astronomy, physics, science, Space, thought experiment

If the Sun went Supernova

I have to preface this article by saying that yes, I know I’m hardly the first person to consider this question.

I also have to add that, according to current physics (as of this writing in December 2017), the Sun won’t ever go supernova. It’s not massive enough to produce supernova conditions. But hey, I’ll gladly take any excuse to talk about supernovae, because supernovae are the kind of brain-bending, scary-as-hell, can’t-wrap-your-feeble-meat-computer-around-it events that make astronomy so creepy and amazing.

So, for the purposes of this thought experiment, let’s say that, at time T + 0.000 seconds, all the ingredients of a core-collapse supernova magically appear at the center of the Sun. What would that look like, from our point of view here on Earth? Well, that’s what I’m here to find out!

From T + 0.000 seconds to 499.000 seconds

This is the boring period where nothing happens. Well, actually, this is the nice period where life on Earth can continue to exist, but astrophysically, that’s pretty boring. Here’s what the Sun looks like during this period:

Normal Sun.png

Pretty much normal. Then, around 8 minutes and 19 seconds (499 seconds) after the supernova, the Earth is hit by a blast of radiation unlike anything ever witnessed by humans.

Neutrinos are very weird, troublesome particles. As of this writing, their precise mass isn’t known, but it’s believed that they do have mass. And that mass is tiny. To get an idea of just how tiny: a bacterium is about 45 million times less massive than a grain of salt. A bacterium is 783 billion times as massive as a proton. Protons are pretty tiny, ghostly particles. Electrons are even ghostlier: 1836 times less massive than a proton. (In a five-gallon / 19 liter bucket of water, the total mass of all the electrons is about the mass of a smallish sugar cube; smaller than an average low-value coin.)

As of this writing (December 2017, once again), the upper bound on the mass of a neutrino is 4.26 million times smaller than the mass of an electron. On top of that, they have no electric charge, so the only way they can interact with ordinary matter is by the mysterious weak nuclear force. They interact so weakly that (very approximately), out of all the neutrinos that pass through the widest part of the Earth, only one in 6.393 billion will collide with an atom.

But, as XKCD eloquently pointed out, supernovae are so enormous and produce so many neutrinos that their ghostliness is canceled out. According to XKCD’s math, 8 minutes after the Sun went supernova, every living creature on Earth would absorb something like 21 Sieverts of neutrino radiation. Radiation doses that high have a 100% mortality rate. You know in Hollywood how they talk about the “walking ghost” phase of radiation poisoning? Where you get sick for a day or two, and then you’re apparently fine until the effects of the radiation catch up with you and you die horribly? At 21 Sieverts, that doesn’t happen. You get very sick within seconds, and you get increasingly sick for the next one to ten days or so, and then you die horribly. You suffer from severe vomiting, diarrhea, fatigue, confusion, fluid loss, fever, cardiac complications, neurological complications, and worsening infections as your immune system dies. (If you’re brave and have a strong stomach, you can read about what 15-20 Sieverts/Gray did to a poor fellow who was involved in a radiation accident in Japan. It’s NSFW. It’s pretty grisly.)

But the point is that we’d all die when the neutrinos hit. I’m no religious scholar, but I think it’d be appropriate to call the scene Biblical. It’d be no less scary than the scary-ass shit that happens in in Revelation 16. (In the King James Bible, angels pour out vials of death that poison the water, the earth, and the Sun, and people either drop dead or start swearing and screaming.) In our supernova Armageddon, the air flares an eerie electric blue from Cherenkov radiation, like this…

685px-Advanced_Test_Reactor

(Source.)

…and a few seconds later, every creature with a central nervous system starts convulsing. Every human being on the planet starts explosively evacuating out both ends. If you had a Jupiter-sized bunker made of lead, you’d die just as fast as someone on the surface. In the realm of materials humans can actually make, there’s no such thing as neutrino shielding.

But let’s pretend we can ignore the neutrinos. We can’t. They contain 99% of a supernova’s energy output (which is why they can kill planets despite barely interacting with matter). But let’s pretend we can, because otherwise, the only spectators will be red, swollen, feverish, and vomiting, and frankly, I don’t need any new nightmares.

T + 499.000 seconds to 568.570 seconds (8m13s to 9m28.570s)

If we could ignore the neutrino radiation (we really, really can’t), this would be another quiet period. That’s kinda weird, considering how much energy was just released. A typical supernova releases somewhere in the neighborhood of 1 × 10^44 Joules, give or take an order of magnitude. The task of conveying just how much energy that is might be beyond my skills, so I’m just going to throw a bunch of metaphors at you in a panic.

According to the infamous equation E = m c^2, 10^44 Joules would mass 190 times as much as Earth. The energy alone would have half the mass of Jupiter. 10^44 Joules is (roughly) ten times as much energy as the Sun will radiate in its remaining 5 billion years. If you represented the yield of the Tsar Bomba, the largest nuclear device ever set off, by the diameter of a human hair, then the dinosaur-killing (probably) Chicxulub impact would stretch halfway across a football field, Earth’s gravitational binding energy (which is more or less the energy needed to blow up the planet) would reach a third of the way to the Sun, and the energy of a supernova would reach well past the Andromeda galaxy. 1 Joule is about as much energy as it takes to pick up an egg, a golf ball, a small apple, or a tennis ball (assuming “pick up” means “raise to 150 cm against Earth gravity.”) A supernova releases 10^44 of those Joules. If you gathered together 10^44 water molecules, they’d form a cube 90 kilometers on an edge. It would reach almost to the edge of space. (And it would very rapidly stop being a cube and start being an apocalyptic flood.)

Screw it. I think XKCD put it best: however big you think a supernova is, it’s bigger than that. Probably by a factor of at least a million.

And yet, ignoring neutrino radiation (we still can’t do that), we wouldn’t know anything about the supernova until nine and a half minutes after it happened. Most of that is because it takes light almost eight and a quarter minutes to travel from Sun to Earth. But ionized gas is also remarkably opaque to radiation, so when a star goes supernova, the shockwave that carries the non-neutrino part of its energy to the surface only travels at about 10,000 kilometers per second. That’s slow by astronomical standards, but not by human ones. To get an idea of how fast 10,000 kilometers per second is, let’s run a marathon.

At the same moment, the following things leave the start line: Usain Bolt at full sprint (10 m/s), me in my car (magically accelerating from 0 MPH to 100 MPH in zero seconds), a rifle bullet traveling at 1 kilometer per second (a .50-caliber BMG, if you want to be specific), the New Horizons probe traveling at 14 km/s (about as fast as it was going when it passed Pluto), and a supernova shockwave traveling at 10,000 km/s.

Naturally enough, the shockwave wins. It finishes the marathon (which is roughly 42.195 kilometers) in 4.220 milliseconds. In that time, New Horizons makes it 60 meters. The bullet has traveled just under 14 feet (422 cm). My car and I have traveled just over six inches (19 cm). Poor Usain Bolt probably isn’t feeling as speedy as he used to, since he’s only traveled an inch and a half (4.22 cm). That’s okay, though: he’d probably die of exhaustion if he ran a full marathon at maximum sprint. And besides, he’s about to be killed by a supernova anyway.

T + 569 seconds

If you’re at a safe distance from a supernova (which is the preferred location), the neutrinos won’t kill you. If you don’t have a neutrino detector, when a supernova goes off, the first detectable sign is the shock breakout: when the shockwave reaches the star’s surface. Normally, it takes in the neighborhood of 20 hours before the shock reaches the surface of its parent star. That’s because supernovas (at least the core-collapse type we’re talking about) usually happen inside enormous, bloated supergiants. If you put a red supergiant where the Sun is, then Jupiter would be hovering just above its surface. They’re that big.

The Sun is much smaller, and so it only takes a couple minutes for the shock to reach the surface. And when it does, Hell breaks loose. There’s a horrific wave of radiation trapped behind the opaque shock. When it breaks out, it heats it to somewhere between 100,000 and 1,000,000 Kelvin. Let’s split the difference and say 500,000 Kelvin. A star’s luminosity is determined by two things: its temperature and its surface area. At the moment of shock breakout, the Sun has yet to actually start expanding, so its surface area remains the same. Its temperature, though, increases by a factor of almost 100. Brightness scales in proportion to the fourth power of temperature, so when the shock breaks out, the Sun is going to shine something like 56 million times brighter. Shock breakout looks something like this:

Sun Shock Breakout.png

But pretty soon, it looks like this:

Sun Supernova.blend

Unsurprisingly, this ends very badly for everybody on the day side. Pre-supernova, the Earth receives about 1,300 watts per square meter. Post-supernova, that jumps up to 767 million watts per square meter. To give you some perspective: that’s roughly 700 times more light than you’d be getting if you were currently being hit in the face by a one-megaton nuclear fireball. Once again: However big you think a supernova is, it’s bigger than that.

All the solids, liquids, and gases on the day side very rapidly start turning into plasma and shock waves. But things go no better for people on the night side. Let’s say the atmosphere scatters or absorbs 10% of light after passing through its 100 km depth. That means that, after passing through one atmosphere-depth, 90% of the light remains. Since the distance, across the Earth’s surface, to the point opposite the sun is about 200 atmosphere-depths, that gives us an easy equation for the light on the night side: [light on the day side] * (0.9)^200. (10% is approximate. After searching for over an hour, I couldn’t find out exactly how much light the air scatters, and although there are equations for it, I was getting a headache. Rayleigh scattering is the relevant phenomenon, if you’re looking for the equations to do the math yourself).

On the night side, even after all that atmospheric scattering, you’re still going to burn to death. You’ll burn to death even faster if the moon’s up that night, but even if it’s not, enough light will reach you through the atmosphere alone that you’ll burn either way. If you’re only getting light via Rayleigh scattering, you’re going to get something like 540,000 watts per square meter. That’s enough to set absolutely everything on fire. It’s enough to heat everything around you to blowtorch temperatures. According to this jolly document, that’s enough radiant flux to give you a second-degree burn in a tenth of a second.

T + 5 minutes to 20 minutes

We live in a pretty cool time, space-wise. We know what the surfaces of Pluto, Vesta, and Ceres look like. We’ve landed a probe on a comet. Those glorious lunatics at SpaceX just landed a booster that had already been launched, landed, and refurbished once. And we’ve caught supernovae in the act of erupting from their parent stars. Here’s a graph, for proof:

breakout_sim-ws_v6.png

(Source. Funnily enough, the data comes from the awesome Kepler planet-hunting telescope.)

The shock-breakout flash doesn’t last very long. That’s because radiant flux scales with the fourth power of temperature, so if something gets ten times hotter, it’s going to radiate ten thousand times as fast, which means, in a vacuum, it’s going to cool ten thousand times faster (without an energy source). So, that first bright pulse is probably going to last less than an hour. But during that hour, the Earth’s going to absorb somewhere in the neighborhood of 3×10^28 Joules of energy, which is enough to accelerate a mass of 4.959×10^20 kg. to escape velocity. In other words: that sixty-minute flash is going to blow off the atmosphere and peel off the first 300 meters of the Earth’s crust. Still better than a grisly death by neutrino poisoning.

T + 20 minutes to 4 hours

This is another period during which things get better for a little while. Except for the fact that pretty much everything on the Earth’s surface is either red-hot or is now part of Earth’s incandescent comet’s-tail atmosphere, which contains, the plants, the animals, most of the surface, and you and me. “Better” is relative.

It doesn’t take long for the shock-heated sun to cool down. The physics behind this is complicated, and I don’t entirely understand it, if I’m honest. But after it cools, we’re faced with a brand-new problem: the entire mass of the sun is now expanding at between 5,000 and 10,000 kilometers per second. And its temperature only cools to something like 6,000 Kelvin. So now, the sun is growing larger and larger and larger, and it’s not getting any cooler. We’re in deep dookie.

Assuming the exploding sun is expanding at 5,000 km/s, it only takes two and a quarter minutes to double in size. If it’s fallen back to its pre-supernova temperature (which, according to my research, is roughly accurate), that means it’s now four times brighter. Or, if you like, it’s as though Earth were twice as close. Earth is experiencing the same kind of irradiance that Mercury once saw. (Mercury is thoroughly vaporized by now.)

In 6 minutes, the Sun has expanded to four times its original size. It’s now 16 times brighter. Earth is receiving 21.8 kilowatts per square meter, which is enough to set wood on fire. Except that there’s no such thing as wood anymore, because all of it just evaporated in the shock-breakout flash.

At sixteen and a quarter minutes, the sun has grown so large that, even if you ignored the earlier disasters, the Earth’s surface is hot enough to melt aluminum.

