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It is my understanding that the Church told Galileo that it would be
okay for him to say that it is much easier to describe/predict the
motion of the planets in an inertial reference frame centered on the sun
but that he should not say that the sun IS the center of the solar
system / universe. Galileo was championing a good model for
understanding the motions of the planets but he refused to simply claim
that it was a good model and insisted on claiming that it was reality.