Final answer:
The geocentric model was accepted due to early observations and strong philosophical and religious backing. It was challenged as better astronomical instruments and a mathematical understanding of the universe emerged, leading to the development of the heliocentric model.
Step-by-step explanation:
People initially accepted the geocentric model of the universe due to the combination of observations of planetary motion and philosophical and religious beliefs. The Ptolemaic view, which placed Earth at the center with celestial bodies moving in complex circular paths around it, aligned with ancient observations. As an Earth-centered model, it was bolstered by the authority of tradition and religion, which held sway over scientific thought in the era. Astronomical models at the time were descriptive, and the geocentric model was made more precise by adding epicycles, which are small circles on the paths of larger circular orbits, to account for the irregular movement of planets.
Over time, the geocentric model became less persuasive as more accurate observations became possible, leading to the development of the Copernican heliocentric model. It was Johannes Kepler's mathematical approach that supported the sun-centered view, with his laws of planetary motion providing a more precise explanation of the movements of celestial bodies. The transition from a Ptolemaic to a Copernican view of the universe marked the beginning of modern astronomy and the scientific method.