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 here.

on earth

used for emphasis. What on earth are you doing?; the stupidest man on earth.

It’s a bit confusing, but they aren’t literally referring to “the planet Earth” in an astronomical sense. If you were writing a sci-fi story and comparing the wealth of the richest man on Earth to, say, the richest man on Mars, then it would be capitalized.