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  • 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.

Hello, it's Scott Manley here. Now, I love the Star Wars movies.

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あなたは惑星を破壊するためにどのくらいのパワーが必要ですか? (How Much Power Do You Need To Destroy A Planet?)

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    Harvey Pan に公開 2021 年 01 月 14 日
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