Episode 4: The Astronomical Diaries

April 27, 2021

We step back and look at Babylon's broader political history and see how Babylonian astronomy changes during the rise of the Neo-Babylonian Empire and the Persian Conquest. Then we look at some of the types of astronomical records the Babylonians produced, particularly the Astronomical Diaries, the longest continuous research program of any society in history.


Good evening, and welcome to the Song of Urania, a podcast about the history of astronomy with new episodes every full moon. My name is Joe Antognini. We’ve been talking about the astronomy of Babylonia for a couple of episodes now and I’ve tried to convey to you a feel for the kinds of problems that Babylonian astronomers were trying to solve, the phenomena they were interested in, and some of the methods they used to solve these problems. We looked at some of the ways that they determined how many months would be in a year, how many days were in a month, when lunar eclipses would happen, and we looked at how astronomical phenomena were used as a source of omens. But our examination of Babylonian astronomy has been generally limited to older periods of Babylonian history. In fact, 626 BC, specifically is the year that I will use to demarcate our discussion of the older Babylonian astronomy in previous episodes with the Babylonian astronomy we will discuss in this and future episodes. It is a somewhat arbitrary cutoff for the astronomy of the time, but is a good choice based on the larger political events in the region. At this point I want to take a step back and become a little more familiar with the broader geopolitical situation in ancient Mesopotamia, because the astronomy broadly changes around this time, or at least our modern perception of it does, as does the political situation of Babylon.

Now we have to remember that Babylon always existed in the context of a fairly integrated Mesopotamian world. The political landscape of the near east was largely driven by the so-called fertile crescent. This was, as its name implies, a crescent-shaped swath of land that started with the Nile in the southwest, extended up along the Nile, along the Mediterranean coast through the Levant in modern-day Israel and Lebanon, turned east across the southern border of modern-day Turkey, and then traced its way southeast along the Tigris and Euphrates rivers in modern-day Iraq until it terminated at the Persian Gulf. This area of land was a more-or-less unbroken region with easily available water surrounded by otherwise arid lands.

Because of this continuous stretch of land with relatively accessible water, and good soil, civilizations in this region could easily travel between each other to trade, exchange cultural ideas, and, frequently, fight with each other. Indeed the Hebrew Bible is full of stories of conquest and defeat between the ancient Israelites and dozens of different peoples of the region: Hittites, Canaanites, Kushites, Kassites, Amorites, Babylonians, Assyrians. The list goes on. But the cultures of the region had many similarities as well due to their frequent contact among one another.

The city of Babylon was built along the Euphrates river, perhaps sometime in the late 2200s BC. Sometime in the 1800s BC Babylon gained its independence from neighboring city-states, built walls, and became a city-state in its own right. This began the Old Babylonian Empire, whose most famous ruler was King Hammurabi. As I discussed in Episode 2, our dates for kings during this period are still uncertain with the different chronologies being separated by the 64 year periodicity of the recorded phenomena of Venus.

Around 1600 BC the Old Babylonian Empire was defeated by the Hittite Empire. The Hittites originated in modern-day Turkey, however, and were not able to maintain control over so distant a land. A group originated from the mountains that today border Iraq and Iran, just east of the Tigris river, the Kassites, subsequently took control and reigned for about 400 years. So we had independence for Babylon for a few centuries with the Old Babylonian Empire, followed by about 400 years of Kassite rule.

Then came the Late Bronze Age Collapse. Sometime around 1200 BC, for mysterious reasons, catastrophe struck in the Babylonian Period. Within a span of a few decades, kingdoms all across the fertile crescent collapsed. Sophisticated city economies were replaced seemingly overnight by small, local village economies. This collapse appears to have been more sudden and more thorough than the collapse of the Roman Empire some 1500 years later. Perhaps in part because of this event it is very hard to know much detail about civilizations prior to this. We do have some astronomical records prior to the Late Bronze Age Collapse, some of which I described in earlier episodes, but there are not many. This event may be the origin of the myths of a past golden age described by the Greek writer Hesiod and lost cities and peoples like Atlantis.

Well, the Kassites were among the victims of the Late Bronze Age Collapse. Whatever the cause of the collapse, the native Akkadian peoples were once again able to reassert control over Babylon. But the recovery from the Late Bronze Age collapse was slow and the kingdoms of this Middle Babylonian period were weak. Finally, in 911 BC the Assyrians conquered the lands and Babylon became subject to the Neo-Assyrian Empire. While the chronologies prior to the Late Bronze Age Collapse are uncertain, by the time we get to the Neo-Assyrian empire, the chronology becomes much more secure.

