How planets blow up

[GStone]

I saw this at SCN, posted by Bond, James Bond and I thought I'd put it up here.

http://www.subspace-comms.net/index.php ... 109146#new

Here's an article by scientist and science fiction author Wil McCarthy on the effects of actual singularities at the core of planets, and how that relates to the new movie. It doesn't quite apply, since obviously the magical Red Matter works differently, but it's still a fascinating, in-depth, and accessible article with some very surprising revelations about how things would happen if a singularity started "eating" a planet.
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Scientist Wil McCarthy shows how Star Trek's planets explode

I'm not in the habit of spoiling movies for people who haven't seen them yet, so I hope it's no surprise to say that in J.J. Abrams new Star Trek movie (aptly titled Star Trek), a planet gets crushed into a black hole. I say "no surprise" because stuff like this happens all the time in Star Trek.

Remember how the random explosion of Ceti Alpha Six doomed Khan Noonien Singh and his followers to a brutal desert subsistence on Ceti Alpha Five? Or how the Doomsday Machine cut a swath through the Alpha Quadrant, gobbling up planets along the way? Or the Crystalline Entity, with its habit of devouring entire biospheres?

And let's not forget the Genesis Planet, whose backbone of unstable protomatter doomed it to short life and a quick, violent death. Or the habitable stars that were so casually destroyed by the criminal Dr. Tolian Soran in his quest to return to the spacetime "nexus" where he'd once spent a brief eternity.
Scientist Wil McCarthy shows how \<em\>Star Trek\<\/em\>\'s planets explode

Nor is Star Trek unique in this regard. Stars and planets are regularly destroyed in Star Wars, too, and in lots of other science fiction from the Golden Age right up to the very doorstep of the Singularity.

But here's the thing: destroying a planet takes time. They're big, dense objects, and destroying one is not like popping a balloon or even vaporizing a city with nukes. In fact, a better analogy would be open-pit mining, where solid rock needs to be broken up and carted away, using thousands of tons of dynamite over dozens of years. Even if you drop a bomb or fire a death ray powerful enough to reduce a whole planet to rubble, you still have the problem of gravity; that rubble is going to stay where it is, or at worst, fly apart and then fall back together again. The resulting planet would be loose rather than solid—picture a pile of sand or a dump truck full of gravel—but it would still be round, it would still have gravity, and you could still orbit your spaceship around it. The process would of course kill every living thing on the planet, which is probably good enough for military or political purposes, but the standards of Hollywood are higher; the planet actually has to disappear.

In the case of an explosion, the energies involved are colossal. The Earth (for example) weighs 6 billion quadrillion tons, and even if we ignore the force required to break it into small pieces, we still need to accelerate every scrap of it to escape velocity—over 10,000 meters per second—in every possible direction, to overcome their collective gravity and keep them from falling back together again. That means almost a quadrillion quadrillion gigajoules of kinetic energy. That's the equivalent of every lightning storm on Earth for a million quadrillion years, or the total heat output of the sun for three full decades. Yeah. And of course, to achieve the required visual effect we need to deliver all that energy in a fraction of a second, so even if the Death Star were made entirely out of fully charged Toyota Prius batteries, you'd still need 50 billion billion Death Stars firing simultaneously to make it happen.

Do you get what I'm saying here?

Now, Star Trek gets around this problem by dropping a mysterious substance called "red matter" into the planet's core, touching off some kind of gravitic chain reaction that collapses the whole thing into a black hole. That's a little more reasonable—if a word like "reasonable" can be used to describe the death of 6 billion people and the total erasure of their culture, history and even the biosphere and geology that supported them. But like a lot of Star Trek, what we see on the screen is difficult to reconcile with the known laws of physics.

