Comment by grues-dinner

The momentum of the Earth-moon system is 3.61x10^34 kg.m^2/s, of which 80% is the moon orbiting and 20% is the Earth (https://space.stackexchange.com/questions/50502/how-much-of-...).

KE = p^2 / 2m

Energy in the Moon's orbit: 5.7*10^45J

Energy in the Earth's orbit: 4.4*10^42J

So the lower momentum of the Earth (with a square term) and its (much) higher mass (Moon is 1.2% the mass of Earth) make Earth over 1000 times less energetic. So it's just the Moon that matters here.

Assume every joule extracted is coming directly from that budget and the moving water wasn't going to hit Scotland and turn some into heat anyway. 15.9 TW is average human energy usage.

5.7*10^45J / (15.9 TW * 1 year) = 1.14 * 10^25

So if we generated ALL human power from this method and every joule was taken from the Moon's orbital energy that would otherwise not be taken, we can spin the system down in just over a ten million billion billion years.

This is actually a bit more than I expected, though I knew it would be a lot from basic common sense of 80 billion billion tons moving at 1km/s. So maybe I've flubbed a few (tens of) orders of magnitude? In particular, the 1000:1 Moon:Earth energy ratio sounds plausible when I think about it, but it still was a bit of a surprise.

In any case, I think it's OK.

Edit, OK, so that was bunk, the orbital energy is 3.8×10^28J, so we can unbind the moon and donate it to Jupiter in only 65 million years.