I can explain this!

The oscillating frequency of the earth moon and sun roughly average out over time, and the moon is pretty low density, so it found a roughly equal point in time space.
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I'm not good enough with astrophysics to fact check this, but the immediate question that arose was then ... why wouldn't other moons do the same thing around their planets then? If this was true for our moon, wouldn't we see Phobos and/or Deimos get closer to Mars to create same effect?
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I would guess Air resistance would drag it down if it got close enough for that.
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Depends on the age, frequency and shape. Time averages all things, the moon will go away eventually, but it's still here for now until it changes mass or density (which will happen eventually on its own)
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