physics, Space, thought experiment

Hypothetical Nightmares | Black Holes, Part 3

Imagine taking all the mass in the Milky Way (estimated to be around a trillion solar masses) and collapsing it into a black hole. The result wouldn’t be an ordinary black hole. Not even to astrophysicists, for whom all sorts of weird shit is ordinary.

The largest black hole candidate is the black hole at the center of the quasar S5 0014+813, estimated at 40 billion solar masses. In other words, almost a hundred times smaller than our hypothetical hole. As I said last time, as far as astronomical objects go, black holes are a fairly comfortable size. Even the largest don’t get much bigger than a really large star. Here, though, is how big our trillion-sun black hole would be, if we replaced the sun with it:

Galaxy Mass Black Hole.png

(Rendered in Universe Sandbox 2.)

The thing circled in orange is the black hole. When I started tinkering with the simulation, I was kinda hoping there’d be one or two dwarf planets outside the event horizon, so their orbits could at least offer a sense of scale. No such luck: the hole has a Schwarzschild radius of 0.312 light-years, which reaches well into the Oort cloud. That is, the galaxy-mass black hole’s event horizon alone would extend beyond the heliopause, and would therefore reach right into interstellar space. Proxima Centauri, around 4.2 light-years from Earth, is circled in white.

The immediate neighborhood around a black hole like this would be rough. We’re talking “feral children eating the corpse of a murder victim while two garbagemen fight to the death with hatchets over who gets to empty the cans on this street” kind of rough. That kinda neighborhood. No object closer than half a light-year would actually be able to orbit the hole: it would either have to fall into the hole or fly off to infinity.

That is, of course, if the hole isn’t spinning. As I said last time, you can orbit closer to a spinning hole. But I’m going to make a leap here and say that our galaxy-mass black hole isn’t likely to be spinning very fast. Some rough calculations suggest that, if it were rotating at half the maximum speed,the rotational kinetic energy alone would have several billion times the mass of the sun. I’m going to assume there’s not enough angular momentum in the galaxy to spin a hole up that much. I could be wrong. Let me know in the comments.

Spin or no spin, it’s gonna be a rough ride anywhere near the hole. Atoms orbiting at the innermost stable orbit (the photon sphere) are moving very close to the speed of light, and therefore, to them, the ambient starlight and cosmic microwave background ahead of them is blue-shifted and aberrated into a horrifying violet death-laser, while the universe behind is red-shifted into an icy-cold nothingness.

But, as we saw last time, once you get outside a large hole’s accretion disk, things settle down a lot. When it comes to gravity and tides, ultra-massive black holes like these are gentle giants. You could hover just outside the event horizon by accelerating upwards at 1.5 gees, which a healthy human could probably tolerate indefinitely, and which is very much achievable with ordinary rocket engines. The tides are no problem, even right up against the horizon. They’re measured in quadrillionths of a meter per second per meter.

Of course, if you’re hovering that close to a trillion-solar-mass black hole, you’re still going to die horribly. Let’s say your fuel depot is orbiting a light-year from the hole’s center, and they’re dropping you rocket fuel in the form of frozen blocks of hydrogen and oxygen. By the time they reach you, those blocks are traveling at a large fraction of the speed of light, and will therefore turn into horrifying thermonuclear bombs if you try to catch them.

But, assuming its accretion disk isn’t too big and angry, a hole this size could support a pretty pleasant galaxy. The supermassive black hole suspected to lie at the center of the Milky Way makes up at about 4.3 parts per million of the Milky Way’s mass. If the ratio were the same for our ultra-massive hole, then it could host around 200 quadrillion solar masses’ worth of stars, or, in more fun units, 80,000 Milky Ways. Actually, it might not be a galaxy at all: it might be a very tightly-packed supercluster of galaxies, all orbiting a gigantic black hole. A pretty little microcosm of the universe at large. Kinda. All enclosed within something like one or two million light-years. A weird region of space where intergalactic travel might be feasible with fairly ordinary antimatter rockets.

You’ll notice that I’ve skipped an important question: Are there any trillion-solar-mass black holes in the universe? Well, none that we know of. But unlike some of the other experiments to come in this article, black holes this size aren’t outside the realm of possibility.

I frequently reference a morbid little cosmology paper titled A Dying Universe. If you’re as warped as I am, you’ll probably enjoy it. It’s a good read, extrapolating, based on current physics, what the universe will be like up to 10^100 years in the future (which they call cosmological decade 100). If you couldn’t guess by the title, the news isn’t good. A hundred trillion years from now (Cosmological Decade 14), so much of the star-forming stuff in galaxies will either be trapped as stellar corpses or will have evaporated into intergalactic space that new stars will stop forming. The galaxies will go dark, and the only stars that shine will be those formed by collisions between high-mass brown dwarfs. By CD 30 (a million trillion trillion years from now), gravitational encounters between stars in the galaxy will have given all the stars either enough of a forward kick to escape altogether, or enough of a backward kick that they fall into a tight orbit around the central black hole. Eventually, gravitational radiation will draw them inexorably into the black hole. By CD 30, the local supercluster of galaxies will consist of a few hundred thousand black holes of around ten billion solar masses, along with a bunch of escaping rogue stars. By this time, the only source of light will be very occasional supernovae resulting from the collisions of things like neutron stars and white dwarfs. Eventually, the local supercluster will probably do what the galaxy did: the lower-mass black holes will get kicked out by the slingshot effect, and the higher-mass ones will coalesce into a super-hole that might grow as large as a few trillion solar masses. Shame that everything in the universe is pretty much dead, so no cool super-galaxies can form. But the long and the short of it is that such a hole isn’t outside the realm of possibility, although you and I will never see one.

