Judah D. answered 12/27/24
Versatile Tutor Offering Expertise in Math and Physics
Plato, like many others at the time believed the earth was the center of the universe and subscribed to a geocentric model, where everything orbits around the earth. Further, Plato believed the orbits of the planets and stars to be circular as he viewed this as the simplest kind of endlessly periodic motion. To his credit, the stars in the night sky did seem to sweep out circles about the north star, however, this model could not accurately describe the motion of planets very accurately. Mars would repeatedly move back in forth in what we now call "retrograde motion" and this description also couldn't accurately predict the motion of the moon or sun. To fix this Plato insisted on "epicycles", where planets would circle around smaller orbits within their orbit, creating a spirograph-type orbital shape. This model was inevitably flawed and required an absurd amount of fine-tuning (finding the radius of the epicycle, then the period of the epicycle, etc.) just to get sub-par accurate results for the orbital motion of the planets.
That being said, no other model at the time was taken seriously really until Copernicus proposed his heliocentric model, although it was first arguably written down by Aristarchus. Even then, it was only accepted once Galileo observed the phases of Venus, a phenomenon that could only be accurately described with a heliocentric model, rather than epicycles, as it required venus to orbit about the sun. With the additional work of Kepler finding that planets did not orbit in perfect circles like Copernicus believed, but actually ellipses - a special kind of curve - finally made our model of orbital mechanics extraordinarily accurate out to the farthest reaches of the solar system and beyond in the non-relativistic limit.