During the half millennium of the Roman Era in Ancient Greece, only two astronomers made any major advances. At the beginning of the Roman Era, Posidonius measured the size of the Earth and discovered the relationship between the Moon and the tides. But the triumph of Greek astronomy came 300 years later with the intricate planetary model of Ptolemy, which stood unchallenged for some 1400 years.

Transcript

Good evening and welcome to the Song of Urania, a podcast about the history of astronomy from antiquity to the present with new episodes every full moon, or thereabouts. My name is Joe Antognini.

Last month we took a little detour from the overall narrative of ancient Greek astronomy and looked at one of the most remarkable artifacts from antiquity, the Antikythera Mechanism. But prior to that digression, we had left off talking about Hipparchus and all the wonderful discoveries he made in the 2nd century BC. So I will pick things up from right where we left them. But believe it or not, after Hipparchus’s work in the 2nd century BC, we can more or less skip over the next 300 years. In all that time, there were essentially no new developments in astronomy. Not so long ago, back in the Classical Era, it seemed that there was someone of note to talk about every decade or two, but now Greek civilization has been brought to such a low point that three centuries can pass without really making a mark on the oldest science. If this were a shorter series on the history of astronomy, I would be justified in skipping straight ahead from Hipparchus to Ptolemy.

But devoted listeners to this podcast should know by now that it is not in the character of this podcast to skip over 300 years without saying at least a little about what happened in between and why there is so little to talk about from this period.

But before we really get into that particular puzzle there are a couple of loose ends I want to tie up in Hellenistic Era astronomy. In particular I wanted to mention Conon of Samos and Aglaonice. I should have mentioned Conon of Samos a few episodes back because he lived right through the middle of the 3rd century BC, so he predated Apollonius of Perga by about 50 years and was probably a little younger than Aristarchus. His serious astronomical work was in a series of seven books called De Astrologica, but, in a tale you are by now well familiar with, it does not survive. All we know is that he wrote about solar eclipses, possibly by collecting Egyptian records and possibly observing some himself. But the reason I bring up Conon of Samos is that he is also the subject of a rather charming story about the constellation Coma Berenices, and how it got its name, and I just couldn’t pass it up. As his name implies Conon of Samos was born in Samos, but just like a great number of his countrymen like Pythagoras and Aristarchus, he ultimately moved away and set up shop in a more vibrant intellectual climate, in his case, Alexandria. Conon must have had quite a strong reputation as an astronomer because he was appointed to the position of court astronomer in Ptolemy III’s court.

Now I talked a little bit about the great power politics in the region two episodes ago when I was talking about the geopolitical situation of the city of Rhodes. You may recall that after Alexander the Great had died, his empire fractured and his generals seized whatever regions they could and set up their own splinter states of larger or smaller sizes. Around the eastern Mediterranean there were three main players: the Ptolemaic dynasty in Egypt, the Seleucid Empire in the east, and the Antigonid dynasty in Macedonia. In the centuries after Alexander’s death, these empires were at each other’s throats and went to war on a regular basis. During the time that Conon of Samos was the court astronomer to Ptolemy III, the Ptolemaic Kingdom once again went to war with the Seleucid Empire in what is called the Third Syrian War, and, though they didn’t know it at the time, at this point they were only halfway through the total of six Syrian Wars that these two empires fought.

Ptolemy III was married to a woman named Berenice II, which gets anglicized to Berenice. They were technically related, her grandmother married Ptolemy III’s grandfather, which would make them second cousins, but only by marriage, not by blood. Later, more salacious stories had it that they were brother and sister, though either way, Egyptian high society was fairly sanguine about consanguinity. At any rate, the marriage of Berenice II to Ptolemy III was evidently a happy one, which was a historical rarity among the powerful. When Ptolemy III had to ship off to war in Syria, Berenice II was so distraught at the prospect of her husband being in harm’s way that she made a sacrifice to the gods. But rather than making the usual sacrifice of bulls she decided to make a more radical offering. She cut off her hair, apparently shaving herself bald, and placed her hair in the temple to Arsinoe Aphrodite to beseech the gods for her husband’s safe return.

Now the stories of what happened next differ in their timing, some say it was the next day, others say it was a good while later, but at some point, the queen’s hair disappeared from the temple. Furious not only that it was embarrassing that someone had apparently stolen the queen’s hair, but also that this might ruin the offering she had made and put her husband in peril, the queen brought together all the court officials and demanded answers for what had happened. Among them was the court astronomer Conon of Samos. Probably to the great relief of everyone else in the room, Conon was quick on his feet and immediately explained that Aphrodite had been so pleased with the queen’s offering that she had taken it and placed it in the sky to be honored through the ages. Henceforth, a patch of stars between Boötes and Leo has been known as Coma Berenices, or Berenice’s hair.

This story was quite popular in the ancient world, and it was almost certainly encouraged by the Egyptian state as a kind of propaganda as it made Berenices II look quite good. It emphasized the devotion of the queen to her husband, her piety, and, above all, her favor with the gods. Official depictions of Berenices II often represented her with a shaved head to allude to this story, and later Roman poets set the story in verse which is how it has survived to us today.

A moral we might take from the story today is that sometimes it is not sufficient for an astronomer to know astronomy. Sometimes an astronomer must have a certain, shall we say, creativity as well.

