Questions regarding Luna, Earth's moon and only natural satellite.

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Multiple apparent lunar eclipses last night

I saw something very strange last night that I'm hoping someone can help me explain. I was sitting on my roof with a night-cap at about 3am last night. The moon, about the last quarter, was low in the ...
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In 2016, the summer solstice will coincide with a full moon. How often does this happen?

I found that the solstices work on a 400 year cycle based on this. I can't find anything similar for the lunar cycle. Is there a formula I can use to calculate the date of the full moon?
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Any new info about solar flares hitting the Moon added by the LADEE mission?

This article from 2011 mentions simulations about the sputtering effect caused by a solar flare hitting the Moon: "We found that when this massive cloud of plasma strikes the moon, it acts like ...