Somewhat disappointingly, turning the Moon into a disco ball would not do much for anyone here on Earth. (Sigh.) We're just too far away to see more than a very fleeting sparkle. The solution, obviously, is to place a moon-sized disco ball in low Earth orbit, at about the altitude of the ISS. That would give us quite a show, as the video below illustrates.
My question now is, strictly speaking, what exactly is preventing us from building a disco ball the size of the Moon and putting it into low Earth orbit? The video suggests that it's physics, but you know what? Damn physics, let's make it work anyway. Let's come together as a planet and show physics that it has no idea what it's talking about, and build ourselves a giant disco ball. Why? It's simple: if we do this, when the aliens show up in our solar system, they'll see this thing and it'll be so crazy that they'll be like, "Whoa, let's not try and enslave and/or feast upon the animals on that planet; if they can put a huge disco ball in orbit they're capable of anything." And they'd be right.
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