So that is Conon of Samos. The last astronomer of the Hellenistic Era I wanted to briefly mention, and then I promise we will move on to the Roman Era for real, is Aglaonice, who was active in the late 2nd century or early 1st century BC. She is remarkable for being one of the very few astronomers of the ancient world who was a she. Over the course of our tour of Greek astronomy, we’ve come across a couple of philosophers who thought it worthwhile to teach philosophy to women, Pythagoras and Epicurus being some of the more prominent, but even then their female students by and large went unnamed, or at least the few that are named have nowhere near the prominence as some of their male students do. Now it seems that historical records of Aglaonice’s work have been rather colored by the fact that she was a woman, which makes it unfortunately hard to get at what it was exactly that she did. Many of the representations make her out to be a kind of witch and she was in particular known for her ability to make the moon disappear from the sky. But a more realistic interpretation of this is that she may have been able to predict the occurrence of lunar eclipses, which was certainly possible to do given the state of Greek astronomy at that point. But it’s not known to what extent the more magical elements of her work were embraced by her or imposed on her by authors writing about her. As I’ll talk about later in this episode when I get to Ptolemy, the modern rigorous separation between the sciences like astronomy, physics, and chemistry, and sorcery, divination and magic, did not exist in the ancient world. So while we would think it strange that someone would go about hard-headed astronomical predictions of lunar eclipses on the one hand and then try their hand at sorcery on the other, the ancients had no such hang-ups.

Well with that I promise you that we are officially finished with the astronomy of the Hellenistic Era of Ancient Greece. Way back when we started our journey through Greek astronomy I said that historians generally divide the history of ancient Greece into five periods: The Greek Dark Ages, the Archaic period, the Classical period, the Hellenistic period, and last of all the Roman period. Now this growing civilization of Rome has been making a few appearances in the last couple of episodes. They had been one out of a number of civilizations over in Italy for many centuries, but around the second century BC, their dominion really started to take off after their defeat of the Carthaginians in the Punic Wars and they subsequently began encroaching on the kingdoms that had been spun out of Alexander the Great’s empire, most notably the Macedonian Kingdom. The canonical end to the Hellenistic Age and the start of the Roman Age is 146 BC, when Rome sacked Corinth and took control of the Greek mainland, but as always, the edges between the eras are a little fuzzy and it would take more than a century before Rome brought Ptolemaic Egypt under its heel.

The main feature of Greek astronomy during the Roman Era is really just the lack of it. There are really only two figures of note in the whole half millennium of the Roman Era, Posidonius, and, of course, Ptolemy. Posidonius was born at the beginning of the Roman Era, about a decade after the sack of Corinth. Posidonius was born in the city of Apamea in Syria. Apamea was a bit of an odd town, it had been founded by one of Alexander the Great’s generals, Seleucus, the originator of the Seleucid Empire. Seleucus’s purpose in founding the city was as a way to give land to his veterans. In the ancient world, to secure the loyalty of their troops, generals would often promise their soldiers a plot of land that they could call their own if they served in the army for the requisite number of years. If you were born into a poor, landless family in the ancient world, joining up was really your only realistic route to property ownership. This strategy later ended up proving to be a major systematic problem for Rome because it needed to acquire vast amounts of land to provide to its vast armies. This required it to conquer vast territories, which meant that it needed to raise ever larger armies whose troops would, in turn, require even more land. Well that was centuries to come and at the moment Seleucus did not have quite as serious a problem as Rome did, but to give his soldiers land he had to found a number of cities and Apamea was one. But because he was plopping down a bunch of Greek soldiers in some conquered territory, the surrounding culture was not really Greek. This was not unusual, of course, the Greeks had colonies all throughout the Mediterranean. Alexandria, the main center of Greek intellectual life during the late Hellenistic Era, was really just a small Greek dot in the otherwise culturally foreign country of Egypt.

It seems that from his upbringing in a Greek town surrounded by barbarians, Posidonius became interested in the cultural practices of foreign peoples. Now, the standards of cultural anthropology in his day were not quite what they are today so he was unabashedly ethnocentric. He thought, for example, that the way that the peoples of the Levant went to battle was just ridiculous. He wrote that they go “clutching knives on their belts and filthy, rusting spears. They drag behind them donkeys piled high with all manner of wine, food, flutes, and musical instruments — prepared for a party rather than a battle.”

Well Posidonius was very smart and in his youth moved to Athens to learn at the philosophical schools there, and found that the Stoic school was most to his liking. But sometime when he was in his 30s he began to travel extensively through the Mediterranean and documented the customs of the peoples he encountered. His writings have become one of the most important sources we have on the society of the Celts since they were an illiterate people and didn’t write anything down about themselves. And, of course, if you can’t write anything down about yourself and have to rely on foreigners to describe your society, the descriptions that get handed down through history can end up full of exaggerations. Posidonius, for example, thought that Gaulish women were very beautiful, and remarked on their height — the average Gaulish woman was as tall as the average Greek man, but he felt that the beauty of the Gaulish women was wasted on the Gaulish men since he wrote “the Gaulish men prefer to have sex with each other. They often sleep on top of animal skins surrounded by other males and roll around together on the ground. The young men are unconcerned about proper behavior and will offer their bodies to anyone—and they are highly offended when anyone turns them down.” There is perhaps a story there that Posidonius isn’t telling us.

Well, Posidonius also remarked on the Celtic practice of head hunting and how everywhere you looked in a Celtic settlement there seemed to be the severed heads of their enemies on display. He writes “The Gauls cut off the heads of the enemies they kill in battle and hang them around their horses’ necks. Then, singing a song of victory, they take the bloody weapons from their fallen foes and give them to their servants to carry home. The weapons they hang on their walls like hunting trophies, but the heads they preserve in cedar oil, storing them away carefully in chests.” Now it’s easy to read this has being your typical Greek exaggeration about the barbarities of the barbarians, but modern archaeology seems to suggest that Posidonius may have downplayed the extent of it if anything. We now know from excavations that Celtic temples have the skeletal remains of severed heads and put the heads on display in prominent places. Some have altars made of the bones of thousands of enemy warriors. One of these temples had a structure that supported upright the decapitated bodies of 80 slain warriors, all positioned holding their shields and swords as if ready for battle. The missing heads were undoubtedly displayed somewhere else.

