" In Galileo's time, to depict the world as lacking an absolute physical reference point was, so to speak, inconceivable. And since the cosmos, as it was then known, was contained within the solar system alone, this reference point could only be situated
in the Earth or in the Sun Today, after Einstein and within the perspective of contemporary cosmology, neither of these two reference points has the importance they once had. This observation, it goes without saying, is not directed against the validity
of Galileo's position in the debate; it is only meant to show that often, beyond two partial and contrasting perceptions, there exists a wider perception which includes them and goes beyond both of them." John Paul II
There was no reason to apologise insofar as the division between Pope and Galileo was far more nuanced and involved the limits of the Ptolemaic framework through which the original heliostatic astronomers arrived at their conclusions.
". . . the ancient hypotheses clearly fail to account for certain important matters. For example, they do not comprehend the causes of the numbers, extents and durations of the retrogradations and of their agreeing so well with the position and mean
motion of the sun. Copernicus alone gives an explanation to those things that provoke astonishment among other astronomers, thus destroying the source of astonishment, which lies in the ignorance of the causes." Kepler, 1596, Mysterium Cosmographicum
The recent resolution for the direct/retrograde motions of Venus and Mercury using the central Sun as a stationary reference no longer requires an appeal to the Ptolemaic framework and its secondary use to conclude that the planets move and the Sun is
central to all those motions.
https://www.youtube.com/watch?v=w2uCtot1aDg
On the death of the Pope today, the complex relationships remain as unattended as they did at the time of Galileo, even though a satellite tracking with the Earth resolves these important matters.
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