Kidinnu
Kidinnu (also Kidunnu) (circa 400 BC - circa 310 BC) was a Chaldean astronomer and mathematician. Strabo of Amaseia in Pontus and Pliny the Elder called him Kidenas or Cidenas.Kidinnu was born in Babylon.
He was a contemporary of Eudoxus of Cnidus and his student Callippus of Cyzicus, and principal of the astronomical school in the Babylonian city of Sippar in Akkad (now Abu Habbah, southwest of Baghdad, Iraq).
Probably Kidinnu had made complex methods and equations for calculating the irregular movements of the Moon and other planets and specially of the Sun. Because he was not as attached as Greek astronomers to the constant velocity of planets he was able to get good approximations for their movements. For the Sun, the apparent angular velocity is a minimum in aphelion, when the Earth is farthest from it. So Kidinnu developed from Nabu-rimanni's System A the more refined system (now called System B) used by the Chaldean astronomers to describe more clearly the motions of the Sun and planets. This system used steadily increasing and decreasing values for the planetary positions, sometimes called the zigzag functions.
For the length of the tropical year Kidinnu used 365d 6h.
About 383 B.C Kidinnu obtained still more accurate values for lunar movements, first calculated before him by Nabu-rimanni. For the mean length of the synodic month he had already as a young man mentioned a value of about 29.530614d = 29d 12h 44 m 5s with an error less of 1s. The classical value of 29d 31:50:8:20 (sexagesimal) = 29d + 12h + 793/1080h = 29.53059414...d is also attributed to him; it was confirmed by Hipparchus and used by Ptolemy and later astronomers.
Kidinnu probably introduced the 19-year cycle known as the Metonic cycle into the Babylonian calendar in 383 BC. In this system each year had 12 lunar months, and 7 extra months were inserted at intervals during the 19-year period. This cycle, with the value for the mean synodic month, was later adopted for the Hebrew calendar and has remained in use until today.
Chaldean astronomers had also found changes of the apparent lunar diameter. They had ascertained that the lunar diameter changes from 29' 30" to 34' 16". Actual values are 29' 30" and 32' 55", which are very close. It is not known yet if they knew about the changes of apparent solar diameter, which was later known by Sosigenes of Alexandria.
In about 314 BC Kidinnu knew that the sidereal year was longer than the tropical year and therefore may have been aware of the precession of the equinoxes. He had smoothed the way for the more accurate calculations of Hipparchus since it seems that Hipparchus, who may have worked for a while in Babylon (near Kidinnu's city of Sippar) around 139 BC, knew Kidinnu's work. Kidinnu also influenced Claudius Ptolemy.
