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The dates given for his birth and death are guesses but Callippus of Cyzicus is known to have been working with Aristotle in Athens starting in 330 BC.
We know that Callippus was a student of Eudoxus. We also know that he made his astronomical observations on the shores of the Hellespont, which can be deduced from the observations themselves.
Callippus made accurate determinations of the lengths of the seasons and constructed a 76 year cycle to harmonise the solar and lunar years which was adopted in 330 BC and used by all later astronomers.
The Callippic period is based on the Metonic period devised by Meton (born about 460 BC). Meton's observations were made in Athens in 432 BC but he gave a length for the year which was 1/76 of a day too long. The relation between Callippus's period and that of Meton are explained in [Encyclopaedia Britannica] as follows:
Callippus of Cyzicus (c. 370300 BC) was perhaps the foremost astronomer of his day. He formed what has been called the Callippic period, essentially a cycle of four Metonic periods. It was more accurate than the original Metonic cycle and made use of the fact that 365.25 days is a more precise value for the tropical year than 365 days. The Callippic period consisted of 4 X 235, or 940 lunar months, but its distribution of hollow and full months was different from Meton's. Instead of having totals of 440 hollow and 500 full months, Callippus adopted 441 hollow and 499 full, thus reducing the length of four Metonic cycles by one day. The total days involved therefore became (441 X 29) + (499 X 30), or 27,759, and 27,759 / (19 X 4) gives 365.25 days exactly. Thus the Callippic cycle fitted 940 lunar months precisely to 76 tropical years of 365.25 days.The Callippic period contributed to the accuracy of later astronomical theories.
Callippus introduced a system of 34 spheres to explain the motions of the heavenly bodies. The Sun, Moon, Mercury, Venus and Mars each had five spheres while Jupiter and Saturn had four and the stars had one. This increased the accuracy of the theory while preserving the belief that the heavenly bodies had to possess motion based on the circle since that was the 'perfect' path.
References (2 books/articles)
References elsewhere in this archive:
There is a Crater Calippus on the moon. There is also a Rima Calippus. You can see a list of lunar features named after mathematicians.