Well Babylon managed to throw off the yoke of its oppressors once more in 626 BC. After three centuries of subjugation, a native Babylonian king succeeded in rebelling against the foreign rulers and establishing a Babylonian kingdom at long last, known as the Neo-Babylonian Empire. Under its second king, Nebuchadnezzar II, the Neo-Babylonian Empire conquered a swath of land along the fertile crescent up to Egypt. Among these lands, were of course, the lands of ancient Judea. The Babylonian conquest of Judea features prominently throughout various books of the Hebrew Bible. During the Babylonian captivity, the Temple of Solomon was destroyed, Jerusalem was sacked, and the Jews were driven from their lands. Understandably, Nebuchadnezzar does not come out looking all that great in the Bible. The heroic king of one people is the arch-villain of another.

But the Neo-Babylonian Empire was not to be an empire for the ages. The Neo-Babylonian Empire lasted only about 100 years before the Persian King Cyrus the Great conquered Babylon. Persia had been growing rapidly under King Cyrus. Cyrus had expanded out of modern-day Iran, capturing lands up to modern-day India, Afghanistan, and then swept north above the Neo-Babylonian empire to capture land in Armenia and modern-day Turkey, all the way up to Greece. Cyrus essentially had the Neo-Babylonian empire surrounded on the north, east, and west, and the lands to the south were all desert. So Babylon was not at all in a good position. The tale of its capture is disputed in the historical sources. The Babylonian accounts of this capture are fairly non-eventful. A relatively contemporaneous Babylonian account, the so-called Nabonidus Chronicle, states that Cyrus defeated the Babylonian armies on the banks of the Tigris River at the Battle of Opis and then took several cities without any additional struggle, Babylon being among them.

According to an account written several centuries later by the Babylonian astronomer Berossus, actually one of the few Babylonian astronomers whose name we know, the Babylonian king fled, but soon surrendered to Cyrus who apparently took kindly to a peaceful surrender and gave the deposed king an estate in the country where he lived out the rest of his days. Granted, that estate was in Persia, presumably where Cyrus could keep a closer eye on him, but nevertheless, it appears to be a more generous fate than one might have expected.

The Greek tales of the capture of Babylon are considerably more interesting. In the Greek accounts, after defeating the Babylonian forces at the Battle of Opis, Cyrus faces a problem when he then tries to take Babylon and finds himself confronted with the impenetrable walls of the city. Well, of course the Euphrates river runs through the city to supply it with water. Now the Babylonians were well aware that this was a potential vulnerability, so they had constructed a metal grate that went below the river to prevent anyone from entering the city via the river. But Cyrus had an idea. Cyrus had his troops dig a canal upriver to divert enough water out of the Euphrates to lower the water level so that his troops could pass under the metal grate and into the city. Cyrus had chosen to implement his plan during a festival when the city was distracted so that his forces could enter unnoticed and took the city without much resistance.

Now, modern historians regard the Greek version as fiction, perhaps drawn from folk tales in the region. Nevertheless, one point of contact between the Greek histories and the Babylonian histories was their broadly moralizing character. And this was not limited to these two groups. The ancient Israelite histories are moralizing in the same way, as are later Roman histories. Moral history was the predominant, perhaps exclusive mode of historical writing throughout the ancient world. In moral history, the point of telling the historical story is to convey a moral lesson to the reader. If, for example, you read the historical books of the Old Testament, the Book of Kings, Chronicles, and so forth, you’ll find that how good a Jewish king was depended on how faithful he was to God and the law. If he was faithful and upheld the law, Israel prospered — battles were won, enemies were slain. If he was unfaithful and worshipped other gods, Israel grew weak and lost lands. And if this infidelity went on for too long, Jerusalem itself would inevitably fall, by none other than the Babylonians as it happened. Well if you read the Babylonian histories you see the same story but in reverse. When the Babylonian king is faithful to Marduk, Babylonia suffers no defeat and rules victorious over all. But when kings are not faithful to Marduk, Babylon grows weak and falls prey to foreign invaders.

