Which sentence in this excerpt from great astronomers shows that ptolemy’s theory was flawed, but that he was still the undisputed authority on astronomy for centuries?

You refer no excerpt or sentence so i hope this explanation would help,
Great Astronomers shows that Ptolemy theory was flawed Because Ptolemy stated that Earth is the center of the universe, he got it wrong because many data proves that Sun is the center of the universe. But he still considered an authority in astronomy because he was a mathematical genius that is the first to predict the movement of the planets

So what's needed to be done?