How did Hipparchus study the Moon’s changing motion?

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Engraving of six astronomers, with Hipparchus seated at center and, from left to right, Galileo, Johannes Hevelius, Tycho Brahe, Nicolaus Copernicus, and Ptolemy standing, each holding scientific instruments. — Hipparchus “Six astronomers,” the frontispiece of *Astronomica Institutio* (1692) by Jan Luyts, engraving after drawing by Gerard Hoet. Hipparchus is seated at center with from left to right: Galileo, Johannes Hevelius, Tycho Brahe, Nicolaus Copernicus, and Ptolemy.

Hipparchus studied the Moon’s complex motion primarily to develop a theory of eclipses. He observed that the Moon varies in its apparent speed and periodically diverges north and south of the ecliptic. To account for these distinct periodicities, he utilized values known to Babylonian astronomers and verified their accuracy by comparing historical records of lunar eclipses separated by intervals of several centuries.1

Additionally, in his work On Sizes and Distances, Hipparchus sought to measure the Moon’s orbit relative to Earth’s size. He employed two primary methods:

Parallax observation: He analyzed a solar eclipse that was total in one location and partial in another, attributing the difference to the Moon's parallax against the stars.1
Geometric calculation: He used the visually identical sizes of the solar and lunar discs alongside observations of Earth’s shadow during lunar eclipses to determine the Moon's mean distance from Earth.1

While these efforts provided significant insights, it was later left to Ptolemy to complete a fully predictive lunar model.1