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Eclipses are possible in KSP, as the Mun isn't in an offset orbit, like the Moon in real life. Because of how the game is made, it does not get dark (unless having the Scatterer mod). However, solar panels will say that they are blocked by the planet in the way and not work. Below are some pictures of a Kerbolar eclipse, as viewed from Kerbin and LKO (Low Kerbin Orbit).

A full Kerbolar eclipse can be observed while landed at KSC starting after game time Year 1, Day 351 - 5h, 40m, and ending (being partial again) somewhere around Year 1, Day 352 - 0h, 22m. Not sure of other occurrences or locations, but this one at KSC is confirmed (unless game times and positions of bodies vary between players). Apparently, a Kerbolar eclipse happens every 6 days, according to a random online source (too lazy to do math or test).