One of the things you learn as you continue to write (and read) is that there are very, very few hard and fast rules when it comes to the finer points of the language.
Take our natural satellite. My instinct is to refer to it as the moon, but a case can be made that while moon is a common noun, when referring to our moon specifically, it becomes a proper noun.
After all, if we lived on Jupiter, each of its moons has an individual name, so we refer to Ganymede, the moon of Jupiter.
Similarly with stars. All stars are suns, but our local star is the Sun.
Or is it?
Not as far as I'm concerned. I understand the argument, but the capitalisation just doesn't work for me. The sun rose this morning, just after the moon looks better to me than The Sun rose this morning, just after the Moon or, heaven help us, The Sun rose this morning, just after The Moon, as some have argued.
Simplicity is generally the best approach in debated cases like this. There is, after all, no doubt what I mean when I write the first sentence. Adding the capitals, in this case, interrupts the flow, so I leave them out.
The AP style (the one I tend to use after twenty years as a tech journalist), is clear about it being lower case, whereas the Chicago Manual of Style (which, in my view, tends to overcomplicate things) favours capitals but does not insist on them. NASA, on the other hand, declares that we must use capitals.
So, as with so many other matters, it's up to you – just be consistent.
By the way, I took the picture at the top of this post 🙂