Callippus

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This article is about the astronomer and mathmatician. For the student of Plato and Syracusean tyrant, see Calippus (Syracusean tyrant).

Callippus (or Calippus) (c. 370 BC–c. 300 BC) was a Greek astronomer and mathematician.

He was born at Cyzicus, and studied under Eudoxus of Cnidus at the Academy of Plato. He also worked with Aristotle at the Lyceum, which means that he was active in Athens prior to Aristotle's death in 322. He observed the movements of the planets and attempted to use Eudoxus' scheme of connected spheres to account for their movements. However he found that 27 spheres was insufficient to account for the planetary movements, and so he added seven more for a total of 34. According to the description in Aristotle's Metaphysics (XII.8), he added two spheres for the Sun, two for the Moon, and one each for Mercury, Venus, and Mars.

He made careful measurements of the lengths of the seasons, finding them (starting with the spring equinox) to be 94 days, 92 days, 89 days, and 90 days. This variation in the seasons implies a variation in the speed of the Sun, called the solar anomaly. He also followed up on the work done by Meton of Athens to measure the length of the year and construct an accurate lunisolar calendar. The Metonic cycle has 19 tropical years and 235 synodic months in 6940 days. The Callippic cycle was thought to synchronize the lunar and solar years better than the Metonic cycle, by dropping 1 day after 4 Metonic cycles, a duration of 76 years.

Assuming a synodic month length of 29 days 12 hours and 44+¹/₁₈ minutes, as was commonly used in his era, the Metonic cycle had a mean year of 365 days 5 hours 55 minutes and 25 seconds, whereas the Callippic cycle had a mean year of 365 days 5 hours 36 minutes and 29 seconds. Therefore, compared to the contemporary spring equinoctial mean year of 365 days 5 hours 48 minutes and 52 seconds, the Metonic cycle was too long by 6 minutes and 33 seconds per year, whereas the Callippic cycle was too short by 12 minutes and 23 seconds per year. Thus the absolute error of the Callippic cycle was actually about double the error of the Metonic cycle, because a one day correction per 76 years is too frequent, for it takes around 220 years for the Metonic cycle to drift one day late, or about 11+¹/₂ Metonic cycles per day of drift.

On the other hand, the Athenian calendar New Year began at the summer solstice, and in the era of Callippus the mean summer solstitial year was about 365 days 5 hours 48 minutes and 30 seconds, relative to which the Metonic cycle was about 7 minutes too long and the Callippic cycle was about 12 minutes too short. The superior accuracy of the Metonic cycle vanishes if its cycle length is rounded up to a whole number of days (6940), because that introduces nearly an extra 7+¹/₂ hours of excess length per 19-year cycle.

Calippus had his first cycle start at the summer solstice of 330 BC (28 June in the proleptic Julian calendar). These cycles were used by later astronomers for dating observations.

Calippus crater on the Moon is named for him.