To estimate how long it would take a highly technologically advanced civilization to disassemble the moon, note that the energy needed is under an hour of the Sun's power output, but that (in the absence of unexpected other energy sources) they'd first have to build all the infrastructure needed to harvest this energy. Section 4.2 of Eternity in Six Hours estimates 31 years of exponentially scaling up to turn Mercury into a Dyson swarm, but this seems to depend crucially on the assumption that it (repeatedly) "takes five years to process the material into solar captors and place them in the correct orbit", and I don't understand what those five years are needed for and suspect the authors were being extremely conservative for rhetorical purposes. I don't understand what the limits are on industrial doubling time given superintelligence, but the end of this post is relevant. A doubling time under a week seems to imply a Dyson swarm in under a year, but I don't know and maybe I've missed something. Then you have to add this to uncertainty about time to AGI or similar technologies, takeoff speed, and uncertainty about whether the resulting agent or agents will want the Moon to continue to exist. All things considered, I'd say it's more likely than not that the Moon will still exist in 2039, so it's fine and there's nothing to worry about.
@StevenK What do you mean disassemble the moon? Seems like there should be easier ways to destroy the moon. In three body problem aliens launched a particle at near lightspeed to destroy a star and the explosion destroyed the nearest few planets. Someone might do the same to our star
@StevenK Some pushback against the fast disassembly times in Eternity in Six Hours here, with a response from one of the authors. (Note there's some confusion about different versions.)
In the years since we wrote that paper I have become much more fond of solar thermal conversion (use the whole spectrum rather than just part of it), and lightweight statite-style foil Dyson swarms rather than heavier collectors. The solar thermal conversion doesn't change things much (but allows for a more clean-cut analysis of entropy and efficiency; see Badescu's work). The statite style however reduces the material requirements many orders of magnitude: Mercury is safe, I only need the biggest asteroids.
If this is true, then it seems like an update toward it taking less time.