[TXnMA]

Indeed, Galileo did not understand everything; not many of us (YT included) do... But, do you really think that Copernican mathematics are used for maneuvering Cassini around Saturn and its moons?

[Lonesome in Massachussets]

Um, no. Neither were Galilean mathematics. Galileo made it point to belittle and insult his indulgent patron over about a matter which he clearly did not understand. Galileo was not a mathematical astronomer. I truly believe that without the Vatican trial, Galileo would be a minor figure in the history of science, inferior probably to Edmund Halley or even Robert Hook.