What was Galileo's relationship with Copernicus's ideas?

Copernicus published his famous work, On the
Revolutions of the Heavenly Bodies in 1543 when he was on his deathbed. He
did not wish to create a stir with religious authorities, and in fact dedicated his work
to Pope Paul III. He never viewed the stars through a telescope, but rather determined
all his calculations mathematically. His most important finding was that the solar
system was heliocentric, not geocentric as Aristotle had claimed. In making this
statement, he wrote

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In the middle of all this sits the Sun enthroned.
How could we place this luminary in any better position in this most beautiful temple
from which to illuminate the whole at
once?

There were a number of
errors in his determinations; for instance he believed that the Universe was finite,
that the planets revolved around the sun in perfect circular orbits, and that the
earth's rotation caused the movement of the stars.

Galileo
attempted to reconcile Copernicus' theory with the teachings of the church; however he
was quite stubborn. When church authorities disputed his insistence that the universe
was completely mathematical ( a conflict with the church's teaching) he mocked church
authorities. This is inconsistent with Copernicus, who avoided conflict with the church.
In a letter to Johannes Kepler, another pioneer in astronomy, Galileo
wrote:

Here at
Padua is the principal professor of theology, whom I have repeatedly and urgently
requested to look at the moon and planets through my glass, which he obstinately refused
to do. Why are you not here? What shouts of laughter we should have at this glorious
folly!

When Church
authorities condemned Galileo's work, he responded by publishing Dialogue
Concerning Two Systems of the World, Ptolemaic and Copernican. He suggested
in the work that Copernicus was correct and those who followed the Ptolemaic theory
(largely along Aristotelian lines) were fools; he even referred to the proponent of
Ptolemy's ideas as "Simplico," a thinly veiled reference to Pope Urban VIII who had been
Galileo's friend. Urban repaid Galileo by having him arrested by the Inquisition. Under
threat of torture, he recanted all his previous theories and was ordered to remain under
house arrest for the remainder of his life. Stubborn and feisty to he end, before
entering his virtual prison and seeing the skies for the last time, he looked up and
said of the earth, "It's still moving."