Galileo had become friends with the Pope and thought he was granted permission as the Pope seemed favorable but the manner in which Galileo wrote I think offended the Pope here's a brief account and link:
http://www.dsm.fordham.edu/~moniot/galileo_from_a_different_angle/node6.html:
Galileo's book on the two cosmological systems
During the years after the condemnation of the heliocentric theory, Galileo turned to other scientific investigations. It was during this time that he became embroiled in a controversy with the eminent Jesuit astronomer Orazio Grassi over the nature of comets. Grassi supported the view that comets are bodies moving in orbits beyond the moon. Galileo took the opposing view that comets are mere optical effects caused by vapors rising from the earth. Although we now know that Galileo was on the wrong side of the argument, his irony and wit took their toll on his opponent. He had previously gotten into a dispute with another Jesuit, Christopher Scheiner, over the priority of the discovery of sunspots. (Scholars now believe that neither man was the first.) Undoubtedly these controversies helped cement the Jesuits' opposition to Galileo, an opposition that carried no small weight in Rome.
In 1624 Galileo began working on a book laying out the arguments in favor of the heliocentric theory. This book would eventually appear as the Dialogue on the Two Great World Systems. In it, three characters discuss the Ptolemaic and Copernican systems. One character, named Simplicius, presents the Aristotelian position. Another, Salviatus, takes the Copernican side. And a third, Sagredus, listens to the two and weighs the force of their arguments.
One may well ask why, having barely managed to escape a serious penalty in his first brush with the Inquisition, Galileo did not show more caution, but instead followed a course that was likely to get him into trouble again. At least part of the reason was that he could foresee, as few of his contemporaries could, the harm that would be done if the Church persisted in suppressing a doctrine that he knew was true. In an unpublished essay considered by scholars to have been written by Galileo in 1615 or early 1616, he wrote:
On the other hand, if we were to fix only on what seemed to us the true and certain meaning of Scripture, and we were to go on to condemn such a proposition [as the motion of the earth and the stability of the sun] without examining the strength of the arguments, what a scandal would follow if sense experiences and reasons were to show the opposite? And who would have brought confusion to the Holy Church? Those who had suggested the greatest consideration of the arguments, or those who had disparaged them?
Galileo was encouraged to write his book because his friend and supporter, Maffeo Barberini, had been elected Pope Urban VIII in 1623. The two had had a number of conversations, and Galileo was confident that the Pope, an intellectual and a supporter of the arts and sciences, would be amenable to reforming the decree of 1616. In this, Galileo may have allowed his enthusiasm and optimism to get the better of him. It seems that although Barberini respected Galileo, he, like Bellarmine, did not understand the power of the scientific method to arrive with certainty at the truth. His position on the matter is placed in the mouth of the Aristotelian Simplicius at the end of the Dialogue:
I know that both of you, being asked whether God, by his infinite power and wisdom, might [achieve the effects observed] by any other way ..., I know, I say that you will answer that he could, and also knew how to bring it about in many ways, and some of them above the reach of our intellect. Upon which I forthwith conclude that, this being granted, it would be an extravagant boldness for anyone to go about to limit and confine the Divine power and wisdom to some one particular conjecture of his own.
Galileo spoke with the Pope before beginning work on his book, and received encouragement to move ahead with it. Throughout the book there are disclaimers stating that none of the arguments presented are considered conclusive. He was careful to obtain the necessary licenses before having the book printed. (There are no fewer than four imprimaturs following the title page.) But when the book appeared, the impact was tremendous, since it was in such obvious violation of the letter and spirit of the Decree of the Index of 1616. Anyone reading it could tell that this was not an even-handed presentation of the evidence for and against each of the two theories, but a blast intended to destroy the Ptolemaic position and establish the Copernican one.
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