The sun swells and swells in the sky. Creepy mushroom-shaped plumes of radioactive nickel plasma erupt from the surface. The Earth’s crust, already baked to blackened glass, glows red, then orange, then yellow. The scorched rocks melt and drip downslope like candle wax. And then, at four hours, the blast wave hits. If you thought things couldn’t get any worse, you haven’t been paying attention.

T + 4 hours

At four hours, the rapidly-expanding Sun hits the Earth. After so much expansion, its density has decreased by a factor of a thousand, or thereabouts. Its density corresponds to about the mass of a grain of sand spread over a cubic meter. By comparison, a cubic meter of sea-level air contains about one and a quarter kilograms.

But that whisper of hydrogen and heavy elements is traveling at 5,000 kilometers per second, and so the pressure it exerts on the Earth is shocking: 257,000 PSI, which is five times the pressure it takes to make a jet of abrasive-laden water cut through pretty much anything (there’s a YouTube channel for that). The Earth’s surface is blasted by winds at Mach 600 (and that’s relative to the speed of sound in hot, thin hydrogen; relative to the speed of sound in ordinary air, it’s Mach 14,700). One-meter boulders are accelerated as fast as a bullet in the barrel of a gun (according to the formulae, at least; what probably happens is that they shatter into tiny shrapnel like they’ve been hit by a gigantic sledgehammer). Whole hills are blown off the surface. The Earth turns into a splintering comet. The hydrogen atoms penetrate a full micron into the surface and heat the rock well past its boiling point. The kinetic energy of all that fast-moving gas delivers 10^30 watts, which is enough to sand-blast the Earth to nothing in about three minutes, give or take.

T + 4 hours to 13h51m

And the supernova has one last really mean trick up its sleeve. If a portion of the Earth survives the blast (I’m not optimistic), then suddenly, that fragment’s going to find itself surrounded on all sides by hot supernova plasma. That’s bad news. There’s worse news, though: that plasma is shockingly radioactive. It’s absolutely loaded with nickel-56, which is produced in huge quantities in supernovae (we’re talking up to 5% of the Sun’s mass, for core-collapse supernovae). Nickel-56 is unstable. It decays first to radioactive cobalt-56 and then to stable iron-56. The radioactivity alone is enough to keep the supernova glowing well over a million times as bright as the sun for six months, and over a thousand times as bright as the sun for over two years.

A radiation dose of 50 Gray will kill a human being. The mortality rate is 100% with top-grade medical care. The body just disintegrates. The bone marrow, which produces the cells we need to clot our blood and fight infections, turns to blood soup. 50 Gray is equivalent to the deposition of 50 joules of radiation energy per kilogram. That’s enough to raise the temperature of a kilo of flesh by 0.01 Kelvin, which you’d need an expensive thermometer to measure. Meanwhile, everything caught in the supernova fallout is absorbing enough radiation to heat it to its melting point, to its boiling point, and then to ionize it to plasma. A supernova remnant is insanely hostile to ordinary matter, and doubly so to biology. If the Earth hadn’t been vaporized by the blast-wave, it would be vaporized by the gamma rays.

And that’s the end of the line. There’s a reason astronomers were so shocked to discover planets orbiting pulsars: pulsars are born in supernovae, and how the hell can a planet survive one of those?

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physics, Space, thought experiment

The Moon Cable

It was my cousin’s birthday. In his honor, we were having lunch at a slightly seedy Mexican restaurant. Half of the people were having a weird discussion about religion. The other half were busy getting drunk on fluorescent mango margaritas. As usual, me and one of my other cousins (let’s call him Neil) were talking absolute nonsense to entertain ourselves.

“So I’ve got a question,” Neil said, knowing my penchant for ridiculous thought experiments, “Would it be physically possible to tie the Earth and Moon together with a cable?” I was distracted by the fact that the ventilation duct was starting to drip in my camarones con arroz, so I didn’t give the matter as much thought as I should have, and I babbled some stuff I read about space elevators until Neil changed the subject. But, because I am an obsessive lunatic, the question has stuck with me.

The first question is how much cable we’re going to need. Since the Earth and Moon are separated, on average, by 384,399 kilometers, the answer is likely to be “a lot.”

It turns out that this isn’t very hard to calculate. Since cable (or wire rope, as the more formal people call it) is such a common and important commodity,  companies like Wirerope Works, Inc. provide their customers (and idiots like me) with pretty detailed specifications for their products. Let’s use two-inch-diameter cable, since we’re dealing with a pretty heavy load here. Every foot of this two-inch cable weighs 6.85 pounds (3.107 kilograms; I’ve noticed that traditional industries like cabling and car-making are stubborn about going metric). That does not bode well for the feasibility of our cable, but let’s give it a shot anyway.

Much to my surprise, we wouldn’t have to dig up all of North America to get the iron for our mega-cable. It would have a mass of 3,919,000,000 kilograms. I mean, 3.918 billion is hardly nothing. I mean, I wouldn’t want to eat 3.919 billion grains of rice. But when you consider that we’re tying two celestial bodies together with a cable, it seems weird that that cable would weigh less than the Great Pyramid of Giza. But it would.

So we could make the cable. And we could probably devise a horrifying bucket-brigade rocket system to haul it into space. But once we got it tied to the Moon, would it hold?

No. No it would not. Not even close.

The first of our (many) problems is that 384,399 kilometers is the Moon’s semimajor axis. Its orbit, however, is elliptical. It gets as close as 362,600 kilometers (its perigee, which is when supermoons happen) and as far away as 405,400 kilometers. If we were silly enough to anchor the cable when the Moon was at perigee (and since we’re tying planets together, there’s pretty much no limit to the silliness), then it would have to stretch by 10%. For many elastic fibers, there’s a specific yield strength: if you try to stretch it further than its limit, it’ll keep stretching without springing back, like a piece of taffy. Steel is a little better-behaved, and doesn’t have a true yield strength. However, as a reference point, engineers say that the tension that causes a piece of steel to increase in length by 0.2% is its yield strength. To put it more clearly: the cable’s gonna snap.

Of course, we could easily get around this problem by just making the cable 405,400 kilometers long instead of 384,399. But we’re very quickly going to run into another problem. The Moon orbits the Earth once every 27.3 days. The Earth, however, revolves on its axis in just under 24 hours. Long before the cable stretches to its maximum length, it’s going to start winding around the Earth’s equator like a yo-yo string until one of two things happens: 1) So much cable is wound around the Earth that, when the moon his apogee, it snaps the cable; or 2) The pull of all that wrapped-up cable slows the Earth’s rotation so that it’s synchronous with the Moon’s orbit.

In the second scenario, the Moon has to brake the Earth’s rotation within less than 24 hours, because after just over 24 hours, the cable will have wound around the Earth’s circumference once, which just so happens to correspond to the difference in distance between the Moon’s apogee and perigee. Any more than one full revolution, and the cable’s gonna snap no matter what. But hell, physics can be weird. Maybe a steel cable can stop a spinning planet.

Turns out there’s a handy formula. Torque is equal to angular acceleration times moment of inertia. (Moment of inertia tells you how hard an object is to set spinning around a particular axis.) To slow the earth’s spin period from one day to 27.3 days over the course of 24 hours requires a torque of 7.906e28 Newton-meters. For perspective: to apply that much torque with ordinary passenger-car engines would require more engines than there are stars in the Milky Way. Not looking good for our cable, but let’s at least finish the math. Since that torque’s being applied to a lever-arm (the Earth’s radius) with a length of 6,371 kilometers, the force on the cable will be 1.241e22 Newtons. That much force, applied over the piddling cross-sectional area of a two-inch cable, results in a stress of 153 quadrillion megapascals. That’s 42 trillion times the yield strength of Kevlar, which is among the strongest tensile materials we have. And don’t even think about telling me “what about nanotubes?” A high-strength aramid like Kevlar is 42 trillion times too weak. I don’t think even high-grade nanotubes are thirteen orders of magnitude stronger than Kevlar.

So, to very belatedly answer Neil’s question: no. You cannot connect the Earth and Moon with a cable. And now I have to go and return all this wire rope and get him a new birthday present.

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Cars, physics, thought experiment

A City on Wheels

Writing this blog, I find myself talking a lot about my weird little obsessions. I have a lot of them. If they were of a more practical bent, maybe I could’ve been a great composer or an architect, or the guy who invented Cards Against Humanity. But no, I end up wondering more abstract stuff, like how tall a mountain can get, or what it would take to centrifuge someone to death. While I was doing research for my post about hooking a cargo-ship diesel to my car, another old obsession came bubbling up: the idea of a town on wheels.

I’ve already done a few back-of-the-envelope numbers for this post, and the results are less than encouraging. But hey, even if it’s not actually doable, I get to talk about gigantic engines and huge wheels, and show you pictures of cool-looking mining equipment. Because I am, in my soul, still a ten-year-old playing with Tonka trucks in a mud puddle.

The Wheels

Here’s a picture of one of the world’s largest dump trucks:

liebherr_t282_1

That is a Liebherr T 282B. (Have you noticed that all the really cool machines have really boring names?) Anyway, the Liebherr is among the largest trucks in the world. It can carry 360 metric tons. It was only recently outdone by the BelAZ 75710 (see what I mean about the names?), which can carry 450 metric tons. Although it doesn’t look as immediately impressive and imposing as the BelAZ or the Caterpillar 797F, it’s got one really cool thing going for it: it’s kind of the Prius of mining trucks. That is to say, it’s almost a hybrid.

I say almost because it doesn’t (as far as I know) have regenerative braking or a big battery bank for storing power. But those gigantic wheels in the back? They’re not driven by a big beefy mechanical drivetrain like you find in an ordinary car or in a Caterpillar 797F. They’re driven by electric motors so big you could put a blanket in one and call it a Japanese hotel room. The power to drive them comes from a 3,600-horsepower Detroit Diesel, which runs an oversized alternator. (For the record, the BelAZ 75710 uses the same setup.)

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biology, Dragons, physics, thought experiment

Dragon Metabolism

As you might have noticed, I have a minor obsession with dragons. I blame Sean Connery. And, because I can never leave anything alone, I got to wondering about the practical details of a dragon’s life. I’ve already talked about breathing fire. I’m not so sure about flight, but hell, airplanes fly, so it might be possible.

But I’ll worry about dragon flight later. Right now, I’m worried about metabolism. Just how many Calories would a dragon need to stay alive? And is there any reasonable way it could get that many?

Well, there’s more than one type of dragon. There are dragons small enough to perch on your shoulder (way cooler than a parrot), and there are dragons the size of horses, and there are dragons the size of cathedrals (Smaug again), and there are, apparently, dragons in Tolkein’s universe that stand taller than the tallest mountains. Here’s a really well-done size reference, from the blog of writer N.R. Eccles-Smith:

dragon-size-full-chart

The only downside is that there’s no numerical scale. There is, however, a human. And, if you know my thought experiments, you know that, no matter what age, sex, or race, human beings are always exactly 2 meters tall. Therefore, the dragons I’ll be considering range in size from 0.001 meters (a hypothetical milli-dragon), 1 meter (Spyro, number 3, purple in the image) to 40 meters (Smaug, number 11), and then beyond that to 1,000 meters, and then beyond to the absolutely ludicrous.

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Cars, physics, thought experiment

Supersonic Toyota? (Cars, Part 2)

A while ago, I wrote a post that examined, in much greater and (slightly) more accurate detail what speeds my 2007 Toyota Yaris, with its stock drivetrain, could manage under different conditions. This post is all about Earth at sea level, which has gotta be the most boring place for a space enthusiast. Earth at sea level is what rockets are built to get away from, right? But I can make things interesting again by getting rid of the whole “sensible stock drivetrain” thing.

But first, since it’s been quite a while, a refresher: My Yaris looks like this:

2007_toyota_yaris_9100

Its stock four-cylinder engine produces about 100 horsepower and about 100 foot-pounds of torque. My drivetrain has the following gear ratios: 1st: 2.874, 2nd: 1.552, 3rd: 1.000, 4th: 0.700, torque converter: 1.950, differential: 4.237. The drag coefficient is 0.29 and the cross-sectional area is 1.96 square meters. The wheel radius is 14 inches. I’m totally writing all this down for your information, and not so I can be lazy and not have to refer back to the previous post to get the numbers later.

Anyway…let’s start dropping different engines into my car. In some cases, I’m going to leave the drivetrain the same. In other cases, either out of curiosity or for practical reasons (a rarity around here), I’ll consider a different drivetrain. As you guys know by now, if I’m gonna do something, I’m gonna overdo it. But for a change, I’m going to shoot low to start with. I’m going to consider a motor that’s actually less powerful than my actual one.

