems would be that it is terribly written and nonsensically plotted, not anything to do with its science (or lack of it).

Unfortunately Interstellar is not soft sci-fi. Or at least, on the outside it doesn’t look like soft sci-fi. Instead, Interstellar is masquerading as hard sci-fi. Hard sci-fi differs from soft sci-fi because the science in hard sci-fi does matter. It might take a few liberties, or rely on one or two big assumptions about future science (the possibility of FTL travel is the usual culprit), but otherwise hard science fiction is written to be as faithful to current real-life scientific knowledge as possible. It’s effectively the reverse of soft sci-fi in that the stories it tells are now all about the how of the science that soft sci-fi just ignores; most hard sci-fi tries to come up with plausible solutions to near future problems such as the colonisation of another planet, and the draw of the story is either the science itself, or how human beings would react when confronted with the stark reality of certain modern scientific concepts. Because it’s actively relying on the science as the central support of its story hard sci-fi is consequently much harder to write well than the soft stuff, which is why you don’t often see hard sci-fi in the cinema. Not only do you have to be really up on your science, but if you’re faced with a choice between “something cool happening on screen” and “obeying the laws of physics” you usually have to choose option B, which doesn’t exactly make for a high-grossing summer blockbuster.

Except now we have Interstellar, a seemingly hard science-fiction movie that made all of the money at the box office last year. It did this despite repeatedly invoking real-world scientific concepts such as gravity and relativity, and despite going out of its way to present itself as a “realistic” vision of space travel right down to the not-having-any-sound-effects-during-space-sequences trope. It also did this despite straight up not being a very good movie, but that doesn’t stop the Transformers franchise and so is probably outside the bounds of this discussion.

The first half hour of Interstellar is probably the most interesting. It’s set on a decaying, technologically regressive Earth afflicted by a blight that’s slowly killing off the world’s staple food crops and turning the topsoil to dust. The main character, Cooper, is a washed-out astronaut who is now scratching a living as a farmer, and whose frustration with his world’s backwards, insular outlook on life drives him to seek some form of escape from it. The world-building that goes on here is perfectly respectable, and it felt like the beginning to a half-decent John Christopher novel. But then Cooper gets his wish, and the movie goes completely off the fucking rails.

Cooper is made the leader of a party of astronauts that is sent through a wormhole that appeared 50 years ago to see if they can find any planets suitable for colonisation. A wormhole? Fine, whatever, you’ve got to get the astronauts to another system somehow and so I’ll swallow that – the existence of wormholes isn’t exactly forbidden by the laws of physics, although the existence of a stable wormhole that you can traverse from one side to the other requires some extreme fudging of energy densities¹. On the other side of the wormhole they find three planets orbiting a black hole called Gargantua, which is stated to have 100 million times the mass of our Sun. This makes it a mid-range black hole – we know of supermassive black holes with masses exceeding tens of billions of Suns, while the lower limit is like four Suns or something — but it’s still not exactly the sort of place I’d want to start humanity anew for the following reasons:

• Black holes aren’t very big on the whole providing heat and light for the purposes of sustaining life thing. Interstellar fudges this too by saying that the black hole’s accretion disk is providing a curiously sun-like environment for the orbiting planets, but while it’s true that accretion disks do give off a lot of radiation it’s usually in the form of X-rays and other nasty stuff that would make any planets present decidedly unhealthy places to live.

• Black holes are tidal giants. This is a point that Interstellar chooses to entirely ignore, but black holes will destroy planets long before they go anywhere near the event horizon thanks to tidal stresses. Even big planets do this – Saturn’s rings are basically chunks of moons and planetoids that wandered inside Saturn’s Roche limit, and if a pissant little gas giant can do that imagine the Roche limit a black hole with 100 million times the mass of the Sun will have. In order to survive a planet would have to be a very, very, very long way away from the black hole, which then poses some additional problems for getting adequate amounts of heat and light to sustain life.

• It’s a sodding black hole. I’m seriously struggling to think of a dumber idea than settling a new colony within spitting distance of one. Even digging out a planetoid in deep space and living underground would be more sensible.

But our intrepid heroes aren’t letting this stop them. Despite Michael Caine and Cooper’s daughter blathering on and on about how getting a look inside a black hole will let them “solve the problem of gravity”, the black hole in Interstellar has a curious lack of it and functions almost identically to Earth’s Sun for almost the entire length of the movie. It’s pretty much there for two reasons.

1. To provide the usual deus ex machina that movie black holes do at the end of the film.
2. To allow the writers to make a spectacular hash of the concept of gravitational time dilation.

They waste no time with the second one, as the first thing the astronauts do is make the mind-numbingly stupid decision to land on a planet so deep inside the black hole’s gravity well that seven years will pass in “normal” space for every hour they spend on the surface. I have a number of problems with this sequence.

• You would have to be bloody close to the event horizon of even a 100 million Sun-mass black hole before you experienced that degree of time dilation. Gravitational time dilation is much like relative velocity time dilation, where you don’t experience significant time dilation effects until you’re all the way up to .99c; otherwise it’s something that’s not really noticable on the human scale. As we’ve just established, being that close to the event horizon means your planet just gets pulled apart and there’d be nowhere to land on. For that matter the spaceship would get pulled apart and there’d be no astronauts to land on it.

• There’s a hefty amount of technobabble about how to land on this planet in such a way that it will save fuel. I have bad news for the astronauts: if your planet is sitting at the bottom of a gravity well so deep that you only age one hour for every seven years that pass outside of it, then there’s no amount of fuel that’s going to get you back off the planet’s surface again. We have enough trouble getting out of Earth’s gravity well, for crying out loud.

• One of the reasons they land on this planet is because there’s an all-clear signal being sent from a pathfinder ship that was sent ahead of them several years ago. When they get there they discover that the pathfinder ship is wrecked, but thanks to the time dilation in the planet’s frame of reference the ship has only just crashed. This is a nice idea, with one extremely significant flaw: if the gravity well was that deep then any transmissions from the pathfinder spacecraft would be incredibly redshifted, and it would have been extremely obvious to the astronauts that something was up. Assuming that they weren’t yet another collection of dumb movie scientists, that is.

• I don’t even know what was going on with the ankle deep water and the huge tidal waves that are somehow not spotted by the astronauts on their initial approach. Have they never heard of side-looking radar? And yes, if you’re that close to the black hole you’re going to experience significant tidal effects, as I’ve mentioned several times, but I somehow don’t think that this is what was on the filmmaker’s minds when they shot that scene. Anyway, I’d be more interested in how the planet has managed to retain a liquid ocean without having it all escape into space under the gravitational influence of the black hole. Ditto any atmospheres and, well, solid matter.

There is a lot of stupid concentrated on that first planet, but Interstellar still has a couple more stops to make on its tour of idiocy. First there’s Crazy Matt Damon’s planet, where the ice surface they spend their time tromping around on is apparently a collection of floating solid clouds. Which is ludicrous. Perhaps in response to the frank impossibility of his environment, Crazy Matt Damon goes crazy and attempts to kill the astronauts and steal their spaceship; the ensuing fracas kills the remaining redshirt astronaut and damages the spaceship so badly that Cooper is forced to attempt some sort of slingshot maneuver around the black hole to get Anne Hathaway to the last remaining candidate planet. He does this by burning all of the fuel they have left and then jettisoning the spent shuttle vehicle he’s piloting into the black hole to reduce the spacecraft’s mass. This is not the dumbest thing that happens in the film by a long way; we’ve already established that they must have some sort of magical future fuel/engines that can get them out of any gravity well and so slingshotting around the black hole while dumping unnecessary ballast is actually quite a good idea. Sadly there’s then an extended sequence where Cooper falls into the black hole, which is inevitably very, very stupid indeed.

• First, there was some gobbledygook earlier in the film where Gargantua is described as a “gentle” black hole, where somebody might be able to dip inside the event horizon and escape again with the data required to solve Michael Caine’s gravity equation. This is nonsense. The whole point of the event horizon is that it’s the point of no return: once you cross it, not even light can get back out again. That’s why it’s called the event horizon; we can’t see anything over it. That’s why black holes are black. Once you’re over that horizon, falling towards the central singularity is inevitable.

• This is also the part where Interstellar contradicts its own twisted movie logic as well as the laws of physics. The accretion disk around the black hole is burning with a heat comparable to the surface of the sun. It must be in order to provide the Earth-like light source that illuminates each of the worlds the astronauts have visited, and I think there’s a part where this is outright stated to be fact by somebody or other. Cooper somehow falls through this incredibly hot accretion disk without being burnt to a cinder and reaches the black hole’s event horizon. Maybe they’ve discovered super-asbestos in the future and lined their spacesuits with them or something.

