It's worth noting that geocentrism wasn't held onto for no reason either. At least the ancient Greeks had solid logical reasons for believing it: if the Earth orbited the sun, then there would be parallax visible between the stars since the Earth's position among the stars is changing throughout the year. Yet, there is none. Therefore the Earth is fixed in space.
The error of course is that the stars are really unimaginably far away and hence there is parallax but it's practically indiscernible. The Greeks thought the stars being that far away was the less likely answer to the apparent lack of parallax than the Earth simply being the center of the solar system.