How did Ptolemy’s lunar theory improve on earlier Greek astronomy?

Ptolemy’s primary contribution to lunar theory was the completion of a fully predictive model, building upon the foundational work of his predecessor, Hipparchus. While Hipparchus had successfully identified the Moon's periodicities and confirmed them using historical eclipse records, he left the task of creating a comprehensive, predictive mathematical framework unfinished.1

In his seminal work, the Almagest, Ptolemy addressed the complex motion of the Moon in Books 4 and 5. By applying rigorous geometrical methods, he developed a model that could accurately predict the Moon's position and behavior, including its varying speed and its divergence north and south of the ecliptic. This advancement provided the numerical precision necessary to apply his theories to the prediction of solar and lunar eclipses with greater success than earlier Greek attempts. Ultimately, Ptolemy’s work transformed lunar and planetary astronomy into a highly accurate, predictive science that remained the standard for over 1,400 years.213