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:

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

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

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

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

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

(Source.)

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

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

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

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

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

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

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

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

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

T + 569 seconds

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

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

But pretty soon, it looks like this:

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, which is enough to sand-blast the Earth to nothing in about three minutes, give or take.

T + 4 hours to 13h51m

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

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

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

astronomy, image, pixel art, science, short, Space, Uncategorized

Pixel Solar System

(Click for full view.)

(Don’t worry. I’ve got one more bit of pixel art on the back burner, and after that, I’ll give it a break for a while.)

This is our solar system. Each pixel represents one astronomical unit, which is the average distance between Earth and Sun: 1 AU, 150 million kilometers, 93.0 million miles, 8 light-minutes and 19 light-seconds, 35,661 United States diameters, 389 times the Earth-Moon distance, or a 326-year road trip, if you drive 12 hours a day every day at roughly highway speed. Each row is 1000 pixels (1000 AU) across, and the slices are stacked so they fit in a reasonably-shaped image.

At the top-left of the image is a yellow dot representing the Sun. Mercury and Venus aren’t visible in this image. The next major body is the blue dot representing the Earth. Next comes a red dot representing Mars. Then Jupiter (peachy orange), Saturn (a salmon-pink color, which is two pixels wide because the difference between Saturn’s closest and furthest distance from the Sun is just about 1 AU), Uranus (cyan, elongated for the same reason), Neptune (deep-blue), Pluto (brick-red, extending slightly within the orbit of Neptune and extending significantly farther out), Sedna (a slightly unpleasant brownish), the Voyager 2 probe (yellow, inside the stripe for Sedna), Planet Nine (purple, if it exists; the orbits are quite approximate and overlap a fair bit with Sedna’s orbit). Then comes the Oort Cloud (light-blue), which extends ridiculously far and may be where some of our comets come from. After a large gap comes Proxima Centauri, the nearest (known) star, in orange. Alpha Centauri (the nearest star system known to host a planet) comes surprisingly far down, in yellow. All told, the image covers just over 5 light-years.

image, short, Space

Earth versus Sun

Earth vs Sun at 1 AU.png

Nothing too special here: just a size comparison between the Earth and the Sun. The only difference from the usual ones, is that I’ve based their relative sizes on their angular diameters. For the Sun, I computed the angular diameter at a distance of 1 AU (which is how we see it here on Earth). For the Earth, I computed the angular diameter at a distance of 1 AU minus the diameter of the Sun. In other words, the Earth appears as large as it would if it were sitting at the point on the Solar surface nearest us. This is how the Earth would look as a very unfortunate close-transiting planet.

To paraphrase Carl Sagan: that little blue blob is home. That’s us. Everything that’s ever happened to you happened there.

Now consider that compared to the Sun…

Earth vs Sun Closeup.png

Here’s a closeup of the same image, showing the Earth compared to the weird convection granules on the Sun’s surface.

Both images are from NASA. The Solar image is from the Solar Dynamics Observatory (HMI intensitygram, February 7th, 2016), and the Earth-disk image is from the GOES earth-observing satellite.

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…

physics, Space, thought experiment

Houston, We Have Several Problems: Black Holes, Part 1

There aren’t many movies that I loved as a kid and can still stand to watch as a grownup. I remember loving Beauty and the Beast, but I don’t know if I could watch it now, because I’ve developed an irrational hatred of musical numbers. I certainly couldn’t watch that amazingly cheesy monster truck movie where the guy who drove Snakebite drugged the guy who drove Bigfoot. Apollo 13, though, aged well. It’s high on the list of my favorite space movies. Thanks to that movie (and the much weirder, but still pretty damn good Marooned), this vehicle is comfortably familiar to me:

(From Wikipedia.)

That there is the Apollo 15 command-service module. The command module (astronaut container) is the shiny cone at the front. Because I had cool parents, I got to go to the Johnson Space Center as a kid and see an actual command module, in person. As far as spacecraft go, it’s pretty small. If you stole one, you could hide it in your average garage. Now there‘s a good scene for a movie: some mad scientist with a stolen command module in his garage, tinkering with it while 80’s electronic montage music plays. Turning it into a time machine or something.

Once again, I imagine many of you are wondering what the hell I’m talking about. Don’t fret, there’s always (well, almost always) a method to my madness. Earlier today, I got thinking about the classic thought experiment: What would it be like to fall into a black hole. That thought experiment normally involves just dropping some hapless human (usually without even a spacesuit) right into one. You guys know me, though: if I’m going to do a weird thought experiment, I’m going to go into far more detail than necessary. That’s the fun part!