• Oddly, Cooper would probably survive the tidal forces present at Gargantua’s event horizon. This is because the radius of the event horizon increases more or less linearly with the mass of the black hole, while the strength of the tidal forces obey an inverse square law that means they get exponentially weaker the further out you go. A small black hole on the order of a few solar masses will have a tiny event horizon, but it’ll kill you long before you reach it. A supermassive black hole like Gargantua, on the other hand, will have an event horizon that extends some way beyond the black hole’s lethal radius². Cooper’s death is inevitable once he’s crossed it, but he’d at least live long enough to see what was inside it.

Of course the interior of the black hole turns out to be some pseudo-mystical time travelling bollocks that ties up the story, as I’d been expecting almost from the very beginning of the film. In fact I’d seen every single plot twist bar Michael Caine’s deathbed confession coming the moment the character or concept was introduced because Interstellar is, as I have already stated, a terribly written movie that hews to all of the worst soft sci-fi tropes despite having dressed itself in hard sci-fi clothing. And this is my problem with Interstellar: it’s actually a soft sci-fi movie, but it’s explicitly linked to the present day and repeatedly invokes real-world scientific concepts in the manner of a hard sci-fi movie, right before mangling them horribly because they just get in the way of the story it wants to tell. Unfortunately if you invoke that real-world science as heavily as Interstellar does you have to be partially bound by it, otherwise there’s no point; you might as well have made a more fantastical film with lasers and aliens.

Yet despite mentioning it repeatedly Interstellar doesn’t use its science in any interesting fashion bar its brief (yet incorrect) flirtation with time dilation, and it’s a much weaker film as a result of cloaking itself in a hard sci-fi raiment that, after the most cursory of inspections, turns out to be the emperor’s new clothes. It would have been far better if it hadn’t made a point of making a point out of the science; if it didn’t go out of its way to draw my attention to how wrong it was at every single turn. It wouldn’t have been a good film, but I probably would have been able to suspend my disbelief the whole way through rather than having it repeatedly snap under the weight of the film’s scientific bullshit. As it is not only is the science awful but Interstellar has a worse grasp on its internal logic than the Fast and Furious series does. At least those movies are fun. Interstellar, on the other hand, is a dull, dreary and pointless expedition into the absurd, and I deeply regret having watched it at all.

(I did like the robots, though.)

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The post Interstellar: A Rant appeared first on The Scientific Gamer.

It’s been over a year since the last science post, so I had probably better either a) make another science post or b) rename the site. What I’m about to talk about is more science fiction than proper science, but I was wondering about it and did the research and it’s close enough to the real thing to pass for it if you squint a bit, and most importantly it ends the science drought.

The hokum military fantasy plotline of Call of Duty: Ghosts is kicked off when the baddies hijack a US space station to drop a number of very heavy objects onto the continental United States, devastating the country and providing the developers with an excuse for one of the more mediocre first person shooters I’ve played in recent years. As with most concepts explored in Call of Duty, while the way its portrayed in the game is complete nonsense the idea of launching weapons into space that can bombard targets below is a legitimate one that’s been around for a very long time –since before we actually got into space in the first place,  in fact — and Ghosts even references a specific one: its Loki satellite has an obvious link to Project Thor, a proposal originating from the 1950s but which was being mentioned in news reports as recently as four years ago under its sexier nickname: Rods from God.

As the particular variant of kinetic bombardment that’s been drawn up by the US, Rods from God is by far the most well-known version of the kinetic bombardment idea, even worming its way into popular consciousness via “entertainment” products like CoD: Ghosts and the execrably awful GI Joe: Retaliation. The idea is that you would have a pair of satellites in orbit: a command and control satellite that handles targeting and guidance and a launcher satellite that houses the actual projectiles, which in this case are long, thin rods composed of a very dense material (tungsten is the one usually cited due to its frankly ludicrous density of 19.3 g cm^-3 – for comparison, lead clocks in at a measly 11.3 g cm^-3) and whose only attachment would be a set of small fins required to steer the rod through the atmosphere to its target. The high material density is required to maximise the projectile’s mass, and hence its kinetic energy once it strikes its target; kinetic energy is a function of mass times velocity squared, and the velocity of something dropped from orbit is in theory going to be pretty damn fast.

Now, the popular depictions of kinetic bombardment mentioned above portray these rods as being absurdly destructive, striking with the force of a nuclear weapon and wiping entire cities off of the map. The reason I’m writing this post is because I got curious: tungsten may be dense, and orbital velocities may be pretty fast, but how much kinetic energy would one of these rods actually have once it reached the Earth’s surface? The rods can vary in size, but the larger versions are mentioned as being 6m long with a 30cm diameter, giving them a mass of roughly 8,000 kg. Assuming we want our rod to hit with the force of a small nuclear weapon (15 kilotons of TNT, say, or 63 terajoules), we’d have to ensure that it hits the Earth’s surface travelling at a velocity of

For reference the fastest man-made object in existence is the New Horizons probe, currently in the penultimate year of its journey to Pluto and cruising at a cool 16.26 kilometres per second relative to the Sun — and it managed that only with the aid of a gravitational slingshot provided by Jupiter. Clearly, then, the idea of one of these rods striking with the force of a nuclear weapon is somewhat overstating their destructive capacity, especially since you’d lose a lot of the kinetic energy on the way down thanks to the Earth’s atmosphere. The question now is: how much kinetic energy would one of these rods realistically have once it reached the surface? There’s a bunch of complicated ways we can figure this out, but I’m going to cheat and simply assume that the rod is going to be slowed down enough by its passage through the atmosphere that it will be moving at terminal velocity when it hits the ground. The equation for working out terminal velocity is

Where m is the mass of the object, g is its acceleration due to gravity (9.81 m s^-1), ρ is the density of the medium through which the object is falling (in this case air with a density of 1.225 kg  m^-3), A is the projected area of the object (the rods are very long and thin and present only a small surface area along their direction of travel), and C_d is the drag coefficient of the falling object (I’m using the drag coefficient of a cone, since my assumption is that the tip of the rod will be cone-shaped). Plug all of these numbers into the equation and the terminal velocity of the rod comes out at

This gives the rod a kinetic energy of around 14.5 gigajoules, which sounds like a lot but which, when converted to something more analogous to explosive force, is equivalent to only 3.46 tons of TNT. That’s plenty of power, more than enough to wreck a small neighbourhood, but a single kinetic impactor isn’t going to be destroying a city any time soon.

More than that, though, there’s the question of practicality to consider. Rods from God do have a couple of advantages over regular missiles – dropping them from space would give any prospective target little to no warning before they struck, and the sheer density of the rod would give it an awful lot of penetrating power ideal for destroying hardened targets – but they have to be weighed up against the massive disadvantages inherent in the concept, first and foremost of which is that in order to drop an 8 ton rod onto somebody’s head you first have to lift it up into orbit. With typical launch costs currently standing at around $5,000 per kilo at the cheap end, putting just one of these rods into orbit would cost a whopping $40,000.000. Putting a whole array of them (plus launch system) up there would be ruinously expensive – and before you say “But Hentzau, a single stealth bomber costs a billion dollars,” you have to bear in mind that that price tag includes the R&D and engineering work required to develop the bomber in the first place. There would be similar costs involved in developing a kinetic bombardment array that would massively inflate the cost, and all for something that has less destructive capacity than a WW2-era Lancaster bomber,  and whose job can easily be performed by much cheaper conventional missiles and/or bombs. Little wonder, then, that the Rods from God concept has never made it out of the pages of science fiction.

The post Rods From God appeared first on The Scientific Gamer.

Taz asks

 Can you do a rundown of Halo from a scientific perspective? I’ve really enjoyed your writing about Armageddon and would like to hear your thoughts on the game that has (since its début in 2002) become a phenomenon. Tanks in advance!

My answer to this one isn’t particularly scientific in any rigorous sense of the word, nor does it have much to do with the Halo universe itself, but I’m going to do it anyway because it’s still kind of fun. Or at least I think so, anyway.

Most elements of the Halo universe are conventionally sci-fi – magic spaceships, magic faster than light travel, magic anti-gravity, all the stuff you really need to hand-wave away in order to make possible the intergalactic space war that forms the background for the Halo story. I can’t quibble with any of that, in the same way that I don’t quibble with the existence of wizards and undead in the Myth series: it’s necessary for the setting. However, what I can quibble with is the thing they put front and centre of the Halo games: the Halos themselves.