An Electric Go-Kart Motor

There are people out there who do really high-quality gas-to-electric conversions. I don’t remember where I saw it, but there was one blog-type site that actually detailed converting a similar Toyota to mine to electric power. That conversion involved a large number of batteries and a lot of careful engineering. Me? I’m just slapping this random go-kart motor into it and sticking a couple car batteries in the trunk.

The motor in question produces up to 4 newton-meters (2.95 foot-pounds). That’s not a lot. That’s equivalent to resting the lightest dumbbell they sell at Walmart on the end of a ruler. That is to say, if you glued one end of a ruler to the shaft of this motor and the other end to a table, the motor might not be able to break the ruler.

But I’m feeling optimistic, so let’s do the math anyway. In 4th gear (which gives maximum wheel speed), that 4 newton-meters of torque becomes 4 * 1.950 * 4.237 * 0.700 = 21 Newton-meters. Divide that by the 14-inch radius of my wheels, and the force applied at maximum wheel-speed is 59.060 Newtons. Plug that into the reverse drag equation from the previous post, and you get 12.76 m/s (28.55 mph, 45.95 km/h). That’s actually not too shabby, considering my car probably weighs a good ten times as much as a go-kart and has at least twice the cross-sectional area.

For the electrically-inclined, if I was using ordinary 12 volt batteries, I’d need to assemble them in series strings of 5, to meet the 48 volts required by the motor and overcome losses and varying battery voltages. One of these strings could supply the necessary current of 36 amps to drive the motor at maximum speed and maximum torque. Ordinary car batteries would provide between one and two hours’ drive-time per 5-battery string. That’s actually not too bad. I couldn’t ever take my go-kart Yaris on the highway, but as a runabout, it might work.

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Uncategorized

Cosmic Soup

I once heard someone (I think it was Neil deGrasse Tyson, but I might be wrong) describe the universe with a really cool analogy: it’s just like soup. You take onions and carrots and celery and mushrooms and rice and stick them in some water. Starting out, it’s not a soup. It’s a disgusting bunch of vegetables floating in some nasty cold water. But as it cooks, all the ingredients leach good stuff into the water and flavor each other, and eventually, you’ve got soup.

Which is a surprisingly good analogy for how our universe formed (at least, according to the best cosmological models we have as of January 2015 (I hate having to add that every time, but it’s true)). First, there was the big bang, which we know little about. The big bang cooled down and gave us a bunch of hydrogen, a little helium, and a tiny trace of lithium. Then it got too cold to make heavier atoms. Luckily, gravity kicked in. The hydrogen and helium (with some help from whatever the hell dark matter actually is) clumped together to form gas clouds. Those gas clouds collapsed to form stars. Those first stars were huge and bright and hot and died young. They died in massive supernovae, releasing heavy elements from their cores and creating new heavy elements on the spot from their high-energy radiation. Slowly, these heavier elements accumulated in the interstellar medium. Eventually, they started getting incorporated into the molecular clouds that went into forming new molecular clouds (I’m getting a horrible unwholesome image of a room full of people breathing each other’s flatulence; that’s why Neil deGrasse Tyson is on TV and I’m sitting here in my corner). These new molecular clouds could collapse to form not only stars, but also things like planets. And this went on and on until we reached today, which is (we think) about 14 billion years later. We’ve got chemistry all over the damn place. There’s chemistry in the sky and chemistry in the oceans and chemistry up to the tops of the highest mountains. My brain is full of chemistry (and from the sound of that sentence, my chemistry’s a little off again tonight…)

But what if it had happened differently? I mean, I’m pretty pleased with how our cosmic soup turned out (seeing as it allowed me to exist and all, which was nice of it), but you’ve got to admit that hydrogen, helium, and a tiny bit of lithium is pretty bland. It’s like that watery potato soup they give orphans in Christmas movies. Sure, it’ll keep you alive, but it’s not all that interesting. So what would happen if we started out with some different ingredients? What would we end up with then?

Let’s find out!

The Gumbo Universe: This universe starts out with a little of everything. Like I said, our universe started out with hydrogen, helium, lithium, and almost nothing else. And there’s a good physical reason for that: it cooled off so fast that there wasn’t time for anything more complicated than helium and lithium to form. It’s like flash-freezing: you don’t get any interesting crystals if you cool your water down too fast.

But in the Gumbo Universe, there are no such limitations. The universe starts out with all of the stable elements. The abundance of a given element is determined by its atomic number. Helium is ten times rarer than hydrogen. Lithium is ten times rarer than helium. And so on. The Gumbo Universe is 90% hydrogen, 9% helium, 0.9% lithium, 0.09% beryllium, 0.009% boron, 900 parts per million carbon, 90 parts per million nitrogen, 9 parts per million oxygen, 900 parts per billion fluorine, 90 parts per billion neon, and so on until uranium, element 92, which would make up only 90 atoms out of every 1, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000.

To my surprise, the Gumbo Universe’s hydrogen-to-helium ratio is pretty close to ours. But this universe has a massive overabundance of lithium, beryllium, and boron. These elements aren’t heavy by human standards (lithium floats in water, although not for very long, since it tends to catch fire and explode), but they might as well be lead boots as far as the cosmos is concerned. All these surplus heavy elements mean stars are going to form sooner, be denser, and probably start fusion sooner. Collisions with high-speed protons (i.e., the hot hydrogen atoms surrounding the metal-rich cores of these weird stars) will rapidly convert most of the lithium to helium (which also happens in our universe). The same thing will happen to the boron (interestingly, proton-boron fusion is being studied in our universe, since it doesn’t produce neutron radiation, which (because it’s evil) damages DNA and turns innocent substances radioactive). And when those beryllium atoms get hit by alpha particles (which are the same thing as hot helium nuclei, which, again, we’re going to have plenty of), they’ll turn into carbon and neutrons. The same thing happened in our universe, which is why, in element abundance graphs like the one in this paper, there’s a massive dip in abundance from lithium to beryllium to boron. Actually, physics ensures that, since the element composition of the Gumbo Universe starts out pretty similar to that of our universe, its ultimate composition is probably going to be similar, too.

Its structure, on the other hand, won’t be. At my estimate, I’d need at least four separate PhD’s and a supercomputer (which still I don’t have. Stupid thrift stores. Never have anything good.) to provide even a good guess what state the stuff in the Gumbo Universe would be like. I suspect the stars would be smaller, since their heavy-element cores would let them ignite fusion earlier, and their light would blow away what remained of their molecular clouds. These stars would probably be red dwarfs (or their exotic cousins), but probably wouldn’t be as long-lived as red dwarfs in our universe. As for galaxies, they’d probably still form (galaxy formation is driven mainly by the gravitation of matter and dark matter (whatever the hell it is)). As for whether they’d be larger or smaller than the galaxies in our universe, I can think up good arguments for both. I can see them being smaller because so many stars would form so quickly, which would blow away a lot of gas and slow star-formation rates, meaning lots of little galaxies a lot closer together. But then again, if the stars in the Gumbo Universe are red-dwarf-like, then their radiation pressure will be pretty weak, which might actually let galaxies grow larger than they do in our universe. I leave that as an exercise to the reader (which is the smart-ass way of saying “I can’t be bothered.”)

But what about the question that has plagued us (probably) since the dawn of thought: Could there be life forms in the Gumbo Universe? (Okay, I’m guessing Galileo didn’t ask himself that exact question, but you know what I mean. Although for some reason, I’m thinking Galileo would have really liked gumbo.) That’s really hard to answer. We know there’s life in our universe, but we don’t know how hard it is for life to form, how long it lasts once it forms, and whether it tends toward simplicity or complexity. But my guess is that the Gumbo Universe would be even more fertile than our own. It would have the elements needed to make life (hydrogen, carbon, oxygen, nitrogen, phosphorus, sulfur, et cetera) right from the start. And to boot, with its smaller stars, it would (probably) have fewer supernovae, which means larger portions of the galaxies would be habitable, since supernovae are probably very unhealthy for life as we know it.

The Julia Child Universe: Julia Child was famous for a lot of things. She was famous for her PBS cooking shows, for her attention-getting voice, for her love of cooking, and for being shockingly tall (6’2″ (188 cm), if IMDB is to be believed). I grew up watching her, but she was cooking on TV when my parents were children. She was famous for her show The French Chef, and one of her most famous recipes (and also the last meal she ate before she died, if Wikipedia is right) was her french onion soup. French onion soup is pretty much just finely-chopped onions simmered in beef stock.

And why on Earth, you may be asking, am I talking about TV chefs and onion soup? Because the French Onion Soup universe, like french onion soup itself, has very few ingredients. The French Onion Soup universe is made entirely of Uranium-238. You might be saying “That’s absolutely ridiculous.” And you’d be right. But I’ve never let that stop me before.

Well, to nobody’s surprise, the Julia Child Universe would be weird. We’d start out with a bunch of gaseous uranium plasma which would gradually cool and coalesce into little dust grains. Those dust grains would collapse. Since fusing two uranium nuclei requires an external energy input, there wouldn’t be any ordinary stars to begin with. There would, however, probably be medium-temperature white dwarfs and neutron stars, which would form straight from the interstellar medium, shortcutting all that hydrogen-burning nonsense stars in our universe have to go through. And, for the same reason all the planets in our solar system don’t get sucked into the sun and all the stars in our galaxy didn’t get sucked into the supermassive black hole at the center (the reason mostly being angular momentum), there would probably also be uranium planets.

Uranium-238 is pretty stable. It’s stable enough that, if you swallow it, your biggest problem isn’t that you just swallowed something radioactive; your biggest problem is that uranium is a toxic heavy metal. But it is radioactive, and when you’ve got enough of it in one place, that radioactivity adds up. U-238 is, for instance, one of the reasons Earth’s interior stays hot enough to be fluid.

But now we’re talking about planet-sized masses of U-238. If Earth were made entirely of uranium, it would have a radius of something like 4,000 kilometers, 60% of its actual radius. It would also produce 5e18 watts of heat from alpha decay (at least at the start of its life), which would be enough to make it glow cherry-red and probably melt.

Sadly, no planet is immortal, even when it’s made of solid uranium. U-238 decays (with a half life of 4.468 billion years) into Thorium-234, releasing an alpha particle (helium nucleus). Over time, the alpha particles will steal electrons from the uranium and thorium atoms, and all those uranium planets will develop helium atmospheres. But it doesn’t end there: Thorium-234 decays (by emitting an electron) with a half-life of 24 days into metastable Protactinium-234 (metastable meaning the nucleus is excited, and will therefore probably release a gamma ray). Regular Protactinium-234 decays by electron emission to Uranium-234, with a half life of 1.17 minutes. Uranium-234 is also an alpha emitter, meaning it decays into Thorium-230 and helium. Thorium-230 decays into helium and Radon-226, which has a half life of around one and a half thousand years. (And for those who are picky and obsessive like me, yes, there would be small quantities of other elements produced by things like spontaneous fission and cluster decay, but I’m keeping things simple.)

This is one weird planet we’ve got. By the time enough of it has decayed to give it an atmosphere as substantial as Earth’s, it’s still probably hot enough to glow. And that atmosphere is just about as toxic as you can imagine: it’s composed primarily of helium, so your voice would be all funny. The helium would also be scorching-hot, so your voice would get really funny. And it would be extremely dense and seriously radioactive, making it even worse than Venus’s atmosphere (which is the closest thing I can imagine to actual Hell).

But the decays would go on. Radon-226 is a noble gas. It decays into Radon-222 (again, by alpha decay), and then into Polonium-118 (not the kind of Polonium people use to poison Russian guys). As it decayed, there would be a fine snow of extremely radioactive isotopes, which would probably give the air an extremely faint blue glow. Most of those isotopes have half-lives measured in minutes or seconds (or microseconds), but you’d most likely end up with measurable quantities of Polonium-210 (that’s the kind you use to very suspiciously murder Russian guys), Lead-210, and Bismuth-210. But all roads that start at Uranium-238 eventually reach Lead-206 (sounds like a really terrible Johnny Cash parody). Lead-206 is stable, and makes up about a quarter of the lead atoms we find here on Earth (there are other stable isotopes). So, after around 4.4 trillion years, there would be less than one one thousandth of the original U-238 left. Pretty much everything else would be either lead or helium.