The historian Philip Freeman points out the contrasting attitudes of the Greeks and the Celts in their treatment of the dead. To the Greeks burial of the dead was an absolute necessity. Only a barbarian, literally or figuratively, would let a dead body remain unburied. You may recall back in Episode 16 when I was talking about Archytas that there was a poem that describes a sailor coming upon the dead body of the philosopher after a shipwreck and pouring some sand on him so that his soul would not be condemned to wander the Earth for a hundred years. In Sophocles’s play Antigone, the entire plot revolves around the king of Thebes, Creon, refusing to permit the burial of his enemy Polyneices, and how this brings about a conflict between Antigone’s duty to the gods and her duty to the state. But the Celts had a different attitude toward the dead. Gruesome though it would have seemed to the Greeks, to display a slain warrior’s head in a prominent location was the highest honor you could give to him. Cowards were left to rot in the battlefield. But the heads of the bravest warriors were kept close in the hopes that he who possessed it could be imbued with some of the spirit of a great warrior.

Well, living among the head hunting and warlike Celts was clearly not Posidonius’s favorite part of his grand tour of Europe. Perhaps the thing he was most excited to see was the Atlantic Ocean. He had heard rumors about this strange body of water and wanted to investigate its properties for himself. In particular he wanted to see if it was true what was said about how it exhibited tides. Tides are present in the Mediterranean Sea, but really only barely. The difference between high tide and low tide in the eastern Mediterranean is only around an inch or so. But on the shore of a real ocean, the difference between high tide and low tide is several feet. So, for a full month, Posidonius stayed in a house near the ocean in the town of Cádiz, on the southern coast of Spain, west of the strait of Gibralter. And for that month he basically did nothing but watch the ocean. He took hourly measurements of the height of the ocean, along with measurements of the position and phase of the Moon and found that the two were related. Honestly it must have been the most relaxing scientific investigation in history. From his observations Posidonius concluded that there was an intimate connection between the moon and the tides. Now he was not the first to suggest such a connection, but he was the first who had the data to back it up.

Well, Posidonius’s travels eventually came to an end and he ended up settling in Rhodes and became the head of the Stoic school there, ultimately earning for himself the reputation of being the most learned man of his day, and students traveled far and wide to learn at his school. Among his students were none other than Pompey and Cicero.

Well in addition to his study of the tides, Posidonius also measured the size of the Earth and the size of the Sun. His measurement of the size of the Earth was similar to the ideas we have heard before. He noted that at Rhodes the star Canopus would only ever peak above the horizon. But in Alexandria it would get up to 7 and a half degrees above the horizon. Alexandria was more or less due south from Rhodes and he estimated that they were about 5000 stades apart. From this, he was able to calculate the circumference of the Earth to be 240,000 stades, only about 6% too small from its true value. Unfortunately for Posidonius, his measurement wasn’t quite as accurate as Eratosthenes’s was, Erathosthenes you might recall, got within 1% of the true value. But Eratosthenes also seems to have gotten lucky and made a couple of mistakes that happened to almost exactly cancel each other out. Well, Posidonius also got fairly lucky because he, too, made two errors, Canopus isn’t exactly on the horizon in Rhodes, it’s more like a degree above it, and the distance is also shorter than he assumed, but these two mistakes ended up partially cancelling out, just not quite as perfectly as they had done for Eratosthenes. Nevertheless, Posidonius’s measurement was a good indication of the state of Greek science of the day and how not only was the spherical shape of the Earth by this point a settled question, but the approximate size of the Earth was well known as well.

To estimate the size of the Sun Posidonius also did something similar as Eratosthenes had done. You might remember that Eratosthenes had noticed that in the Egyptian town of Syene, the Sun cast no shadows on the summer solstice. Posidonius made an even stronger assumption than this and claimed that this was true in a region around the city with a diameter of 300 stades, or about 47 kilometers. Where Posidonius got this information we do not know. But he argued that this implies that some part of the Sun is directly above every part of this 300 stade region around Syene. This means that you can then draw a cone from the center of the Earth, through this circle around Syene, out to the Sun. If you know the size of the Earth and the distance to the Sun, this would tell you the size of the Sun. Now lucky for Posidonius he already had a measurement of the size of the Earth on hand, but he actually doesn’t use it. He instead used a value of 300,000 stades rather than the 240,000 that he had measured. He probably did this to keep the numbers nice and round, but it also does suggest that he probably wasn’t super confident in his own results. Well what about the second part — he also needed to know the distance to the Sun. For this, he just assumed that the distance to the Sun was 10,000 times the radius of the Earth. The only basis for this assumption was that Archimedes had made the same assumption in the Sand-Reckoner when he was trying to estimate how many grains of sand could fit in the universe. But Archimedes, in turn, had no real basis for this assumption. So, with no real justification, Posidonius just assumed that the Sun was 10,000 times farther away than the radius of the Earth and ended up with a diameter of the Sun of 3,000,000 stades. Well Posidonius ended up getting closer to the true diameter of the Sun than he had any right to be given that he essentially made up one of the numbers in his measurement and the technique as a whole is fairly dubious. His value of 3,000,000 stades would correspond to a diameter of about 500,000 kilometers, which is less than a factor of 3 smaller than its modern value of 1.4 million kilometers. Not bad for being, in effect, a blind guess.

