I guess, because Newton could not explain the precession of Mercury that gravitation needed papal approval, especially if Newton ridiculed Ptolemy, which I don't believe he did, although he, like many brilliant people, was caustic.
As for the comet, this reminds me of a Lincolnism, wherein he resisted initial calls for the Emancipation Proclamation by noting that it would be "as effective as the Pope's bull against the comet." Of course, Lincoln did issue the proclamation and initially at least, it was as effective as the "Bull against the comet." There is some doubt whether this bull actually existed - it seems to have been promoted by Laplace, who actually worked out many important equations relating to tides, and a hell of a lot of other things about which Galileo could not have known. Fortunately for humanity, Laplace was not threatened by discredited and absurd priests.
I looked up that asshole Maffeo Barberini on Wikipedia - and I had to look him up, because he's a historical curiosity of no moral or intellectual value - which is about as deep as I'm willing to go.
From what I understand, his real problem was that Galileo put his arguments in the mouth of "Simplicio."
This, um, tortured defense of this awful human being, Maffeo Barberini, who took time out of fighting wars for the papacy to threaten Galileo, seems to make an argument that if I call Roy Moore a childish idiot because he is a creationist, and he has me arrested, then it will be my fault.
One hears some pretty incredible historical distortions on the internet, but this one is, I think, a classic.
Barberini was a big factor in the relative rise of English science, since he made science illegal in Italy, more or less, just as Trump will be a factor in the rise of Chinese science, since science no longer needs just for politicians to leave it alone; it needs politicians to support science, which in China they do.
One really can't take the Holy "See" seriously in this case. The case of Galileo and his relationship with the warrior "Prince" Maffeo Barberini is a disgrace to the Catholic faith, although, apparently, in 1993, the church finally conceded that, um, the Pope wasn't an infallible arbiter of the state of the physical universe and that Galileo wasn't a bad guy after all.
I don't think one can "slander" Maffeo. He was a fool with questionable morals and a swelled head, sort of like the orange idiot of today. This is a fact. He is immune to "slander," since slander is a criticism that has no basis in fact.
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