Back to the original question, I quote from the ultimate authority -- namely, our own BA in his new book.
He discusses
tidal evolution, that is, the way the tides affect the Earth-Moon system. He explains that Earth's rotation is slowing, and that eventually it will rotate once a month, keeping the same face toward the moon at all times.
But...
Quote:
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...by the time all this happens, the Sun will be well on its way to turning into a red giant, frying the Earth and the Moon.
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This suggests we're talking about several billion years.