Well, this is mostly the extent of Posidonius’s astronomy, at least his contributions to astronomy that aren’t really embarrassing. He also did make an estimate of the distance to the Moon but it relies on even sketchier arguments if you can believe it. There is much more that could be said of Posidonius the philosopher, he was one of the greatest intellects of his day and made contributions to a huge number of different fields, mathematics, history, ethics, geology and really all the branches of knowledge of the time. But we must move on to explore the rest of the vast wasteland that is Greek astronomy during the Roman Era.

After Posidonius died around 50 BC there are really no astronomers of note for about two centuries. Now I don’t want to mislead you with the impression that there was no astronomy at all in the intervening two centuries. That is certainly not the case. We have various artifacts that show that astronomy was indeed still practiced throughout this time, there are star charts, almanacs were drawn up, and after all people still needed to keep track of the calendar. There are some physical artifacts like celestial globes which were probably used to teach astronomy. And of course horoscopes from the time survive as well. But there wasn’t really anything new here. The astronomers of this period seem to have just been following the techniques developed by earlier astronomers and developed no new techniques of their own. As a consequence very few of their names survive. Ptolemy records that an astronomer named Agrippa observed an occultation of the Pleiades by the Moon in 92 AD, but other than that nothing about this fellow is known. Ptolemy also says that Menelaus of Alexandria observed occultation of the stars Spica and Acrab by the Moon when he was in Rome in 98 AD. We know a little more about the work of Menelaus since he developed the mathematics of spherical geometry in a book called Sphaerica which does survive. Although his motivation for studying spherical geometry was its application to astronomy, today he is more remembered as a mathematician than an astronomer.

All that said, while it appears that the astronomers of this period could do the basic things required of their job, generate almanacs, predict lunar eclipses, update the calendar, and so forth, some of the more cutting edge discoveries from earlier times had gotten a bit garbled. In particular, Hipparchus’s discovery of the precession of the equinoxes seems to have been either misunderstood, disbelieved, or ignored by many subsequent astronomers. Hipparchus had claimed that the position of the vernal equinox drifted westward at a rate of more than a degree per century. But other astronomers, left nameless in the sources, instead said that the location of the equinoxes oscillates. It drifts westward over the course of 640 years and then turns around and goes back the other way for another 640 years. And, in particular, they said that precession had reversed itself in the year 158 BC. Now how they came up with this bizarre theory requires a bit of speculation, but needless to say, they don’t come out looking good. What probably happened is that long ago Eudoxus had placed the location of the vernal equinox 8 degrees into the constellation Aries since this was consistent with the way that the Babylonians had marked the signs of the zodiac. Remember that in the ancient world, the locations of the constellations were not as precisely determined as they are today. Much later Pliny had done the same thing and put the vernal equinox 8 degrees into the constellation Aries. But midway in between these two, Hipparchus had put the location of the vernal equinox at the beginning of the constellation of Aries, not 8 degrees in. So probably some astronomers saw this variation and assumed that it implied that the locations of the equinoxes oscillated about, with the reversal occurring around the time that Hipparchus was active. The problem, though, is that the boundaries of the zodiac were not well defined in the sky. Their location was set by the location of the equinoxes, not the other way around. Hipparchus had just used a different convention than earlier and later astronomers, so this 8 degree discrepancy was unrelated to the true precession of the equinoxes.

And so with that we can just hop lightly over a period of about two hundred years and arrive at the last major figure in Greek astronomy — Claudius Ptolemy. In terms of the longevity of his influence it is hard to find any other scientist throughout history who beats Ptolemy. The model of the planetary motions that Ptolemy proposed stood virtually unchanged and unchallenged for nearly 1500 years. He and Plato were the only two figures out of the dozens I have discussed in the history of Greek astronomy, whose works were continually read, commented upon, and taught, maybe excepting Homer and Hesiod if we’re going to be generous and count them as astronomers. So it is sad to say that for such an influential astronomer we know next to nothing about him personally. His reputation stands on the weight of his work alone. For all intents and purposes, Ptolemy is simply the author of the Almagest and the Tetrabiblos and nothing more.

We can infer that he lived in the 2nd century AD based on the dates of some observations he records in the Almagest. His first observation was in 127 AD and his last was in 150 and he made his observations in Alexandria, so it is assumed that that is where he lived. Given that his name was Ptolemy and lived in Alexandria you might suppose that he was a member of the Ptolemaic dynasty, and some later medieval scholars did make this assumption, but there is no evidence for it. He was probably a Roman citizen since Claudius is a Roman name, and his family had probably been Roman citizens for several generations since oftentimes families would take as a Roman name the name of the emperor who extended them citizenship, and Claudius was emperor in the middle of the 1st century AD. You might think that it’s a bit unfair to the Romans that I’m including him in with the Greeks rather than showcasing him as the greatest Roman astronomer to ever live, but although he was a Roman citizen, the Romans by this point were no longer as picky as they once had been about extending citizenship to foreigners in conquered lands. So although legally he was a Roman citizen, culturally, he was almost certainly coming out of the Hellenistic tradition.

Well if we can’t say much about Ptolemy the man we at least have to say much about Ptolemy’s works. And fortunately there is a great deal to say there. Ptolemy has the excellent fortune of having had almost all of his works survive in complete form. Sometimes it survives in a Latin or Arabic translation rather than the Greek original, and sometimes those translations are of dubious quality, but nevertheless that’s doing head and shoulders better than almost any other figure from antiquity.

