Keep in mind that idioms follow their own rules. Down to earth, what on earth, and move heaven and earth do not capitalize the planet, and four corners of the earth or salt of the earth take the definite article.

“On earth” (e.g. “richest man on earth”) is one of those idioms, so the E is lowercase. See the first entry here.

Idiom:

on earth

Among all the possibilities: Why on earth did you put on that outfit?