Which ancient astronomer developed a geocentric model of the universe explaining the observable motions of the planets?

Answer: Ptolemy

Explanation:

Ptolemy also called Claudius Ptolemaeus, a Greek mathematician in his theory proposed that the earth was at the centre of the solar system while all other planets revolves round it. This explains the geocentric model of the universe, as " geo" represents earth while "centric" represents 'in the centre of".

Ptolemy