Well evidently King Nabonidus was not faithful to Marduk because he was defeated by the Persian King Cyrus in 626 BC and Babylon lost its independence. Now you might have expected that the foreign conquest of Babylon would have been bad for Babylonian astronomy. It certainly had the potential for catastrophe. But nothing of the sort happened under King Cyrus the Great. To the contrary, Babylonian astronomy under Cyrus the Great flourished. Why this is is not exactly clear. The Persian Empire was not particularly interested in Babylonian astronomy and didn’t subsidize or support it in any direct way. After all, a large part of Babylonian astronomy was concerned with diving the intentions of the gods Marduk, Ishtar, and Nergal. What did the Persians care what the local gods of the Babylonians had to say? And this went the other way — without a Mesopotamian king to interpret omens for, what was the point of Babylonian astrology? During this period the influence of astrology wanes relative to the more scientific astronomical observations, using the anachronistic term “scientific”. Mesopotamian astrology loses some of its judicial character and develops a more personal flavor. This actually presents a bit of conundrum — why bother keeping these detailed astronomical records if you couldn’t do any valuable astrology with them? Perhaps the priests were carrying on their tradition for a time when a Babylonian king would reign once again.

Well at any rate, King Cyrus was a remarkably pluralistic kind of king. Unlike the Babylonians, he did not care what gods his subjects worshiped as long as they paid him tribute and sent him their quota of conscripts to fill his armies. He permitted a large degree of local autonomy, including religious freedom, throughout his empire. It was thanks to this broad religious tolerance that the Jews were permitted to return to Judea, rebuild the temple, and begin worshiping the god of Abraham according to their traditional rites once again. Like the Babylonian conqueror Nebuchadnezzar, King Cyrus, too, appears in several places in the Hebrew Bible, but unlike Nebuchadnezzar, he gets a much better treatment.

By the time of his death, the Persian Empire under King Cyrus had become the largest the world had yet seen. Such a vast empire necessitated a new kind of governance, and Cyrus was highly adept at appropriating local customs and institutions to build a decentralized empire that he could manage from the distance of his capital in Pasargadae. One of the most remarkable artifacts from the period is the Cyrus Cylinder, discovered in 1879. It was traditional for Babylonian kings to begin their reign with a public declaration of the reasons for their legitimacy and to perform certain rituals. Among these was a practice of burying their declaration in a new building’s foundation. This practice had no analog in Persia, but Cyrus nevertheless found it useful to appropriate in order to rule Babylon. In his declaration, written on a cylinder now called the Cyrus Cylinder, he states that the previous Babylonian king, Nabonidus, had been unfaithful to Marduk, and that Marduk had smiled upon Cyrus, and used Cyrus to smite the unfaithful Babylonian king. Quote:

Nabonidus brought the daily offerings to a halt; he interfered with the rites instituted within the sanctuaries. In his mind, reverential fear of Marduk, king of the gods, came to an end. He did yet more evil to the city every day. He brought ruin on them all by a yoke without relief. Enlil-of-the-gods became extremely angry at their complaints. Exalted Marduk, Enlil-of-the-gods, relented. He changed his mind about all the settlements whose sanctuaries were in ruins, and the population of the land of Sumer and Akkad who had become like corpses, and took pity on them. He inspected and checked all the countries, seeking for the upright king of his choice. He took the hand of Cyrus, king of the city of Anshan, and called him by his name, proclaiming him aloud for the kingship over all of everything.

Now Cyrus, of course, as a Persian, did not care in the least what the Babylonian god Marduk thought of him or Nabonidus for that matter. But Marduk could be invoked as a useful bit of propaganda to establish the legitimacy of his rule in the eyes of the Babylonians.

Well, nothing in this world is permanent, and the Persian empire was no exception. But Babylon was never to regain its independence after Cyrus’s conquest. Babylon remained under Persian control for another two hundred years until 331 BC, when Alexander the Great swept in and exiled many of the residents of the city. Babylon as a city never really recovered from this exile. After Alexander’s death, control fell to one of his generals, and shortly thereafter the city was recaptured by the Persians, who held it for nearly a millennium until the development of Islam in the mid-seventh century AD. Babylon then fell into the rapidly expanding Muslim Empire, but by this point had essentially ceased to exist as a city. About a century after the foundation of Islam, the nearby city of Baghdad was founded and eventually grew to encompass the ruins of the ancient city of Babylon.

