This is getting too far into the weeds on judging Ptolemy's intentions and motivations. It also applies more modern standards of scientific rigour to work that

This is getting too far into the weeds on judging Ptolemy's intentions and motivations. It also applies more modern standards of scientific rigour to work that was done before they existed. This is a common anachronism (and fallacy) people make throughout history. the heliocentric view was known long before Ptolemy I am aware that Aristarchus of Samos put forth a heliocentric view. Unfortunately for him, it wouldn't be until the development of Kepler's Laws (ca. 1609-1619) that a heliocentric model could be made to yield better predictions (in all cases) than the Ptolemaic model. Yes, even though Copernicus developed the more modern heliocentric theory (before 1543) he could not reduce the errors in his predictions because he held onto the assumption of perfect circular orbits dating back to Plato. Few astronomers at the time accepted his theory, and even Tycho Brahe (who you cite) constructed his own model which was mathematically equivalent to Copernicus's but placed the Earth at the centre of the system.