How long will it take for the Earth to become tidally locked to the Moon?

mofobro

According to an article I read,
http://www.badastronomy.com/bad/misc/tides.html

the earth will one day become tidally locked to the moon the way the moon is locked to the earth today, so that the same face of the earth always faces the moon.

If this is true, how long will that process take?

Chronos

Tidal braking is slowing the earth's rotation by about a millisecond per century. Assuming that was to remain constant, it would take so long for earth to become tidally locked with the moon, our sun would have long since become a white dwarf. We do, however, know the assumption of constant braking is invalid. Tidal braking also causes the moon to receed from earth which will diminish the braking effect over time. We also know that earth will lose its oceans within a few billion years, which will eliminate the source of most tidal braking. In short, the answer effectively becomes nearly eternity.

onomatomanic

A slightly better rule-of-thumb is that the Earth loses a third of its rotational energy per billion years. Over 5 billion years, that yields a factor of (2/3)^5 ~ 32/243 ~ 1/7.5 and hence a factor of between 2.5 and 3 for the rotational period (inverse square dependence on energy). So, if things were to continue going smoothly, the day would be some 60 hours long by the end. However, as Chronos said, the oceans are expected to evaporate long before that, which will make further braking far less effective.