The idea that medieval people believed in a flat Earth is not true. The shape and approximate size of the Earth was knowm since ancient times (3rd century BC).

Columbus was not turned down at first because people believed he'd fall off the edge of the Earth; they knew he could not have possibly reached Asia, the distance was too great. It was only pure luck (finding America) that saved him. A venture capitalist in those times would have been rational not to buy into the expedition.

As for geocentrism, that has some merits. But note that Ptolemy and his followers were really hindered by a lack of good astronomical data. Using methods of those times, an epicyclical model of the planets was pretty accurate and could have been refined further. The model of Copernicus was deemed superior because it needed fewer epicycles to make the math right. The breakthrough came only after Kepler got the very accurate Huygens observations (taken over 20 years); after he had enough datapoints, he could come up with his famous laws.

And so, let's not blame the Ancients right away. They were not as ignorant as we may believe.