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Linguofreak

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Or with the sun. ;) I don't know which one dominates, would have to calculate it.

The moon dominates for the moment, but once (or even before) the two are tidally locked, the action of tidal effects from the sun on the whole Earth-Moon system will either start sending the moon back in, or separate it from the Earth. Once the moon separates from or dives back into the Earth, solar tidal effects will eventually cause Earth to lock to the sun (and the moon too, if it leaves Earth).

However, before any of this happens, the sun will expand into a red giant, most likely leading to the destruction of both the Earth and moon.

And even this is only a consideration if the apocalypse doesn't happen first.
 
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