No cities on the Moon: a billion tons of water is not enough for sustainability

We show that, with reasonable consumption rate estimates, that (1) power is not a strong constraint on the lunar population but (2) the roughly 1 billion tons of water potentially present in the Permanently Shadowed Regions near the lunar poles is insufficient to support a population of one million using ISS-level (98%) recycling for more than about one century. Unless recycling can be improved by factors of about 10, or a similarly greater water supply is discovered, this result precludes large-scale long-term human habitation of the Moon.