The Halos are ring-shaped megastructures with a diameter of 10,000km and what looks like a width of around 300-400km. On the inner surface of the ring is a fully-functioning biosphere with a breathable atmosphere, water, plant life and weather regions. The ring is spun to provide enough faux-gravity in the form of centrifugal force to keep all this stuff stuck to the inside of the ring. This kind of space habitat is not a new idea; it was first popularised in Larry Niven’s Ringworld and became a common part of the late Iain M. Banks’ Culture novels, with the Culture Orbitals being truly vast structures on the scale of millions of kilometres which dwarfed the comparatively titchy specimens on offer in Halo. If you’re trying to build somewhere for people to live in space and have access to ridiculously advanced levels of engineering technology, then a ring-shaped structure is not the worst idea in the world. While I can think of a lot of better ways to do it I can’t think of any reason why a ring wouldn’t work.

On the face of it setting Halo on a ringworld isn’t so terribly unscientific, then. They’d work as space habitats. But there are two problems with the implementation of ringworlds as seen in Halo. The first is rather prosaic: even the backwards human race is shown to have some form of artificial gravity system functioning on all of its spaceships. If you have artificial gravity then the primary – indeed the only – reason you would build your space habitat in the shape of a ring is negated; access to artificial gravity technology means that you no longer need to spin something to get the things on its inside surface to stay on, and so the question arises of why the hell you did that in the first place.

The second problem partially deals with the first, in that we discover during the course of the first game that the Halos aren’t actually intended to be space habitats at all. Instead the Halos are ancient superweapons designed to wipe out all sentient life within a large radius (I think a range of tens of thousands of light years is mentioned in the first game, with a network of seven Halos being enough to wipe clean the entire galaxy). Now, maybe the Halos weren’t built in a ring shape because the builders wanted people to live there. Maybe they have to be ring-shaped in order to carry out their function of galaxy-wide genocide. Who knows how these things work. Unfortunately this theory is somewhat sabotaged by the fact that there is a working biosphere on the inside surface of the Halo that is capable of supporting life, which would require the builders of Halo to go to a not inconsiderable amount of extra effort to get it all to work. If Halo is not supposed to be a space habitat then why the hell does it resemble one so exactly?

Of course the answer is that a ringworld is a pretty striking setting for an FPS which certainly seems to have done Halo no harm whatsoever; nobody who played it is going to forget booting it up for the first time and seeing the world curving up over their heads. That’s fine. The plot of Halo isn’t especially coherent anyway, so some inconsistency over what exactly the Halos are for versus how they’re designed is to be expected. However, the question did get me thinking as to what other useful things could you do with a ring-shaped megastructure. The resulting list was a fairly short one, consisting as it did of a single item: energy gathering via Dyson structures.

If you read or watch sci-fi at all you’ve probably heard of the Dyson sphere concept, at least in passing. A Dyson sphere is a shell of matter constructed around a star in order to maximise the amount of energy you can harvest from that star. Make the shell dense enough and there’d be practically no wastage; you’d  be able to gather 100% of the star’s energy output, which is a truly ludicrous amount of power. After the shell harvests all this power it would then be transmitted elsewhere so that the civilization that built the shell could do something useful with it.

Some misconceptions about the Dyson “sphere”: that it is a solid object, and that it has to take the shape of a sphere. A lot of sci-fi writers made the mistake of having their Dyson spheres be solid shells of matter enclosing their parent star. This is stupid for several reasons; if we’re considering structures on this scale we have to assume that the technology would exist to make the shell solid,  but a solid shell would be gravitationally neutral in relation to its parent star since it would envelope it uniformly at a constant distance. Each part of the shell would cancel out another part of the shell, which raises the interesting hazard of having the parent star drift into the side of the shell (or vice versa) since neither of them is gravitationally stable compared to the other. There’s also the minor niggle that there might not actually be enough construction material present within the star’s solar system in order to actually make a solid shell.

So solid Dyson spheres truly are science fiction, with no possibility that even a hyper-advanced race would be able to make one without circumventing a fair number of the laws of physics. Happily for us they are just a corruption of Freeman Dyson’s original idea, which was to have an orbiting array of satellites gobbling up a star’s energy output. While it would still be a massive engineering project this is much more plausible, and while not having a solid structure means the shell is going to be less than 100% efficient it does have the advantage that you can start the shell simple and work up from there. The simplest form of the shell is – you guessed it – a ring-shaped array of satellites all orbiting the parent star on the same plane. Scaling up would result in multiple interconnecting rings with very complex orbital characteristics, but if somebody could sit down and work out the maths there’s no real reason why it couldn’t be done.

Which does rather beg the question: why would you want to?

The answer to this is somewhat speculative and has to do with another commonly-referenced sci-fi concept called the Kardashev scale. The Kardashev scale isn’t any kind of absolute measure, but instead functions kind of like the Drake equation in that it’s supposed to jog us out of our stolid, Earth-based ways of thinking: assuming most technological barriers could eventually be overcome, then what would be the major limiting factor on a civilization’s progress? The answer is energy, and the Kardashev scale attempts to class a given civilization’s level of technological advancement by the quantity of energy it can harness/has access to. The scale as originally formulated by Kardashev goes like this:

• Type I Civilizations have the capability to utilise the entirety of the energy resources provided by their home planet.

• Type II Civilizations have progressed further and are capable of tapping into all or most of the energy generated by their parent star.

• Type III Civilizations have progressed furthest, and have found a way to harness the energy output of an entire galaxy.

Now, clearly that’s not remotely scientific in the least, and the concept of a Type III civilization in particular boggles the mind; we’re talking about completely utilising the energy of at least a hundred billion stars simply to service the needs of your civilization. Our own civilization can only make use of a fraction of the energy provided by the Earth – it doesn’t even rank as a Type I on the Kardashev scale — and from there it’s very difficult to imagine what the hell you’d need so much energy for. But that’s the point in the scale. It’s supposed to get us thinking about how large a civilization could grow if it were unconstrained by 20^th – now 21^st – century technology and modes of thinking.

It’s a fair bet humanity will make it to Type I status eventually, since this roughly corresponds to fusion power, nanotechnological capability and all that other World of Tomorrow stuff that never quite seems to turn up. We can just about envisage a Type II civilization, as while the idea of building rings of energy-gathering satellites around the Sun is quite outlandish it isn’t that infeasible either; we probably will be able to do that at some point if we don’t kill ourselves off through some kind of horrible climate catastrophe/Malthusian apocalypse. The sort of things a Type III civilization would get up to, on the other hand, are very firmly beyond our technological horizon, and the Kardashev scale is the only thing that’s really punched through that barrier to give us some idea of the scale and capability that a true far future civilization might eventually possess. It’s also acted as an enabler for dozens of hack sci-fi writers to produce oodles and oodles of poorly-formatted bollocks¹, but then no good idea ever went unsullied by that particular fraternity.

Anyway, Kardashev is one of those abstract things that’s supposed to drive other more scientific ideas, and this is something that it most certainly has succeeded in doing. You go to the Wikipedia page on the subject and you’ll find a dozen ways of reclassifying, improving on or extending the scale to incorporate this case or that case, but the sole warning on how seriously it should be taken is the line towards the end which states

It has been argued that, because we cannot understand advanced civilizations, we cannot predict their behavior. Thus the Kardashev scale may not be relevant or useful for classifying extraterrestrial civilizations.

I’d go farther than that, in that the Kardashev scale may not be that useful for classifying advanced human ones either. Most attempts to predict the future even fifty years down the line end up being laughable in hindsight, and it only gets worse as you get further and further away from our modern technological touchstones, so all this stuff I just said about ringworlds and Dyson spheres will probably end up being a load of old balls as well. Even scientists like to dream sometimes, though, and since using structures like these to gather practically unlimited quantities of power that are free for the taking would probably lead to post-scarcity societies like those seen in Star Trek and the Culture novels I’d say it’s a dream worth holding on to.

The post With This Ringworld I… Do What, Exactly? appeared first on The Scientific Gamer.

Janek asks

I would be interested in a further post detailing roughly how we’ve calculated the size of the observable universe.

Okay. Actually I’m more than happy to answer this because the answer is relatively short and it’ll let me bunk off science posts for a week.