Ptolemy continues a trend that we’ve been seeing in that his works are very specialized. Most of the early Greek philosophers I talked about, Pythagoras, Heraclitus, Parmenides, Aristotle, they were interested in just about everything. And of course everything includes astronomy, so they wrote about astronomy. But as we start to get into the Hellenistic Era, generally speaking astronomers became more specialized. Astronomers like Apollonius or Aristarchus would write about sister subjects like mathematics or geography, but they generally weren’t writing so much about, say, ethics or epistemology. Now, after saying all this I have to caveat it that this is a generalization and there were exceptions. Thales, the first Greek astronomer I talked about is really only known for his astronomy. And I just spent the first half of this episode telling you about Posidonius, who was interested in just about everything under the Sun, along with the Sun itself for good measure. But Ptolemy’s works are very much in line with the kinds of works one would expect from an astronomer working toward the end of antiquity. He writes about astronomy, of course, but his other works are on closely related subjects. He wrote a book on optics, a book on geography, and a work on mathematics. To modern eyes the one work that would seem a little bit out of place is called Harmonikon and concerned music theory. But given the prevailing philosophies of the time, this was not really far outside his domain of expertise. Music theory in ancient Greece was intimately associated with the mathematics of ratios, the main question of the day being how determine the set of musical intervals that would produce the most harmonious music.

But really there is just one work that Ptolemy is known for, and this is, of course, the Almagest. Really its original Greek title was Mathematike Syntaxis, which translates roughly to Mathematical Treatise. This was a bit of a banal title, which later astronomers felt was ill-suited to a work of its scope and influence, so it came to be known as the Great Treatise since it represented the culmination of the whole of Greek astronomy. During the Islamic Golden Age, the work was translated into Arabic and the informal title, the Great Treatise also made its way into the Arabic title, Al-Majisti, which drops the rather self-evident treatise part, and left us with the superlative title, The Greatest. Once the work made its way back to the West it retained a Latinized version of this Arabic title, going from Al-Majisti, to The Almagest. Though, to be a bit pedantic, calling it The Almagest is a bit redundant, like saying an ATM machine, since the article “al” in Arabic means The. So saying The Almagest literally would translate to The The Greatest. That said it’s not the most redundant title out there. That honor would have to go to the Battle of The El-Alamein, which would literally translate to the Battle of the the the Amein.

Anyway before we get into the meat of the text I would be remiss if I didn’t relate the motto that Ptolemy begins his work with because it is really quite charming:

In studying the convoluted orbits of the stars my feet do not touch the Earth, and, seated at the table of Zeus himself, I am nurtured with celestial ambrosia.

Well the book begins by laying out same basic assumptions or axioms that will be the foundation for the planetary theory that makes up the bulk of the work. These assumptions should be familiar to us by now. He assumes that the heavens are a sphere centered upon the Earth. This is clear because if the heavens were centered somewhere other than the Earth, the stars would not trace circles in the sky as we observe them to do. Furthermore, the Earth is a sphere which does not rotate. Now he does consider the possibility that the Earth might rotate and actually acknowledges that this would make for a far simpler model. But he decides that it cannot be so basically on Aristotelian grounds. Earth is, after all, the heaviest element, and if the Earth were rotating the heaviest element would be moving faster than the air or aether, which is far lighter. Moreover, the exceedingly rapid motion of the Earth would cause great winds, and because the Earth would be rotating so quickly from west to east, we should never observe anything in the sky like birds or clouds move in the direction of the east. We see birds fly east or west with equal probability. How can this happen if the Earth is moving so rapidly in one direction as this hypothesis suggests. So, Ptolemy discards that hypothesis and concludes that more complicated a hypothesis or not, the Earth just does not rotate.

Now the Almagest was quite comprehensive in its scope, but it was most influential for its theory of planetary orbits so let’s start there. Ptolemy, of course, is closely associated with the theory of epicycles, but as I talked about in Episode 20, the theory of epicycles had been around for something like 300 years by this point, perhaps originating with Apollonius of Perga, or perhaps an earlier astronomer. To recap the basic theory of epicycles up until Ptolemy, the idea was that each planet revolved around a little circle called an epicycle, and the center of the epicycle, in turn, revolved in a great big circle around the Earth, called the deferent. For the superior planets, the period of the motion on the deferent was sidereal period, and for the inferior planets it was one year. And for all the planets, the motion along the epicycle had a period equal to the synodic period of the planet.

This basic theory was really quite good at explaining the main features of the planetary motions. It explained the retrograde motion that was seen once a year, it predicted the positions of the planets quite well, and it even accounted for other features like the fact that planets would get brighter at opposition, because according to the epicycle model, they would then be closer to the Earth. But in Episode 21 we learned that Hipparchus had noticed a problem with the basic epicycle model. Since everything is moving in perfect circles the motion should be exactly periodic. But Hipparchus noticed that the retrograde motion was not quite uniform. Sometimes the planet travelled backwards a different distance. And the time spent in retrograde motion varied as well. Not by much, but enough to be noticeable. Sadly, Hipparchus lacked the data to really do anything more than notice that there was a problem. But Ptolemy, working 300 years later, had more data to draw upon.

To model these variations in retrograde motion, Ptolemy introduced a new concept to the epicycle model, called the equant. In the original model, the center of the epicycle moved uniformly around the deferent, which was a perfect circle centered on the Earth. Ptolemy offset this circle from the Earth a little bit. But that wasn’t all. Ptolemy then placed a point on the opposite side from the center of the deferent as the Earth. This point he called the equant. Ptolemy then threw out the basic assumption that had been a part of Greek astronomy since the time of Plato, that orbits consist of uniform circular motions. Instead, he said that the planet appeared to move uniformly when viewed at the location of the equant, rather than at the center of the deferent. In other words, the angular velocity of the planet would be constant relative to the equant, but would vary relative to the center of its orbit.

The consequence of this is that each planet’s orbit gained a kind of eccentricity, eccentricity literally meaning out of the center. Not exactly the same eccentricity as an ellipse has, but the offset circle produced a behavior that was very similar. Due to this offset and the variable angular velocity, a planet’s motion would not be constant over time, sometimes it would be faster, and sometimes slower. Moreover, because sometimes the epicycle would be closer to the Earth, it would appear larger, and the planet would travel a larger distance in retrograde motion. Other times, the epicycle would be on the other side of the equant and it would appear smaller, producing less retrograde motion.

