Well, this only made me more curious ;-) So I found a paragraph on the name of the Moon on the Polish wikipedia: https://pl.wikipedia.org/wiki/Ksi%C4%99%C5%BCyc#Nazwa_i_etymologia
With the help of Google Translate I figured out that 'Księżyc' originally only referred to the young moon - between new moon and first quarter. The young moon was regarded as the son of the 'old' moon and thus called 'prince'. :-)
" księżyc, księży, księżna, księga, książę, książęcy, książka, ksiądz" , English translation: moon - priestly, priest's - princess, duchess - book - prince, duke - prince's, princely, duke's - book - priest
My guess is these words are related, because the aristocracy, the nobility and the clergy studied Astronomy through books.
Fyi, although "Earth" is the name of this planet, almost nobody uses it like a name, i.e., without the definite article "the". Just like we don't say "Sun has 8 planets", we don't say "Earth has one moon". It's "The sun has 8 planets", and "The Earth has one moon."
Also, when writing about "the universe", it's not capitalized.
Well, I can find quite a few examples; apart from NASA, how about this one: https://www.forbes.com/sites/startswithabang/2019/07/19/everyone-missed-an-apollo-11-mistake-and-it-almost-killed-the-astronauts-returning-to-earth/#7903ad57cbd8 .
"Universe" doesn't seem to appear in this lesson anyway, but there seems to be some support for capitalising it when referring to the one we're living in.
A quick Google search for the phrase will return vastly more hits with "universe" uncapitalized, and it includes the definite article, e.g.,
https://www.scientificamerican.com/article/the-evolution-of-the-universe/ (in this one, it's capitalized in the title, but, of course, that's a title--everywhere else it's lower case)
https://spaceplace.nasa.gov/universe-slime/en/ (an exercise for kids on the NASA website)
I don't have an account to access the detail pages in the Chicago Manual of Style, but other sites describe what it and other style guides say about capitalization of "earth", "moon", and "sun", e.g.,
There is much argument on the capitalization topic, though, and there is much argument about when to use the proper name "Earth" versus "the earth". So I guess there isn't a hard and fast rule about it when referring to our planet.