Kidinnu
and Babylonian astronomy

Tablet with a list of eclipses 
between 518 and 465, 
mentioning the death of king
Xerxes (British Museum).

The Babylonian astronomers had been observing the skies for centuries and had recorded their observations in astronomical diaries, astronomical almanacs, catalogues of stars and other texts. We possess observations of Venus written down under king Ammisaduqa (1702-1682?BC), detailed stellar catalogues from the eighth century -our Zodiac was invented in Babylon-, and astronomical diaries from the seventh century until the first century BC.

Because there were many data available to Babylonian astronomers, their results could be pretty accurate. An example is the length of the so-called synodic month, i.e., the period between two full moons. The astronomer Nabû-rîmannu (c.490 BC?) concluded that it lasted 29.530641 days. Kidinnu arrived at 29.530594 days, which is only 4.32 seconds more than the modern estimate of 29.530589 days. A similar result is the length of the solar year, which Kidinnu calculated at 365 days, 5 hours, 44 minutes, 12.52 seconds, instead of 48 minutes, 45.17 seconds. In other words, his error was only 4½ minutes. His accuracy was in fact greater than that of the astronomer Theodor von Oppolzer in 1887. (Kidinnu's results are known from Greek sources.)

Using these data, astronomers were able to predict lunar eclipses and -later- solar eclipses with some accuracy. Their tool was the so-called Saros-cycle: this is the period of 223 synodic months (or 18 years and 11.3 days) after which lunar and solar eclipses repeat themselves. E.g., when you know that there has been a solar eclipse on May 18, 603 BCE at dawn, you can be confident  (The first solar eclipse that was predicted in this way, was that of June 15, 763 BCE.)

The importance of these predictions can not be exaggerated. The Assyrians and Babylonians regarded lunar eclipses as evil omens, directed against their kings. Now that they were predictable, it was possible to appoint substitute kings who would bear the brunt of the gods' wrath. The real king would remain unharmed and the continuity of the state's policy was guaranteed.

Another result of the observations was a nearly perfect calendar. In the reign of king Nabonassar -in 747 BC to be more precise- the astronomers of Babylon recognized that 235 lunar months are almost identical to 19 solar years. (The difference is only two hours.) They concluded that seven out of nineteen years ought to be leap years with an extra month.

At first, intercalary months were announced by the king (who had an astronomical adviser), but after Babylon had been captured by the Persian king Cyrus the Great in 539 BC, priestly officials took over. They started to look for a standard procedure for the intercalation of months. It was introduced in 503 BC (if not earlier).
 

As this table shows, there are six years when a second month Addaru is added, and one year with an extra Ululu. The result is that the first day of the month Nisanu (New year's day) was never far from the vernal equinox (the first day of spring), so that the civil calendar and the seasons were never out of step. This system is often called the cycle of Meton, to commemorate the Greek astronomer who introduced it in the West. It is still used in the Jewish calendar.

At an unknown moment in the fourth century BC, a second procedure for the intercalation of months was invented. This time, a cycle of 76 years was used, and the limits of variability in the start of the year were further narrowed. The new system was already known in 331 BC, because in that year the Macedonian conqueror Alexander the Great captured Babylon and ordered the astronomical diaries to be translated into Greek. This is known from a very late Greek source, Simplicius; the truth of his words, however, is established, because he correctly translates the Babylonian title, massartu, with têrêseis, which is illogical in Greek but keeps the double meaning of 'guarding' and 'observing'. The new knowledge was immediately applied in Greece: the astronomer Callippus of Cyzicus, a pupil of the philosopher Aristotle, recalculated the length of the lunar month and proposed a new calendar, in which he used the longer cycle. His new era, which was used by all later Greek astronomers, started at June 28, 330 BC, eight months after the capture of Babylon.

This calendar reform may have been the work of Kidinnu. We have already seen that he reached extremely accurate estimates of the length of the solar year and the synodic month. Consequently, he had all the necessary knowledge to establish this cycle. There is, however, no hard proof  for this. On the other hand, it is unlikely that someone who has discovered the length of the year and month refrains from thinking about the calendar.