The point is, I’m going to start off my series on black holes by imagining what would happen if you dropped a pristine command module into black holes of various masses. The command module needs a three-person crew, and my crew will consist of myself, a young David Bowie, and Abraham Lincoln. Despite what you may think, no, I’m not on drugs. This is all natural, which, if you think about it, is much scarier.

A Mini Black Hole

As XKCD pointed out, a black hole with the mass of the Moon would not be a terribly dramatic-looking object. Even accounting for gravitational lensing, it would be next to impossible to see unless you were close to it, or you were looking really hard, or you had an X-ray/gamma-ray telescope. Nobody knows for sure whether black holes with masses this small actually exist. They might possibly have formed from the compression of the high-density plasma that filled the early universe, but so far, nobody’s spotted their telltale radiation.

But me, Bowie, and Lincoln are about to see one, and far too close.

At 1,700 kilometers, we’ve already gone from flying to falling. There’s nothing exciting happening, though, because as physicists always say, from a reasonable distance, a black hole’s gravitational field is no different from the gravitational field of a regular old object of the same mass. The tidal acceleration (which is the real killer when it comes to black holes) amounts to less than a millionth of a gee. Detectable, but only just.

At 100 kilometers, the tides are noticeable. Lincoln’s top-hat (which he foolishly left untethered. There wasn’t time to explain space flight and free-fall to a 19th-century politician) is slowly migrating to the end of the cabin. The tidal acceleration (the difference in pull between the center of the CM and either of its ends) is similar to the gravity of Pluto. The command module is stretching, but no more than, say, a 747 flexes in flight. Only detectable with fancy things like strain gauges.

At 10 km, we’re really motoring. Traveling at 31 kilometers per second, we’ve broken the record set by Apollo 10 for the fastest-moving humans. Bowie’s crazy Ziggy Stardust hair is getting misshapen by differential acceleration, which by now amounts to almost a full gee. Anything untethered (Lincoln’s hat, Bowie’s guitar, my cup of coffee, et cetera) is stuck at either end of the cabin.

At 5 km, we’re all shrieking in pain. The stray objects at the ends of the cabin are starting to get smashed. We’re all being stretched front-to-back (since that’s how you sit in a command module). The tides are pulling the command module like a rubber band, but a command module’s a compact and sturdy thing, so apart from some alarming creaking of metal, and maybe some cracking in the heat shield, it’s still in one piece.

All three of us die very quickly not long after the 2.5 km mark. Since the university still won’t let me use their finite-element physics package (well, more accurately, they won’t let me in the physics department…), I can only conjecture what will kill us, but it’ll either be the fact that the blood in our backs is being pulled toward the black hole much harder than the blood at our fronts (probably turning us very nasty colors and causing lots of horrible hemorrhages), or the fact that the command module has been stressed beyond its limits and sprung a leak. I’d wager the viewports would shatter before anything else happened, as their frames start to bend out of shape.

Time dilation hasn’t really kicked in, even by 500 meters, so an observer at a safe distance would see the CM crumple in real-time. The cone collapses like an umbrella being closed. Fragments of broken glass, shards of metal, control panels, shattered heat shield, and pieces of a legendary rocker, a melancholic President, and an idiot are spilling out of the wreckage.

By 10 meters, the command module is no longer falling straight down. It’s started falling inward, compressing side-to-side even as it stretches top-to-bottom. The individual components and fragments cast off from the wreck stretch and pull apart. Metal panels tear in two. Glass shards crack. Bits of flesh tear messily in half. The fragments divide and divide and divide. As they approach the event horizon, they explode into purple-white incandescent plasma: because the atoms are falling inward towards a point, they slam sideways into each other at high speeds. All 13,000 pounds of command module and crew either help bulk up the black hole, or form a radiant accretion disk denser than lead and smaller than a grape.

A 5-Solar-Mass Black Hole

In black hole thought experiments, the starting-point is usually a 1-solar-mass black hole. That makes sense: as far as astronomical objects go, the Sun is nicely familiar. But like I said before, scientists aren’t sure if there are any 1-solar-mass black holes anywhere in the Universe. As far as we know, all black holes in this mass range form from stars, and supernova leftovers smaller than something like 3 solar masses can still be supported by things like radiation pressure, degeneracy pressure, and the fact that atoms don’t like other atoms too close to them. In practice, there aren’t any known black hole candidates smaller than about 3 solar masses. There are a couple around 5 solar masses, and 5 is a nice round number, so that’s what I’m going with. We’re resetting this weird-ass experiment and dropping me, Bowie, and Lincoln into a stellar black hole.