So once upon a time there was an astronomer called Edwin Hubble. Hubble’s career is notable for a number of firsts – such as the identification and use of the standard candles known as Cepheid variables found within the Andromeda and Triangulum galaxies to prove that these were indeed galaxies and not merely nebulae as had previously been assumed, thus incidentally proving that the universe extended beyond the bounds of the Milky Way – but the one that ended up getting his name attached to it was the discovery of something called the Hubble constant which basically defines our universe. Astronomers spend a lot of their time nailing down increasingly accurate values for the Hubble constant; part of the motivation for the whole CMB thing is to get better measurements of H_o.

So the Hubble constant is kind of a big deal, and what it is and how it works is best explained by telling the story of how Hubble found it in the first place. After having such success with the Cepheid variable approach to Andromeda and Triangulum (if you need Cepheid variables explained I go over them in one of my first posts here, and the Wikipedia article is here) Hubble decided to see just how many other galaxies he could find with Cepheid variables in them in order to build up a picture of what our universe really looked like. The Cepheids let him measure how far away these particular galaxies were, but while he was observing them he noticed something odd: the light from some of the more distant galaxies displayed a significant degree of redshift. It was already known that galactic redshift was related to their recession velocity thanks to work done by Vesto Slipher a few years earlier, and so Hubble was able to make a graph of galactic distance versus recession velocity that looked much like the following:

It’s a straight line relationship (albeit one with a fair amount of scatter), which is convincing evidence that the recession velocity of a particular galaxy is directly proportional to its distance away from . In other words,

where v is the recession velocity of the galaxy, d is its distance from us, and Ho is the Hubble constant. The expression above forms Hubble’s law, which states that the further away from us something is the faster it will be moving – and since that movement is caused by the expansion of space, Hubble’s law is effectively a relationship which governs that phenomenon. This means that what exactly the precise value of the Hubble constant is is going to have a profound impact on our views of how the universe is expanding, which is why scientists are so interested in obtaining increasingly accurate measurements of it. It also incidentally allows us to get a rough idea of galactic distance by measuring the redshift, converting it into a recession velocity, and plugging it into Hubble’s law along with the current value of the Hubble constant (67.80 ± 0.77 km s^-1 Mpc^-1 as of the most recent measurements obtained by the Planck probe).

So in theory when we look at things we have a fairly good way of figuring out how far away they are from us. All we have to do is find the thing that’s furthest away, plug its redshift into Hubble’s law, and from that calculate the approximate radius of our observable universe, right? Unfortunately — as with most things in astronomy – the reality is nowhere near that simple. Whenever you read an article reporting the discovery of the most distant astronomical object yet discovered, that article will likely quote two things: the object’s redshift, which is a thing that can be directly measured via observation, and its age, which can be reliably calculated from its redshift. What it won’t quote, unless it’s been written by an idiot, is its distance from us. This is due to several factors which complicate Hubble’s law immensely, most notably:

• That the simplified version of the law I described above – which incidentally is the one we teach to reasonably intelligent people up to and including undergraduate level¹    – assumes that the redshifted light we see from galaxies moving away from us is caused by a simple Doppler effect; that is, that the galaxies are moving away from us through space, like a boat sailing on the ocean. What’s actually happening is that the space itself is expanding and carrying that boat away from us on a tidal wave, which requires a far more complex treatment of the redshift.
• That the rate of galactic expansion has been constant and unchanging throughout its entire history. This is not true, as we now think that the universe is accelerating in its expansion. You know that value of Hubble’s constant we calculated just this year using the Planck probe? That’s the value of Hubble’s constant now. We have little to no idea what the value of Hubble’s constant was ten billion years ago, and the various cosmological models that attempt to establish this differ wildly in their predictions of how it’s changed over time.

These two factors together not only make the use of galactic redshift to calculate distance a rather iffy proposition at the best of times, but that second one also makes it effectively impossible to gauge the distance of the really old stuff we find. And if we can’t put an accurate number on those distances, this means it’s impossible to directly measure the volume of our observable universe.

If that’s the case, though, then why do astronomers throw around a precise number for the radius of the observable universe (currently about 46 billion light years)? It’s because they’re not using the term observable in the same way that you (or I) might. To them, “observable” does not mean “Can we see it right now?” Instead, the observable universe is simply the radius inside which light emitted from objects at some point over the entire history of the universe could theoretically reach us here on Earth. It doesn’t matter if the light actually does get here or not, or whether somebody manages to detect it, or whether we can make sense of what we eventually see; if the light has the potential ability to reach us, then the part of the universe that would hypothetically emit it falls within the bounds of the observable universe.

This simplifies the calculation of the radius of the observable universe immensely; instead of trying to establish actual physical boundaries you simply dial things back all the way to the oldest thing that could possibly exist and be observed and try to derive a distance measurement to that. In the case of our universe this happens to be the cosmic microwave background radiation, which is a collection of extremely redshifted particles released at the moment of photon decoupling². That 46 billion light-year number is derived from our observations of the surface of last scattering, a collection of points in the sky where photons from the CMB are only just now reaching us here on Earth. The great advantage of using the CMB to calculate this radius is that it isn’t just one object; since it exists over the entire sky it provides an awful lot of data which allows astronomers to average out those huge uncertainties in using redshift to gauge distance I described above. This means that it’s a reasonably solid number, although there’s no reason a more detailed observation of the CMB wouldn’t cause it to change in future.

So that’s how we arrived at a definition for our observable universe. There’s stuff inside it that we haven’t seen — and likely never will – because our instruments aren’t good enough, but that doesn’t change the fact that we could see it with sufficiently advanced equipment. It’s possible that the boundaries of the observable universe could move outwards if we figure out a way to see stuff without relying on electromagnetic radiation (observations of neutrino emissions and gravity waves could allow us to look back beyond the moment of photon decoupling, for example) but I wouldn’t hold your breath; that stuff is very definitely future science.

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The post The Hubble Bubble. appeared first on The Scientific Gamer.

In which I tackle one of the things that for a long time seemed like a colossal fudge to me, but which has an ever-increasing weight of evidence supporting it: inflation theory.

How big is the universe, really? Nobody knows, and it’s entirely probable that nobody will ever know. We’re limited in our measurements to observations of the bits of it we can actually see; all we have access to are the stars and galaxies which are close enough to have their light crawl slowly, painfully across the ever-expanding fabric of spacetime to be received by our telescopes within the 13.7 billion year lifetime of the universe. Anything emitting radiation which takes more than 13.7 billion years to get here will forever be locked behind a causal event horizon that we’re unlikely to ever penetrate, and not having access to an unknown proportion of the universe makes it pretty difficult to estimate the overall size of the thing. However, even the bits of it we can see raise some pretty interesting questions.

For starters, the  universe — everything we can see — appears to be about 93 billion light years across. A common misconception is that since the universe is 13.7 billion years old, and light travels one light year per year, then the observable universe must have a 13.7 billion light year radius. This is not true; the fact that the fabric of spacetime is stretching and expanding underneath the light as it wends its way through the cosmos means that by the time it reaches us the distance between us and the source has grown to several times what it was when the light set out on its journey. This also has the effect of stretching the light itself, spreading it out into longer wavelengths and shifting it into the red part of the spectrum; this redshifted light is what tells us space is expanding in the first place, and is distinct from the Doppler effect caused by a simple moving body which is used to explain shifting wavelengths to schoolchildren.

So that’s why the observable universe is so big. Thinking about it, though, this just presents us with more problems. Consider the case of two galaxies situated a long way away from us, one on each side of the Milky Way at opposite ends of the universe, whose light is only just now starting to be detected by our telescopes. Logic dictates that since the speed of light is an absolute limit and since the light has twice as far to go until it reaches the other galaxy, neither galaxy can see the other, and that the only reason we can see both is that we happen to be conveniently situated at the midpoint between the two. From the perspective of each of these galaxies the other is locked behind that causal event horizon I mentioned earlier. No information can travel faster than light, and so these galaxies are effectively out of causal contact — they cannot influence each other in any way, and never have been able to influence each other.

(Everyone with me so far?)

This gives rise to something called the horizon problem: if these two galaxies lie beyond each other’s cosmic horizons, and are completely isolated from each other and unable communicate information to each other in any way whatsoever, then why are they so similar? Everywhere we look in the universe we see two things: homogeneity, and isotropy. This is a fancy way of saying that forces act uniformly throughout the universe, and that when viewed on a large scale the distribution of matter and energy is astonishingly even (this is one of the reasons the increasingly accurate measurements of the cosmic microwave background are such a big deal, which we’ll get to later). Which would be fine, except the fact that large portions of the universe are (apparently) out of casual contact with each other means this should be impossible. Think about molecules of gas that have been pumped into a container; initially different parts of the gas will have different kinetic energies, and thus different temperatures, but eventually the gas will reach thermal equilibrium as the gas molecules bounce off of each other and communicate their energy to all the other gas molecules in the container. If two parts of the gas were isolated from each other in the same way that the portions of the universe containing these galaxies are, though, we would expect them to have different thermal energies and different temperatures since there’s no way for one part of the gas to communicate its thermal energy to the other. So it is with the universe in general: if these two galaxies are out of causal contact then they should have evolved along dissimilar lines and look at least broadly different to us, and each different region of space should have its own unique character. Instead, the whole damn thing is the same to us no matter which direction we look in.

