Final answer:
The apparent planetary motions are explained by Kepler's laws, stating that planets move in elliptical orbits with the Sun at one focus, not by uniform circular motions as previously thought in the Ptolemaic system.
Step-by-step explanation:
The apparent motions of the planets can be accounted for by assuming they move in elliptical orbits with the Sun at one focus, according to Kepler's laws of planetary motion.
Initially, the Ptolemaic model, with its epicycles and deferents, explained planetary motion as uniform circular motions. Later, astronomers realized that this model was not sufficient to accurately represent the observed behaviors of the planets. It was through Tycho Brahe's accurate observations that Johannes Kepler was able to derive three fundamental laws of planetary motion which took into account that planets travel in elliptical orbits, not perfect circles.
Furthermore, Isaac Newton's universal law of gravitation and his laws of motion explained why these planetary orbits occurred, attributing the motion to gravitational forces and inertia. Kepler's first law states that planetary orbits are ellipses with the Sun at one focus, emphasizing non-uniform, elliptical motion rather than uniform circles. This marked a significant shift in understanding and laid the groundwork for modern astronomy.