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My understanding is that Brahe was actually trying to find good data
that would verify the Ptolemaic system (or more accurately his and/or
latter day versions of that system.)
I think this was an ambiguous antecedent. Kepler was outside, but
Galileo inside. As I understood Brahe actually was doing his
observations with the support of the Pope, but Kepler ran off with
his notebooks after Brahe's death.
I find it hard to think of Galileo as being outside the influence
of the Catholic Church. He seems like a pretty go insider to me.
He needed some sort of circular inertia to explain the continue
motion of the planets. Just a guess, perhaps he appealed to the
ideal circular motion as why they continued.