the Sun or the sun?

I was proofreading something that referred to "the Sun," but I wasn't sure if it should be capitalized. My hunch was that it shouldn't be, but when I did a search online, I found conflicting results. For instance, NASA capitalizes it in a student worksheet, but they could be doing that for stylistic purposes. Meanwhile, The Atlantic, which seems to take language and writing seriously, does not capitalize it.

After seeing various examples online, I assumed it's standard practice to not capitalize it, until I saw a discussion on Quora, with an answer by a highly educated science person: "The International Astronomical Union rules in this context, and they say that the names of each planet, each planetary satellite, each asteroid, each comet, each star, each stellar/planetary system, and each galaxy is a proper name and, therefore, a proper noun to be capitalized." Then he says that not capitalizing it is fiction-oriented. But the Massachusetts Institute of Technology, aka MIT, one of the most prestigious science and technical institutions on the planet, instructs people to not capitalize it. And the MLA style guide (by the well-known Modern Language Association) makes the same conclusion.

So I'm assuming it should not be capitalized, thus I corrected what the author wrote. Now that I'm writing about it, it doesn't seem like a big deal, but when I saw it, it made me think about it for the first time, since I don't usually have to deal with the issue. I even discussed it with a professional writer, who didn't really know the answer either, which made me even more curious and concerned about doing the right thing.