One of the issues with geocentrism that heliocentrism fixed was the existence of epicycles. When viewed from the surface of the Earth, the Moon and Sun have even and continuous motion across the sky. The planets however, have varible speed and often exhibit retrograde motion (where they move backwards through the sky). In a geocentric model one solution was the introduction of epicycles: instead of moving around Earth in rings, the planets orbit in rings-on-rings, like a theme park teacup ride. This motion is complex and proved difficult to explain- no one could come up with a better explanation that “God just likes it that way.” The heliocentrist model eliminated epicycles altogether because the planets are orbiting the Sun in nearly circular orbits, so the bizarre motion is the result of the difference with Earth’s orbit. The simpler planetary motion of the heliocentric model let us develop more comprehensive theories about the motion of bodies in general.
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