September 18, 2014
Ethan Siegel [Starts With a Bang]
How to destroy an Alderaan-sized planet.
“What’s that star?
It’s the Death Star.
What does it do?
It does Death. It does Death, buddy. Get out of my way!” -Eddie Izzard
It’s one of the most iconic sequences in all of film: the evil galactic empire takes the captured princess to her home planet of Alderaan, a world not so different from Earth, threatening to destroy it unless she tells them the location of the hidden rebel base. Distressed but loyal to her cause, she lies, giving them the name of a false location, which they have no way of knowing. Nevertheless, they give the order to fire, and despite her protestations, this is what happens next.
I want you to think about this for a moment:
A battle station the size of the Moon,
With a mysterious, unexplained power source at its core,
Charges up and fires a laser-like ray at an entire, Earth-sized planet,
And completely destroys it.
Not only does the Death Star completely destroy Alderaan from the force of its blast, it does so in a matter of seconds, and kicks off at least a substantial fraction of the world into interplanetary space with an incredible velocity.
See for yourself!
From a physics point of view — and using the Earth as a proxy for Alderaan — how much energy/power would it take to cause this destruction, and what are the physical possibilities for actually making this happen?
First off, let’s consider the planet Earth, and force binding it together.
As Obi-Wan famously said, “It surrounds us and penetrates us; it binds the galaxy together.” But the force binding the Earth together isn’t the mysterious one from the Star Wars Universe, but simply gravitation. And the gravitational binding energy of our planet — which is the minimum amount of energy we’d have to put into it to blast it apart — is an astounding 2.24 × 10^32 Joules, or 224,000,000,000,000,000,000,000,000,000,000 Joules of energy!
To put that in perspective, think about the entire energy output of the Sun, a “mere” 3.8 × 10^26 Watts.
It would take a full week’s worth of the Sun’s total energy output — delivered to an entire planet in the span of a few seconds — to cause that kind of reaction!
Remember what goes on inside an actual Sun-like star: hydrogen is burned via the process of nuclear fusion into heavier isotopes and elements, resulting in helium. Each second in the Sun, 4.3 billion kilograms of mass are converted into pure energy, which is the source of the Sun’s energy output. Let’s imagine that’s exactly what the Death Star is doing, in the most efficient way possible.
We could simply have the Death Star fire a beam of light into the planet (e.g., laser light), requiring that it generate all that energy on board itself, and then firing it at Alderaan. This would be catastrophically inefficient, however: imagine a solid material structure — even one as big as our Moon — trying to generate, direct and expel all that energy in just a matter of a few seconds. Releasing that much energy in one direction (2.24 × 10^32 Joules), would cause a Moon-mass object to accelerate in the opposite direction to a speed of 78 km/s from rest, something that clearly didn’t happen when the Death Star was fired.
In fact, there was no discernible recoil at all! And that’s not even considering how such intense energy would be managed, since it would heat up everything surrounding it (by simple heat diffusion) and quite clearly melt the tubes inside. But there’s another way this planetary destruction could’ve happened, predicated on one simple, indisputable fact: Princess Leia is made up of matter, and not antimatter.
Since she’s made of matter and grew up on Alderaan, we can assume Alderaan is made of matter as well, meaning that if if the Death Star instead fired pure antimatter at Alderaan, it would only need to supply half the total energy, since the target (Alderaan itself) would provide the other half of the fuel.
If this were the case, “only” 1.24 trillion tonnes of antimatter would suffice to provide the minimum amount of energy needed to blast that world apart. In the grand scheme of things, that isn’t so big.
Image credit: montage by Emily Lakdawalla of the Planetary Society, via http://www.planetary.org/blogs/emily-lakdawalla/2008/1634.html, all credits as follows: NASA / JPL / Ted Stryk except: Mathilde: NASA / JHUAPL / Ted Stryk; Steins: ESA / OSIRIS team; Eros: NASA / JHUAPL; Itokawa: ISAS / JAXA / Emily Lakdawalla; Halley: Russian Academy of Sciences / Ted Stryk; Tempel 1: NASA / JPL / UMD; Wild 2: NASA / JPL
Here are some of the larger asteroids and comet nuclei known in the Solar System; 1.24 trillion tonnes is only about the mass of the asteroid 5535 Annefrank, or one of the smaller asteroids in this montage. It’s larger than Dactyl and smaller than Ida, and denser than any of the cometary nuclei like Halley or Tempel.
