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 an almost 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…



…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 really 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 (Ha ha!), 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:


(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 per second, 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 sterile red 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?

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.

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:


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:


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:


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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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?


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:


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:


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:


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.


(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:


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.


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: