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For every year, the moon is orbiting further away from earth.

What distance has the moon been from earth at the closest?

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This may prove difficult to answer since some theories about the formation of the moon state that it was a part of earth that separated when earth got hit by a very large meteorite. If this were true, then the moon was 'inside' the earth so to say –  Eduardo Serra Jan 21 at 22:53
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up vote 4 down vote accepted

If we accept the Giant impact hypothesis, which says that the Moon was once a part of the Earth pushed away by a big impact, the answer is obviously 0.

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Arguably it wasn't yet the Moon at that point, just a cloud of molten or vaporized rock and debris. At some vaguely-defined point, it became a coherent object. I wonder how far from Earth it was at that point. –  Keith Thompson Jan 24 at 22:00
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@KeithThompson It was not, for sure, inside the Roche Limit. –  Envite Jan 27 at 9:15
    
Excellent point. It's likely that much of the debris from the collision was quickly thrown outside the Roche Limit (and that much of the debris that wasn't thrown outside that limit fell back onto the Earth). So the question is, what was the distance of the bulk of the debris at the time when it first coalesced into a single coherent body? A real answer to that question would require running a detailed computer model of the event (something that's probably already been done). –  Keith Thompson Jan 27 at 16:53
    
I think a more interesting interpretation of the question might be, "when the moon first accreted into a discrete body or was captured into orbit, how close was it?" –  Larry Gritz Jan 27 at 17:56
    
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