But that’s not the end. During its transformation to Lead-206, Uranium-238 has given birth to no less than 8 alpha particles, which will ultimately become helium atoms, So, after a long time, the mass of the Julia Child Universe would consist of 84.5% Lead-206 (by mass) and 15.5% Helium-4. 15.5% of one solar mass (in our universe, and when it’s made out of hydrogen) is enough stuff to make a proper star (albeit a small one). It’s harder to make a star out of helium, though, since helium atoms take more energy to fuse together. Stars weighing 15.5% of a solar mass generally can’t burn helium. That is, unless they have enormously dense, hot cores with crushing gravity. Which would most certainly be the case of some of our uranium white dwarfs and our neutron stars. So, for a brief while, stars would burn in our weird-ass sky. I say “a brief while” because, when you compress it to such high pressures and densities, helium tends to detonate more than burn. Our stars would last a few hours or a few days, burning purplish-white with fusion energy.

Helium fusion is a little complicated, which is why it takes stellar pressures to get it going. First, two helium nuclei fuse to form Beryllium-8. Then, another helium nucleus fuses with Beryllium-8 to form Carbon-12, which is the carbon on which our chemistry is based. But it gets better: it turns out that you can keep adding helium nuclei until you get all the way up to Iron-56 and Nickel-56, after which the fusion no longer releases energy. You’d end up with most of the ingredients for life as we know it, although they’d all be stuck on the surface of white dwarfs and neutron stars. Still, Frank Drake and Robert L. Forward made a passable case for life on a neutron star in Dragon’s Egg, so who knows? And white dwarfs tend to hold their heat for billions of years, so you might see very flat critters crawling around on miniature lead stars.

Surprisingly, even this weird universe would ultimately produce planets made of more familiar stuff. It turns out that collisions between neutron stars can produce elements like thorium and gold, and other elements which could fission into lighter elements. Neutron star collisions are pretty violent things, so some of this stuff would get flung out into space. Neutron stars have a death-grip on their matter, so I imagine it wouldn’t be nearly enough to form an actual proper hydrogen star, but it would probably be enough to form a planet.

Imagine it: a planet made of gold, iron, carbon, and uranium, with an atmosphere of helium and carbon dioxide, inhabited by radiation-hardened snails with lead shells. Sound implausible? How could it possibly be more implausible than the star-nosed mole?

The “Blinded by the Light” Universe: Can you tell my mom made me listen to too much classic rock when she was driving me to school? Until now, all our hypothetical universes have been made of matter: protons, neutrons, and electrons. But what if the mass of the universe was composed entirely of photons? That is, particles of light.

This one’s a lot trickier. In order for anything really interesting to happen, the universe has to expand in just the right way, and there has to be just the right number of photons. If the universe expands too fast (which can happen when there are too few photons) or too slow (if there are too many photons), it’ll end up as a diluted infrared soup (the former case) or a singularity (the latter). But if everything goes just right, and the universe expands and then comes to a halt while at least some of the photons have energies above 1022 kiloelectronvolts (meaning wavelengths shorter than 0.0012 nanometers), then interesting stuff can happen.

The universe is really weird. A gamma ray with an energy of 1022 kiloelectronvolts effectively has twice the mass of an electron. Thanks to quantum mechanics (the giver of headaches, by royal appointment), a gamma ray with an energy equal to or greater than 1022 keV can suddenly turn into an electron and a positron (its antiparticle). Normally, photons can’t interact with each other, since they have no charge. But if one photon should collide with another photon that’s momentarily popped apart into two charged particles, then they can interact. Sometimes, they can even bounce off of each other (see this Wikipedia article for a brief introduction).

But what exactly does that mean? Well, to be honest, I’m not sure. Photons are complicated. They have energy and angular momentum and all sorts of other stuff they didn’t teach in the English department. I don’t know whether life or intelligence of any kind could exist in this universe. But I imagine interesting structures could emerge, as long as there were enough high-energy gamma rays left over. I’m imagining a Feynman diagram big enough to wallpaper an airplane hangar, covered in a terrifying spiderweb of lines, photons bouncing off photons and transferring angular momentum back and forth. Let’s face it, that wouldn’t be any wilder than the universe we have: a soup of photons bouncing off of electrons, and electrons shuffling between atoms made of protons and neutrons.

The Universe is Made of Spiders: The Spider Universe has no explanation. It consists entirely of spiders which weave airtight tubular webs containing long-lived radio-isotopes. Plaques of mold feed on these isotopes. Fruit flies feed on the mold. Spiders feed on the fruit flies, and endlessly weave. Their air-filled tunnels are no thicker than your finger, and spread so thinly that each is separated from its nearest neighbor by the diameter of a star. But they’re all connected. Even though no single spider will ever travel from one node to the next in its lifetime, there is a steady traffic of genes to and fro. An endless parade of spiders, back and forth, back and forth in a network far more fragile and gossamer than the thinnest gold leaf.

In case you’re worried I just had a seizure there, I didn’t. I think. You see, according to recent physics, the universe as it exists today will collapse if its density is greater than one hydrogen atom per cubic centimeter. Locally, the density can be much higher (like, for example, on Earth). The same applies to mysterious networks of radioactive spiderwebs that appeared from nowhere at the beginning of time with no explanation. And when you consider that our current cosmological models pretty much all say “First there was the Big Bang, which for some reason created a bunch of energy and matter (but more matter than antimatter, for some reason). We don’t know why, but then everything else happened”, the spider thing doesn’t seem so far-fetched. Okay, maybe a little far-fetched, but isn’t it cool that we still have stuff to learn about the start of the universe?

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Carousel planet.

As you might imagine, I’m a big fan of bizarre science fiction. Peter Watts, Charles Stross, Edgar Allan Poe (who was such a good writer that he almost convinced me that you really could travel to the Moon by balloon). Lately, I’ve been reading Hal Clement’s Mission of Gravity, a charming and very well-thought-out book about a massive planet which spins so fast (once every eighteen minutes) that it’s flattened into the shape of a throat lozenge, with a polar gravity somewhere between 250 and 600 gees (instantly lethal to a human explorer), but an equatorial gravity of 3 gees (miserable, but survivable, especially with mechanical support). He called his planet Mesklin. Get your peyote jokes in while you can.

Thinking about Mesklin kindled in me a brief but powerful obsession with fast-rotating planets. And, in the spirit of the thought experiment (and to justify the ungodly amount of time I spent researching the subject), I thought I’d share what I found.

Planets and stars are massive things, so their gravity tries to pull them into spheres. If you think about it, this makes sense: over geological and astronomical timescales, rock flows like liquid. Therefore, it’s not unreasonable, for the sake of simplification, to treat planets like they’re made of an incompressible fluid.

To massively oversimplify things, gravity makes planets spherical because, once they’re spherical, there are no low spots left for the rock to flow into. In a sphere, the weight of the fluid is perfectly and evenly balanced by the pressure it generates in response to compression. Objects like this are said to be in hydrostatic equilibrium, and that’s one of the requirements an object must meet to be a planet according to the International Astronomical Union. (Don’t get too excited, though: this has nothing to do with why they decided Pluto wasn’t a planet.)

But all this talk of spheres and hydrostatic equilibrium ignores one important thing: every planet rotates. Some rotate very slowly. Venus, for instance, rotates so slowly that its day is longer than its year (243 Earth days versus 224 days; I’d hate to see a Venusian calendar). Others rotate really fast: Jupiter rotates once every 9.9 hours. Most of the other equilibrium objects (meaning: planet-like thingies) in the solar system fall in between these two extremes.

This means that none of the planets are actually perfectly spherical. Rotation of an object generates a centrifugal acceleration (and, incidentally, also generates a lot of arguments about the difference between centrifugal and centripetal). Although from the viewpoint of someone standing on the planet, centrifugal accelerations and forces act like regular accelerations and forces, they’re technically “fictitious”: they’re a consequence of the fact that something that’s moving likes to go in a straight line, but in a rotating body, all the bits of mass are being forced to move in a circle by the rotation of the reference frame, and therefore must behave like they have a force acting on them, even though they don’t.

For the Earth and most of the other planets, these centrifugal effects are small. Ignoring other effects, when you’re standing on Earth’s equator, you experience an upward acceleration of about 0.003 gees. That means every kilogram of matter feels 3.4 grams lighter on the Equator than it does at the poles. 3.4 grams is less than the mass of most small coins, so it’s not something that’s going to ruin your day.

It does, however, have an effect. Gravitational acceleration is directed towards the Earth’s center of mass. Centrifugal acceleration is directed away from the earth’s axis of rotation, and therefore opposes gravitational acceleration, the opposition being largest at the equator and smallest at the poles. As a result, the Earth is not quite spherical. It’s very slightly lozenge-shaped (or Skittle-shaped or Smartie-shaped; the technical term is oblate). The difference is small: measured at the equator, the Earth has a radius of 6,378.1 kilometers. Measured at the poles, it has a radius of 6,356.8 kilometers. That’s a difference of 21 kilometers, which is a lot higher than any mountain on Earth, but on the scale of a planet, it isn’t that much. Here, have a visual aid:

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Here, the green ellipse represents the cross-section of a perfect sphere with the same volume as Earth. The red ellipse is the cross section of the real Earth. If you look closely, you can see that the red ellipse falls a hair’s-breadth below the green one near the poles.

Saturn is a more extreme case. Saturn has a much larger radius than Earth, and it rotates faster, and centrifugal acceleration is the square of angular velocity (rotation speed) times the radius of the circle in question. So Saturn is flattened a lot more than the Earth. So much so, in fact, that you can see it in photographs:

(Image courtesy of JPL/NASA.)

But I keep getting distracted by the pretty rings and the absolutely horrifying thunderstorm (seriously: that knotty thing in the southern hemisphere is one huge thunderstorm), so here’s a graph:

saturn

If you can’t see the difference this time, chances are you’re reading this in Braille, in which case I’m sorry if my alt-text is unhelpful, but that stuff confuses me.

The squashed-ness of an ellipse (or an ellipsoid like the Earth or Saturn) is described by its flattening (also called oblateness), which is the difference between the equatorial and polar radii divided by the equatorial radius. Earth’s flattening is 0.003, meaning its polar radius is 0.3% smaller than its equatorial. Saturn’s flattening is 0.098, allmost a full ten percent.

You may notice that I’ve managed to go almost a thousand words without getting into the hypothetical stuff. Well, fret no longer: what I wanted to know is whether or not there’s a simple formula to calculate flattening from parameters like mass, radius, and rotation rate. The math involved is actually quite tricky. As the planet gets more and more flattened, the matter at the equator moves far enough away from the center of mass for it to experience significantly less gravity than the matter at the poles, which magnifies the flattening effect. Flattening also moves enough of the mass away from the center that you can’t do the usual thing and treat the planet as a dimensionless point. Nonetheless, clever folks like Isaac Newton and Colin Maclaurin worked through these problems in the 18th century, and this is what they got. The flattening of a planet is (approximately)

(5/4) * [((2 * pi) / (rotation period))^2 * (planet’s radius)^3] / [Newton’s gravitational constant * planet’s mass]

I know that looks ugly, but trust me, it’s a lot less complicated than the math Newton and Maclaurin had to do to get there.

This formula is, at best, an approximation. It doesn’t give the Earth’s flattening to very high accuracy, because the formula assumes the Earth is equally dense throughout, which is not even close to the truth. Still, it’s a convenient approximation. It tells us, for instance, that if the Earth’s day was only 3 hours long, the Earth would be 27% smaller through the poles than through the equator (a flattening of 0.27). Compared to a spherical Earth, it would look like this:

earth

And there are actual objects out there that are this squashed. The star Altair, for instance, is 1.79 times as massive as our Sun, and while our sun rotates once every 25 days (give or take), Altair rotates once every 8.9 hours. Altair is also close by–only 16 light-years–which means it’s one of the few stars whose surface we’ve actually imaged in any detail. Altair looks like this:

(Image courtesy of the University of Michigan.)

Altair’s oblateness is about 0.25. Just for giggles, here’s what it would look like if the Sun was that oblate:

Oblate Sun

(This image was made using the wonderful and extremely moddable program Celestia, which is the best planetarium software in the world, and is absolutely free.)

You might think Altair is an extraordinary case, a freak of nature. But as it turns out, a lot of large stars spin very quickly and are very oblate. Vega, which is one of the brightest stars you can see from the Northern Hemisphere, is almost as oblate as Altair. Achernar is even more oblate: it spins so fast that it has a belt of loose gas around its equator; it’s close to the maximum rate at which a star can spin without flying apart.

Now Altair is a pretty weird-looking object, but you know me well enough to know that I like extremes, and while an oblateness of 0.25 is pretty extreme, it’s not super-extreme. (Can you tell I’m a child of the ’90s?) If we spun the Earth faster, could we make it even flatter?

Sure. Up to a point. The mathematicians Carl Jacobi and Henri Poincaré both worked on the problem of fast-rotating self-gravitating fluids. They discovered that the pancake-shaped planet is the most stable configuration as long as its oblateness is less than 0.81, which, for Earth, means a rotation period of about 2 hours. Here’s what that would look like.

