In a manner relating to or coming from outside Earth; in an otherworldly way.
From 'extraterrestrial' + '-ly' (forming adverbs). This adverb developed naturally alongside the adjective in 20th-century science fiction and serious astronomy.
When a sci-fi author wants to say something happened 'in an alien way,' they use this adverb—it's how you describe something that's clearly not following Earth's usual rules.
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