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Aristotle and Ptolemy believed in a geocentric model of the universe, meaning everything orbits the Earth. In this model of the universe, the planets orbit the Earth in perfect circles which didn't explain why planets changed brightness or looked like they were sometimes moving in a different direction. To try and explain these flaws, the model used epicycles, imaginary points moving in imaginary circles with planets orbiting those points.

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Indian astronomer, Aryabhatta,  propounded a heliocentric model in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to a stationary Sun.

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Copernicus developed a Heliocentric model of the universe, meaning that the sun is at the center of the universe. This model also explained that the moon orbits the Earth. It still used epicycles but had planets moving at the same constant speed which would make sense if they were actually moving in perfect circles like the thought.

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Kepler supported the heliocentric model of the universe but he used elipsys for the orbits of planets instead of perfect circles.

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Galileo pointed his telescope at jupiter and observed some of its moons. He also presented compelling information supporting the heliocentric theory when he observed venus's phases.

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The current understanding of the model of the solar system is a heliocentric model where the planets orbit around the sun. To be more exact, everything orbits around the center of mass in the middle of the solar system.