Callipus

c. 370-c. 300 b.c.

Greek Astronomer and Mathematician

Callipus is famous for refining the planetary theory of Eudoxus by adding additional spheres. He also made accurate determinations of the lengths of the seasons and constructed a 76-year period to more accurately align the solar and lunar cycles. This Callipic cycle remained the standard for dating and correcting astronomical observations for many centuries.

One of the greatest astronomers of ancient Greece, Callipus was born sometime around 370 b.c. in Cyzicus, located in Hellespontine Phrygia on the southern shores of the Propontis (known today as the Sea of Marmara). According to Simplicius, he studied with Polemarchus (fl. c. 340 b.c.), a former student of Eudoxus (c. 408-c. 355 b.c.). Callipus followed Polemarchus to Athens. He eventually came to live with Aristotle (384-322 b.c.), who encouraged him to devote his efforts to improving the Eudoxean system of concentric spheres.

Plato (c. 428-347 b.c.) first challenged astronomers to explain the apparently irregular movements of celestial bodies in terms of uniform circular motions. Eudoxus accepted this challenge "to save the phenomena" and developed a system of concentric spheres with Earth as their common center. Each planet, as well as the Sun and Moon, was attached to a single sphere. This, in turn, was part of a set of inter-connected spheres, each of which rotated about its own axis at a different rate and orientation. The combined motions were then adjusted to approximate the observed movements of the body in question. Eudoxus employed 27 spheres: three each for the Sun and Moon, four each for the five planets, and one for the fixed stars.

Callipus realized that the Eudoxus's system required the Sun to move with an apparent constant velocity against the background of the fixed stars. This implied that the seasons were of equal length, which was contrary to common knowledge. Based on his own careful observations, Callipus accurately determined the lengths of the seasons. To account for his results, he found it necessary to refine the Eudoxean model by adding two more spheres for each of the lunar and solar models and one additional sphere each for the mechanisms of Mercury, Venus, and Mars. This brought the total number of spheres to 34.

Aristotle further modified this system, but unlike Eudoxus and Callipus, he maintained the spheres were material bodies. Accordingly, certain presuppositions of Aristotelian physics needed to be satisfied. This required 22 additional spheres, for a total of 56. Unfortunately, all concentric-sphere models were incapable of explaining or reproducing certain phenomena, specifically the variation in the apparent diameters of the Sun and Moon and the requirement that the hippopede (horseshoe-curve) of retrograde motion repeat itself exactly from one orbit to the next. Nevertheless, the Aristotelian version of Eudoxus's system survived for many centuries and greatly influenced Hellenistic (Greek) astronomy.

By accurately determining the lengths of the seasons (94, 92, 89, and 90 days respectively from the time of the vernal equinox), Callipus reconciled the lunar and solar calendars. The Athenian astronomer Meton (fl. fifth century b.c.) previously established a 19-year luni-solar calendric cycle. Callipus showed that this Metonic cycle was slightly too long. To bring the calendars into alignment, he combined four 19-year Metonic cycles, dropping one day from each.

The resulting 76-year Callipic cycle provided a much more accurate measure for the year. It also became the reference standard by which later astronomers recorded their observations. The existence of this calendric standard made it possible to correct and correlate observations much more accurately. This in turn greatly contributed to the development of future astronomical theories.

STEPHEN D. NORTON