At 380,000 kilometers (the distance from the Earth to the Moon), the tidal acceleration is detectable, but not noticeable. Good thing we’re free-falling (I should’ve made Tom Petty the third crewmember…), because if we were held stationary (say, by a magic platform hovering at a fixed altitude above the hole), we’d be flattened by a lethal 469-gee acceleration. Good thing, too, that we’re in an enclosed spacecraft: if the black hole has an accretion disk orbiting around it, we’re probably close enough that an unshielded human would be scalded to death by its heat, light, and X-rays. For our purposes, though, we’ll assume this black hole’s been floating through interstellar space for a long time, and has already cannibalized its own accretion disk, rendering it almost dark.

As we reach 10,000 km from the black hole, the same thing happens that happened with the mini black hole. David Bowie, who has gotten out of his seat to have a second tube of strawberry-banana pudding, finds it difficult to climb back to his couch against the gravity gradient. He’s being gently pelted by loose objects. Lincoln is just sitting in his couch looking very grave. I’m screaming my head off, so I miss all of this.

At 5,000 kilometers, the command module starts to creak. David Bowie is now stuck upside-down at the top of the cabin. I, having lost my shit and tried to open the hatch to end it quickly, have fallen to the bottom and broken my coccyx. Lincoln is still sitting in his couch looking very grave. We’re experiencing a total acceleration of over a million gees. If we tried to maintain a constant altitude, that million gees would turn us and the command module into a sheet of very thin and very gory foil. We’re moving almost as fast as the electrons shot from the electron gun of an old CRT TV.

Between 5,000 and 1,000 kilometers, the command module starts popping apart. It’s not as fast as the last time. First, the phenolic plastic of the heat shield cracks and pulls free of the insulation beneath. Then, the circular perimeter of the cone starts to crumple and wrinkle. (True story: the command module was built with crumple zones, just like a car, so that it didn’t pulp the astronauts too much when it hit the ocean at splashdown.) Not long after, the pressure hull finally ruptures, spewing white jets of gas and condensation in all directions like a leaky balloon. Then, the bottom of the pressure hull bursts. Think of a sledgehammer hitting a sheet of aluminum foil. All the guts of the command module spill out: wires, seats, guitars, apples (I was hungry), tophats, shoes, hoses, spare spacesuits, screaming idiots (I fell out). We’re moving 10% of the speed of light.

By 100 kilometers, the command module has spaghettified into a long stream of debris. The individual metal parts, although badly warped by being torn from their mountings, are mostly holding together, though they’re really starting to stretch. Anything softer is shattering/pulping/shredding. The black hole’s event horizon is the largest object in the sky: a fist-sized black disk of nothingness surrounded by a very pretty mandala of distorted stars and galaxies. It looks something like this:

(Screenshot from the unbelievably awesome (and free) program Space Engine.)

We can’t see it, though: we’re all dead.

By 25 kilometers, we’re just a stream of fine dust hurtling towards the event horizon at close to the speed of light. For an observer at a great distance, our disintegration proceeds in slow motion, both from the massive speed at which we’re traveling, and from the time-dilating effects of extreme gravity.

As we scream through 14.8 kilometers, we’ve almost reached the event horizon. The individual atoms the command module used to be made of are accelerating apart, spraying the whole CM into a narrow stream of plasma. Outside observers, though, just see the incandescent dust slow to a halt, change color from electric-arc purple to brilliant blue-white to the color of the sun to the color of hot steel to red-hot to black. What happens when we hit the singularity not long after is anybody’s guess. By definition, at a singularity, the equations you’re working with just quit making sense.

Sagittarius A*

There’s a very massive and very dense thing at the center of the Milky Way. It has about 3.6 million times the mass of the Sun, and because there’s a star (poetically called S0-102) that orbits pretty close to it (relatively speaking, anyway: its closest-approach distance is still larger than the distance from the Sun to Pluto), we know it has to be quite small, and therefore quite dense. According to our current understanding of physics, any mass like that would inevitably collapse into a black hole no matter what. The short version: it’s probably a black hole. (Note 1: as of this writing in November 2016, radio astronomers have finally committed to using a gigantic virtual telescope to take a picture of the actual event horizon in 2017, which is awesome) (Note 2: Though the actual mechanism for their formation isn’t known, some astrophysicists have done simulations suggesting that they formed from super-massive stars in the early universe. These days, the largest stars are a few hundred solar masses, with the largest stars for which we have firm evidence weighing around 120 solar masses. That’s massive, but not super-massive. These super-massive primordial stars contained thousands of solar masses. The one in that article massed 55,500. Some may have exceeded a million.)

Because a black hole (or, at least, its event horizon) is as compact as you can make anything, black holes tend to be really small compared to normal objects of similar mass. A Moon-mass black hole would look like a black dust-grain. An Earth-mass one would look like a pea. A Sun-mass one (and remember, there’s a lot of stuff in the Sun) would be the size of a small town. The 5-solar-mass hole we considered a second ago would be the size of a city. Sagittarius A*, though, containing so much mass, is actually a proper astronomical-sized object: 15 times larger than the Sun. If some deity with a really sick sense of humor replaced the Sun with Sgr A*, it would hang in the sky, a little smaller than a fist at arm’s length. We would also all be dead. For many reasons: no sunlight, radiation from the accretion disk, and the fact that we’d be orbiting so fast that grains of dust would heat the upper atmosphere lethally hot.

At 1 AU (the average distance from the Earth to the Sun), Sgr A*’s event horizon is much larger in the sky than the Moon. We’re accelerating at 1800 gees, but we don’t feel it, because we’re in free-fall. The tidal acceleration is minuscule: less than a micron per second per second. Once again, we’re pretending the black hole has no accretion disk, because if it did, its radiation would probably have incinerated us by now.

By the time we pass through Mercury’s orbit (0.387 AU) (assuming we actually are in this nightmarish black-hole solar system), we’re going one-third the speed of light, accelerating at over 15,000 gees. The tides are still detectable only by specialized instruments.

By 0.1 AU, we’re moving three-quarters the speed of light. David Bowie is singing “Space Oddity”, because I’ve smuggled a durian fruit onboard and threatened to cut it open if he doesn’t. Lincoln is starting to get sick of this shit, but this just gives him that same grave expression he has in all his photographs. The tides are detectable by instruments, but probably not by our human senses. Hitting a stationary dust particle the size of a bacterium unleashes a burst of light as bright as a studio flash.

At 0.071 AU, we pass through the event horizon without even realizing it. Falling into a black hole intact is a little like having a gigantic black bag closed around you: the event horizon already covers more than half of the sky, thanks to the fact that the black hole bends light toward the horizon. The sky shrinks into an ever-diminishing circle in a black void. The circle grows brighter and bluer with every passing second.

By 0.05 AU, stray objects are drifting to the ends of the cabin again: the tides are finally picking up. David Bowie is holding me down and punching me repeatedly, because he’s sick of me resurrecting him and killing him over and over. Lincoln is letting him do it, because frankly, I’ve cracked his statesman’s patience with my bullshit. We’re only 30 seconds from the singularity.

Even at 0.01 AU, the tides aren’t stretching the capsule. The effects might be palpable, but they’re nothing compared to what we’ve already been through in the previous experiments. We’re riding down a shaft of blue-shifted light, concentrated into a point straight overhead: everything that’s fallen into the hole recently can’t help but curve inward, until it’s falling almost ruler-straight towards the singularity.

At one Sun radius from the singularity, the differential acceleration is approaching one gee. Things are starting to get uncomfortable. David Bowie has stopped punching me, because he’s fallen to the top of the capsule again. Lincoln, though, still has the strength to pick up a pen and stab me in the sternum. He’s cursing at me, and as I start to bleed to death, I observe that Lincoln is much more creative with his swears than I would have given him credit for.

At 150,000 km, we start to get woozy on account of the blood in our bodies pooling in all the wrong places. We narrowly avoid a collision with Matthew McConaughey in a spacesuit, who has gone from muttering about quantum data to describing the peculiar aging patterns of high-school girls.

At 50,000 km, moving very, very nearly the speed of light, the command module finally starts to disintegrate. Seconds later, we spaghettify, just as before, and strike the singularity. And, once again, we run afoul of the fact that physicists have very little idea what happens that deep in a gravity well. For reference, at 100 meters from the singularity (and ignoring relativistic effects and pretending we can use the Newtonian equation for tides down here), the differential acceleration is measured with twenty-digit numbers. If the capsule were infinitely rigid and didn’t spaghettify, by the time its bottom touched the singularity, the tides would be measured in 25-digit numbers. If, somehow, we’d survived our trip to the singularity, we’d be accelerating so fast that, thanks to the Unruh effect, empty space would be so hot we’d instantly vaporize.

And here’s where physics breaks down. If I’m reading this paper right, the distance between any point and the singularity is infinity, because space-time is so strongly curved near it.

Imagine that space is two-dimensional. It contains two-dimensional stars with two-dimensional mass. That curves two-dimensional space into a three-dimensional manifold. The gravity well (technically, the metric) around a very dense (but non-black-hole) looks roughly like this:

(From Wikipedia.)

If you measure the circumference of the object, you can calculate its diameter: divide by two times pi. But when you measure its actual diameter, you’ll find it’s larger than that, because of the way strong gravitation stretches spacetime. In the case of a black hole, spacetime looks more like this:

(From the paper cited above.)

The cylindrical part of the trumpet is (if I’m understanding this correctly) infinitely long. The “straight-line” distance through the black hole, on a line that just barely misses the singularity, is much larger than you’d expect. But the distance through the black hole, measured on a line that hits the singularity is infinite. All lines that hit the singularity just stop there.

But, to be honest, I really don’t know what it’d be like down there. Nobody does. The first person to figure out what gravity and particle physics do under conditions like that will probably be getting a shiny medal from some Swedes.

Cars, physics, Space, thought experiment

A Toyota in Space

I talk all the time about the weird nerdy epiphanies I had as a kid. One of those epiphanies involved driving a car around on the outside of a space station. I realized that the car would have to bring along its own air supply, because an internal combustion engine can’t run on vacuum. I know that sounds obvious, but when you consider I was like nine years old at the time, it’s almost impressive that I figured it out. Almost.

Now that I’m older, I realized “Hey! I can actually figure out how much air I’d need to bring with me!” Conveniently, the worldwide craze for automobiles (some say they’ll replace the horse and buggy. I think that’s a pretty audacious claim, sir.) means that all sorts of vital statistics about gasoline engines are known. For instance: the air-fuel ratio. It’s as simple as it sounds. It’s the mass of air you need to burn 1 mass unit of fuel. The “ideal” ratio is 15:1: combustion requires 15 grams of air for every gram of fuel burned. Of course, if you’ve watched Mythbusters, you’ll know that stoichiometric (ideal) mixtures of air and fuel detonate, often violently. You don’t actually want that happening in a cylinder. You want subsonic combustion: deflagration, which is rapid burning, not an actual explosion. Supersonic combustion (detonation) produces much higher temperatures and pressures. At best, it’s really rough on the. At worst, it makes the engine stop being an engine and start being shrapnel. So, in practice, mixtures like 14:1 and 13:1 are more common. I’ll go with 14:1, although I freely admit I don’t know much about engines, and might be talking out my butt. No change there.

Either way, we now know how many mass units of air the engine will consume. Now, we need to know how many mass units of fuel the engine will consume. There are lots of numbers that tell you this, but for reasons of precision, I’m using one commonly used in airplanes: specific fuel consumption (technically, brake specific fuel consumption). The Cessna 172 is probably the most common airplane in the world. It has a four-cylinder engine, just like my car, though it produces 80% more horsepower. Its specific fuel consumption, according to this document, is 0.435 pounds per horsepower per hour. The Cessna engine produces 180 horsepower, and my car produces 100, so, conveniently, I can just multiply 0.435 by 100/180 to get 0.242 pounds per horsepower per hour. Assuming I’m using 50% power the whole way (I’m probably not, but that’s a good upper limit), that’s 50 horsepower * 0.242, or 12.1 pounds of gasoline per hour.

So, we know we need 12.1 pounds of gasoline per hour, and from the air-fuel ratio, we know we need 169.4 pounds of air per hour. That’s all fine and dandy, but I’m not sure how much room 169.4 pounds of air takes up. Welders to the rescue! According to the product catalog from welding-gas supplier Airgas, a large (size 300) cylinder of semiconductor-grade air has a volume of 49 liters, and the air is stored in that bottle at about 2,500 PSI. (I don’t know what you actually do with semiconductor-grade air, but it’s got the same ratio of gases as ordinary air, so it’ll do.) At room temperature, the bottled air is actually a supercritical fluid with a density 1/5th that of water. Therefore, each cylinder contains about 10 kilograms (22 pounds) of air. Much to my surprise, even when it’s connected to an air-hungry device like an internal combustion engine, a single size-300 cylinder could power my car for over seven and a half hours.