Oblate Earth

This is one weird planet. If the Earth were rotating this fast, Australians would experience a gravity of much less than 1 gee. Hurricanes would have much smaller diameters because of the increased power of the Coriolis effect. If we pretend that, somehow, human evolution proceeded normally in spite of the pancake Earth, cultures that developed in northern Asia, North America, and parts of South America might spend a very long time absolutely convinced that the Earth was flat, because to them, it would very nearly be true. Cultures in India, China, the Middle East, central Africa, and central North and South America, on the other hand, probably wouldn’t know what to think: If you looked north or south, the horizon would be much farther away than if you were looking east and west.

Of course, if the Earth was spinning that fast, it would look nothing like it does today. For one thing, it would probably be a lot colder: for one thing, there would only be a small equatorial belt where the sun could ever pass directly overhead, and everywhere else would get its sunlight at an angle, which is what causes our winters. Human beings as we know them couldn’t live near the poles, where the gravity would approach 8 gees. Fighter pilots can handle that, but that’s only for short periods, and only after a lot of physical conditioning and centrifuge training, and with the help of pressure-equalizing suits. If we stick with the prevailing theory that modern humans began their outward migration in Africa, then they would probably only be able to spread as far north as Spain, Italy, Greece, southern Ukraine, Uzbekistan, India, China, and Japan. Their southward migration would be limited to south Africa, Australia, and possibly New Zealand. Human beings would have to grow a hell of a lot stouter and tougher to survive the trek through the high-gravity regions to cross the Bering Strait into the Americas.

But if you think this is weird, you ain’t seen nothin’ yet. Jacobi, Poincaré, and others that came after them discovered something else: a pancake-shaped body with an oblateness of 0.81 is a maximum. As you keep adding angular momentum to it, it doesn’t just keep flattening out, and its rotation actually slows down. That’s because, above oblateness 0.81, the pancake shape is no longer stable. Above oblateness 0.81, the stable configuration is the so-called Jacobi ellipsoid, which looks like a badly-made rugby ball or a really disturbing suppository:

Scalene Earth

This would be an even weirder planet to live on than the pancake Earth from before. The tips of the ellipsoid would be the best place to live, since the gravity there would be weakest and they would have the best chance of getting direct sunlight. On the other hand, the bizarre geometry might make for some crazy civilization-ending weather patterns around the tips. Still, that’d be better than the wild centrifugal-Coriolis storms whirling east and west from the planet’s narrow waist. If, once again, human migration starts in Africa, it probably wouldn’t proceed much farther east than Europe and the Middle East, which would not only have the lowest gravity, but would have a better chance of having tolerable weather and getting regular rainfall.

You might be thinking “What does all that have to do with anything?” I get that question a lot. Well, it turns out that there are objects in our own solar system which spin fast enough to distort into this shape. One of the largest is the dwarf planet Haumea, which is larger than Pluto along all but its shortest axis, and is larger than the Moon along its longest. Haumea’s been stretched into this bizarre shape by its rapid rotation: once every 3.9 hours.

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(Source and licensing.)

Now, you have to re-define oblateness when you’re working with scalene ellipsoids like these. Because each of their three axes are a different length, there are actually three separate oblatenesses. The one we’re concerned with, though, is the oblateness of the cross-section taken parallel to the longest axis. We’re interested in this because it turns out that, just like the symmetrical lozenge-shaped Maclaurin spheroid became unstable beyond oblateness 0.81, the suppository-shaped Jacobi ellipsoid becomes unstable beyond a long-axis oblateness of 0.93. At this point, the Earth would be shaped a little like a torpedo or a cartoon cigar.

But what would happen as you pumped more angular momentum into it? Until now, we’ve been able to get a pretty good approximation by assuming that the Earth is a zero-viscosity fluid of uniform density. But the results of exceeding the Jacobi limit depend strongly on Earth’s material properties. Simulations of such fast-spinning fluids have been performed, and depending on how they compress under pressure, sometimes they deform into asymmetric cones before splitting in two, and sometimes they lose mass from their tips, which carries away angular momentum and slows their rotation until they return to the Jacobi equilibrium.

There is reason to believe that the Earth would take the fission route rather than the mass-shedding route. The Earth, after all is a solid object made of fairly strong stuff. Stars that spin too fast (like Achernar) tend to lose mass, since gas doesn’t hold together too well. Planets, on the other hand, tend to break into smaller planets.

There’s more evidence to believe that the Earth would fission: similar things have happened to other objects in our solar system. Here’s a picture of a weird-looking object:

(Source.)

You could be forgiven for thinking that this was an X-ray picture of a bone from an extinct squirrel. In fact, it’s an asteroid: 216 Kleopatra, which is 217 kilometers long and about 91 in diameter. It’s what’s known as a contact binary: a pair of objects orbiting so close together that they touch. The theory is that, a long time ago, Kleopatra was hit by a glancing blow from another asteroid, which broke it apart and gave it so much angular momentum that it couldn’t even pull itself into a Haumea suppository shape. Contact binaries are right on the border between “One object spinning fast” and “Two objects orbiting very close together.” It might look something like this:

Contact Binary Earth

This would be an even weirder place to live than the others. Picture this: you step outside your house one summer evening. The sun has already set, but the other lobe of the world reflects enough light to give the yard a pleasant glow. You can’t see the waist of the world from here, but you know it’s there. At this very moment, planeloads of businesspeople are flying vertically up through the waist to the continents on the other side, and cargo ships are sailing up the massive waterfall that connects the two halves of the planet. As the shadow of your half of the world creeps across the opposite half, you see city lights coming on on the other side. Weird, right?

What’s weirder is that, as in the case of the absurdly oblate objects we looked at before, contact binaries are not all that rare. Many asteroids are contact binaries. The comet 67P/Churyumov-Gerasimenko (which, as of this writing, is being explored by the Rosetta spacecraft) might be a contact binary. Weirder still, there are contact binary stars. It seems strange that an object like a star could survive direct contact with another star, but contact binary stars actually form a whole class, called W Ursae Majoris variables, after W Ursae Majoris, a double star which looks like a peanut.

(Source.)

Contact binary stars don’t behave like any other kind of star. That’s partly because they’re essentially one star with two cores, which means the whole surface tends to stay at the same temperature when it normally wouldn’t; it’s also partly because of the huge angular momentum you get when two stars orbit that close together.

The universe can be a really weird place, but I have to admit, for all its messiness, it can be pretty aesthetically-pleasing, too. I mean, look at all those pretty ellipses up there. They’re smooth and curved like eggs (or parts of human anatomy, if you stretch your perverse imagination). And they’re proof that we humans can be clever when we work at it. Isaac Newton figured out his flattening formula using math and physics he helped invent, and this was in a time when hardly anybody had indoor plumbing. Now, we’ve got Rosetta getting ready to drop a lander on a comet, and next year (2015), we’re going to get our first up-close looks the giant dwarf planets Pluto and Ceres. We’ve got plenty of flaws, don’t get me wrong, but we can be pretty cool sometimes.

(And speaking of cool, someone made an amazing animation of the transition from spherical Earth to Maclaurin spheroid to Jacobi Ellipsoid to Poincare pear:

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Shaving too.

The hilarious and bizarre Mitch Hedberg once said “Every time I go and shave I assume there’s someone else on the planet shaving, so I say ‘I’m gonna go shave, too.'” Because I am an obsessive fool who can’t leave anything alone, I started wondering if you could actually reasonably say that. I mean, there are a lot of people in the world, and a lot of people who shave, so it’s entirely possible that there’s someone shaving every second of the day.

This is a perfect place for Fermi estimation, or, if you prefer, back-of-the-envelope calculation. It’s a great method for getting a quick idea of the scope of a problem.

There are about 7 billion people on Earth. In many cultures, only the men shave. Let’s assume that half of the people in the world are men. That gives us 3.5 billion potential shavers. But, except in rare cases, men don’t start shaving until their beards begin growing at puberty. Let’s say beard growth starts at age 15. A randomly-chosen person could be pretty much any age, let’s say from 0 to 70. Only that percentage of men between 15 and 70 shave, which comes out to 79%, or 2.756 billion.

It takes me about 15 minutes to shave. Let’s assume that all the men in the world shave every day at a random time of day (this ain’t a realistic asumption, lemme tell you, but it’ll help compensate for the fact that most of the men in the world are in a different timezone than me, and for other weird factors like that.) There are 96 15-minute blocks in a 24-hour day. The probability of a man picking a particular 15-minute block to shave is 0.01. Therefore, the probability of a man not picking a block to shave is 0.99. The probability of every shaving-age man not picking the block in which I’m shaving is 0.99^(2,756,000,000), or 2.045e-12029404. When you see a negative exponent that large, your number is, by any sensible definition, zero.

Mitch had it right. So, from now on, when I shave, I’ll say “I’m gonna shave, too.”

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A great big pile of money.

When I was little, there was always that one kid on the playground who thought he was clever. We’d be drawing horrifying killer monsters (we were a weird bunch). I would say “My monster is a thousand feet high!” Then Chad would say “My monster is a mile high!” Then I would say “Nuh-uh, my monster is a thousand miles high!” Then Taylor would break in, filling us with dread, because we knew what he was going to say: “My monster is infinity miles high!” There would then follow the inevitable numeric arms race. “My monster is infinity plus one miles high!” “My monster is infinity plus infinity miles high!” “My monster is infinity times infinity miles high!” Our shortsighted teachers hadn’t taught us about Georg Cantor, or else we would have known that, once you hit infinity, pretty much all the math you do just gives you infinity right back.

But that’s not what I’m getting at here. As we got older and started (unfortunately) to care about money, the concept of “infinite money” inevitably started coming up. As I got older still and descended fully into madness, I realized that having an infinite amount of printed money was a really bad idea, since an infinite amount of mass would cause the entire universe to collapse into a singularity, which would limit the number of places I could spend all that money. Eventually, my thoughts of infinite wealth matured, and I realized that what you really want is a machine that can generate however much money you want in an instant. With nanomachines, you could conceivably assemble dollar bills (or coins) with relative ease. As long as you didn’t create so much money that you got caught or crashed the economy, you could live really well for the rest of your life.

But that’s not what I got hung up on. I got hung up on the part where I collapsed the universe into a Planck-scale singularity. And that got me thinking about one of my favorite subjects: weird objects in space. I’ve been mildly obsessed with creating larger and larger piles of objects ever since. Yes, I do know that I’m weird. Thanks for pointing that out.

Anyway, I thought it might be nice to combine these two things, and try to figure out the largest pile of money I could reasonably accumulate. My initial thought was to make the pile from American Gold Eagle coins, but I like to think of myself as a man of the world, and besides, those Gold Eagles are annoyingly alloyed with shit like copper and silver, and I like it when things are pure. So, instead, I’m going to invent my own currency: the Hobo Sullivan Dragon’s Egg Gold Piece. It’s a sphere of 24-karat gold with a diameter of 50 millimeters, a mass of 1,260 grams, and a value (as of June 29, 2014) of $53,280. The Dragon’s Egg bears no markings or portraits, because when your smallest unit of currency is worth $53,280, you can do whatever the fuck you want. And you know what? I’m going to act like a dragon and pile my gold up in a gigantic hoard. But I don’t want any arm-removing Anglo Saxon kings or tricksy hobbitses or anything coming and taking any of it, so instead of putting it in a cave under a famous mountain, I’m going to send it into space.

Now, a single Dragon’s Egg is already valuable enough for a family to live comfortably on for a year, or for a single person to live really comfortably. But I’m apparently some kind of ridiculous royalty now, so I want to live better than comfortably. As Dr. Evil once said, I want one billion dollars. That means assembling 18,769 Dragon’s Eggs in my outer-space hoard. Actually, now that I think about it, I’m less royalty and more some kind of psychotic space-dragon, which I think you’ll agree is infinitely cooler. 18,769 Dragon’s Eggs would weigh in at 23,649 kilograms. It would form a sphere with a diameter of about 1.46 meters, which is about the size of a person. Keen-eyed (or obsessive) readers will notice that this sphere’s density is significantly less than that of gold. That’s because, so far, the spheres are still spheres, and the closest possible packing, courtesy of Carl Friedrich Gauss, is only 74% sphere and 26% empty space.

You know what? Since I’m being a psychotic space-dragon anyway, I think I want a whole golden planet. Something I can walk around while I cackle. A nice place to take stolen damsels and awe them with shining gold landscapes.