Let's assume a droplet of red matter weighs 1 billion metric tons. It clearly weighs a lot less than that, or a Volkswagen-sized sphere of the stuff would be impossible to haul around even with the best warp drive in the universe. But we're being generous here, if "generous" is a word I can use to describe, well, you know. In the first place, you wouldn't need a fancy-schmancy mining drill boring a hole to the planet's center, because no material would be strong enough to hold the red matter up. It would drop right through the crust, mantle and core like a cannonball through a pile of feathers. In fact, it would zip right through the planet and out the other side, crisscrossing through it over and over again until friction finally slowed it down and stopped it. That could take days, but let's say (again, generously) that red matter has some special property that allows it to stop dead the moment it reaches the planet's center. All you have to do is drop it from a thousand kilometers up, and the rest is history.

First problem? Planets are big, as I said, and to reach the center of an Earth-like one you need to fall through more than 6,000 kilometers of solid material. This takes even longer than you might guess, because once you're inside the planet you start to experience less of its gravity, until at the center you're completely weightless, because the gravity of all that rock and magma is pulling outward equally in every direction. Once you're in, there's less and less force to accelerate you. Including the 1,000 kilometers of initial altitude, the fall alone would take 2.8 minutes.

Second problem? Even if a black hole forms right away, it's simply not that destructive. Remember: It only weighs a billion tons—one quadrillionth of the mass of the planet around it. It has a fierce gravitational pull, yes, but that drops off rapidly with distance. An object 6 centimeters away would experience almost 2,000 times the pull of Earth's gravity, but just 2.6 meters away the pull is equal to Earth's surface gravity, and a few meters beyond that, it's negligible. So the object will very quickly gobble up everything within a few meters—adding at most a few million tons to its weight—and then very slowly gobble up the stuff farther up. Remember, too, that while the magma at Earth's core is very hot and is under tremendous pressure, it's also weightless, sitting in the one spot where the world's gravity cancels out completely. And it's extremely viscous, acting in many ways more like a solid than liquid. So imagine it dripping and oozing, forming droplets in the superheated cavern that has suddenly opened up in the planet's center. These droplets gradually drift toward the black hole (which is a microscopic pinpoint that still has no more mass than a small asteroid) and are consumed by it. Or maybe the cavern walls squirt like volcanic fountains, or maybe even swell and expand inward to relieve the pressure and fill the void. Either way, the core-stuff—mostly iron, with bits of other heavy metals mixed in—is like taffy; it can only flow so fast.

Rolling the clock forward a few minutes, we find the cavern is now half a kilometer across, and the black hole is eight times as massive as it was at the start. And yet the gravitational pull on the cavern walls is smaller than ever, barely two thousandths of the gravity pressing you into your chair while you read this. It's only the pressure of the rock and magma above, and the lack of any real structural integrity, that keeps the walls collapsing at all. Really, this is not going to be a speedy process! I don't really know exactly how fast it would unfold—we'd need some very sophisticated fluid dynamics simulations to figure that out. And with the black hole sucking in all the light and heat emitted by the cavern walls, they might even start to cool off and solidify, turning into solid iron. And that would end the party right there.

But let's say that doesn't happen. Let's say the red matter is vibrating, wiggling back and forth down there, striking the cavern walls to keep everything stirred up and crumbly. It didn't stop dead at the core at all, just slowed way down, so it's in there tracing Spirograph patterns through the magma while the planet turns around it. Whee! Eventually (and this could still take days), it has eaten away the planet's entire core. By now the planet has a real problem, because the black hole has started to gain a significant amount of mass, and the layer that sits above the core—the mantle—is a lot lighter and runnier than the stuff below it. It collapses inward with much less resistance, and the reverberations are felt throughout the planet, which is now ringing like a bell and cracking under the stress of a billion simultaneous earthquakes. The void around the hypermass is now 2,000 kilometers wide, and the pull of gravity at the margins is 40 gee, so things are starting to happen a lot more quickly. For the people on the surface, this is bad news indeed, and anyone who can get off the planet has probably done so by now.

And yet.