The Opposite Extreme

But what about really tiny black holes? In the first post in this series, I talked about falling into a black hole with the mass of the Moon. But what about even smaller holes?

Hobo Sullivan is a Little Black Pinhole

Yeah, I feel like that sometimes. I mass about 131 kilograms (unfortunately; I’m working on that). If, by some bizarre accident (I’m guessing the intervention of one of those smart-ass genies who twist your wishes around and ruin your shit), I was turned into a black hole, I’d be a pinprick in space far, far smaller than a proton. And then, within a tenth of a nanosecond, I would evaporate by Hawking radiation (if it exists; we’re still not 100% sure). When a black hole is this small, Hawking radiation is nasty shit. It would have a temperature of a hundred million trillion degrees, and I’d go off like four Tsar Bombas, releasing over 200 megatons of high-energy radiation. Not enough to destroy the Earth, but enough to ruin the year for the inhabitants of a medium-sized country.

There’s no point in trying to work out things like surface tides or surface gravity: I’d be gone so fast that, in the time between my becoming a black hole and my evaporation, a beam of light would have traveled a foot or two. Everything around me is as good as stationary for my brief lifetime.

A Burial Fit for a Pharaoh. Well, for a weird pharaoh.

Things change dramatically once black holes get a little bigger. A hole with the mass of the Great Pyramid of Giza (around 6 billion kilograms) would take half a million years to evaporate. It would still be screaming-hot: we’re talking trillions of Kelvin, which is hot enough that nearby matter will vaporize, turn to plasma, the protons and neutrons will evaporate out of nuclei, and then the protons and neutrons themselves will melt into a quark-gluon soup. But, assuming the black hole is held in place exactly where the pyramid once stood, we won’t see that. We’ll only see a ball of plasma and incandescent air the size of a university campus or a big football stadium, throbbing and booming and setting fire to everything for a hundred kilometers in every direction. The Hawking radiation wouldn’t inject quite enough energy to boil the planet, but it would probably be enough (combined with things like the fact that it’s setting most of Egypt on fire) to spoil the climate in the long run.

This isn’t an issue if the black hole is where black holes belong: the vacuum of space. Out there, the hole won’t gobble up Earth matter and keep growing until it destroys us. Instead, it’ll keep radiating brighter and brighter until it dies in a fantastic explosion, much like the me-mass black hole did.

Can’t you just buy a space heater like a normal person?

It’s starting to get cold here in North Carolina. Much as I love the cold, I’ve been forced to turn my heater on. But, you know, electric heating is kinda inefficient, and this house isn’t all that well insulated. I wonder if I could heat the house using Hawking radiation instead…

Technically, yes. Technically in the sense of “Yeah, technically the equations say yes.” Technically in the same way that you could technically eat 98,000 bacon double cheeseburgers at birth and then go on a 75-year fast, because technically, that averages out to 2,000 Calories per day. What I mean is that while the numbers say you can, isolated equations never take into account all the other factors that make this a really terrible idea.

A black hole with the mass of a very large asteroiod (like Ceres, Vesta, or Pallas) would produce Hawking radiation at a temperature of 500 Kelvin, which is probably too hot to cook with, but cool enough not to glow red-hot. That seems like a sensible heat source. Except for the fact that, as soon as you let it go, it’s going to fall through the floor, gobble up everything within a building-sized channel, and convert that everything into superheated plasma by frictional effects as it falls into the hole. And except for the fact that if you’re in the same neighborhood as the hole, you’ll simultaneously be pulled into it at great speed by its gravity, and pulled apart into a bloody mass of fettuccine by tidal forces. And except for the fact that, as the black hole orbits inside the Earth, it’s going to open up a kilometer-wide tunnel around it and superheat the rock, which will cause all sorts of cataclysmic seismic activity, and ultimately, the Earth will either collapse into the hole, or be blasted apart by the luminosity of the forming accretion disk, or some combination thereof.

Back to the Original Extreme

But there’s one more frontier we haven’t explored. (I was watching Star Trek yesterday.) That is: the biggest black hole we can reasonably (well, semi-reasonably) imagine existing. That’s a black hole with a mass of around 1 x 10^52 kilograms: a black hole with the mass of the observable universe. Minus the mass of the Earth and the Sun, which make less of a dent in that number than stealing a penny makes a dent in Warren Buffett’s bank account.

The hole has a Schwarzschild radius of about 1.6 billion light-years, which is a good fraction of the radius of the observable universe. Not that the observable universe matters much anymore: all the stuff that was out there is stuck in a black hole now.

For the Earth and Sun, though, things don’t change very much (assuming you set them at a modest distance from the hole). After all, even light needs over 10 billion years to circumnavigate a hole this size. Sure, the Earth and Sun will be orbiting the hole, rather than the former orbiting the latter, but since we’re dealing with gravitational accelerations less than 3 nanometers per second per second, and tides you probably couldn’t physically measure (4e-34 m/s/m at the horizon, and less further out, which falls into the realm of the Planck scale), life on Earth would probably proceed more or less as normal. The hole can’t inflict any accretion-disk horror on the Sun and Earth: there’s nothing left to accrete. Here on Earth, we’d just be floating for all eternity, living our lives, but with a very black night sky. If we ever bothered to invent radio astronomy, we’d probably realize there was a gigantic something in the sky, since plasma from the Sun would escape and fall into a stream orbiting around the hole, but we’d never see it. What a weird world that would be…

Then again, if the world’s not weird by the end of one of my articles, then I’m really not doing my job…

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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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