Well, a billion dollars’ worth of Dragon’s Eggs isn’t going to cut it. The sphere’s surface gravity is a pathetic 2.96 microns per second squared. I’m fascinated by gravity, and so I often find myself working out the surface gravity of objects like asteroids of different compositions. Asteroids have low masses and densities and therefore have very weak gravity. The asteroid 433 Eros, one of only a few asteroids to be visited and mapped in detail by a space probe (NEAR-Shoemaker), has a surface gravity of about 6 millimeters per second squared (This varies wildly because Eros is far from symmetrical. Like so many asteroids, it’s stubbornly and inconveniently peanut-shaped. There are places where the surface is very close to the center of mass, and other places where it sticks way up away from it.) The usual analogies don’t really help you get a grasp of how feeble Erotian gravity is. The blue whale, the heaviest organism (living or extinct, as far as we know) masses around 100 metric tons. On Earth, it weighs 981,000 Newtons. You can also say that it weighs 100 metric tons, because there’s a direct and simple equivalence between mass and weight on Earth’s surface. Just be careful: physics dorks like me might try to make a fool out of you. Anyway, on Eros, a blue whale would weigh 600 Newtons, which, on Earth, would be equivalent to a mass of 61 kilograms, which is about the mass of a slender adult human.

But that’s really not all that intuitive. It’s been quite a while since I tried to lift 61 kilograms of anything. When I’m trying to get a feel for low gravities, I prefer to use the 10-second fall distance. That (not surprisingly) is the distance a dropped object would fall in 10 seconds under the object’s surface gravity. You can calculate this easily: (0.5) * (surface gravity) * (10 seconds)^2. I want you to participate in this thought experiment with me. Take a moment and either stare at a clock or count “One one thousand two one thousand three one thousand…” until you’ve counted off ten seconds. Do it. I’ll see you in the next paragraph.

In those ten seconds, a dropped object on Eros would fall 30 centimeters, or about a foot. For comparison, on Earth, that dropped object would have fallen 490 meters. If you neglect air resistance (let’s say you’re dropping an especially streamlined dart), it would have hit the ground after 10 seconds if you were standing at the top of the Eiffel Tower. You’d have to drop it from a very tall skyscraper (at least as tall as the Shanghai World Financial Center) for it to still be in the air after ten seconds.

But my shiny golden sphere pales in comparison even to Eros. Its 10-second fall distance is 148 microns. That’s the diameter of a human hair (not that I’d allow feeble humans on my golden dragon-planet). That’s ridiculous. Clearly, we need more gold.

Well, like Dr. Evil, we can increase our demand: 1 trillion US dollars. That comes out to 18,768,769 of my golden spheres. That’s 23,649,000 kilograms of gold. My hoard would have a diameter of 14.6 meters and a surface gravity of 29.6 microns per second squared (a 10-second fall distance of 1.345 millimeters, which would just barely be visible, if you were paying close attention.) I am not impressed. And you know what happens when a dragon is not impressed? He goes out and steals shit. So I’m going to go out and steal the entire world’s economy and convert it into gold. I’m pretty sure that will cause Superman and/or Captain Planet to declare me their nemesis, but what psychotic villain is complete without a nemesis?

It’s pretty much impossible to be certain how much money is in the world economy, but estimates seem to be on the order of US$50 trillion (in 2014 dollars). That works out to 938,438,439 gold balls (you don’t know how hard I had to fight to resist calling my currency the Hobo Sullivan Golden Testicle). That’s a total mass of 1.182e9 kilograms (1.182 billion kilograms) and a diameter of 54 meters (the balls still aren’t being crushed out of shape, so the packing efficiency is still stuck at 74%). 54 meters is pretty big in human terms. A 54-meter gold ball would make a pretty impressive decoration outside some sultan’s palace. If it hit the Earth as an asteroid, it would deposit more energy than the Chelyabinsk meteor, which, even though it exploded at an altitude of 30 kilometers, still managed to break windows and make scary sounds like this:

This golden asteroid would have a surface gravity of 0.108 millimeters per second squared, and a 10-second fall distance of 0.54 centimeters. Visible to the eye if you like sitting very still to watch small objects fall in weak gravitational fields (and they say I have weird hobbies), but still fairly close to the kind of micro-gravity you get on space stations. I can walk across the room, get my coffee cup, walk back, and sit down in 10 seconds (I timed it), and my falling object would still be almost exactly where I left it.

Obviously, we need to go bigger. Most small asteorids do not even approach hydrostatic equilibrium: they don’t have enough mass for their gravity to crush their constituent materials into spheres. For the majority of asteroids, the strength of their materials is greater than gravitational forces. But the largest asteroids do start to approach hydrostatic equilibrium. Here’s a picture of 4 Vesta, one of the other asteroids that’s been visited by a spacecraft (the awesome ion-engine-powered Dawn, in this case.)

(Image courtesy of NASA via Wikipedia.)

You’re probably saying “Hobo, that’s not very fucking spherical.” Well first of all, that’s a pretty damn rude way to discuss asteroids. Second of all, you’re right. That’s partly because of its gravity (still weak), partly because its fast rotation (once every 5 hours) deforms it into an oblate spheroid, and partly because of the massive Rheasilvia crater on one of its poles (which also hosts the solar system’s tallest known mountain, rising 22 kilometers above the surrounding terrain). But it’s pretty damn spherical when you compare it to ordinary asteroids, like 951 Gaspra, which is the shape of a chicken’s beak. It’s also large enough that its interior is probably more similar to a planet’s interior than an asteroid’s. Small asteroids are pretty much homogenous rock. Large asteroids contain enough rock, and therefore enough radioactive minerals and enough leftover heat from accretion, to heat their interiors to the melting point, at least briefly. Their gravity is also strong enough to cause the denser elements like iron and nickel to sink to the center and form something approximating a core, with the aluminosilicate minerals (the stuff Earth rocks are mostly made of) forming a mantle. Therefore, we’ll say that once my golden asteroid reaches the same mass as 4 Vesta, the gold in the center will finally be crushed sufficiently to squeeze out the empty space.

It would be convenient for my calculations if the whole asteroid melted so that there were no empty spaces anywhere. Would that happen, though? That’s actually not so hard to calculate. What we need is the golden asteroid’s gravitational binding energy, which is the amount of energy you’d need to peel the asteroid apart layer by layer and carry the layers away to infinity. This is the same amount of energy you’d deposit in the asteroid by assembling it one piece at a time by dropping golden balls on it. A solid gold (I’m cheating there) asteroid with Vesta’s mass (2.59e20 kg) would have a radius of 147 kilometers and a gravitational binding energy of about 1.827e25 Joules, or about the energy of 37 dinosaur-killing Chicxulub impacts. That’s enough energy to heat the gold up to 546 Kelvin, which is less than halfway to gold’s melting point.

But, you know what? Since I don’t have access to a supercomputer to model the compressional deformation of a hundred million trillion kilograms of close-packed gold spheres, I’m going to streamline things by melting the whole asteroid with a giant draconic space-laser. I’ll dispense with the gold spheres, too, and just pour molten gold directly on the surface.

You know where this is going: I want a whole planet made of gold. But if I’m going to build a planet, it’s going to need a name. Let’s call it Dragon’s Hoard. Sounds like a name Robert Forward would give a planet in a sci-fi novel, so I’m pleased. Let’s pump Dragon’s Hoard up to the mass of the Earth.

Dragon’s Hoard is a weird planet. It has the same mass as Earth, but its radius is only 66% of Earth’s. Its surface gravity is 22.64 meters per second squared, or 2.3 earth gees. Let’s turn off the spigot of high-temperature liquid gold (of course I have one of those) for a while and see what we get.

According to me, we get something like this:

Gold Tectonics

The heat content of a uniform-temperature sphere of liquid gold depends on its volume, but since it’s floating in space, its rate of heat loss depends on surface area (by the Stefan-Boltzmann law). The heat can move around inside it, but ultimately, it can only leave by radiating off the surface. Therefore, not only will the sphere take a long time to cool, but its upper layers will cool much faster than its lower layers. Gold has a high coefficient of thermal expansion: it expands more than iron when you heat it up. Therefore, as the liquid gold at the surface cools, it will contract, lose density, and sink beneath the hotter gold on the surface. It will sink and heat up to its original temperature, and will eventually be displaced by the descent of cooler gold and will rise back to the surface. When the surface cools enough, it will solidify into a solid-gold crust, which is awesome. Apparently, my fantasies are written by Terry Pratchett, which is the best thing ever. I’ve got Counterweight Continents all over the place!

Gold is ductile: it’s a soft metal, easy to bend out of shape. Therefore, the crust would deform pretty easily, and there wouldn’t be too many earthquakes. There might, however, be volcanoes, where upwellings of liquid gold strike the middle of a plate and erupt as long chains of liquid-gold fountains. It would behave a bit like the lava lake at Kilauea volcano, in Hawai’i. See below:

What a landscape this would be! Imagine standing (in a spacesuit) on a rumpled plain of warm gold. To your right, a range of gold mountains glitter in the sun, broken here and there by gurgling volcanoes of shiny red-hot liquid. Flat, frozen puddles of gold fill the low spots, concave from the contraction they experienced as they cooled. To your right , the land undulates along until it reaches another mountain range. In a valley at the foot of this range is an incandescent river of molten gold, fed by the huge shield volcano just beyond the mountains. Then a psychotic space-dragon swoops down, flying through the vacuum (and also in the face of physics), picks you up in his talons, carries you over the landscape, and drops you into one of those volcanoes.

Yeah. It would be something like that.

As fun as my golden planet is, I think we could go bigger. Unfortunately, the bigger it gets, the more unpredictable its properties become. As we keep pouring molten gold on it, its convection currents will become more and more vigorous: it will have more trapped heat, a larger volume-to-surface area ratio, and stronger gravity, which will increase the buoyant force on the hot, low-density spots. Eventually, we’ll end up with convection cells, much like you see in a pot of boiling water. They might look like this:

Benard Cells

Those are Rayleigh-Bénard cells, which you often get in convective fluids. I used that same picture in my Endless Sky article. But there, I was talking about supercritical oxygen and nitrogen. Here, it’s all gold, baby.

Eventually, the convection’s going to get intense enough and the heat’s going to get high enough that the planet will have a thin atmosphere of gold vapor. If it rotates, the planet will also develop a powerful magnetic field: swirling conductive liquid is believed to be the thing that creates the magnetic fields of Earth, the Sun, and Jupiter (and all the other planets). This planet is going to have some weird electrical properties. Gold is one of the best conductors there is, second only to copper, silver, graphene, and superconductors. Therefore, expect some terrifying lightning on Dragon’s Hoard: charged particles and ultraviolet radiation from the Sun will ionize the surface, the gold atmosphere (if there is one) or both, and Dragon’s Hoard will become the spherical terminal in a gigantic Van de Graaff generator. As it becomes more and more charged, Dragon’s Hoard will start deflecting solar-wind electrons more easily than solar-wind protons (since the protons are more massive), and will soak up protons, acquiring a net positive charge. It’ll keep accumulating charge until the potential difference explosively equalizes. Imagine a massive jet or bolt of lightning blasting up into space, carrying off a cloud of gold vapor, glowing with pink hydrogen plasma. Yikes.

After Dragon’s Hoard surpasses Jupiter’s mass, weird things will begin happening. Gold atoms do not like to fuse. Even the largest stars can’t fuse them. Therefore, the only things keeping Dragon’s Hoard from collapsing altogether are the electrostatic repulsion between its atoms and the thermal pressure from all that heat. Sooner or later, neither of these things will be enough, and we’ll be in big trouble: the core, compressed to a higher density than the outer portions by all that gold, will become degenerate: its electrons will break loose of their nuclei, and the matter will contract until the electrons are squeezed so close together that quantum physics prevents them from getting any closer. This is electron degeneracy pressure, and it’s the reason white dwarf stars can squeeze the mass of a star into a sphere the size of a planet without either imploding or exploding.

The equations involved here are complicated, and were designed for bodies made of hydrogen, carbon, and oxygen instead of gold (Those short-sighted physicists never consider weird thought experiments when they’re unraveling the secrets of the universe. The selfish bastards.) The result is that I’m not entirely sure how large Dragon’s Hoard will be when this happens. It’s a good bet, though, that it’ll be somewhere around Jupiter’s mass. This collapse won’t be explosive: at first, only a fraction of the matter in the core will be degenerate.As we add mass, the degenerate core will grow larger and larger, and more and more of it will become degenerate. It will, however, start to get violent after a while. Electron-degenerate matter is an excellent conductor of heat, and its temperature will equalize pretty quickly. That means that we’ll have a hot ball of degenerate gold (Degenerate Gold. Add that to the list of possible band names.) surrounded by a thin layer of hot liquid gold. Because of the efficient heat transfer within the degenerate core, it will partly be able to overcome the surface-area-versus-volume problem and radiate heat at a tremendous rate.  The liquid gold on top, though, will have trouble carrying that heat away fast enough, and will get hotter and hotter, and thanks to its small volume, will eventually get hot enough to boil. Imagine a planet a little larger than Earth, its surface white-hot, crushed under a gravity of 500,000 gees, bubbles exploding and flinging evaporating droplets of gold a few kilometers as gaseous gold and gold plasma jet up from beneath. Yeah. Something like that.

But in a chemical sense, my huge pile of gold is still gold. The nuclei may be uncomfortably close together and stripped of all of their electrons, but the nuclei are still gold nuclei. For now. Because you know I’m going to keep pumping gold into this ball to see what happens (That’s also a line from a really weird porno movie.)

White dwarfs have a peculiar property: the more massive they are, the smaller they get. That’s because, the heavier they get, the more they have to contract before electron degeneracy pressure balances gravity. Sirius B, one of the nearest white dwarfs to Earth, has a mass of about 1 solar mass, but a radius similar to that of Earth. When Dragon’s Hoard reached 1.38 solar masses, it would be even smaller, having a radius of around 3000 kilometers. The stream of liquid gold would fall towards a blinding white sphere, striking the surface at 3% of the speed of light. The surface gravity would be in the neighborhood of 2 million gees. If the gravity were constant (which it most certainly would not be), the 10-second fall distance would be 2.7 times the distance between Earth and moon. Now we’re getting into some serious shit.

Notice that I specified three significant figures when I gave that mass: 1.38 solar masses. That is not by accident. As some of you may know, that’s dangerously close to 1.39 solar masses, the Chandrashekar limit, named after the brilliant and surprisingly handsome Indian physicist Subrahmanyan Chandrasekhar. (Side note: Chandrashekhar unfortunately died in 1995, but his wife lived until 2013. Last year. She was 102 years old. There’s something cool about that, but I don’t know what it is.) The Chandrasekhar limit is the maximum mass a star can have and still be supported by electron degeneracy pressure. When you go above that, you’ve got big trouble.

When ordinary white dwarfs (made mostly of carbon, oxygen, hydrogen, and helium) surpass the Chandrasekhar limit by vacuuming mass from a binary companion, they are unable to resist gravitational contraction. They contract until the carbon and oxygen nuclei in their cores get hot enough and close enough to fuse and make iron. This results in a Type Ia supernova, which shines as bright as 10 billion suns. It’s only recently that our supercomputers have been able to simulate this phenomenon. The simulations are surprisingly beautiful.

I could watch that over and over again and never get tired of it.

Unfortunately, even though it’s made of gold (which, as I said, doesn’t like to fuse), the same sort of thing will happen to Dragon’s Hoard. When it passes the Chandrasekhar limit, it will rapidly contract until the nuclei are touching. This will trigger a bizarre form of runaway fusion. The pressure will force electrons to combine with protons, releasing neutrinos and radiation. Dragon’s Hoard will be heated to ludicrous temperatures, and a supernova will blow off its outer layers. What remains will be a neutron star, which, as I talked about in The Weather in Hell, is mostly neutrons, with a thin crust of iron atoms and an even thinner atmosphere of iron, hydrogen, helium, or maybe carbon. Most or all of the gold nuclei will be destroyed. The only thing that will stop the sphere from turning into a black hole is that, like electrons, neutrons resist being squeezed too close together, at least up to a limit.

But you know what? That tells us exactly how much gold you can hoard in one place: about 1.38 solar masses. So fuck you, Taylor from kindergarten! You can’t have infinity dollars! You can only have 0.116 trillion trillion trillion dollars (US, and according to June 2014 gold prices) before your gold implodes and transmutes itself into other elements! So there!

But while I’m randomly adding mass to massive astronomical objects (that’s what space dragons do instead of breathing fire), let’s see how much farther we can go.

The answer is: Nobody’s exactly certain. The Chandrasekhar limit is based on pretty well-understood physics, but the physics of neutron-degenerate matter at neutron star pressures and temperatures (and in highly curved space-time) is not nearly so well understood. The Tolman-Oppenheimer-Volkoff limit (Yes, the same Oppenheimer you’re thinking of.) is essentially a neutron-degenerate version of the Chandrasekhar limit, but we only have the TOV limit narrowed down to somewhere between 1.5 solar masses and 3 solar masses. We’re even less certain about what happens above that limit. Quarks might start leaking out of neutrons, the way neutrons leak out of nuclei in a neutron star, and we might get an even smaller, denser kind of star (a quark star). At this point, the matter would stop being matter as we know it. It wouldn’t even be made of neutrons anymore. But to be honest, we simply don’t know yet.

Sooner or later, though, Karl Schwarzschild is going to come and kick our asses. He solved the Einstein field equations of general relativity (which are frightening but elegant, like a hyena in a cocktail dress) and discovered that, if an object is made smaller than its a certain radius (the Schwarzschild radius), it will become a black hole. The Schwarzschild radius depends only on the object’s mass, charge, and angular momentum. Dragon’s Hoard, or rather what’s left of it, doesn’t have a significant charge or angular momentum (because I said so), so its Schwarzschild radius depends only on mass. At 3 solar masses, the Schwarzschild radius is 8.859 kilometers, which is only just barely larger than a neutron star. Whether quark stars can actually form or not, you can bet your ass they’re going to be denser than neutron stars. Therefore, I’d expect Dragon’s Hoard to fall within its own Schwarzschild radius somewhere between 3 and 5 solar masses. Let’s say 5, just to be safe. There are suspected black holes with masses near 5.

That’s the end of Dragon’s Hoard. The physics in the center gets unspeakably weird, but the gold-spitting space dragon doesn’t get to see it. He’s outside the event horizon, which means the collapse of his hoard is hidden to him. He just sees a black sphere with a circumference of 92.77 kilometers, warping the images of the stars behind it. It doesn’t matter how much more gold we pour into it now: it’s all going to end up inside the event horizon, and the only noticeable effect will be that the event horizon’s circumference will grow larger and larger. But fuck that. If I wanted to throw money down a black hole, I’d just go to Vegas. (Heyo!) Dragon’s Hoard isn’t getting any more of my draconic space-gold.

But one last thing before I go. Notice how I suddenly went from saying Schwarzschild radius to talking about the event horizon’s circumference. That’s significant. Here’s a terrible picture illustrating why I did that:

CurvedSpacetime

Massive objects create curvature in space-time. Imagine standing at the dot on circle B, in the top picture. If you walk to the center-point along line A, you’ll measure a length a. If you then walk around circle B, you’ll get the circle’s circumference. You’ll find that that circumference is 2 * pi * a. The radius is therefore (circumference) / (2 * pi) But that only holds in flat space. When space is positively curved (like it is in the vicinity of massive objects), the radius of a circle will always be larger than (circumference) / (2 * pi). That is to say, radius C in the bottom picture is significantly longer than radius A in the top one, and longer than you would expect from the circumference of circle D.

In other words, the radius of a massive object like a star, a neutron star, or a black hole, differs from what you would expect based on its circumference. The existence of black holes and neutron stars has not actually been directly confirmed (because they’re so small and so far away). It is merely strongly suspected based on our understanding of physics. The existence of spacetime curvature, though, has been confirmed in many experiments.

Imagine you’re standing in a field that looks flat. There’s a weird sort of bluish haze in the center, but apart from that, it looks normal. You walk in a circle around the haze to get a better look at it. It only takes you fifteen minutes to walk all the way around and get back to your starting point. The haze makes you nervous, so you don’t walk straight into it. Instead, you walk on a line crossing the circle so that it passes halfway between the haze and the circle’s edge at its closest approach. Somehow, walking that distance takes you twenty minutes, which is not what you’d expect. When you walk past the haze at a quarter-radius, it takes you an hour. When you walk within one-eighth of a radius, it takes you so long you have to turn back and go get some water. Each time, you’re getting closer and closer to walking along the circle’s radius towards its center, but if you actually tried to walk directly into its center, where the haze is (the haze is because there’s so much air between you and the stuff beyond the haze, which is the same reason distant mountains look blue), you would find that the distance is infinite.

That’s how black holes are. They’re so strongly-curved that there’s way more space inside than there should be. The radius is effectively infinite, which is why it’s better to talk about circumference. As long as the black hole is spherically symmetric, circumferences are still well-behaved.

But the radius isn’t actually infinite. When you consider distance scales close to the Planck length, Einstein’s equations butt heads with quantum mechanics, and physicists don’t really know what the fuck’s going on. We still don’t know what happens near a black hole’s central singularity.

Incidentally, the Planck length compared to the diameter of an atom is about the same as the diameter of an atom compared to the diameter of a galaxy. The Universe is a weird place, isn’t it?

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The weather in hell.

Neutron stars are horrifying things. They’re born in supernova explosions, which can shine with the light of 10 billion suns for weeks on end. But even after the fireworks, they’re still scary as hell. A neutron star compacts over 1.44 times the sun’s mass into a sphere about 20 kilometers across (about the size of a city). Apart from black holes, they’re the most extreme objects we know about (There may actually be more extreme variants, but none have been conclusively observed, and thank goodness: what we’re dealing with is scary enough.).

Everything about a neutron star is horrifying. Their surfaces broil at temperatures of over 100,000 Kelvin, which is twice as hot as the hottest stars. The young ones can get hotter than 1,000,000 Kelvin. Red-hot metal emits red light because most hot objects emit a so-called blackbody spectrum, with the most intense wavelength (color) of light depending on temperature. Iron near its melting point (1811 Kelvin) emits strongest at a wavelength of 1.6 microns, which is in the near-infrared (which is not the kind of infra-red the Predator used to hunt Arnold Scwharzenegger). To our eyes, the iron would look bright red-orange. The sun, with a blackbody temperature of about 5800 Kelvin, emits most strongly in the blue-green part of the spectrum (it looks yellow on Earth partly because of atmospheric scattering and partly because the human eye is a lot less sensitive to indigo and violet than it is to blue, yellow, orange, and red). At 100,000 to 1,000,000 Kelvin (and above), neutron stars would have about the same purplish-blue color as lightning bolts or the most powerful electric arcs, and they would emit most of their light in the deadly far-ultraviolet and really deadly X-ray. If you replaced the Sun with a 1,000,000-Kelvin neutron star, the Earth would only receive five times less energy than it does from the Sun. That’s ridiculous, considering all that energy is coming from an object the size of downtown Tokyo. (Speaking of which, that gives me an idea for a new Godzilla movie…) Of course, almost all of that energy would be in the x-ray and ultraviolet portions of the spectrum, and therefore would blow off the ozone layer and kill us all. But what would this blog be if I didn’t kill humanity every article?

But let’s handwave the radiation away (in true Star Trek fashion) and say you were able to get close to the neutron star.

Sorry. You’re still dead. Say you replaced Earth with a 2-solar-mass neutron star. If you were in the International Space Station, you’d probably survive the tidal forces, but they would be enough that if you oriented yourself feet-down, you’d feel a noticeable and unpleasant stretch: your head and feet would experience a difference in acceleration of about 0.4 gees. If you were orbiting at 4,000 kilometers, you’d experience a very painful 1.5-gee stretch (and, incidentally, you’d be completing one orbit every 3 seconds, which is ridiculous). By the time you got within 1,000 kilometers of the neutron star, your feet and your head would experience a difference in acceleration of 100 gees, more than enough to pull half your blood to your feet and the other half to your brain, stopping your heart and giving you lethal cerebral hemorrhages at the same time.

But as bad as things are in the neutron star’s neighborhood, they’re even worse on its surface. This is where the “Hell” part comes from. I’ve read through a few papers on neutron star structure (and skimmed many more). It’s hard to get a straight answer on what neutron stars are like on the inside (partly because it’s really hard to simulate the imponderable conditions near the core), but here’s neutron star structure as  I understand it:

Neutron Star Structure

At the top is the atmosphere, crushed to a thickness of between 10 centimeters and 10 meters (definite numbers are hard to find) by a gravity of 200 billion gees. Most neutron star atmospheres are pure hydrogen or pure helium, but sometimes, because of the insane pressures and temperatures, the atoms undergo fusion, leaving behind a carbon atmosphere. Below that is a crust that, thanks to the way nuclei get smashed together in supernovae, is mostly iron ions, their electrons wandering around with little regard for the nuclei.

