It had been known since Ancient Greek times that the planets didn’t simply travel in circles around the Earth. Instead, they were seen as travelling along “epicycles”, kind of like spirograph shapes. As more celestial bodies were discovered and more detailed measurements of their motion were taken (especially the measurements by Tycho Brahe and his team), these epicycle models became increasingly complicated. The original heliocentric model had the planets travelling in perfect circles around the Sun – this simply wasn’t accurate. But the same new measurements that were causing problems for the geocentric model led to an improved version of the heliocentric model in which the planets have elliptical orbits with the Sun at one of the foci. So now there were two equally accurate models, but one was straightforward and the other was wildly complicated and getting more so over time.
There were various secondary factors too. Observations of comets and of the phases of Venus clearly contradicted certain variants of the geocentric model. Not enough to be a death knell for the whole thing, but enough for various people to recognise that their particular understanding of the planets was wrong and start questioning their astronomical beliefs more broadly. And then the debate was essentially put to rest by Newton outlining a straightforward mechanism that explained why the planets would have elliptical orbits (this is the result you get if you have two bodies attracting each other with a force inversely proportional to the square of the distance between them).
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