Final answer:
Ptolemy was responsible for creating the Ptolemaic model, a geocentric system used to predict planetary positions for about 1,500 years until the heliocentric model gained prominence.
Step-by-step explanation:
The individual who developed a system for predicting planetary positions that remained in use for some 1,500 years was Ptolemy. Ptolemy, a Greek philosopher and mathematician living in the second century AD, devised what is known as the Ptolemaic model. This geocentric model, with its complex system of epicycles and deferents, explained the observed epicyclic motions of planets without involving any actual cause and effect.
Despite the lack of simplicity and different rules for each planet, the model's mathematical precision was remarkably reliable for the time, enabling it to persist until it was eventually replaced by the heliocentric model championed by Copernicus, Kepler, and others.