So that in a nutshell is a political history of the city of Babylon. I spent some time dwelling it and the rise of the Neo-Babylonian empire and its fall to King Cyrus the Great because it seems to be a symbolically and perhaps causally significant period in the history of astronomy. One important development in astronomy shortly after the Persian conquest was the discovery of the Metonic cycle. As we discussed in earlier episodes, perhaps ad nauseam, one of the principal issues of astronomy was determining when an extra month should be added to the year since the length of a month does not neatly divide the length of a year. Up until this point, the addition of extra months was fairly ad hoc. Priests added the extra month whenever it became apparent that an extra month was needed. We see from civil records that during the reign of King Cyrus Babylonian astronomers continued to insert extra months with no discernible pattern. But about ten years later, during the reign of his successor, King Cambyses II, the Babylonian astronomers had begun a regular eight year cycle. The extra month would be added on the years three, six, and eight. This worked for a little while, but the length of this cycle in lunar periods is still noticeably off from eight years, by about one and a half days. So after three of these eight year cycles the astronomers had evidently noticed that they were drifting too far from the solar calendar, and had to break the cycle and add an extra extra month. Now, the error across three of these eight-year cycles was still only 4 and a half days. That is, the date of, for example, the spring equinox, had drifted by only four and a half days according to the lunar calendar. So it is actually something of an achievement that the astronomy of the Babylonians was sophisticated enough that they could detect a relatively small error like that early on and correct it. But they didn’t stop with yet another ad hoc correction. Within another cycle or two, by about 480 BC, Babylonian astronomers had refined their method of intercalation and discovered the 19 year Metonic cycle. This puts the extra months on the third, sixth, eighth, eleventh, fourteenth, seventeenth, and nineteenth year. The Metonic cycle is highly accurate and drifts by only six and a half minutes per year. Once the Babylonians had hit upon the Metonic cycle in the early fifth century they never again needed to deviate from it for the next five hundred years. Within a generation or two of the Persian conquest, the seemingly arbitrary and chaotic addition of months to the calendar at random intervals that had so plagued Babylonian society became a thing of the past.

But the Metonic cycle is not the only way in which astronomy changes around the time of the Persian conquest. More broadly, it is around this time that the Babylonian astronomical records become much more numerous, detailed, and varied. These records are of course interesting in their own right — after all in the centuries after the Persian conquest the Babylonians had developed the most sophisticated mathematical astronomy the ancient world would see for centuries. But these records were also critical directly or indirectly for astronomy for centuries, even millennia to come. Later Greek astronomers such as Ptolemy relied heavily on the detailed records kept by Babylonian astronomers to develop their planetary models. And in turn, as the parameters of the planetary models became outdated, it later prompted the development of updated records in the Middle Ages, first by Islamic astronomers in Spain and later by Christian astronomers in Spain. And it was these records that Copernicus used to develop his heliocentric model of the Solar System.

So what exactly are these Babylonian astronomical records? We’ve already discussed some of the older records in earlier episodes. There are some fragmentary, incidental records — inscriptions on monuments, references to dates in civil contracts, etc. But the earliest systematic set of astronomical records is the Enuma Anu Enlil, which literally means, “When the gods Anu and Enlil”. The Enuma Anu Enlil consists of 70 tablets written sometime between 1600 and 1000 BC, though some parts of it may date back to 2000 BC. The Enuma Anu Enlil is almost entirely a collection of some 7000 omens. I read through some of these omens in the last episode and you may have noticed their somewhat formulaic character. Each omen consists of a protasis followed by an apodosis. The protasis is written in the past tense and describes the phenomenon. For example, “In Nisannu the sunrise looked sprinkled with blood and the light was cool.” Then this is followed by the apodosis, which is written in the future tense and provides the omen. So to complete the previous omen, “rebellion will not stop in the country, there will be devouring by Adad.”

A second set of tablets of prime importance is the Mul.Apin. This was much shorter than the Enuma Anu Enlil — only two tablets instead of 70 and would appear to be more scientific to the modern eye. The Mul.Apin was a sort of astronomical treatise that summarized the astronomical knowledge of the time. The Mul.Apin started by listing the locations of important stars and the dates of their heliacal risings. It drew connections between various stars noting which stars would be overhead or setting when other stars were rising. It described the course of the Sun in the sky over the year, described how the length of the day and night varied, and presented a method to compute which years needed extra months. And while the Mul.Apin was a more rigorously scientific text by modern standards, it does, of course, include a collection of omens as well. One very clever development that first appears in the Mul.Apin was the introduction of a sort of formal “astronomical year” which lasted exactly 360 days. This astronomical year of course had no real relation to the actual year, but was simply a formal device to make calculations over many years easier. A problem that Babylonian astronomers faced, particularly in the earlier centuries was that they were adding days to months and months to years essentially at random. If they wanted to compare observations across decades it was a bit of a nightmare to use real dates since you’d have to keep track of all the years that had an extra month or two randomly inserted. The 360-day year was a way to avoid this mess. You could do all your calculations with this 360 day year and then at the end convert from the astronomical year to the actual year. Astronomers today do something similar with the Julian day, or at least the observational astronomers do. The Julian day is the number of days since January 1, 4713 BC, a distant enough day in the past that we can be assured that nothing of interest happened on that day. You can then do your calculations ignoring any edge cases like leap years or leap seconds. If you are, for example, trying to predict the position of the planets, most modern day astronomical software will do these calculations using Julian days. Then afterwards it can take into account all the leap days and leap seconds to convert to the real wall clock time.

