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

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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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Connection between Earth, Moon, Theia, and astroid belt?

Are there other fragments aside from the Moon that resulted from the collision of Earth and "Theia" (as it's called in recent main-stream press stories)? And if not, why not? And what happened to ...
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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 ...