Even when a good percentage of this unfortunate world has been sucked inside the black hole, the mass of the total system cannot exceed the mass of the planet, plus the (comparatively tiny) mass of the droplet of red matter that triggered the cataclysm. If that's not clear, let me state it another way: throughout the ordeal, the gravity on the planet's surface never changes. Never. And when the surface finally begins to collapse—probably several days after the start of the process—its bits and pieces (both living and non) still have more than 6,000 kilometers to fall before they reach the center. The gravity gradients are all different now—the pull grows stronger, not weaker, as you get deeper inside the planet—but even so the fall takes 2.3 minutes, which is much longer than the final collapse we see in the movie.

Actually, it's even more complicated than that, because even after swallowing an entire Earth-sized planet, the black hole is only 9 millimeters across. That's a very small target; much of the falling debris is going to miss it altogether and fall instead into highly elliptical orbits around it. That situation is unstable; objects would be banging and grinding against one another for years. Some would be knocked into the black hole in a shrieking burst of X-rays; others would be ejected from its gravity and escape into space. As for a shock wave, I don't think we'd see one. I'm not saying there wouldn't be energy released—in fact, as more and more matter fell onto the black hole, it would probably look like a continuous H-bomb explosion. But aside from light and charged particles, I don't think anything would escape from the gravity well. The energy required for gas or grit to escape from the region adjacent to black hole's surface is simply too great. Once you get close enough, you're trapped for good. And yet, within a few days friction would slow most of the flailing debris objects down until they were in circular orbits. In a miniature, speeded-up version of the evolution of Saturn, the black hole would acquire a ring of orbiting rubble.

And here's the funny part: some of the debris in that ring might be living people. Close to the event horizon the tidal stresses are enough to tear a person apart into component atoms, but a hundred kilometers farther out, the stresses would be felt but would not be lethal. Such a disaster would be a rough ride indeed, but anyone wearing a spacesuit, or holed up in a submarine, or trapped in a bank vault or an underground military bunker, would have a small but possibly nonzero chance of surviving. In a world of 6 billion, there might just be a few bewildered refugees floating here and there. The odds are even better for plant seeds and bacterial spores, some of which have been shown to survive the vacuum, radiation, heat and cold of outer space. And if we're talking clonable DNA, well, there should be plenty of that, albeit smeared across billions of chunks of jagged rock. There would also be artifacts, including any satellites or space stations in orbit around the planet before the disaster started. Remember, the gravity they experience would not change either; their orbits would hardly quiver. Point is, while the planet would of course be a total loss, a determined salvage operation could probably find enough bits and pieces of its history and biology to cobble together, on some other similar planet, a rough approximation of the way things used to be.

So. The planet's destruction would be nowhere near as quick or as total as Star Trek's otherwise capable writers and director would have us believe. Then again, given that the whole sequence occupies only a few minutes of the storyline's 2.1-hour runtime, you should probably go see it anyway, as millions of people have already done. True to the Star Trek franchise, it's a tense, fun and ultimately hopeful story that will likely kick off a whole new sequence of rebooted cinematic glory.
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Sources:
McCarthy, Wil: The Collapsium, Appendix C, Technical Notes, Del Rey Books, 2000
Wikipedia: The Free Encyclopedia (en.wikipedia.org): "lightning", "Prius", "iron", "Earth"
The Internet Movie Database (www.imdb.com): Star Trek
www.rottentomatoes.com: Star Trek
C. Balto and S.M. Cali: PaperTech Astronomical Data I, Papertech Marketing Group, 1985

Wil McCarthy is a rocket guidance engineer, robot designer, nanotechnologist, science-fiction author and occasional aquanaut. He has contributed to three interplanetary spacecraft, five communication and weather satellites, a line of landmine-clearing robots and some other "really cool stuff" he can't tell us about. His short writings have graced the pages of Analog, Asimov's, Wired, Nature and other major publications, and his book-length works include the New York Times notable Bloom, Amazon "Best of Y2K" The Collapsium and most recently, To Crush the Moon. His acclaimed nonfiction book Hacking Matter is now available as a free download.

http://scifiwire.com/2009/05/columnist- ... thy-st.php