I have always used "Earth" (capitalized) as a formal noun, referring to our home planet by name. I have always used "earth" as a common noun to refer to what is also called "dirt" or "soil" or "ground." Lately, I've been seeing many instances where the uncapitalized "earth" is used as the formal noun. Most recently, in the current issue of Discover magazine.
Use of the word "moon" has always been inconsistent. When capitalized, it should be Earth's moon, aka "Luna" or "Selene" (depending on your mythology). When not capitalized, it's the generic term for a natural body in orbit around a planet.
Google is no help, since it doesn't seem to distinguish caps, and mainly returns hits about UFOs. I'm still a novice with N-grams, and can't seem to extract any info there.
What's the consensus about when to capitalize "Earth" ???
I wonder if this counts as an instance of "the name of the whole is also the name of one of the parts". Think of "day" = "the sunlit period from dawn to dusk" vs. "day" = "a twenty-four hour period".
Or of "Classical music" = "art music of Europe from 1750 to 1820" vs. "classical music" = "art music of Europe from about the eleventh century to the present".
In my personal writing, I would agree with you about Earth vs. earth. As for Moon vs. moon, I would use Moon to refer specifically to Earth's moon in a planetary sense. I would not capitalize it otherwise. As a rule of thumb, if it makes sense to substitute the noun phrase Earth's moon for the word moon or the words the moon, I would capitalize it as Moon. For example, I would write a full moon, rather than a full Moon, but I would write that Man has only recently set foot on the Moon.
If I write moon in lower case, it could also mean Uranus is visible.
I believe it does not matter what you are referring to, rather if you are using the word as a proper name. The first comparison that came to my mind was "mother." "Let's go see Mother." = proper name. "Let's go see my mother." = common noun. "That woman is a mother." = common noun. In the first two cases mother refers to the same person but one is her name. I have just explained something that everyone likely knows and agrees upon. This compares to earth. "I live on Earth." = proper name. "I live on the earth." common noun. (this one could be debated) "Many believe that there could be another earth somewhere in our universe." = common noun (no debate) I do not believe "moon" fits into the discussion. It is comparable to "planet" which is never capitalized because it is never a proper name. It is often not specified as Earth's moon because it is understood, like "I am going home", obviously my home. Using "earth" to refer to dirt is never capitalized.
Dick, I agree with your comments about Earth/earth. But "Moon" as a proper noun has some convincing etymology. From Wiki:
The English proper name for Earth's natural satellite is "the Moon".[7][8] The noun moon derives from moone (around 1380), which developed from mone (1135), which derives from Old English mÅna (dating from before 725), which, like all Germanic language cognates, ultimately stems from Proto-Germanic *mÇ£nÅn.[9]
The principal modern English adjective pertaining to the Moon is lunar, derived from the Latin Luna. Another less common adjective is selenic, derived from the Ancient Greek Selene (Σελήνη), from which the prefix "seleno-" (as in selenography) is derived.[10]
I maintain Earth's moon is the "Moon." If you want to talk about the "moons" of Mars, they are just "moons" but also have proper noun names (Phobos and Deimos). I will pass on the debate of whether there is another "Earth" in the cosmos. Since that just raises the additional puzzle of capitalizing "Cosmos" or "Universe," which I've also seen used inconsistently in print.