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How did the eccenter model explain the Sun’s changing apparent speed?

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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.

The eccenter model explains the Sun’s changing apparent speed by positing that the Sun travels at a constant speed along a perfect circular path, but the center of that circle is slightly displaced from Earth.12

Because the center of the Sun's orbit is off-center relative to Earth, the distance between the Sun and Earth varies throughout the year. When the Sun is at its closest point to Earth, it appears to travel more rapidly across the zodiac; conversely, when it is at its farthest point, it appears to move more slowly.12

Hipparchus was the first to successfully calculate the direction and magnitude of this displacement, determining that the off-centeredness of the Sun’s circle was approximately 4 percent of its radius. He based these calculations on the observed, unequal lengths of the seasons, providing a geometrically accurate model that remained standard in astronomy until the 17th century.13