It is worth noting that both the Enuma Anu Enlil and Mul.Apin were widely circulated texts in ancient Mesopotamia. Or at least were widely circulated by the standards of the time. There were multiple copies of these tablets — these were not one of a kind texts. And Babylonian scribes were apparently intimately familiar with them. Even very late in the history of Babylon, the scribes who computed sophisticated predictions of planetary positions called themselves “scribes of the series Enuma Anu Enlil.” The earliest copy we have of the Mul.Apin dates back to 687 BC based on a date in the inscription, but a number of copies of the text appear in the archaeological record shortly thereafter which suggests that the original composition was earlier. In fact, the Mul.Apin can even be used to date itself using the dates of heliacal risings. Remember, these are the days of the year when a star is first visible in the morning after it had disappeared from the night sky. Heliacal risings aren’t exactly constant. They drift a small amount every year due to the precession of the Earth’s rotation. This isn’t very noticeable from one year to the next, but over the centuries it adds up. By comparing the listed dates of heliacal risings in the Mul.Apin to their true dates over the centuries, archaeoastronomers were able to date the original composition of the Mul.Apin to around 1300 BC +/- 150 years. Now, this is likely underestimating the true errors somewhat because this technique unfortunately has to make a number of assumptions. These assumptions are all reasonable, but reasonable is not the same thing as true. For example, many of the stars in the list of heliacal risings are actually small constellations. Is the date of the heliacal rising the date when the first star in the constellation is visible? When the brightest star in the constellation is visible? When half the constellation is visible? When the whole constellation is visible? Different assumptions here give drastically different dates. We are also assuming that the helical risings recorded in the Mul.Apin are accurate. We know from certain events where we can compare Babylonian observations against precisely computed configurations of the heavens that the Babylonians were not always the most rigorous observers. Perhaps they had fudged the heliacal risings to round the numbers a little bit and this biased the data. How would we know? A slight bias upwards or downwards could shift the calculated date by centuries. Further since all the dates listed are with respect to this fictitious 360 day year, how are we supposed to convert from the fictitious astronomical year to the real year? The Mul.Apin does not tell us so we have to make some assumptions. All we can say is that it seems likely that the Mul.Apin was composed earlier than 687 BC, probably by several centuries. But as with so many other things in ancient history, that is about all we can say for sure.

The Enuma Anu Enlil and Mul.Apin are the two major astronomical texts written prior to the Neo-Babylonian empire. But after the rise of the Neo-Babylonian empire the number of astronomical records grows tremendously. During the Neo-Babylonian and especially during the rule of Babylon by the Persian Empire we see a huge increase in the number of documents of all kinds available — civil contracts, letters to the king from officials in far-flung lands, royal proclamations and so on. There are perhaps a few explanations of this. Of course, one reason is survivorship bias. The later we get in history the more likely something is to have survived. But also the Neo-Babylonian and especially the Persian empires were far larger than the kingdoms that had come before them. They needed to coordinate their activities over vast territories and so needed to communicate in writing more frequently and in more detail. Furthermore, as populations and civilizations grew, they became more complex and could support more sophisticated kinds of civil interactions, which also required more detailed civil contracts.

This held true of astronomical records as well. One of the most important kinds of records for the development of astronomy was the so-called Astronomical Diaries. It is believed that these records began around 750 BC during the reign of King Nabonassar. The reason for this assumption is that much later, the great Greek astronomer Claudius Ptolemy chose the year 747 BC as the starting date for his astronomical tables in The Almagest because, as he writes, “for we have ancient observations completely preserved from that period to the present.” But the oldest astronomical diary we today know of dates back to 652 BC. The early records are patchy, but by the Persian conquest, we end up with a nearly unbroken string of records that lasts until 61 BC. This continuous chain of observations for six or seven centuries constitutes the longest scientific research program in history.

