The sun had its turn, so now it’s time for the moon.
Moon used to be mona (no, not related to the name, like at all) in Old English, and before that it was menon- in Proto Germanic, and then in Proto Indo European it was me(n)ses-, which meant both moon and month and of course is where month comes from. In fact me(n)ses comes from me-, which means “to measure”, because the phases of the moon used to be a standard of time (which you were probably aware of; one cycle of the moon used to be one month).
Lunar showed up in the early fifteenth century meaning crescent-shaped—it didn’t actually refer to the moon until the seventeenth century! At least, not in English. It’s from the Old French lunaire, which is from the classical Latin lunaris, relating to the moon. Interestingly the word luna showed up before lunar, coming about in the late fourteenth century and actually meaning the moon, coming from the Roman goddess Luna. The word can actually be traced back to the Proto Indo European leuksna-, from leuk-, light (and the origin for most light related words). And hey, the reason lunatic is obviously related is because when it showed up in the late thirteenth century it meant someone with periodic insanity caused by the changes of the moon. In fact it comes from the Late Latin llunaticus, moon-struck.
Selene of course is the Greek equivalent of Luna and although English uses the Latin goddess more, Selene still pops up in places. Selenium, for example, was named for the moon. Selene can also be traced to the Proto Indo European swell-, to shine or beam, and gave us the words swelter and sultry. So. You know. That’s a thing.
Tony Jebson’s page on the Origins of Old English