I am a non-native English speaker. Since school, I was taught "on the earth" is equal to "in the world", and "on earth"'s meaning should be "indeed". But nowadays, I find "on earth" has replaced "on the earth" in many articles. So I want to make sure is it right to use "on earth" to replace "on the earth"?
The word earth is commonly used to mean two things 1) soil, dirt, the substance that keep the trees upright and help you to grow beans and tomatoes, the material of the world; the ground, the world 2) the second meaning of earth is the planet Earth; a member of the Solar system of the planets; the third orb from the Sun. (that is called Astronomical sense)
When it is used in astronomical sense (2) it takes the definite article the and it is capitalized at the same time.
What on earth you are talking about? Means what you say is astonishing, or clarify your meaning, it is not easily understandable. Down to earth means humble, and approachable. come down to earth means be real, stop being high and mighty etc.
on the earth DOES NOT MEAN equal to;
on earth DOES NOT MEAN indeed
Not in American speech anyway.
Following usage manuals are gold standard, recognized and highly regarded and used in the USA.
New Oxford Style Manual :NOSM
Fowlers Modern English Usage (Burchfield Editor): FMEU.Bu.
Merriam-Webster Dictionary of English Usage: M-W.DoEU
Garners Modern American Usage: GMAU Published by Oxford by Brian Garner and
NYT Manual of Style and Usage: NYT-SM, Editor dos NYT
Earth: NOSM: Capitalize only in astronomical contexts, and in a list of planets.
FMEU.Bu.: Frequently with the initial capital when considered as a planet of the solar system; in such contexts like Mars, Venus it is normally used without the definite article (but the Planet Earth)
GMAU : in reference to planet we live on, earth is usually preceded by the and is not capitalized. But when Earth is referred to as a proper noun it is capitalized and it stands alone!
In reference to the stuff that the planet is made of Roy Copperud states lower case earth without the means soil.
The excavation is left large pile of earth. The American Usage and Style: The Consensus p.117 1980
NYT-SM: Lowercase except in the specialized context of astronomy. Particulary in juxtaposition with other bodies:
How do Mars and Earth fit in that pattern.
So the summary is even the GURUs do not agree 100 % !
Except capitalize when you mean the Planet Earth: everyone seems to agree on that one.