Like the Enuma Anu Enlil, the astronomical diaries have a very regular kind of structure. Each record contains data from six or seven months, and each month generally contains six observations or so. Most of the observations concerned the moon. The entry would begin by noting whether or not the previous month was full and had 30 days or empty and had 29 days. This would establish the start of the next month. The astronomer would note how long it was between sunset and moonset. At the middle of the month, the astronomer would record a number of similar intervals: the time from moonset to sunrise; the time from moonrise to sunset; the time from sunrise to moonset; and the time from sunset to moonrise. This would help to establish whether or not this month would have 29 or 30 days. And then at the end of the month the astronomer would note the time from moonrise to sunrise. Otherwise throughout the month the date and position of the Moon would be recorded if it passed by one of the 30 reference stars.

But in addition to the motions of the moon, the diaries would typically record notable phenomena of the planets. They would note which zodiacal sign the planet was in, how far it was away from the nearest of the 30 reference stars and in what direction the planet was relative to that star. Moreover, there were special points in a planet’s orbit, like opposition, which we will talk about in more detail in a moment, whose date would be recorded. The diaries also contained other information that was of note to the astronomer which we would not consider to be astronomical today such as unusual weather or even prices of commodities like barley, dates, sesame, and wool. In fact sometimes the commodity data was quite detailed and prices would be given for various days of the month or even different times of the same day.

The astronomical diaries are really quite a remarkable series of documents. It is impressive for a civilization to have meticulously maintained these series of records for some seven centuries. And these records required a great deal of training to produce. Of course it would have taken a good deal of training to learn how to produce these observations. But more than that, the astronomical measurements themselves were written with cuneiform in the Akkadian language. By the time of the Neo-Babylonian Empire in the 600s BC, Akkadian had largely fallen out of use as a spoken language in Mesopotamia in favor of Aramaic. The use of Akkadian was confined to priests and scribes for formal, written documents, similar to the use of Latin in medieval Europe. And just as it was no small feat for the Catholic Church to train a body of scholars to write in the dead tongue of Latin, it must have been no small feat for the city of Babylon to train its astronomers to keep regular observations and record them in the dead tongue of Akkadian. But nevertheless this feat was accomplished, all the way up to the first century BC. And in fact some cuneiform records of other kinds continue to be produced throughout the first century AD, with the last one we have dating from 75 AD. Why did the Babylonians support this endeavor for so long? This seems to be a bit of a mystery. After the conquest of King Cyrus, they didn’t have a king to provide omens for. Maybe they were doing it in case a Mesopotamian king came to throw off the yoke of foreign domination. And, of course, astronomical recordkeeping was likely a component of a broader set of religious ritual. Some of the tablets we have warn that the information contained therein is a secret kind of knowledge. But this is all a bit speculative on my part and there doesn’t seem to be any definite explanation for why the Babylonians maintained such detailed astronomical observations for such a long period of time.

Well, as I mentioned earlier, the Babylonians generally didn’t record the position of the planets in general. They only recorded planetary positions at certain special points in a planet’s orbit. This actually was an issue for later astronomers because although the Babylonian records continuously spanned a long time, they were fairly sparse in terms of the general planetary motion since they tended to only record planetary positions at special times. These special positions that the Babylonians recorded have variously been called planetary phases or stations. Claudius Ptolemy even complained about the Babylonians only recording positions at the planetary stations in the Almagest saying,

Most of the old observations were thrown together carelessly and grossly. The more continuous of them contain stations and … the stations cannot indicate the exact time, since the planet’s local motion remains imperceptible for many days before and after its station; and the apparitions not only make the places immediately disappear along with the stars as they are seen for the first or last time, but also can be utterly misleading as to the times because of the differences in the atmosphere and in the eye of the observer.

Now, as Ptolemy concedes, this was only true of the older Babylonian observations. The later diaries, starting during the fifth century BC, start to record more detail about planetary motion, in particular when the planet entered a new constellation of the zodiac. And here we see something very interesting, because if we work out where these planets were on the dates of the recording, we find that these transitions from one constellation to the next are all 30 degrees apart. Even though the size of the actual pattern of stars on the sky that made up each zodiacal constellation varied, for the purposes of recording astronomical observation, the ecliptic was divided into 12 equal regions of 30 degrees apiece, which we today call the signs of the zodiac. Earlier observations of the constellation a planet was in were complicated by the fact that the constellations were of irregular extents and did not have clearly defined boundaries. There may have even been regions of the sky that didn’t have any constellations at all! So this development of zodiacal signs in the fifth century BC greatly simplified the recording of planetary positions.

