Callippus (; grc, Κάλλιππος; c. 370 BC – c. 300 BC) was a Greek astronomer and

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History O ...

Biography

Callippus was born at Cyzicus, and studied under

Eudoxus of Cnidus Eudoxus of Cnidus (; grc, Εὔδοξος ὁ Κνίδιος, ''Eúdoxos ho Knídios''; ) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his original works are lost, though some fragments are ...

at the

Academy An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy, ...

Plato Plato ( ; grc-gre, wikt:Πλάτων, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greeks, Greek philosopher born in Athens during the Classical Greece, Classical period in Ancient Greece. He founded the Platonist school of thou ...

. He also worked with Aristotle at the

Lyceum The lyceum is a category of educational institution defined within the education system of many countries, mainly in Europe. The definition varies among countries; usually it is a type of secondary school. Generally in that type of school the ...

, which means that he was active in Athens prior to Aristotle's death in 322 BC. 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 Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of consci ...

'' (XII.8), he added two spheres for the Sun, two for the Moon, and one each for Mercury, Venus, and Mars. Callippus made careful measurements of the lengths of the seasons, finding them (starting with the spring

equinox A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and set ...

) 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 Meton of Athens ( el, Μέτων ὁ Ἀθηναῖος; ''gen''.: Μέτωνος) was a Greek mathematician, astronomer, geometer, and engineer who lived in Athens in the 5th century BC. He is best known for calculations involving the eponymo ...

to measure the length of the year and construct an accurate lunisolar calendar. The

Metonic cycle The Metonic cycle or enneadecaeteris (from grc, ἐννεακαιδεκαετηρίς, from ἐννεακαίδεκα, "nineteen") is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year. The recu ...

has 19

tropical year A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time fro ...

s and 235

synodic month In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month. Variations In Shona, Middle Eastern, and Euro ...

s in 6,940 days. The Callippic cycle synchronizes days per orbit and rotations per orbit within the Metonic cycle, noting the difference of one after 4 Metonic cycles, a duration of 76 years. Distinguishing rotations and days infers knowledge of the precession cycle. Callippus started his observation cycle on the summer solstice in 330 BC (28 June in the

proleptic Julian calendar The proleptic Julian calendar is produced by extending the Julian calendar backwards to dates preceding AD 8 when the quadrennial leap year stabilized. The leap years that were actually observed between the implementation of the Julian calendar i ...

). The cycle's begin position, the stellar position and sidereal hour timing the eclipse, are used by later astronomers for calibrating their observations in relation to subsequent eclipses. The Callippic cycle of 76 years appears to be used in the

Antikythera mechanism The Antikythera mechanism ( ) is an Ancient Greek hand-powered orrery, described as the oldest example of an analogue computer used to predict astronomical positions and eclipses decades in advance. It could also be used to track the four-yea ...

, an ancient astronomical mechanical clock and observational aide of the 2nd century BC (discovered in Mediterranean waters off Greece). The mechanism has a dial for the Callippic cycle and the 76 years are mentioned in the Greek text of the manual of this old device. The crater Calippus on the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

is named after him.

References

*Kieffer, John S. "Callippus." ''Dictionary of Scientific Biography'' 3:21-22.

External links

*
Online Callippic calendar converter as used in Ptolemy's ''Almagest''
{{Authority control 4th-century BC Greek people Ancient Greek astronomers Ancient Greek mathematicians Aristotelian philosophers 370s BC births 300s BC deaths 4th-century BC mathematicians