But you guys know me by now. You know much I like to over-think. And I’m gonna do it again, because there are a lot of things you have to consider when driving a car in a vacuum that don’t come up when you’re driving around in air.

Thing 1: Waste heat. This is a major issue for spacecraft, which live in a vacuum (unless you’ve really screwed up). The problem is that there’s only one good way to expel waste heat in a vacuum: radiation. Luckily, the majority of automobile engines are already radiator-cooled. Normally, they depend on heat flowing from the engine to the cooling water, into the metal fins of a radiator, and into the atmosphere. In vacuum, the cooling will run engine-water-radiator-vacuum. The engine produces 100 horsepower at maximum, which is about 75 kilowatts. A radiator operating at the boiling temperature of water radiates about 1,100 watts per square meter, for a total area of 68 square meters, which means a square 27 feet (8.2 meters) on a side. You could play tennis on that. Luckily, the radiator is two-sided, which cuts the radiator down to a square 19 feet (5.8 meters) on a side. It’s still going to be larger than my car, but if I divide it into ten fins, it would only be absolutely ridiculous, rather than impractically ridiculous. That’s already my comfort zone anyway.

Thing 2: Materials behave differently in a vacuum. Everything behaves differently under vacuum. Water boils away at room temperature. Some of the compounds in oil evaporate, and the oil stops acting like oil. Humans suffocate and die. To prevent that last one, I’m going to have to beef up my car’s cabin into a pressure vessel. And since I’m doing that, I’ll go ahead and do the same to the engine bay, so that I don’t have to re-design the whole engine to work in hard vaucuum. I’ll make the two pressure vessels separate compartments, because carbon monoxide in a closed environment is bad and sometimes engines leak.

I’ll also have to put a one-way valve on the exhaust pipe, because my engine is designed to work against an atmospheric pressure of 1 atmosphere, and I feel like working against no pressure at all would cause trouble. I’m also going to have to change the end of my exhaust pipe. I’ll seal it off at the end and drill lots of small holes down the sides, to keep the exhaust from acting like a thruster and making my car spin all over the place.

Thing 3: Lubrication. A car’s drivetrain and suspension contain a lot of bearings. There are bearings for the wheels, the wheel axles, the steering linkages, the universal joints in the axles, the front and rear A-arms… it just goes on and on. Those bearings need lubrication, or they’ll seize up and pieces will break off, which you very rarely want in engineering. Worse, in vacuum, metal parts can vacuum-weld together if they’re not properly protected. We can’t enclose and pressurize every bearing and joint. That would make my car too bulky, for one. For two, there would still have to be bearings where the axles came out of the pressurized section, so I’ve gotta deal with the problem sooner or later. Luckily, high-vacuum grease is already a thing. It maintains its lubricating properties under very high vacuum and a wide range of pressures, without breaking down or gumming up or evaporating. We’ll need built-in heaters to keep the grease warm enough to stay greasy, but that’s not too big a hurdle.

Thing 4: Tires. My car’s owner’s manual specifies that I should inflate my tires to 35 psi (gauge). I’ll have to inflate them to a higher gauge pressure in vacuum, since they’ll have almost no pressure working against them. If I don’t, they’ll be under-inflated, and that’ll make them heat up, and in vacuum, that goes from a minor problem to a potentially fatal tire-melting and tire-bursting disaster. Actually, I think I’ll eliminate that risk altogether. I’ll do what most rovers do: I’m getting rid of pneumatic tires altogether. Because my car’s going to be fast, heavy and have a human passenger, I can’t do what most rovers have done and just make my wheels metal shells. I need some cushioning to stop from rattling myself and my car to pieces.

nasa_apollo_17_lunar_roving_vehicle

That’s Gene Cernan driving the Lunar Roving Vehicle (the moon buggy). It’s about five times lighter than my car, but it proves that airless tires can work at moderate speed. Michelin is also trying to design airless rubber tires for military Humvees, and while they don’t absorb shocks quite as well as pneumatic tires, they can’t puncture and explode like pneumatic tires. So I’m going with some sort of springy metal tire, possibly just composed of spring-steel hoops or something like that.

