Excerpts from the Wikipedia article on Tycho; you can see Tycho, the greatest naked-eye astronomer, was a proponent of some incorrect assumptions:
Kepler tried, but was unable, to persuade Tycho to adopt the heliocentric model of the solar system. Tycho advocated for a system with an unmoving Earth for reasons of physics, astronomical observations of stars, and religion.
In regards to physics, Tycho held that the Earth was just too sluggish and heavy to be continuously in motion.
Tycho used basic geometry to show that,
assuming a small parallax that just escaped detection, the distance to the stars in the Copernican system would have to be 700 times greater than the distance from the sun to Saturn. Moreover, the only way the stars could be so distant and still appear the sizes they do in the sky would be if even average stars were gigantic — at least as big as the orbit of the Earth, and of course vastly larger than the sun. And, Tycho said, the more prominent stars would have to be even larger still. And what if the parallax was even smaller than anyone thought, so the stars were yet more distant? Then they would all have to be even larger still.[59] Tycho said
Deduce these things geometrically if you like, and you will see how many absurdities (not to mention others) accompany this assumption [of the motion of the earth] by inference.
Whether or not other scientists accepted the heliocentric theory depended in part on their religious beliefs and pressures from the Catholic church; from the Tycho Wikipedia article:
Persistence of the Tychonic system, especially in Catholic countries, has been attributed to its satisfaction of a need (relative to Catholic doctrine) for "a safe synthesis of ancient and modern". After 1670, even many Jesuit writers only thinly disguised their Copernicanism. But in Germany, Holland, and England, the Tychonic system "vanished from the literature much earlier"
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There is a difference in the amount of retrograde motion observable in the inner planets compared to the outer planets which is best explained (in the sense of Occam's razor) by the heliocentric model. This difference was known, but the implications may have been resisted, in Galileo's time. It was the retrograde motion, at least in part, that motivated Ptomely's epicycles.
For those interested, a review of this material is at:
http://www.opencourse.info/astronomy/introduction/05.motion_planets/
Fascinating as this may be for some of us (me, for example) I agree we should drop this discussion because it is deviating from the thread topic. But let's be aware of the important scientific and logical principles involved; the logical principles are not dissimilar to those that apply to any complexity, including the investigation of murder/rape cases.