Nevertheless, although this allowed the planetary positions to be recorded at more frequent intervals, records of the planetary stations were really of primary importance because they formed the longest chain of observations. So what are the planetary stations? Well they are different for the superior planets and the inferior planets. The superior planets are those planets in our modern model which have orbits outside that of the Earth, so Mars, Jupiter, and Saturn, and the inferior planets are those which have orbits inside that of Earth, so Mercury and Venus. Let’s look at the stations of a superior planet first. The first station that the Babylonians had is easy enough: it is the first appearance. After the planet has been behind the Sun for some time, this would be the point at which the planet is once again visible in the morning sky just before sunrise, much like a heliacal rising of a star.

The next phase deals with a phenomenon that is of paramount importance to the history of astronomy, namely retrograde motion. Now, most of the time, a superior planet will slowly drift eastwards in the sky relative to the background stars. The reason for this is that the planet is revolving around the Sun, and this motion causes its position in the sky to change relative to the background stars. Easy enough. The catch here is that when we observe the planet we are ourselves moving as well. Now, most of the time, the motion of the Earth is in some other direction relative to the planet, so we still observe its usual eastward drift. The exception comes around the time that the Earth is between the Sun and the planet. Because the Earth revolves around the Sun faster than any of the superior planets, around this time, the Earth ends up overtaking the planet and passing it by. This causes the planet to appear to move backwards on the sky from our vantage point, just as a slower car on the highway appears to move backwards as you overtake it in a faster car. So occasionally the general eastward drift of a superior planet is interrupted and it starts to drift westward on the sky for a time before slowing down, stopping, and resuming its usual eastward drift. This period of westward motion is what is called retrograde motion, and explaining this phenomenon was really the principal problem in astronomy for about two thousand years.

Well, the Babylonians had no explanation whatsoever for this phenomenon, but they did notice it that it happened. In their astronomical diaries, one of the planetary stations they made note of was what is called the first stationary point, where the planet stops its eastward drift and starts moving westward. Then they noted opposition, which is the point at which the planet is on the opposite side of the sky from the Sun. Then the fourth station was the second stationary point, where retrograde motion ceased, and the planet began moving eastward once more. Finally the last station they noted was the last night that the planet was visible before it disappeared behind the Sun.

The stations of the inferior planets are somewhat similar in nature. But the inferior planets differ from the superior planets in that their motion is limited and they cannot wander too far away from the Sun. Venus can only ever be seen at most 47 degrees away from the Sun, and Mercury only 28 degrees away. The first station is the opposite from that of the superior planets. Rather than appearing in the morning sky, the planet first appears in the evening sky. It then drifts eastward relative to the background sky for some time before hitting its first stationary point, where it stops its eastward drift and then starts to move westward relative to the background stars. At this point the planet starts its period of retrograde motion. But unlike the case of a superior planet, an inferior planet continues its retrograde motion right past the Sun. So it disappears from the evening sky for a time and later on reappears in the morning sky just before sunrise. Then it continues its westward drift before it stops, turns around and starts to drift in the usual eastward direction. Then it eventually catches up to the Sun and disappears, starting the cycle once more. So the Babylonians recorded six stations for the inferior planet: first appearance in the evening, the first stationary point in the evening, disappearance from the evening sky, the first appearance in the morning sky, the stationary point in the morning, and the disappearance from the morning sky.

I went into a fair amount of detail about the planetary stations because they are important for understanding the last class of astronomical records which we will discuss. We could broadly call these mathematical astronomy tablets. These themselves came in a number of different types. The simplest of these are what are known as the “Goal Year texts.” The goal year texts were a very simple way of producing what are called ephemerides, or predictions of planetary positions. Now, thanks to their meticulous recordkeeping, Babylonian astronomers began to notice patterns in the positions of the planets. And one of the fortunate things about the planetary motions is that while they can seem somewhat arbitrary month to month — seemingly at random the planet will stop its usual motion and turn around and go backwards — over decades the behavior is almost completely periodic. The Babylonian astronomers may have noticed that, for example, one month Saturn was at opposition in the constellation of Leo and wondered when and where Saturn would arrive at the next station, the second stationary point. If they went back to their records, they would have found that the last time Saturn was at opposition in the constellation of Leo was 59 years prior. Then by consulting their records they would have found that Saturn had reached its secondary point about two months and one week later, about six degrees away from where it was at opposition. Well if they waited another two months and one week, they would have observed history repeat itself — Saturn would arrive at its second stationary point about six degrees away from opposition, just as it had 59 years ago.