This should be impossible — hence our calling it the horizon problem rather than the horizon curiosity or the horizon discrepancy or whatever — but obviously it’s happened somehow, and so we’ve had to come up with a mechanism by which different regions of the universe which have been out of communication with each other since the dawn of time have somehow acquired such similar physical properties. The theory goes that very shortly after the beginning of the universe — we’re talking 10^-36 seconds here — it underwent a phase of rapid and massive expansion, growing to 10^78 times the size in just 10^-33 seconds. Much like a scrunched up sheet suddenly being stretched out to its full flat length this period inflation had the effect of smoothing out irregularities in the structure of the universe, removing nearly all of the inhomogeneity and (eventually) resulting in the uniform structure we observe around us today. This explains why those two galaxies have evolved like the regions of space that contained them were once in causal contact with each other: they were, since the entire universe originates from this one small causally connected part of space. After this period of dramatic inflation the expansion of the universe slows down¹, achieving its current, relatively sedate character.

Inflation theory explains why the universe is homogenous, why it is flat (see the sheet analogy above) and why there are no magnetic monopoles when particle physics says there should be (too complicated to go into here). However it always seemed to me like a classic case of post hoc ergo propter hoc; writing the theory solely to fit observed phenomena without making any falsifiable predictions is bad science (hello string theory). It’s a good thing the cosmic microwave background is a thing that exists, then, since it provides actual experimental evidence that inflation theory might have something concrete to it. The CMB is residual thermal radiation left over from the formation of the universe, and it is very nearly uniform throughout the entire sky. When the CMB was first observed by the COBE satellite back in 1993, though, it was observed to contain tiny irregularities on the scale of one part in  10⁴; these irregularities just happen to match those we’d expect to see if you took a relatively small region of hot gas and suddenly expanded it to the size of a universe. Quantum fluctuations in the hot gas would suddenly be magnified to the point where they have a significant effect on the macro scale of things, and despite their tiny scale the resulting irregularities were sufficient to provide a starting point for the clumping together of matter to form dust clouds, to form stars, to form galaxies. This is one of the reasons the CMB is such an intense target of study for astrophysicists, with the far more accurate WMAP probe being launched in 2001 and the Planck spacecraft following that up in 2009; it basically explains why we even have a universe in the first place, and better measurements of those irregularities (called anisotropies) give us a much improved understanding of how things all began, and incidentally provide a compelling reason why inflation theory might not be such a bit of flim-flam after all.

(Of course exactly how and why inflation happened is still a bit of a mystery. But then science wouldn’t be any fun if we knew everything, would it?)

The post Inflation Theory. appeared first on The Scientific Gamer.

Two years before the outbreak of World War Two the Japanese introduced a new high-level diplomatic cypher that the US named Purple. Purple was a cutting-edge cryptosystem that proved fiendishly difficult to break, using machine-generated cyphertext with a similar level of complexity to the Enigma devices — but unlike Enigma the US were unable to capture any working Purple devices to give them clues as to the design of the system. All they had to go on was underlying patterns in the cyphertext and the cribs (or operational errors) that represented the few chinks in Purple’s armour. Nevertheless, by 1941 the SIS had constructed an analogous device that successfully decoded Purple messages based on just this information, in effect making a perfect working replica of the Purple device without ever having seen one themselves.

The reason I’m telling you about this little historical curio is because it’s a very good analogy for our current models of particle physics. We have directly or indirectly observed most of the particles predicted by the Standard Model now, much like the US cryptographers reading the Japanese cyphertext. However, using that particle bestiary to construct a model of how things work at subatomic scales is a different matter entirely. Historically all we’ve been able to do is observe the aftereffects of a particle interaction and try to infer the exact mechanism from that alone, and this is why reading up on our current models of particle physics starts to sound like a foray into the mind of the more tinfoil-hatted among us¹. It’s also why the subsequent discovery of particles predicted by these models using high-energy particle accelerators is considered to be such a success story, since this validates the model in the same way that the analogue Purple machine producing word-perfect decrypts demonstrated that the US analysis and reproduction of the encyphering process was sound. It will be useful to keep this in mind during the next couple of posts; while the Standard Model is very counterintuitive in places it both makes accurate predictions about particle behaviour and has had the proposed mechanisms which explain that behaviour confirmed experimentally. It’s as solid a piece of work as you’ll ever find in science.

This particular post is going to be on what are called the fundamental forces: gravity, electromagnetism, strong nuclear and weak nuclear. I’ve mentioned them offhandedly during previous posts but have never gone into what they mean in detail, largely because I couldn’t remember if they actually taught this stuff in school or not. Then I realised that if I couldn’t remember learning it there it’s highly unlikely anyone else does, taught or not, and so it’s going to be useful to pin down exactly how each force works and what they affect.

All matter — even the weird stuff, like dark matter — is made up of a class of particles called fermions. Fermions are defined by their inability to occupy the same quantum space as another fermion; this gives matter its reassuring habit of forming rigid structures and not collapsing into an amorphous mess of quantum goo. A “force” (in the sense that we’re using the word here; it’s becoming trendier to refer to them as the fundamental interactions instead to avoid confusion) is the physical representation of one fermionic particle exerting influence on another. In order to exert influence there has to be some sort of transmission of information between the two fermions, and this is achieved via a “virtual”² carrier particle of a different type called a boson. Unlike fermions, the defining feature of a boson is that it can occupy the same quantum state as another particle; this makes them incapable of forming solid structures like fermions but it also gives them the ability to permeate everything in the form of a quantum field³ — electromagnetic, gravitational, you name it. Exactly what field you get will depend on the type of boson involved, as three of the four fundamental forces has a specific boson associated that gives it its particular characteristics.

The four fundamental forces are:

Strong nuclear⁴: Transmitted by gluons. The strong nuclear force is the strongest of the fundamental forces by a couple of orders of magnitude — hence its name — but its other defining characteristic is its absolutely tiny range of influence, which only stretches out to about the thickness of an atomic nucleus. The strong nuclear force is responsible for binding quarks into protons and neutrons, and protons and neutrons into atomic nucleii. The strength of the strong nuclear force makes it very difficult to split atomic nucleii up, but its miniscule range ensures that your hands do not suddenly glue themselves inseparably to your computer keyboard.

Weak nuclear: Transmitted by W and Z bosons. About 100,000,000,000,000 times weaker than the strong nuclear force and with an even shorter range; this is because the W and Z bosons are particularly massive bosons which decay very quickly and can’t travel far, barely making it beyond a few particle lengths before fizzling out. Exactly what the weak nuclear force does is a little complex and requires some understanding of advanced particle physics⁵, but basically it makes it possible for neutrons to decay into protons and thus enables the whole radioactivity shindig.

Electromagnetism⁶: Where it starts to get interesting. You’re already familiar with the carrier particle for electromagnetism: it is the humble photon, billions of which are emitted from our Sun every second to light up the Solar System, but which are also exchanged in a virtual form between particles exerting an electromagnetic force on each other. Electromagnetism is only about a hundred times weaker than the strong nuclear force (vastly stronger than gravity) and appears to have an effectively infinite range; however things aren’t flying around the universe propelled by electromagnetism because it’s a force which both repels and attracts in equal measure, and when measured over a large system (i.e. human scale objects) things tend to have equal quantities of positive and negative charge. It’s only on the chemical/atomic scale that electromagnetism becomes dominant. For large systems, the dominant force is…

Gravity: By far the weakest of the four fundamental forces (the strong nuclear force is *counts on fingers* a hundred million billion billion billion times more powerful), it nevertheless dominates large systems because like electromagnetism gravity has an infinite range, but unlike electromagnetism gravity always attracts, which means it trumps all three of the other forces over large distances. Curiously there’s not currently any room in the Standard Model for a boson associated with gravity (one is proposed — the graviton — but it’s still wildy theoretical) making it the only force without a carrier particle, and the exact mechanism by which gravity exerts its influence on an atomic scale is still a mystery to us⁷.