So this, in its bare bones, is the theory of epicycles, deferents, and equants, which Ptolemy created and stood more or less unchallenged for some 1400 years. Ptolemy’s theory has a reputation for being fearsomely complicated, but really the mechanics of it are quite straightforward, even if they are admittedly a little weird. You have planet moving in a little circle, and that little circle moves in a big circle somewhat offset from the Earth. But it doesn’t move uniformly about that circle, it instead moves in such a way that its angular motion is uniform with respect to a point on the opposite side of the center of the deferent from the Earth. That is all there is to it. So what are we to make of this theory?

Well there are two ways we can approach it. First I think it would be worthwhile to see how it fits in with our modern understanding of the orbits of the planets. Now of course since the time of Kepler our understanding of planetary motions is that the plants move in elliptical orbits where one focus is centered on the Sun. But the motion along the ellipse is not uniform. According to Kepler’s second law, the planets sweep out equal areas in equal times, so when they are closer to the Sun they move faster and when they are farther from the Sun they move more slowly.

So with that in mind, the purpose of the epicycle is quite clear. In Ptolemy’s theory, all the planets revolved about the Earth, but in reality, they revolve about the Sun, as does the Earth. The epicycle is nothing more than the orbital motion of the Earth superimposed upon the planet. The relationship between the epicycle and the Earth’s orbit was unfortunately obscured by the way that Greek astronomers measured the periods of motions about the epicycle. For them, they measured the period from the time that the planet was closest to Earth on the epicycle to the next time that it was closest to Earth on the epicycle. But because the epicycle was moving around the deferent as this was happening, and all the planets moved at different speeds around their deferents, they all had different periods. But if instead you measure the motion about the epicycle relative to the background stars, you find that it is exactly one year for all the planets. So the epicycle essentially served to transform a heliocentric system into a geocentric system.

Okay, so what about Ptolemy’s main innovation, the equant, what is that doing? In the original theory, all the motions were perfectly circular. But today we know that the orbits of the planets are not circular, they are elliptical. Now, it turns out that the orbits aren’t very elliptical. If I drew the orbit of Mars, which has a fairly high eccentricity, you’d have a hard time telling it apart from a circle. But the fact that the orbits are not quite circular manifests itself in two ways. The retrograde motion we see in the superior planets happens when the Earth overtakes a planet in its orbit. But because the orbits are a little elliptical, sometimes the planet is a little closer to Earth and sometimes it’s a little farther away. If it happens to be closer you’d expect to see more retrograde motion, and if it’s farther you’d expect to see less. This is pretty well modeled by taking the center of the circle of the planet’s orbit and shifting it a little bit away from the Earth.

This then leaves the last part of the theory, the uniform motion about the equant, what’s going on there? By shifting the center of the orbit of the planet away from the Earth, we have actually created a reasonable approximation of an elliptical orbit, at least for orbits that aren’t too eccentric. Shifting the center away from the Earth now puts the Earth at one of the foci of the ellipse. Now, of course, in reality the Sun is at one of the two foci, but we have essentially used the epicycle to swap the Earth and the Sun. But, what is still unaccounted for is Kepler’s second law, namely that the planet does not move uniformly on its orbit. Now, back in school, when you first learned about the planets moving in elliptical orbits and that the Sun was at a focus of the ellipse, you may have wondered, well, an ellipse has two foci — the Sun is at one focus, but what’s going on at the other focus? Usually the response is that there’s nothing special about the second focus. From a physical perspective this is true, there’s no special gravity or anything at the second focus. But, the second focus in an elliptical orbit does have one special property. It turns out that, at least for modest eccentricities, if you sit at the second focus and observe the planet’s motion around you, you will see that it is approximately uniform. The math to derive this is a little annoying but it all falls out of Kepler’s laws. At the second focus of an elliptical orbit, the angular velocity of the planet is approximately uniform. So, with this in mind, the purpose of the equant immediately becomes clear. In modern terms, the Earth is at one focus of a planet’s elliptical orbit, and the equant is at the other. As such the orbital motion of the planet is uniform about the equant, not the center of the deferent. So, really rather remarkably for a theory that gets a lot of things fundamentally wrong, Ptolemy’s model of planetary motion captures the main features of the true, elliptical orbits of the planets. It gets the retrograde motions about right, along with their variations, and it gets the non-uniform motions of the planets about right as well.