Thing 4: Fuel. If I was sensible, I’d have chucked the whole idea of powering a vacuum-roving Toyota with a gasoline engine. (Actually, I’d have chucked the whole idea of a vacuum-roving Toyota and started from scratch…) We know I’m not sensible, so I’m going to demand that my Lunar Toyota run on gasoline. 10,000 liters of gasoline (I like to mix units, like an idiot) will let me drive 42,500 kilometers. Enough to go around the Moon’s equator three (almost four) times. You might think that carrying a small tanker’s worth of gasoline to the Moon is an impossible feat, but when you consider that the mass of my car (about 1,000 kilograms) plus the mass of all that gasoline (7,300 kilograms) plus tankage is less than the weight of the Apollo Command-Service Module and the Lunar Module, not only does the Apollo program seem that much more audacious and impressive, but it becomes possible to talk sensibly (sort of…) about putting my car, my air tanks, and a lifetime supply of gasoline on the Moon. That also takes care of…

…Thing 5: Getting my car on the Moon. We can just use a Saturn V, or wait for the engineers to finish building the Falcon Heavy or Space Launch System. Lucky for me, the rocket scientists have already solved the problem of landing a heavy vehicle, too: the ballsy sky-crane landing used during the Curiosity rover’s descent would almost certainly work just fine for my car, since it’s only 200 kilograms heavier than Curiosity. The fuel and air can just be landed under rocket power, or by expendable airbags.

So it wasn’t all that insane for my nine-year-old self to imagine driving an ordinary street car around on the Moon. That is, from the point of view of fueling and aspirating (ventilating? aerating? Providing air to, is what I mean…) the engine and the passenger. But the physics of driving around in vacuum and/or under low gravity pose another challenge, and that challenge is interesting enough to get a post of its own. Watch this space!

Addendum, Cars, physics, Space, thought experiment

Addendum: A City On Wheels

While I was proofreading my City on Wheels post, I realized that I’d missed a golden opportunity to estimate just how heavy a whole city would be. When I was writing that post, I wanted to use the Empire State Building’s weight as an upper limit, because I was pretty sure that would be enough space for a whole self-sufficient community. Trouble is, the weight of buildings isn’t usually known. The Empire State Building’s weight is cited here and there, but never with a very convincing source. I couldn’t figure out a way to estimate its weight that didn’t feel like nonsense guesswork. That’s why I used the Titanic’s displacement as my baseline.

The reason estimating the mass of a building was so tricky is that, generally, buildings are far form standardized. Yeah, a lot of houses are built in similar or identical styles, but even if you know their exact dimensions, converting that into a reasonably accurate weight turns into pure guesswork, because you don’t know what kind of wood was used in the frame, how much moisture the wood contained, how many total nails were used, et cetera. But, just now, I realized something. There is a standardized object that represents the shape, size, and weight of a dwelling pretty well: the humble shipping container.

31-shipping-container-house-01-850x566

You may notice that that’s not a shipping container. It’s a bunch of shipping containers put together to make a rather stylish (if slightly industrial-looking) house. Building homes out of shipping containers is a big movement in the United States right now. They’re cheaper than a lot of alternatives, and they’re tough: shipping containers are built to be stacked high, even while carrying full loads. For example:

cscl_globe_arriving_at_felixstowe_united_kingdom

The things are sturdy enough that they far exceed most building codes, when properly anchored. Their low price, their strength, and the fact that they’re easily combined and modified, has made them popular as alternative houses.

Because different shipping containers from different manufacturers and different countries often end up stacked together, they all have to be built to the same standard. Their dimensions, therefore, are standardized, which is good news for us. I re-imagined the rolling city as a stack of shipping containers approximately the size of the Titanic, with their long axes perpendicular to the ship’s long axis. You could fit two across the Titanic‘s deck this way, and 110 along the deck, and if you stacked them 20 high, you’d approximate the Titanic’s shape and volume. To account for the fact that the people living in these containers are going to have furniture, pets, physical bodies, and other inconvenient stuff, I’ll assume that each container would have twelve pieces of the heaviest furniture I could think of: the refrigerator.

Amazon is a great thing for this kind of estimation, because from it, I learned that an ordinary Frigidaire is about 300 pounds. Multiply that by twelve, add the mass of the container itself (3.8 metric tons each), round up (to keep estimates pessimistic), and you get 6 metric tons per container. Considering that a standard 40-foot intermodal container (which is the standard I worked with) can handle a gross weight (container + cargo) of over 28 metric tons, we’re nowhere near the load limit for the containers. There are 4,400 containers in all, for a total mass of 26,400 metric tons. Increase the mass by 25% to account for the weight of the nuclear reactor, chassis, and suspension, and we get 33,000 metric tons. That’s still a hell of a lot, but it’s only just over half of the 50,000 tonnes we were working with before.

