I read that the lunar orbit undergoes apsidal precession in which the major axis of the elliptic orbit shifts. Does the lunar orbital plane precess as well?
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$\begingroup$ Yes, see the Draconic month, en.wikipedia.org/wiki/Lunar_month#Draconic_month $\endgroup$– Peter KravchukCommented Jul 6, 2016 at 7:01
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Yes, it does. This is known as nodal precession and has a period of 18.6 years. There is a wikipedia article that covers both nodal and apsidial precession of the moon.
Remarkably, this effect was known and accurately measured by the Babylonians in ancient times, since it is important for predicting eclipses.