"Apsis" is the technical term for this, and can stand for either of two things. The one of interest to us and with respect to the body involved is called "perigee". An astrologer named Richard Nolle is perhaps responsible for the common term that came into prominence.
What term?
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"Supermoon". "Apsis" is when an object is nearest or farthest to the entity it orbits. "Perigee" is when the moon is closest (the "peri-") to the earth (the "-gee").