Final answer:
There was a span of over 1,200 years between the acceptance of the geocentric theory and the heliocentric theory, but it took nearly 300 years from Copernicus's proposal for the heliocentric model to be universally acknowledged.
Step-by-step explanation:
The period between the acceptance of the heliocentric theory, proposed by Nicolaus Copernicus, and the ancient geocentric model, endorsed by Ptolemy, spans over a considerable amount of time. The geocentric model was the accepted cosmological system for more than 1,200 years following Ptolemy's death. It wasn't until Copernicus put forward his heliocentric theory in 1514, suggesting the Sun, not the Earth, was at the center of the universe. This idea, however, was debated and tested for many years due to a historical reliance on philosophical thought over empirical observation, as advocated by the long-standing tradition carried by the Catholic Church and ancient Greek philosophy. It would take nearly 300 years for the heliocentric model to be universally acknowledged as correct, following observational evidence provided by astronomers like Galileo.