So those are the forces and what they do. But why are they important? Well, you might recall a couple of weeks back I mentioned elementary particles like quarks being the basic building blocks of all other particles; they’re the smallest things we know of in the universe and if you manipulate them right you can use them to build a universe. Fundamental forces are similar to this in that these four forces — strong nuclear, weak nuclear, gravity and electromagnetism — are in theory responsible for everything that happens in the universe. Think of a particular phenomenon, no matter how exotic, and when you pare it down to its most basic physical causes you should identify one or more of these four forces as the culprit.

Thus it should be possible to explain everything in the universe using these forces. However, even though we’ve narrowed it down to just four forces that’s not enough for physicists. Much like string theorists are trying to “simplify” the Standard Model even further by positing that all particles are made up of tiny vibrating strings, it’s also possible that these four fundamental forces all spring from a common source, which is why one of the current scientific holy grails is unifying all four forces into a Theory of Everything that describes… well, everything. We’ve already managed to combine electricity and magnetism into electromagnetism, and then electromagnetism and the weak nuclear force into electroweak theory⁸, but reconciling the other forces — and especially gravity — is going to be another of these great scientific challenges for the next century I keep talking about. If we can do it, though, it’s going to lead to a revolution in scientific thinking that’ll probably exceed the eventual advances made through quantum theory. It’s a tantalising thought if nothing else.

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The post Fundamental Forces. appeared first on The Scientific Gamer.

After last week’s dark matter post in which I mentioned that the outer planets are orbiting more slowly than the inner ones due to Kepler’s third law, Jim commented

In my head Neptune was going super-fast but over a gigantic distance which explained the longer time.

BIG MISTAKE.

Kepler’s laws are a good topic of discussion because while they do have relatively complicated mathematical expressions to describe them, they are also easily and concisely summed up in the form of simple words. Kepler’s laws are as follows:

1) The orbit of every planet is an ellipse, with the Sun at one of the foci.

2) A hypothetical line tethering a planet to the Sun will sweep out equal areas during equal periods of time.

3) The square of the period of the orbit is proportional to the cube of the semi-major axis of its orbit.

Sounds easy enough, but there’s still some snags in there; for example, what is a semi-major axis? Why is the line covering equal areas such a big deal? And if we go around the Sun why isn’t it at the centre of the ellipse rather than “at one of the foci”?  These are excellent questions, little Jimmy, and answering them goes a long way towards explaining why the solar system works the way it does.

Starting with the first law, the orbit of every planet (and everything else that goes around the Sun) being an ellipse has some profound implications for certain characteristics of those orbits such as the orbital velocity and where exactly the Sun is going to be in relation to the orbiting body. An ellipse looks like this:

The semi-major axis of an ellipse is the longest line that can be drawn from the ellipse’s edge towards its centre. An object found at the point where the major axis intersects with the ellipse will be at the furthest distance from the centre possible. The semi-minor axis is the reverse; it’s the shortest line that can be drawn from the edge of the ellipse towards its centre. The focii of the ellipse are two points located on the major axis which are equidistant from the centre. Exactly what that distance is is calculated by subtracting the square of the semi-minor axis from the square of the semi-major axis, and then taking a square root of the total.

(Everyone got that?)

For bodies orbiting the Sun, it is always located at one of the focii of the elliptical path they follow. If you have a body orbiting in a circular (or practically circular) orbit, then the length of the semi-major axis will be identical to the length of the semi-minor axis, and the distance of the focii from the centre of a circular orbit will turn out to be zero — which is why we go around the Sun in a nice, orderly fashion instead of screaming in for a close approach on a highly elliptical path like a comet. Turning an orbit into a circle also greatly simplifies laws two and three; since a body on a circular orbit will always be at a fixed distance from the Sun it will always have a fixed velocity, and you can calculate its orbital period by cubing its distance from the Sun at any point, since that distance is always the same.

However, while we can calculate the dynamics of circular (or near-circular¹) orbits using laws intended for ellipses, not all orbits are circular. Comets and Kuiper belt objects in particular tend to follow highly elliptical orbits; comets will famously make close approaches to the Sun during which they display a prominent tail due to surface outgassing blasting off ice and other particulate matter before retreating to the outer solar system and beyond, and Kepler’s laws explain their behaviour too.

This is the orbit of a hypothetical comet. As you can see it closely resembles the diagram of the ellipse with the Sun located at one of the focii, so that’s law one taken care of. Law two states that if we draw a hypothetical line between the Sun and the comet as it orbits around it, that line will sweep out equal areas in equal times. If you’re having difficulty visualising how this would work there is a neat animation on Wikipedia that illustrates it;  the blue shaded zone always has a constant area, and each slice of the ellipse in the red zone also has the same area and represents the distance an orbiting body will travel over a fixed period of time at that point in its orbit. The equal area thing basically means that if the area swept out by the imaginary line is a function of the distance of the comet from the Sun multiplied by the comet’s velocity, and if that area is always constant over a given period of time, then in order to keep that area constant as the comet’s distance from the Sun increases and decreases over time the velocity of the comet must increase and decrease too. When it is far away from the Sun the comet’s velocity will be small. When it is at its point of closest approach the comet’s velocity will be at its fastest.  This is a geometric representation of the comet converting gravitational potential energy into kinetic energy — and thus additional velocity — as it falls in towards the sun, and then losing that kinetic energy again as it moves outwards against the pull of the Sun’s gravity. The second law therefore tells how how the the velocity of an orbiting body will change as its distance from the Sun changes, which is crucial for plotting exactly where a comet or an asteroid is going to end up at a given point in the future. When astronomers find an Earth-threatening asteroid, Kepler’s second law is one of the things they’ll use to figure out if it’s going to hit us or not.

Finally there’s Kepler’s third law, which is the most interesting of the lot when you apply it to circular orbits. “The square of the period of the orbit is proportional to the cube of the semi-major axis of its orbit” doesn’t exactly roll off the tongue, but what this boils down to is that if the orbital period is determined by the distance of the orbiting body from the Sun, and if the orbital circumference — the distance that body covers over the orbital period — is also determined by the distance of the orbiting body from the Sun, as per 2πr, and if the orbital velocity is constant, as it must be for a circular orbit according to Kepler’s second law, then what you end up with is:

The velocity of a body in a circular orbit is a single, constant number which is also determined by the distance from that body to the Sun. In other words, if you’re X million kilometres away from the Sun there is only one velocity you can travel at to achieve a circular orbit; travelling faster than this will cause your orbit to shift outwards into an elliptical shape (or maybe even escape the solar system entirely), and travelling slower than this will cause you to fall inwards towards the Sun. This is best contextualised using the hoary old analogy of the cannon on a mountain firing a cannonball around the Earth. If it’s travelling too fast it’ll escape the Earth’s gravity and fly away from the Earth; too slow and it’ll succumb the the Earth’s gravity and crash into the surface. It needs to be travelling at a velocity that is just right in order to achieve a stable orbit.

This means that for each planet orbiting the Sun there is only one velocity it can possibly be moving at, determined by how far away from the Sun it is. This velocity decreases the further away from the Sun you go, with the orbital velocity of Mercury being 47.87 km/s compared to the orbital velocity of Neptune, a mere 5.42 km/s. Being able to calculate typical orbital velocities from just how far away from the Sun a planet or an asteroid is is very useful for several branches of solar system science; I’m most familiar with it as a way of estimating impact velocities — and consequently how destructive they’re going to be — as while these will vary depending on the direction of travel of both the impacting body and the body being impacted (head-on collisions are obviously more energetic) it’s perfectly possible to get upper and lower bounds from models based on Kepler’s second law. (For your information the typical impact speed of an asteroid hitting the Earth is likely to be between 10 and 70 kilometres per second, which is fast enough for even a small chunk of rock to really mess up somebody’s day. If you’re dealing with stuff in the Kuiper belt the range of impact speeds is much smaller — around 1 to 9 kilometres per second — since everything out there moves so slowly.) So again, Kepler’s laws aren’t just for orbital dynamics; they’re also useful for figuring out how we’re all going to die in some horrifying apocalyptic nightmare scenario!