So, this then brings us to the second way we can try to understand Ptolemy’s model — through his own eyes. How did Ptolemy manage to come up with this idea? Now, unfortunately he does not just come out and tell us. But we can kind of reverse engineer how he might have gone about it. The biggest problem he had to solve was the variable retrograde motion, and that problem had a fairly straightforward solution. Shift the center of the planet’s orbit away from the Earth, and boom, problem solved. Sometimes the planet is close and there’s more retrograde motion, and other times it’s farther away and there’s less. But how did he come up with the idea of the equant? What probably happened is that he had also known that the planet’s overall motion, independent of the retrograde motions, was not uniform. Now, once again, there is a simple solution to this — just shift the planet’s circular orbit away from the Earth. This would make it appear to move non-uniformly when viewed on the Earth. But then when he went to actually calculate the magnitude of these offsets he would have found that they didn’t match. In fact, the offset needed to explain the non-uniformity of the planet’s motion would have been twice the offset needed to explain the variation in the size of the retrograde motions. Having been presented with these two conflicting offsets, he may have just smushed them together. The physical center of the planet’s orbit was the smaller offset and explained the variation in the size of the retrograde motion, but then he imposed a uniform motion about the second offset to explain the non-uniformity in the epicycle’s progress across the sky relative to the Earth. Since the planet only needed to be physically closer for one of these offsets, this hack basically held together, even if it did more or less abandon the centuries-old principle that the planetary motions had to be explained using uniform circular motions. Now at this point I think it’s worth noting that I don’t think there is much evidence that there was something sacred about this particular requirement, that planetary models had to be composed of uniform circular motions, if we can even call it a requirement. It started all the way back with Plato who, of course had his own philosophical justifications for preferring such models. But centuries later, by the time we get to Ptolemy, and even in the earlier time of Apollonius or Hipparchus, it’s not really clear that they were philosophically wedded to this idea. More probably the reason that uniform circular motions dominated Greek planetary models is that uniform circular motions are really, really easy to work with. Modern mathematical concepts that we take for granted like algebraic geometry and trigonometry, were not well developed in ancient Greece. When you read the original texts, these astronomers had to spend pages and pages in intricate geometrical arguments to prove propositions that we could do in a handful of lines of trigonometry today, and in many cases ancient Greek astronomers couldn’t even get exact results, but could only calculate approximations. But circles were something they could easily work with, so it’s no surprise that circles formed the foundation of their planetary models.

Now one detail that I’ve elided is that Ptolemy found that he did need to make an extra tweak to get things to work for Mercury. The inferior planets are a bit trickier to model in a geocentric model because the epicycle now has to be quite large since the planet is now on the inside of the Earth’s orbit. To model Mercury’s different amounts of greatest eastern and western elongations, he had to put the center of the deferent on its own little orbit that had a period that was one half the period of the epicycle around the deferent. This had the effect of turning Mercury’s orbit into an oval shape which more closely approximated its true elliptical shape. Even still, the model didn’t do a great job with Mercury which is a tricky planet to model anyway — really it’s motion wasn’t well explained until the 20th century with the development of the general theory of relativity. But fortunately for Ptolemy, it’s also a tricky planet to observe, it only appears low on the horizon right after sunset or before sunrise, so the errors in the model would have been hard to detect.

Well, there is one other component to Ptolemy’s planetary theory. So far I have only been talking about the ecliptic longitude of the planets, which, to be fair, is the most prominent component of planetary motions. The positions of the planets are confined to the zodiac, but in addition to moving through all the longitudes through the zodiac, they do also move north and south of the ecliptic a little bit as well. This latitudinal motion was essentially ignored by Apollonius and Hipparchus, but Ptolemy does consider it. What he does is he orients the deferent of each planet at some angle relative to the ecliptic. Now, this works pretty well, but the epicycle cannot be oriented at this angle — it is exactly parallel to the ecliptic. This makes perfect sense in the modern context, the epicycle is just the orbit of the Earth, so it has to be exactly on the ecliptic. But things couldn’t be quite so simple for Ptolemy. For whatever reason, he found it more natural for the epicycle to be inclined at the same angle as the deferent, but then adds an additional, little epicycle, oriented perpendicular to the ecliptic, which, in effect, keeps the planet’s motion along the epicycle parallel to the ecliptic. For what it’s worth, Ptolemy himself recognized that this was not the most elegant theory. He writes:

Let nobody, looking at the imperfection of our human contrivances, regard the hypotheses here proposed as too artificial. We must not compare human beings with things divine.” “The simplicity itself of celestial processes should not be judged according to what his held simple among men.

Ptolemy also discussed in some detail a theory of the Sun’s orbital motion, but there’s not much to say on the subject because, perhaps surprisingly, Ptolemy didn’t really make any modifications to Hipparchus’s models of the Sun’s motion. He discusses the phenomenon of precession, but seems to have made it into a nice round number, 1 degree / century, which was way too small. Strangely, if you back out what the precession should have been from his star catalog, you get a number that is much closer to the truth, 1 degree / 78 years, but for whatever reason Ptolemy did not use that value even though he could have. He also just continued to use Hipparchus’s measurement of the location of perihelion, the point in the Earth’s orbit where it is closest to the Sun, and where the Sun moves fastest on the sky. This location gradually changes over time, so over the three centuries between Ptolemy and Hipparchus, his assumption about where perihelion was came to be more than 5 degrees off. Taken all together, all these inaccuracies meant that Ptolemy’s solar calculations were not very good. He could be off by as much as 1 and a half degrees which is really quite a lot and could have been measured by him fairly easily. It’s hard to say why his solar theory is so much worse than his planetary model and lunar theory. It’s possible that he just had less interest in precision measurements of the Sun’s position or that he lacked the equipment to do them.

Well the last celestial body to model is the Moon, and unlike with the Sun, Ptolemy made some real advances here. As with everything else, he started with Hipparchus’s epicycle model as his foundation. But he noticed that Hipparchus’s epicycle model of the Moon was not always quite accurate. The position of the Moon would line up with the prediction at new moon and full moon, but it could be off during first and third quarters. But even then, it wasn’t always off, just sometimes. But when it was, the moon could be more than two and a half degrees away from where it was supposed to be according to Hipparchus.