In fact, if we were to compare 5535 Annefrank with Earth — an Alderaan-sized planet — it would be about one tenth the size of what Ida looks like.
Image credit: Matt Francis of Galileo’s Pendulum, via http://galileospendulum.org/2012/03/05/moonday-a-bite-sized-moon/
In other words, the “antimatter” asteroid that would theoretically destroy an entire planet would barely be a single pixel in the above image!
It’s not completely inconceivable that such a small amount of antimatter could be generated and fired at a planet! Storing that much antimatter in a Death Star-sized object might be the hard part, but here’s the thing: just like matter binds to itself through the electromagnetic force and — if you get a large amount of “stuff” together — through gravitation, antimatter behaves exactly in the same way.
We’ve been able to create neutral antimatter and store it, successfully, for reasonably long periods of time: not mere picoseconds, microseconds or even milliseconds, but long enough that it’s only our failure to keep normal matter away from it that causes it to annihilate in short order.
It isn’t unreasonable that an advanced technological civilization — one that’s mastered hyperdrive and faster-than-light travel — could harness, say, the energy from an uninhabited star and use it to produce neutral antimatter. The way we do it on Earth in particle accelerators is relatively simple: we collide protons with other protons at high energies, producing three protons and one antiproton as a result. That antiproton could then be merged with a positron to produce neutral antihydrogen. You might wish for rocky, crystalline structures based on elements like silicon or carbon, but under the right conditions, hydrogen can produce a crystal-like structure.
The quark structure of the proton. The color assignment of individual quarks is arbitrary, but all three colors must be present. Forces between quarks are mediated by gluons
The quark structure of the antiproton.
Image credit: NASA/R.J. Hall, via http://en.wikipedia.org/wiki/File:Jupiter_interior.png
In the interiors of gas giants like Jupiter and Saturn, the incredibly thick hydrogen atmosphere extends down for tens of thousands of kilometers. Whereas the pressure at Earth’s atmosphere is around 100,000 Pascals (where a Pascal is a N/m^2), at pressures of tens of Gigapascals (or 10^10 Pascals), hydrogen can enter a metallic phase, something that should no doubt happen in the interiors of gas giant planets.
If we could achieve this state of matter, hydrogen would actually become an electrical conductor, and is thought to be responsible for the intense magnetic field of Jupiter. All the laws of physics suggest that if this is how matter behaves, and we can do this with hydrogen, then this must also be how antimatter — and hence, antihydrogen — behaves, too.
So all it would take, if you want to destroy an (Earth-like) planet like Alderaan, is a little over a trillion tonnes of metallic antihydrogen, and to transport it down to the planet’s surface. Once it hits the planet’s surface, it should have no trouble clearing a path down near the core, where the densities are highest.
Image credit: Wikimedia Commons user AllenMcC, via http://www.gps.caltech.edu/uploads/File/People/dla/DLApepi81.pdf.
And as matter-and-antimatter annihilate according to E=mc^2, the result is the release of pure energy. So long as it’s more than the gravitational binding energy of the planet — and that’s not a whole lot of antimatter, mind you — the result could be literally world-ending!
Image credit: user Jugus of the Halo Wikia, via http://halo.wikia.com/wiki/Shield_0459. It’s the same idea.
But if you wanted to destroy an entire planet, it would only take a small amount of antimatter to do the job: just 0.00000002% the mass of the planet in question. For comparison, a single antimatter star — and not necessarily a behemoth, but something like a relatively common A-star like Vega — would be able to undo an entire Milky Way-sized galaxy.
When you think about it, it should make you really, really glad that matter won out over antimatter in the Universe, and that there aren’t starships, planets, stars and galaxies made out of antimatter out there. The way the Universe is destructing — slowly and gradually — is more than sufficient as-is.
Leave your planet-destroying comments at the Starts With A Bang forum here!
See the full article,with video, here.
ScienceSprings relies on technology from