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As in the case of Pluto and its moon Charon, both the bodies are tidally locked to each other, will the Earth ever be tidally locked to the Moon? Is there any effect on the rotation of the Earth because of the Moon that may cause tidal locking of Earth to the Moon?

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As explained in this article by Neill DeGrasse Tyson, the tidal forces between the Earth and the moon do indeed slow down the rotation of the Earth each year, the same process that caused the moon's rotation to become tidally locked with its orbit of the Earth. This effect would eventually cause the Earth's rotation to be tidally locked with the moon as well, if nothing else interfered with the system. However, wikipedia says in the Tidal acceleration article that the process of the Earth's rotation slowing down until it becomes tidally locked with the moon will not have completed before the time the Sun becomes a red giant and likely swallows both of them:

About 2.1 billion years from now, the continual increase of the Sun's radiation will likely cause Earth's oceans to vaporize,[11] removing the bulk of the tidal friction and acceleration. Even without this, the slowdown to a month-long day would still not have been completed by 4.5 billion years from now when the Sun will probably evolve into a red giant and likely destroy both Earth and the Moon.[12][13]

The article references the books Solar System Dynamics by Murray and Dermott, p. 184, which can be read on google books here--the book calculates a time of around 50 billion years for the Earth's rotation to become tidally locked with the moon, although they mention that "for heuristic purposes, we treat the orbit of the Moon as equatorial and neglect the influence of the solar tides", and presumably they don't take into account the vaporization of the oceans mentioned in the wiki article, and I'm also not sure if they take into account the fact that the moon's orbital radius is slowly increasing over time as discussed in this article (and also in the Tyson article above). But these latter two effects would only lengthen the time needed for tidal locking, I would think.

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