Another discovery is mentioned in a scholion (commentary) on the Handy tables by Ptolemy of Alexandria (second century AD). According to the scholiast, Kidinnu discovered that 251 synodic months are identical to 269 anomalistic months. (An anomalistic month is the period between two moments when the moon is closest to the earth, 27,55 days.) This discovery shows considerable skill in observation, because it is very difficult to see with the naked eye that the moon is sometimes closer than on other times. The distance varies between 356,000 and 407,000 kilometers and the diameter of the moon varies only 11%.

The Roman author Pliny the Elder (23-79) knows another discovery of Kidinnu.

The star next to Venus is Mercury, by some called Apollo. It has a similar orbit, but is by no means similar in magnitude or power. It travels in a lower circle, with a revolution nine days quicker, shining sometimes before sunrise and sometimes after sunset, but according to Cidenas [Kidinnu] and Sosigenes never more than 22 degrees away from the sun.

[Pliny the Elder, Natural History 2.39]

Kidinnu's greatest discovery, however, is a system to predict the motion of the moon. Modern scholars call it System-B. In the last years of the fifth century, the Babylonian astronomers discovered that the moon does not always move at the same speed. At first, it seems as if the moon accelerates, later it seems to go slower. The explanation is the elliptic shape of the moon's orbit: when it is near the earth, it moves faster because of the earth's gravity.

Several astronomers have tried to describe this phenomenon. (As far as we know, no Babylonian, Greek or Roman has ever suggested an explanation.) The first system, called System-A, assumes that the moon has two constant speeds, and this idea makes predictions more accurate than when we assume a constant motion. Unfortunately, we do not know who invented this improvement.

Kidinnu's system was a further refinement. The moon's velocity changes as a function of time: first, it increases in steps (of a day each) from minimum to maximum speed, later the velocity decreases again. This system was very accurate. From now on, the Babylonian astronomers were able to predict the lunar phases and positions. A similar system was used for the movements of the sun and the five planets (which the Babylonians called Nabû, Ištar, Nergal, Marduk and Ninurta). This is essentially an arithmetical system, and it is probably no coincidence that Strabo in our first quotation connects Kidinnu with mathematics.

It has been argued in the 1930's that Kidinnu also discovered the precession, that is the slow reorientation of the earth's axis. He was certainly in the position to discover this phenomenon. In our age, the stars seem to rotate around the Pole Star, but in Kidinnu's age, the north pole of heaven was somewhere halfway the Little Bear and the Dragon. Kidinnu must have known that in the days of the legendary king Hammurabi (1792-1750 BC), the earth's axis was directed to a point inside the Dragon and he must have been able to conclude that the axis of the earth was slowly changing its direction. However, there are no indications that he really reached this conclusion, and the theory that Kidinnu discovered the precession has now been abandoned. The Greek astronomer Hipparchus of Nicaea (second century BC) was the first to understand the nature of the precession.

Only one fact about Kidinnu's life is known: he must have lived in the fourth century, because the first System-B-tablets can be dated in that age. (One tablet is dated c.375 BC.) An undated cuneiform chronicle mentions that a man named Kidinnu is put to the sword; the same text mentions a king Darius and a name that looks like 'Alexander'. It is tempting to assume that Kidinnu was executed by Alexander the Great on August 13, 329 BC, but it is far from certain that this is the correct reading of the tablet. Besides, one would expect an earlier date, because System-B originated almost half a century earlier.

It has been argued that the 'Sudines' mentioned by Strabo is responsible for the translation of Kidinnu's work into Greek. It is tempting to connect this hypothesis with the fact that Alexander the Great had the Babylonian astronomical diaries translated, but it is probably better to resist this temptation. However this may be, it is certain that the Greek translation was used by the Greek astrologer Critodemus (c.260 BC), by Hipparchus of Nicaeae and Ptolemy of Alexandria, who all knew System-B and accepted Kidinnu's values for the length of the year and the synodic month and his equation of 251 synodic months with 269 anomalistic months.

To honor the great Babylonian astronomer, a crater on the far side of the moon has been called Kidinnu (35.9N 122.9E). It is a small crater, however, with a diameter of only 56 kilometer.

Literature

A brief introduction to Babylonian astronomy, written by Asger Aaboe, can be found in volume 3, part 2 of Cambridge ancient history (2^nd edition, 1991), chapter 28b, "Babylonian mathematics, astrology and astronomy". Hermann Hunger's and David Pingree's Astral sciences in Mesopotamia (1999 Leiden) is less accessible but offers a wealth of information.