And there were similar periodicities for the other planets in the sky. Mars would repeat its behavior every 47 and 79 years, Jupiter every 71 and 83 years, Venus every 8 years, and Mercury every 46 years. The premise of a Goal Year text was simple then. If you wanted to compile a table of predictions of planetary positions, all you would have to do is go back and copy the records from 59 years ago for Saturn, 71 years ago for Jupiter, 47 years ago for Mars, etc. Then you would have a more or less accurate prediction of the positions for the year to come.

Now we have evidence from other records that this technique was in use around the Persian invasion, but despite its simplicity, goal year texts do not actually appear as a distinct form of record until around 300 BC. Well where do these numbers like the 59 year periodicity of Saturn come from? While the Babylonians did not have a physical model to explain their origin, they did seem to have a model of planetary motion that was somewhat more sophisticated than just copying earlier records because occasionally they do make small adjustments in their goal year texts.

To understand this we need to understand two different kinds of periodicities in planetary motions. The first period, called the sidereal period, is what we normally think of when we talk about the orbital period of a planet. In our modern heliocentric model of the Solar System, the sidereal period is simply the time it takes the planet to make one revolution around the Sun. From a geocentric perspective, that is from our perspective looking at the planet here on Earth, the sidereal period is the time it takes the planet to return to the same background star on the sky. For Saturn the sidereal period is slightly less than 29 and a half years. There is another important kind of period however, called the synodic period. This is the time it takes the planet to return to the same configuration relative to the Earth and the Sun. So, for example, if the Earth is between the Sun and Saturn, this is the time it takes for the Earth to come between the Sun and Saturn once again, or, in other words, the time from one opposition to the next. In the case of Saturn the synodic period is about one year and two weeks. Now, as you might expect, the sidereal period gets bigger, the more distant the planet is. But, perhaps counterintuitively, the synodic period actually decreases for the more distant planets. In the limit that a planet is infinitely far away, well, it’s just like a background star, and its synodic period is exactly one year. For the synodic period, the closer the planet is to Earth is the determining factor. The reason for this is that what is important for the synodic period is the relative velocity between the Earth and the other planet. For the planets closer to Earth, they are actually moving closer to the Earth’s speed, so their relative motion compared to the Earth is quite slow. As a consequence, Mars has quite a leisurely synodic period of nearly two years and one month, the longest synodic period of all the planets in the Solar System.

Well, if you are interested not only in whether or not an opposition has occurred, but also where it has occurred, you need to take into account both the sidereal and the synodic period. Because it’s not enough to use the synodic period to figure out when, for example the next opposition will be, because the next opposition won’t necessarily be in the same zodiacal sign. The planet will return to the same zodiacal sign after a sidereal period. So in essence, you have these two periods, the synodic and sidereal periods, and you need to find something like the least common multiple of these two periods. Well you can’t really do this exactly because the periods aren’t integers. But you need to find the smallest number of synodic and sidereal periods that makes approximately an integer.

This is easiest to see with Saturn. So the sidereal period of Saturn is about 29 and a half years and the synodic period is about one year and two weeks. So, if you wait a single sidereal period that will have been about 28 and a half synodic periods. No good. Saturn will be in the same spot in the sky relative to the background stars, it will, say, be back in Leo, but because of that extra one half a synodic period it will be at conjunction instead of opposition. So the Sun will be in Leo, too, rather than on the opposite side of the sky! But if you now wait two sidereal periods, that will have been about 59 years and about 57 synodic periods. 56.91 synodic periods, to be exact. But close enough for Babylonian astronomy. And that will put Saturn back at opposition.

And you can follow the same procedure to figure out what these periodicities are for the other planets in the sky. Because the periods aren’t exact multiples of each other, there are multiple long-term periodicities that you can find. This is why the Babylonians sometimes used periods of 71 years for Jupiter and other times 83 years. Both are approximately integer ratios between the synodic and sidereal periods of Jupiter. Furthermore, because these ratios aren’t exact integers, over time errors accumulate. This meant that the goal year texts had to be updated based on the most recent series of observations rather than just copying the same phenomena centuries out into the future.

Well, the Goal Year texts were a pretty straightforward technique in the Babylonian mathematical astronomy tablets. In fact it might be a bit of a stretch to even call it mathematical astronomy. But the Babylonians also produced a series of much more sophisticated astronomical calculations. However, as much as I would like to discuss them with you now, our discussion of the Babylonian tablets in this episode is getting a bit lengthy, and the more complicated tablets will require some time to explain, so these texts will have to wait for our next episode. Then we will dive into how the Babylonians produced their most accurate planetary and lunar ephemerides, a pair of techniques known as System A and System B. I hope you will join me then. Thank you for listening, and until the next full moon, clear skies.