Callippus of Cyzicus ( c.370 BC – c.310 BC) was a Greek philosopher and a pupil of Eudoxus’ school of astronomy. His main achievement was an extension of Eudoxus’ homocentric sphere model which attempted to explain the motions of the Sun, Moon, planets and fixed stars in terms of a system of spheres centered on the Earth.

By introducing 7 new spheres to the 27 required in Eudoxus’ model, Callippus was able to achieve a level of accuracy for the planetary orbits that was as good as the available observations! The additional spheres added to the Sun accounted for the varying velocity of the Sun during the year – a notable failing of the earlier model.

The table below summarises the number of spheres requried in Callippus’ model.

Object Eudoxus Callippus
The Sun 3 5
The Moon 3 5
Mercury 4 5
Venus 4 5
Mars 4 5
Jupiter 4 4
Saturn 4 4
Fixed Stars 1 1
Total 27 34

Callippus also made accurate measurements of the lengths of the seasons, and was able to bring the solar and lunar years into alignment through a Callippic period of 76 years. His cycle combined 441 × 29-day months (12,789 days) and 499 × 30-day months (14,970 days), giving a total of 27759 days. Dividing this by 76 years gave an estimate of the tropical year (the length of time between successive equinoxes) of 365.25 days, a duration that has been used ever since.

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