The uppermost layers of the crust are made of almost-normal mater, albeit crushed to insane densities. But as you get deeper, the weight of the crust above puts extreme pressure on the nuclei. Suddenly, nuclei that have half-lives measured in seconds on Earth become as stable as ordinary gold or lead, because the pressure keeps decay products from escaping. The higher the pressure, the easier it is for extra neutrons to slip into nuclei. The nuclei get heavier and heavier and closer and closer together as you go down. Then, a few hundred meters below the surface, you encounter the “neutron drip,” where neutrons start leaking out of nuclei and roaming free. (On Earth, loose neutrons decay with a half-life of about 10 minutes. In the neutron star, once again, the pressure makes them stable.) This region gives us one of the coolest scientific terms ever devised: “nuclear pasta.”

Say it. Nuclear pasta. That sounds like something from an awesomely shitty ’70’s superhero movie. But, according to our current physics, it’s a real thing.

Because like charges repel, a nucleus wants to fly apart, since it’s full of chargeless neutrons (which don’t attract or repel anything) and positive protons (which fiercely repel each other). The strong nuclear force (or Strong Force, which sounds like the name of a badly-translated kung fu movie) provides the glue that holds nuclei together. At small distances, it’s far stronger than the electromagnetic force that causes like charges to repel (thus the name). But it decays very quickly with distance: beyond about a millionth of a nanometer, it gets vanishingly weak. Nuclei that are too large for the strong force to span their whole diameter tend to be unstable.

For this reason, nuclei also repel each other when brought close together. But deep in a neutron star’s crust, the pressure begins to overwhelm the repulsion. The protons still repel each other, but now there are places where they’re forced so close together that the strong force starts winning out. The nuclei grow oblong, and then they fuse into long tubes of protons and neutrons, like subatomic sausage (Subatomic Sausage. Another good band name.). This is the eponymous “pasta phase.” As you go down and the pressure goes up, these tubes get closer together and adjacent ones merge into two-dimensional sheets. This is called the “lasagna phase.” If you go on Google Scholar and type in “nuclear pasta”, you can find an actual peer-reviewed university-supported scientific paper that uses the phrase “lasagna phase” with a straight face. That makes me smile.

Deeper down, parts of the sheets come into contact, and you end up with a weird latticework of nuclear-matter tubes called the “gyroid phase.” Below that is a phase where you have cylindrical holes surrounded by nucleus-stuff, a sort of negative of the pasta phase. Then you get spherical holes. Then, the electromagnetic repulsion just gives up entirely, and the neutron-star matter reaches the density of an atomic nucleus, which is so huge (2 x 10^17 kilograms per cubic meter) that a piece the size of a grain of sand (a cube 500 microns on an edge) would weigh as much as a small cargo ship (25,000 metric tons). Of course, without the pressure provided by a whole neutron star to compress it, that grain would expand rapidly, and you would be spread over a large area. So don’t go removing pieces of neutron stars and carrying them around. Ain’t safe.

This is the outer part of the core. So far, the electrons have pretty much been minding their own business, ignoring the pained cries of the protons and neutrons as they were squeezed unnaturally close (the bastards). Deeper down, the pressures get so high that the electrons and protons combine to form neutrons, releasing a neutrino. Below a certain depth, it’s just a soup of neutrons crammed shoulder-to-shoulder. This soup has some weird properties, which we’ll get to later.

Below the neutron fluid, physicists aren’t quite sure what happens. Funnily enough, we here on Earth don’t have a lot of experience with soups of pure atomic-nucleus fluid. It’s possible that, in the depths, quarks could leak out of the individual neutrons, or even weirder stuff could happen, but we just don’t know. Most diagrams of neutron star structures either just put a question mark at the center or list a bunch of exotic particle names and then put a question mark. I won’t even attempt to guess what’s going on down there. I’ve got hellish weather to talk about.

But would there even be weather on a neutron star? That’s hard to say. Neutron stars have powerful magnetic fields, which could very well hold the plasma in the atmosphere in place, or at least make it awfully hard for it to move around. But, if you think about it, the temperature difference between the bottom and the top of a neutron star atmosphere is between 900,000 and 2,500,000 Kelvin, which is several thousand times the 350-Kelvin temperature difference that drive’s Earth’s weather. I’ll be working under the assumption that the atmosphere of a neutron star is able to circulate. If anybody has better information than me, feel free to set me straight.

In the last article, I talked about “scale height,” which is a nifty number that tells you how high you have to go for the atmosphere on a planet to be e times (about 2.7 times) less dense. Because their gravity is so monstrous, even the superheated plasma in a neutron star’s atmosphere is crushed tight against the surface. The Earth’s scale height is about 8,500 meters. The scale height in a neutron star’s atmosphere (depending on whether it’s made of hydrogen, helium, carbon, or something else, and depending on temperature) can range from a fraction of a millimeter to a few centimeters. On Earth, if you go up two scale heights, you’re higher than most airliners ever fly. If you go up 12 scale heights, you’re in space. I couldn’t find any really reliable numbers on the surface density of neutron-star atmospheres, but let’s assume it’s the same as the density of the sun’s core: 150,000 kilograms per cubic meter. The gravity is so strong that even the deepest neutron star atmospheres reach outer-space densities within half a meter. If I could stand on a neutron star (which, I will remind you, is a bad idea), the atmosphere would just about reach my knees. Right before I evaporated and then collapsed into a one-atom-thin layer of plasma.

Lucky for us, since the density profile of an atmosphere is exponential, many of its features will scale nicely from more familiar examples, like the atmospheres of stars and planets. Here, I’m pretty much making shit up, but the shit I’m making up is informed by some real-world knowledge. It’s also based on a few assumptions. I’m assuming, for one thing, that our neutron star is a pulsar, a neutron star spun up like a top by the infall of matter from a binary companion. I’m further assuming that this neutron star has about the same rotation rate as PSR J1748-2446ad, the fastest-spinning pulsar yet discovered (as of June 2014). It spins 716 times a second. Let’s imagine there was a single spot on the pulsar that emitted radio waves (in reality, there’s one at each magnetic pole, but one spot is usually looks brighter to us on Earth). If you could hear the signal it emitted, it would sound about like this (TURN DOWN YOUR SPEAKERS! It’s not a pretty sound.):

716-Hertz Pulsar

Even for an object like a pulsar, which is small in astronomical terms, spinning 716 times per second is ridiculous. It means that the matter at the equator is moving at 15% of the speed of light. It also means the Coriolis effect is gonna come kick some ass.

For those of you who find the Coriolis effect as confusing as I once did, here’s a brief explanation. Imagine you roll a ball inward from the edge of a frictionless spinning carousel. In the reference frame of the ground, the ball just travels straight to the center, across the other side, and off the edge. But if you were rotating with the carousel, the ball wouldn’t appear to travel in a straight line. This is because, according to you, the ball has both the inward velocity the outside observer sees and a radial velocity tangent to the circle’s circumference, since it’s not moving and the carousel is. This radial velocity is at its highest at the carousel’s edge, so as the ball approaches the center, it’s moving faster than the carousel’s surface, since the inner parts have lower radial velocities. Therefore, it appears to curve across the carousel as though acted upon by a force, pass through the center, and curve back out, describing a (roughly) semicircular trajectory. I know that’s the dunderhead layman’s explanation, but since I’m a dunderheaded layman, what do you expect?

The Coriolis effect is why low-pressure systems swirl anti-clockwise over Earth’s Northern hemisphere (and clockwise over the Southern hemisphere): the Earth is a sphere, so as you move towards the poles, you’re closer to the Earth’s axis of rotation. The faster the rotation of the body in question, the stronger the Coriolis effect and the tighter the circulation. Since our pulsar is spinning so damn fast, the circulation will be very tight, and since the bottom of the atmosphere is so much hotter than the top, the motion will be quite violent. Here’s my guess at what the pulsar’s atmosphere will look like:

Neutron Star Surface Weather Small

Here, I’m calling upon the concept of inertial circles. The radius of an inertial circle is given by:

(speed of the moving fluid) / (2 * angular velocity of planet * sin(latitude, with the poles being plus or minus 90 degrees and the equator 0))

An inertial circle is the path a body would take on a planet’s surface under the influence of the Coriolis effect alone. On Earth, if you assume a wind speed of 100 MPH (about 44 meters per second), then the inertial circle at a latitude of 45 degrees has a radius of about 480 kilometers, which is about right for a hurricane. I’ll make the very naive assumption that the winds on a neutron star will scale up in proportion to the increase in the temperature difference (from about 320 Kelvin (and 44 meters per second) on Earth to as much as 2,500,000 Kelvin on a neutron star). Neutron star winds will therefore have speeds on the order of 1,700 kilometers per second (Dorothy’s not going to make it to Oz in this tornado. Forget an F-5. We’re looking at an F-68000.) At a latitude of 45 degrees, a neutron star hurricane will have a radius of about 250 meters:

Hurricanes

Imagine standing up to your knees in glowing gas. Spreading out around you is a brilliant electric-purple hurricane the size of a football stadium. At its center, it has an eye a few meters across, which feeds down into a needle-thin funnel with gas swirling at 0.1% of the speed of light.

I would guess that our pulsar wouldn’t have features like jet streams. For one thing, pretty much any movement in the atmosphere is going to be twisted into a circle by the Coriolis effect and turn into a cyclone. For another thing, the magnetic field would probably put the brakes on big swathes of moving fluid. A neutron star, having such a violent, hot atmosphere, would have hellish weather, and its surface would be paved with hurricanes. I imagine it would look something like this:

Neutron Star Weather

(Yes, I mixed up North and South and scribbled them out. Yes, I do know that I’m an idiot.)

The magnetic poles of neutron stars are often not aligned with the geographic poles (also true of Earth!), so there would probably be spots where the emerging magnetic field, all bunched up and concentrated, would stop the gas from moving much at all, even if the field was weak enough to let it move around everywhere else. These are also the spots where material tends to fall onto neutron stars, so they would have perpetual hot high-pressure systems (much like Louisiana or North Carolina). I took the liberty of adding magnetically-dampened high-pressure cyclones around these poles, and putting hurricanes everywhere else.

But this isn’t the only possible weather on a neutron star. Wherever you have fluid, gravity, and a density and/or temperature gradient, you can have weather-like phenomena. They happen in Earth’s atmosphere, they happen in Earth’s oceans, they happen on Venus, and they happen on the Sun. I’ve just spent quite a while talking about the weather on the surface of a neutron star, but there could also be weather in the interior. Beneath the crust, where the protons and electrons combine and it’s almost all neutrons, the material stops being solid and becomes a neutron liquid. But it’s not just any liquid. It’s a neutron superfluid. Superfluids are weird shit. They behave more or less like liquids, except that they have zero viscosity. Bizarre, but true. Water has a non-zero viscosity: as your pipe gets smaller, it gets harder and harder for water to move at a given velocity. Viscosity is pretty much the internal friction within the moving fluid. Viscosity determines the minimum size a stable vortex can have. Water has a viscosity of about 8.9 x 10^-4 pascal-seconds. But superfluids like liquid helium-4 have a viscosity of zero. The viscosity isn’t just very small, it’s actually zero. Superfluids can slip through any hole (that sounds dirty), and because of capillary action (which allows a wet spot on a paper towel to spread out), and because there’s no viscous friction to oppose it, they can crawl up and out of containers.

That’s all awesome, but, for my money, one of the coolest things about superfluids is what happens when they start swirling. Normally, when you rotate a container of fluid, the fluid starts to rotate with the container. Essentially, the whole container of fluid becomes one giant vortex.

This doesn’t happen in superfluids. No matter how large or small the rotating container, the superfluid forms lots and lots of extremely tiny vortices, their number depending only on the spin rate. If spin a glass of water at 1 revolution per minute, you’ll get one big, slow vortex. If you fill the same glass with superfluid helium-4 and rotate it at 1 RPM, you’ll get thousands of them. Don’t know what the hell I’m talking about? Here’s a truly beautiful video of swirling superfluid helium in action:

And here’s a terrible picture I drew of the same phenomenon:

Superfluid

This is basically quantum mechanics acting on a large scale, which often happens when things get cold enough. Since superfluid helium has zero viscosity, when it has to form vortices, the vortices are infinitely small, or rather, as small as the fact that the helium is made of atoms will allow them to be. This is called “quantization of vortices,” and is extremely weird, and most likely also happens in the superfluid interiors of neutron stars. These tiny vortices will be oriented along the axis of rotation, so they’ll be parallel to the crust near the equator and perpendicular near the poles (with additional changes depending on the magnetic field and whether the rotation is  faster in some regions than in others, which is usually how it works out). So if you look at it from the bottom up, you get knee-deep plasma tornadoes the size of football stadiums. And if you look at it from the top down, you get a field of weird nuclear pasta crawling with trillions and trillions of microscopic tornadoes piercing a neutron sea. I’ve said it before and you know I’ll say it again: astronomy is awesome.

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