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Dark matter cropped up in the news again recently (scientists think they might have detected something which may or may not be produced by dark matter; this happens every four or five years or so with no conclusive result so I wouldn’t hold your breath), so I thought now might be a good time to write something about it on the blog. This is particularly difficult — or easy, depending on how you look at it — since we currently know next to sod-all about dark matter and its even more mysterious counterpart, dark energy. It’s even been said that our calling it dark matter reflects more on our total and utter lack of understanding of what it actually is than any intrinsic properties on the part of the dark matter itself. Still, while we’ve never been able to directly observe dark matter (indeed, this may not ever be possible depending on what the dark matter eventually turns out to be) we have  been able to infer its existence from certain odd phenomena that don’t make any sense without something that fits the rather broad description we have of it, so we can at least have an interesting discussion about that.

(Well, I say discussion. Mostly this is going to consist of me writing at you, and you hopefully taking it all in.)

There’s a word that’s going to crop up a lot in this post. That word is baryonic, which is a term used to describe the overwhelming majority of visible matter in the universe. A baryon is a particle made up of three quarks — the quark is what’s called an elementary particle, which means that it is a particle with no known substructure and which is effectively a base building block from which you construct other particles — and which is subject to the four fundamental forces: electromagnetism, strong nuclear, weak nuclear and gravity. The protons and neutrons that give atoms most of their mass are baryonic particles, and so anything made up of atoms is called baryonic matter. Literally everything we can see (and quite a few things that we can’t, except with very high-tech observing equipment) is made of baryonic matter — you, me, the Earth, stars, galaxies, the whole works. So when a scientist is throwing around the term “baryonic” in the context of dark matter, what they mean is that it’s something that behaves rather conventionally according the laws of the physics: we can see it, we can detect it, we can predict how it will behave and what properties it will have.

There are also an apparent minority of things in the universe that are non-baryonic in nature. Most familiar to us are the electrons which orbit atomic nucleii in a fuzzy cloud, which are members of a family of particles called leptons. Like quarks, leptons are also elementary particles, but with the crucial difference that — for reasons that I’m not going to go into here for the very good reason that I barely understand them — they are not subject to the strong nuclear force which binds atomic nucleii together. This means that if you have a lepton which carries no charge and is electrically neutral you wind up with something that isn’t subject to electromagnetism either; the resulting particle is called a neutrino and it is, famously, a complete bastard to detect thanks to it ignoring two of the four fundamental forces. The other two aren’t much help either; we cannot use gravitational interaction to detect neutrinos because they have next to no mass, and the weak interaction is an incredibly short range force that is only really relevant if your neutrino is in physical contact with another particle. This is why the only way we can spot neutrinos is by detecting the aftereffects of them ramming into other particles and exchanging charge, resulting in the creation of a muon/electron which moves faster than light in water (not the same thing as faster than light in a vacuum) and an associated burst of Cherenkov radiation. And even then dedicated neutrino detectors hundreds of metres underground with billions of neutrinos sleeting through them every second will spot only a few of these.

Still, despite the difficulty we have finding it we’ve seen enough of it to know that all this non-baryonic stuff tends to have next to no mass, and that the total mass of estimated non-baryonic matter inside a given galaxy is going to be negligible in comparison to all the heavy baryonic stuff like stars and planets. This is why this graph is such a big problem for modern physics.

This is a graph of the rotation curve of a typical galaxy. The way this works is that the rotation velocity of individual stars as they orbit the galactic core is dictated by the distribution of mass throughout the galaxy. With much of a typical galaxy’s visible mass concentrated within the galactic core we would expect to see a rotation curve broadly similar to that of a solar system’s planets orbiting the central star: this is described by Kepler’s third law, which says that orbital velocity will decrease exponentially as you get further away from the star, and which is the reason why Mercury has an orbital period of 88 days and Neptune has an orbital period of 165 years — not only is Neptune covering a larger distance thanks to the increased orbital radius, but it’s doing it more slowly¹ to boot.

Now, the problem here is that this expected behaviour is represented on the above graph by the dashed line. What’s actually happening is represented by the red one, which is that the orbital velocity of matter within a galaxy remains constant no matter how far you travel out from the galactic core. This is patently absurd considering the distribution of visible mass within a typical galaxy, and yet it’s a relationship (or lack of one) that’s been proven to hold firm no matter how many galaxies we look at. There are only two ways that we can make this flat rotation curve fit in with our established laws of physics. One is to rewrite the laws of physics, which is what a vocal minority of physicists are attempting with Modified Newtonian Dynamics (or MOND). The other is to accept the existence of a hitherto unsuspected and almost completely invisible collection of matter within every galaxy that can distort the galactic mass distribution to the point where the flat rotation curve becomes possible. There are substantial issues with each approach, but since this is a post about dark matter — and because MOND is having difficulty getting traction in mainstream scientific consensus — I’ll be talking about the second one here.

As I said earlier, the name “dark matter” reflects both the fact that it’s next to impossible to detect conventionally as well as the almost total paucity of information we have about the nature of the dark matter itself. What little we know is inferred from the effect it has on the stuff we can see, like the galactic rotation curve. We know that it’s subject to gravity, since without its gravitational interactions with baryonic matter we wouldn’t know it was there in the first place. We know that there must be a staggering amount of it present in every galaxy in order to distort the curve away from its expected shape to the degree that it does, to the point that the baryonic matter component of a galaxy — all those stars, planets, and dust clouds — comprises only 15% of its actual mass. The other 85% is dark matter, coexisting in the same place (and possibly even in the same space) but otherwise eerily beyond our perception. And despite the idea being around for a good seventy years now, those two facts are just about all we know about the stuff.

Not that that stops scientists from speculating about what it might be, of course. The two major candidates for dark matter are referred to — and you’ll have to imagine me gritting my teeth as I say this — as MACHOs and WIMPs. MACHO stands for MAssive Compact Halo Object, and represents the idea that the galactic halo (the bit just outside the visible rim) might be full of extremely small, dense and dark objects like neutron stars and black holes. These MACHOs would be composed of regular baryonic matter, but they’d be impossible to spot directly thanks to being situated in a region of the galaxy with very little ambient radiation to make them show up, not to mention being distinctly non-luminous themselves. Unfortunately there are a couple of drawbacks to this idea: first, you’d need a truly ridiculous number of MACHOs in order to multiply the galaxy’s known mass by seven, and second… well, it’s complicated, but let’s just say that our current models of the Big Bang indicate that it created X amount of baryonic matter. Adding these MACHOs to the mix takes the amount of baryonic matter present in the universe to quite some way above X. There’s simply not enough regular matter around to create the required number of MACHOs.

So MACHOs are falling out of favour as potential candidates for dark matter. This leaves WIMPs, or Weakly Interacting Massive Particles. These are hypothetical non-baryonic particles somewhat like neutrinos — they are not subject to the strong nuclear force, which means they barely ever interact with other particles/atomic nucleii, and their absence of charge means they are also unaffected by electromagnetism. However, they do differ from neutrinos in that a WIMP — as its name implies — is a relatively heavy particle. It has to be in order to inject enough mass into a galaxy to produce that distorted rotation curve. There is no known particle in the Standard Model² that combines this hard-to-detect nature with a heavy mass, so if scientists ever do manage to find one the Standard Model is going to need a fair bit of rewriting. They haven’t yet, despite a number of seemingly-promising signs that they might exist; this is largely because in addition to being immune to the two major forces used to detect regular particles our hypothetical WIMPs are also very, very slow, which means we can’t use the same method we use to find neutrinos. Still, you should never underestimate the ingenuity of scientists when faced with a seemingly-impossible challenge; here’s just one of the proposed detection methods cribbed from Wikipedia:

Halo WIMPs may, as they pass through the Sun, interact with solar protons and helium nuclei. Such an interaction would cause a WIMP to lose energy. The resulting slower WIMP would not have enough energy to escape the gravitational pull of the sun and thus would be “captured” by the Sun. As more and more WIMPs thermalize inside the Sun, they begin to annihilate with each other, forming a variety of particles including high-energy neutrinos. These neutrinos may then travel to the Earth to be detected in one of the many neutrino telescopes.

Which seems to be saying that if WIMPs exist we should be seeing an excess of neutrinos being emitted from the Sun. Exactly how many extra neutrinos we see is going to depend both on the properties of the WIMPs and the mass of the Higgs boson, another scientific puzzle that has yet to be satisfactorily resolved. So it’s not just a matter of building better instruments; we need to nail down a couple of other crucial discoveries before we can properly get to work on finding WIMPs. And that’s if they even exist at all; both the MACHO and WIMP theories might be completely wrong for all we know. Maybe MOND actually has some legs. Maybe it’s one of the more obscure theories, like RAMBOs. Maybe it’s none of these things. Dark matter is one of those intriguing glimpses into the future of physics that’s just out of our grasp because we lack the necessary framework to properly describe it, much like all the not-so-minor discrepancies in our theory of the universe before general relativity and quantum mechanics came along. I suspect unravelling its exact nature is going to be one of the great scientific mysteries of the 21st century, and the one thing you can be sure of is that it’s going to take a lot more than a single experiment on board the ISS to do it. Keep that in mind when the next round of “Dark matter detected” stories hits the news in a couple of years’ time.

