From Longman Dictionary of Contemporary Englishmoon over somebody/something phrasal verbold-fashionedLOVE to spend your time thinking about someone that you are in love with She sits mooning over his photograph for hours. → moon→ See Verb table
Examples from the Corpus
moon over • It's bad enough that Timothy's mooning over her like a schoolboy, wet behind the ears.• In less unreasonable moments he was disgusted with this mooning over Leanna.• And Alice had better get off her high horse and realize there was more to life than mooning over Lester Stoner.• We could see the moon over the papyrus swamps.• I raise my arm, my finger traces a bird on the shape of the moon over the trees in front of me. 