字幕表 動画を再生する 英語字幕をプリント Hello, it's Scott Manley here. Now, I love the Star Wars movies. When I first saw Star Wars as a four-year-old, it pretty much framed my life and sent me off in my spaceship obsessed course in life. Now, Star Wars movies are actually pretty light in terms of physics and science. They're often misclassified as science fiction, when I prefer to call them high-tech fantasy. But there's one very important question for which we can invoke real-life physics. Just what kind of power does it take to destroy a planet? I mean, three of the seven movies involve devices that are able to destroy planets, and I should mention that there's a couple of minor spoilers here. And, as it turns out, it's pretty easy to figure out how much energy you would actually take to destroy a planet. Indeed, in 2001, a paper addressed this issue by calculating the gravitational binding energy of these spherical planet. You know, physicists love approximating things to spheres, by the way, at least with planets that's closer to reality. And with the gravitational binding energy, it's a pretty simple concept for any Kerbal Space Program player. We know that the escape velocity is the critical speed above which an object will escape to infinity and never fall back. Now, imagine that you grab a rock from the surface of the planet and shoot off at escape velocity. It's an easy equation to figure out how much energy is required. And repeat that, bit by bit, rock by rock, as you go on, you're actually gonna need slightly less energy because as you throw bits into space, there's less mass of the planet left behind to hold them down. But then wait, if you add them all up, using calculus, you get a very simple equation. The energy is 3/5 times the gravitational constant, times the mass of the planet squared, and divided by the radius of the planet. Now, for earth, that number is about 2.25 times 10 to the 32 joules, or in -illion speak, 225 million trillion trillion joules. However, in the same paper, they went on to calculate that for larger planets like Jupiter. The energy would be even higher, something like 2 times ten to the 36 Joules. That said, 2 trillion trillion trillion Joules. The authors hypothesize that the Death Star may, in fact, be able to destroy this by shutting down some of its non-critical system like life support. And they wouldn't put that past the Empire, given there are spotty record on providing basic workplace safety features like handrails. Now, this paper is actually underestimating the power of this technological terror, and by extension, the power of the Force. In Star Wars, we see the destruction of Alderaan, in but a few second, the planet explodes, sending fragments away. But assuming that Alderaan is similar to the earth, that exploding ball of plasma is exploding at many times the escape velocity. Look at this demo in Universe Sandbox to show just how slow escape velocity is when you're comparing it to the size of the earth. It's not particularly dramatic, unless, of course, you're on the surface of that planet. This is, of course, done because Star Wars is a movie, and the audience expects special effects to wow them rather than bore them. If we re-examine the sequence in slow mode, we can see that, within a second, the ball of pulverized planet is about two to three times the size of the original planet. So, the substantial part is moving at over 10,000 kilometers per second. We're dealing with velocities many times higher than the escape velocity, and the gravitational binding energy is really a small correction compared to the kinetic energy required to accelerate a planet's worth of mass up to these speeds. To be fair, this is an explosion, and it's more like a range of velocities. But even if we take, say, a baseline of 1000 kilometers per second, the energy required to obliterate Alderaan in this manner that will satisfy movie goers, is about 3 times 10 to the 36 joules, are, once again, 3 trillion trillion trillion joules. Now, in The Force Awakens, we have a new generation of planet busting super weapon that can project its beam of destruction over interstellar distances and destroy entire solar systems. But, moreover, it's powered by a star, which gives me another opportunity to invoke real physics. Our Sun emits roughly 3.85 times 10 to 26 watts of power, or again, in -illion speak, 385 trillion trillion joules per second, which means that for our law and estimate, it would take about a week of the sun's energy output to obliterate Alderaan, or 250 years, if you look at my higher estimates. Now, in the 10-billion-year life span of a star, that isn't so bad. But I do have some straight out problems with this. Maybe I missed it, but it seems to me that they weren't planning on moving Starkiller Base around. After all, the energy required to move a planet into hyperspace is probably similar to the energy required to destroy a planet by moving its different pieces at several kilometer per second in different directions. But if you had to consume the entire star to do that, then you would need another star, and if it can't move, well, you gonna get another star, it seems like bad planning. I mean, you don't even need mathematics to figure this out. Okay, look, scriptwriters, hello! Look, there's a way to fix this. There are stars that have luminosities that are something like a million times higher than the sun. They're short-lived, but they can generate the energy required for epic planet busting for millions of years, long enough for any movie franchise. Starkiller Base could soak up all the power it wanted to from the outer layers of these stars, and it could then even make the star turn from blue through red to black, as the energy was siphoned off, giving those X-wing pilots a way to gauge how long they had left in a visually arresting style. And then, of course, after the siphoning stopped, the star would return to normal energy output and be ready for firing again in a few days' time. Of course, the scriptwriters never asked me. Regardless, if you really wanna go into planetary destruction to strike fear into the hearts of your enemies, the Empire and the First Order are going way overboard, making millions of voices cry out in terror. It just requires obliterating the top, a 0.1% of the planet near the surface. The other 99.9% of a planet is generally things like magma that isn't particularly hospitable to life. I'm Scott Manley. Fly safe.