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I was researching a fun post about the apocalypse today when I suddenly came across a disaster scale I’d never even heard of before. It’s the Volcanic Explosivity Index, which is a way of measuring the magnitude of volcanic eruptions via the amount of ejecta they produce – not a perfect way of ranking volcanic eruptions, if you ask me, but probably the only one that’s really possible given all the different ways a volcano can explode. It then struck me that it might be a good idea to spend a little while talking about the major disaster scales and why they’re set up the way they are, since it’ll be a good setup for whenever I do get around to the apocalypse, as well as ensuring that next time you read a news report about an earthquake you’ll have some idea of what the experts mean when they say it measured 5.8 on the Richter scale.

So let’s start with the Richter scale, which is the obvious one everyone thinks they know about. The Richter scale operates on a logarithmic scale, which is a method of measuring quantities that increase exponentially while keeping them all on the same piece of graph paper – or in this case, on the same ten point measurement device. This means that each point on the Richter scale represents an increase of ten times the power of the previous point on the scale; an earthquake measuring 3.0 on the Richter scale is ten times more powerful than one which measures 2.0, and a hundred times more powerful than one which comes in at 1.0. It’s this measurement quirk more than anything else that leads to most local reported earthquakes coming in at around the 4.0—5.5 mark, since the scale has to cover the entire range of possible earthquakes from tiny microtremors to vast world-ending ruptures in the earth’s crust. 4.0 is the point at which earthquakes become noticeable by the majority of humans, and at 5.0 they start causing minor property damage; these sound like large numbers on a ten point scale but you have to remember that even a 5.0 earthquake is a thousand times less powerful than the 8.0s which cause tsunamis and kill thousands of people in places which are – hopefully – a long way away.

Anyway, what you should take away from this is that the first six points on the Richter scale represent comparatively weak earthquakes that have little chance of killing anyone; the news reports are usually just quoting them to make them seem bigger than they really are. The lethal stuff doesn’t really start until after 6.0, and the good news is that you only tend to experience one of those if you live in close proximity to a tectonic plate boundary. I would also draw your attention to the final point on the conventional Richter scale – 10.0 – which says that an earthquake of this magnitude has never been recorded. That’s not to say it can’t happen, just that it would take something rather extraordinary to prompt that sort of geological upheaval, like the earth being walloped by a bloody great asteroid. We don’t notice earthquakes below 4.0 and the range of known earthquakes only goes up to 9.9, so as far as most people are concerned the Richter scale actually operates between 4.0 and 9.9, and suddenly your local earthquake measuring 5.1 on the scale doesn’t really seem like all that much.

Then there’s the Volcanic Explosivity Index, which works much the same way as the Richter scale (except at lower bounds between 0 and 3 due to the way low-end volcanic eruptions work) except it measures the quantity of volcanic ejecta rather than the amplitude of the shockwaves passing through the earth. The difficult thing to get your head around here is that the VEI measures things in terms of volume, and it can be quite hard for the human mind to comprehend just how large a cubic kilometre of ash really is. It’s one of the questions of scale that often trips up undergraduate physicists, actually¹: how many cubic metres go into a cubic kilometre? The answer isn’t a thousand, as a lot of people think; it’s actually one billion, which is a very large number of cubic metres indeed.

Now, unlike earthquakes volcanoes are usually only locally devastating in the short-term, which is one of the reasons why the VEI is focusing on the amount of ejecta – or in other words, the amount of ash – they release. Not only is this a handy way to rank the violence of a given volcano’s eruption, but it’s the ash and gas output over the long-term that will do the major damage on a global scale.  Eyjafjallajokull shut down all flights over Europe with its ash when it erupted in 2010, and that ranks at a relatively titchy 4 on the Volcanic Explosivity Index with 0.1 cubic kilometres of ash output. Krakatoa in 1883 turned the skies around the world an attractive shade of blood red and dropped global temperatures by a full degree Celsius – and Krakatoa only comes in on the VEI index at six out of eight. Once you get out to eight out of eight – the so-called supervolcano eruptions of Yellowstone and Toba, each spewing out over a thousand cubic kilometres of material – you start to see why volcanic eruptions can be globally threatening events. Both Yellowstone and Toba spread so much ash into the atmosphere and onto the Earth’s surface that not only was there a significant drop in the global temperature for years afterwards, but the human, animal and plant populations of the world started to suffer mass dieoffs as the ash either polluted their food/water sources or made it impossible to get enough light to grow. There’s even a theory that posits Toba was responsible for reducing the human race to just a few hundred living individuals, which is why the seven-billion-odd modern humans are descended from a relatively small number of ancestors. Personally I think this is just a little bit too sensational, but it’s inarguable that supervolcano eruptions on this scale would seriously mess up civilization as we know it.

Finally there’s the Torino scale, which is used to rate asteroid impacts. Given that the vast majority of asteroids tend to miss the Earth completely, the Torino scale differs from the others in that it combines both the potential magnitude of the impact event with the probability that the asteroid will actually hit the Earth to produce a single number that indicates just how much we should be worrying about it. Small asteroids that will definitely hit us but will burn up in the atmosphere rank in low positions on the Torino scale. Large asteroids that could explode a small country but which have low probabilities of impacting are also ranked in low positions on the Torino scale. It’s only a combination of a (reasonably) large asteroid and high probability of impact which results in an asteroid having a Torino number attached to it which is larger than one, and if you look at the chart it is impact probability which is the dominant factor in an asteroid managing to place on the higher regions of the scale.  Which is fair enough, really; an object with a 1% chance of impact is something we should definitely keep our eye on, but until we get improved observations of its trajectory and know for sure it’s not a huge worry unless it’s something large enough to potentially end all life on Earth.

So any object with a Torino scale value of 1 or 0 is basically completely non-threatening, and as far as I’m aware the only asteroid that has made it past 2 was 99942 Apophis back in 2004, which was briefly ranked at 4 due to its size (350 metres diameter, which isn’t world-ending but is still pretty big) and the fact that it had a whopping 1% chance of impacting. That it was eventually downgraded to zero should tell you something about the Torino scale: since the bottom four rungs of the scale are based on impact probabilities calculated before detailed observations, this range of numbers basically exists to tell astronomers what they should be focusing their attention on and not to panic the general public. Not that this stops the media from completely misinterpreting what the scale means, of course;  they actually had to rejig the scale categories at one point because asteroids with a Torino value of 1 kept cropping up in news reports as potential threats when in fact these objects posed no unusual danger and just needed a double-check to make sure there was no chance of them hitting.  (This is why 1 is now in its own category as “NORMAL” instead of “MERITING FURTHER ATTENTIONS OF ASTRONOMERS”.)

But what about the upper regions of the scale? It’s the last three points we should really be interested in, which represent certain impacts with increasing levels of destructiveness. Number 8 is localised destructive potential, which basically equates to the detonation of a large nuclear weapon – annoying if you happen to be standing nearby, but not unduly threatening to everyone else. Number 9 represents regional  destructive potential, which is… hmm. If it was an ocean impact we’d probably be talking about something on the level of the 2004 or 2011 tsunamis, but I’m not sure there’s a good analogue for a land impact. Earthquakes don’t really translate that well into asteroid strikes, but maybe just imagine a similar level of devastation to one which wrecks an entire country (so Haiti 2010, Lisbon 1758 etc.) and you’d have some idea of the amount of damage we’re talking about. And then there’s a Torino number of 10, which has the interesting wording of global climactic catastrophe.   An asteroid that ranks at 10 doesn’t have to be large enough to kill millions of people through direct impact damage (although it probably would just as a byproduct), it just has to be able to throw up enough impact debris to cause mass species dieoffs similar to a supervolcano (or a nuclear winter).

Now, if you ask me there should be a number beyond 10. An impact of 10 on the Torino scale is small enough that it still leaves a fair chance of survival for the human race, albeit with vastly reduced numbers. If there was an impact event powerful enough to crack the earth’s crust open there’d be no survivors whatsoever, so maybe there should be a number 11 in its own category of “WE’RE SO SCREWED”. On the other hand the Torino scale exists to communicate information to the public and I suspect the public would find the existence of this category profoundly depressing, so perhaps it’s for the best.

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