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How did Hipparchus explain the unequal lengths of the seasons?

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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 explained the unequal lengths of the seasons by proposing that the Sun travels at a uniform speed along a circular path whose center is slightly displaced from Earth, a model known as an eccentric circle.12

While the Sun maintains a constant velocity, its off-center orbit causes it to appear to move more rapidly through the zodiac when it is closest to Earth and more slowly when it is farthest away. By utilizing the observed dates of two equinoxes and a solstice, Hipparchus was able to calculate both the direction and the magnitude of this displacement, which he determined to be approximately 4 percent of the orbit's radius. This mathematical model successfully accounted for the observed irregularities in the seasons and remained a standard in celestial mechanics until the work of Johannes Kepler.21