@SRM sure, we've got some black paint, and we might be able to craft some paint bots. However... Moon's surface area is about 85% of that of Asia. That's a lot of paint - and remember that Moon already is pretty much "black" already, so acrylic paint won't cut it. And Vantablack is bloody expensive.

I think defending it is significantly easier than 25%. If you've got the budget to put stuff on the moon, obtaining a nuclear device or even conventional warhead that you can use to threaten earth would be quite simple. At the Moment, the ownership of the moon is not important enough that any major country would risk antagonizing a nuclear power with a "legit" claim

@JohnDvorak just need mirrors angled away from Earth. All you’re trying to do is make the moon not shine on Earth. So you can manufacture them here and ship ‘em up. Installation should be straightforward. If budget isn’t a limitation (per the question) then the plausibility of this method is pretty high, IMHO.

@SRM, plausbility of hiding is 0, because you can't hide it's gravity and you can't actually hide its thermal radiation either—it isn't called “black body radiation” for nothing. So it will only look stolen to normal people, but not to astronomers and people of power will know well what is going on from astronomers. I also doubt anybody will actually care—so you've painted moon black, and?

@JanHudec at least, we could finally answer this question…

@JanHudec Not to mention it'd be a black spot in the sky, night and day. We would also notice tides have gone nowhere, and if you have some probes, rovers or satellites functioning around there, that'd be another tell. It'd be like trying to convince someone the Moon doesn't exist.

Duh, no mandatory xkcd what-ifs? Sounds good for stealing the Moon (well, not sure if it will be "usable" after that though)

@Holger Surely it was the Rolling Stones? "I see a full moon and I want to paint it black..."

@JohnDvorak Well that's step 1 of your evil plan: invent a cheap way to create gigatons of Vantablack.

@F1Krazy they said they want but didn’t admit having done it

@JanHudec Who cares about the thermal signature? It's the nightly presence in the sky that is the point of the theft.

To further elaborate on why you need a dyson sphere: If you had the mass of the earth in fuel (5.972e24 kg), and strapped today's most efficient (liquid-oxygen) engine to the moon, it would still not be enough (6.807e24 kg) to bring the moon to escape velocity. But then again, if you get all your fuel from earth...

@JanHudec, I'm not sure how much humans will care if moonlight goes away (but at least some will, for various "reasons of principle" if nothing else), but I'm pretty sure it will have adverse effects on animals and possibly plants.

Re "it wouldn't be any harder to move", Is that accidentally negated?

"Hiding to pretend it was stolen", aside from "still obscuring part of the sky" and "gravity", also has the problem that, unless you have some technology to make the hiding more or less instantaneous, you'll be seen in the process of hiding it, making it even more unlikely that anyone will believe you.

"Hide The Moon" could be improved if the self-replicating nanobots were built with cameras & projection screens. Durning construction, the nanobots would display what its own camera showed behind it, rendering them invisible to @JanHudec's "normal people" (if the tech is good enough), since they could still see the projection of the moon. When enough robots are built to cover the moon front & back, then the cameras behind the moon could capture the starfield for the robots in front of the moon to project to Earth. Voilà! Now the populace might be fooled long enough to be incited to panic...

Additional problem for shrinking Moon: copyright violation. You'd get sued to smitherens by Universal Studios

You can move the moon by essentially converting it into a rocket (xkcd tip: what-if.xkcd.com/13 and I hope you're not too concerned with Earth). Also, there's a Justice League cartoon episode where some bad guys cloak a planet in order to convince some judges that a main character had destroyed the planet and all living things on it. So, just cloaking it somehow would be pretty useful... and that technology is slowly becoming more and more feasible every year (although not to a planetary scale).

Vantablack "hides" it by absorbing light. This is going to cook the moon. It will either disintegrate the paint, or burn up the moon. The lack of atmosphere is going to make heat management a big problem. Vantablack already has heating problems on earth; it'll only get worse on the moon. One way or another you're just shifting the radiation from the visible spectrum to the heat spectrum.

@AlmaDo sounds like a better fit for the "How To" book

An easier way to hide it would be to simply put up a satellite at the L1 point (or really anywhere on the line between them, L1 just requires the least energy to keep stable, but you could go even smaller if closer) big enough to block any light reflected off the moon towards us. This is far more feasible than covering the entire Earth-facing surface of the moon. It would still not affect the gravitational pull, and would leave a black spot in its place, the latter possibly mitigated by displaying an image of the stars behind the moon on a large screen as LHM suggested.

I think you are under rating shrinking the moon. Never underestimate mankind's ability to make ever bigger nukes!

TOW THE MOON: Redirect a constant stream of asteroids, comets, and planetesimals so that they buzz past the moon, slowly altering its course due to gravitational interaction until it breaks orbit. Then continue buzzing it with big rocks so that it goes where you want it to go. FLY AWAY WITH THE MOON: Install large light-sails on the surface of the moon, and hit the sails with a high-energy laser, such as can be built out of mirrors installed around the sun. Bonus points if you supercharge the laser's beam by looping it around a black hole.

A lot of the suggestions for hiding the moon are going to generate a lot of questions the first time there's a solar eclipse.