As you might remember, I wrote off the Titanic-based city on wheels as probably feasible, but requiring a heroic effort and investment. But using the shipping container mass, which is 1.5-fold smaller, I think it moves into the “impressive but almost sensible mega-project” category, along with the Golden Gate Bridge, the Burj Khalifa, the Great Pyramid of Giza, and Infinite Jest.

Another note: There’s one heavy, mobile object whose weight I didn’t mention in the City on Wheels post: the Saturn V rocket. I did mention the Crawler-Transporter that moved the Saturn V from the Vehicle Assembly Building to the launchpad, however. And the weight of the fully-loaded Saturn V gives us an idea of how massive an object a self-propelled machine can move: 3,000 tonnes. Because, to nobody’s surprise, NASA knows the weight of every Apollo rocket at liftoff. Because it’s mildly (massively) important to know the mass of the rocket you’re launching, because that can make the difference between “rocket in a low orbit” and “really dangerous and expensive airplane flying really high until it explodes with three astronauts inside.”

Addendum, Space, thought experiment

Addendum: The Moon Cable

Reader Dan of 360 Exposure, pointed out something that I completely neglected to mention, regarding cable strength. Not only would the Moon Cable be unable to connect the Earth and Moon without breaking (either by being stretched, or by winding around the Earth and then being stretched), but it couldn’t even support its own weight.

There’s a really cool measurement used in engineering circles: specific strength. Specific strength compares the strength of a material to its weight. It’s often measured in (kilonewtons x meters) / kilograms. But there’s another measurement that I like better: breaking length. Breaking length tells you the same thing, but in a more intuitive way. Breaking length is the maximum length of a cable made of the material in question that could dangle free under 1 gee (9.80665 m/s^2) without the cable’s own weight breaking it.

Concrete’s breaking length is only 440 meters. Oak does better, at 13 kilometers (a really bizarre inverted tree. That’d make a good science-fiction story). Spider silk, which has one of the highest tensile strengths of any biological material, has a breaking length of 109 km (meaning a space-spider could drop a web from very low orbit and snag something on the ground. There’s a thought.) Kevlar, whose tensile strength and low density make it ideal for bullet-proof vests, has a breaking length of 256 kilometers. If you could ignore atmospheric effects (you can’t) and the mass of the rope (you can’t), you could tie a Kevlar rope to a satellite and have it drag along the ground. Zylon is even better. It’s a high-tensile synthetic polymer with a higher tensile strength than Kevlar, and a larger breaking length: 384 kilometers. You could attach a harpoon to a Zylon rope and use it to catch the International Space Station (no you couldn’t).

And, funnily enough, specific strength is one of those things that has a well-established upper limit. According to current physics, nothing (made of matter, magnetic fields, or anything else) can have a breaking length longer than 9.2 trillion kilometers. This is demonstrated in this paper, which I could get the gist of but which I can’t vouch for, because I understand the Einstein Field Equations about as well as I understand cricket, or dating, or the politics of Mongolian soccer. But the long and the short of it is that it’s not possible, according to current physics, to make anything stronger than this without violating one of those important conservation laws, or the speed of light, or something similar.

Not that we were ever going to get there anyway. The strongest material that has actually been produced (as of this writing, July 2016) is the colossal carbon tube. Think of a tube made of corrugated cardboard with holes in it, except that the cardboard and the corrugation is made of graphene. Colossal carbon tubes have a breaking length of something like 6,000 km (remember, this is under constant gravity, not real gravity). And that’s theoretical. So we’re not building a giant ISS-catching harpoon any time soon.

You might have noticed that I skipped over the one material that I was actually talking about in the Moon Cable post: steel. There’s a reason for that. I want to leave the big punch in the gut for the very end. For dramatic purposes. Ordinary 304 stainless steel has a pitiful breaking length of 6.4 km. Inconel (which is both surprisingly tough and amazingly heat-resistant, and is often used in things like rocket combustion chambers) only does a little better, at 15.4 km. There’s no handwaving it: you can’t attach the Moon to the Earth with a metal cable.

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 hits 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.

Sublime Curiosity

A zoo for thought experiments.

Category Archives: Space

If the Sun went Supernova

Earth versus Sun

Hypothetical Nightmares | Black Holes, Part 3

Houston, We Have Several Problems: Black Holes, Part 1

A Toyota in Space

Addendum: A City On Wheels

Addendum: The Moon Cable

The Moon Cable