Today this phenomenon is called evection and it’s understood to be due to oscillations in the Moon’s orbital parameters due to the gravitational torque imposed by the Sun. To model it, Ptolemy adopted a similar strategy that he used for the planets. He shifted the center of the Moon’s orbit away from the Sun, and similar to the orbit of Mercury, he then made the offset center revolve around the Earth twice a month. This added a sort of oval shape to the Moon’s orbit such that its position was identical to the original model at new and full moon, but had an offset during first and third quarters. Now, as a model of the Moon’s position, Ptolemy’s theory was remarkably successful. It incorporated what have turned out to be fairly subtle orbital phenomena. But as a physical model it was really quite garbage. The offset that Ptolemy had to shift the Moon’s orbit by was so large that the Moon’s distance to the Earth would have varied by a factor of two. So from first quarter to full moon you would see the moon shrink to half its size, and then grow back to that size from full moon to third quarter. This clearly doesn’t happen and Ptolemy must have known it. Given the various bells and whistles in Ptolemy’s models, it seems pretty clear that he did not exactly regard his models as being perfect physical models of the heavens. Rather, he seems to have been satisfied just with being able to predict the positions of the planets on the sky.

So, now that we’ve seen Ptolemy’s models for the motions of all the heavenly bodies it’s worth stepping back for a moment and asking why it was that the geocentric model persisted for so long. With the benefit of hindsight, we can see that there were some pretty massive clues lurking in Ptolemy’s model that the Sun was at the center of things. If he had measured the period of the epicycles, he would have seen that the period of every planet around its epicycle was exactly one year, just the same as the period of the Sun around the Earth, and this is exactly what you’d expect to see if everything were revolving around the Sun. Furthermore, the inclination of the epicycle was different from the inclination of the deferent, and was the same for all of the planets — again, exactly what you’d expect if the Earth were going around the Sun. More generally, modeling the changes in the ecliptic latitudes was very difficult to do in his geocentric model. Since the orbits of the planets are inclined relative to a point centered on the Sun and not on the Earth, when viewed from the Earth, the whole orbit is offset from the ecliptic, but this offset disappears when the Sun is taken as the center of the system. Lastly the motion of the inferior planets was pretty hard to square with a geocentric theory. If you go and calculate where the center of Venus’s epicycle is, you’d find that it is in exactly the same position as the Sun itself. So there were plenty of clues that the Sun was at the center of things. But, many of these clues can really only be appreciated in retrospect. The center of Venus’s epicycle was indeed the location of the Sun, but just from looking at the parameters of his model, it doesn’t seem that Ptolemy noticed that this was the case. It’s not obvious. In order to discover that the offset of the orbits from the zodiac could be eliminated if the planets were centered on the Sun Ptolemy would have had to try to do that calculation, and he didn’t really have any reason to try it in the first place. More broadly, today we may look at this model and see the influence of the Sun cropping up in the motions of all the planets, and thereby conclude that it would be simpler if the Sun were at the center of the system. But this isn’t always true. The influence of the Sun also shows up in the Moon’s orbit in Ptolemy’s model, but we can’t conclude from that that the Moon revolves around the Sun. So although there are a lot of clues pointing you towards a heliocentric model, it’s understandable that Ptolemy might not have noticed them. What is maybe less understandable is that no one noticed that things could be simplified in a heliocentric system for another 1400 years, but that probably has more to do with broader social factors than anything else. Ptolemy’s work was very, very hard to understand and from late antiquity through the middle ages, there just weren’t a lot of people who were intimately familiar with it and could propose fundamentally new approaches to doing things. But I will have to save a more complete discussion of that subject for when we get to astronomy in the Middle Ages.

Well, although the bulk of the Almagest is concerned with these various models of planetary or lunar motion, in the middle of the treatise Ptolemy also includes a fairly extensive stellar catalog. It’s generally believed that the bulk of Ptolemy’s star catalog was essentially copied from Hipparchus’s original star catalog 300 years earlier. The main reason for this supposition is that Ptolemy definitely knew about precession as he talks about it in his work. But around 800 stars in his catalog have the wrong position. They’re about 1 degree off from where they should be. It seems that what had happened is that Ptolemy took Hipparchus’s measurements, and then applied a correction for precession. But he assumed that the rate of precession was 1 degree per century, when in fact it is more like one degree every 72 years. Over the course of 300 years, he ended up about a degree off. Scholars have also noticed that the positions of most of the stars in the catalog are given in intervals of a sixth of a degree, but some of them are given at fourths of a degree. This seems to indicate that separate instruments were used for those different stars.

Well, in addition to the positions of the stars in his catalog, Ptolemy also singles six stars out and gives them a color. In the Greek he calls them “hypokirros” which literally translates to yellowish. There is an interesting strand of scholarship that puzzles over the bizarre ways in which the ancient Greeks described colors. In the 19th century a popular theory was that ancient Greeks were colorblind. The most famous example is probably from Homer, who consistently describes the color of the sea as “wine dark” even though today we would call the sea blue, or maybe greenish-blue, but certainly not the color of a red wine. And Homer also describes the sky as bronze which seems even more implausible.

Well, in the case of Ptolemy, the six stars he gives a yellowish color to are Aldebaran, Betelgeuse, Arcturus, Antares, Pollux, and Sirius. Today we would describe the first five of these as red, not yellow, and in fact they are literally called today red giants. Sirius is the odd man out in this list. It’s the brightest star in the night sky and is very distinctly blue. It’s a little hard to explain why Ptolemy describes it as yellowish and puts in the same category as an extremely red star like Antares, which is so red that its name literally means “rival of Mars.” To confuse matters even further, Ptolemy isn’t the only one to do this. Many ancient sources describe Sirius as being red, yellow, or copper colored. Up through the 19th century, some astronomers hypothesized that the color of the star had actually changed since ancient times. In antiquity perhaps it really was yellow or red and then at some point changed to blue. Now our understanding of modern astrophysics tells us that stars generally do in fact change their color over the course of their lifetime, but a change in the color of Sirius in particular in a time span of just 2000 years is far too rapid and is definitively ruled out by modern stellar theory. And for what it is worth, Sirius wasn’t universally described as yellow or reddish. The poet Marcus Manilius described Sirius as azure blue. And in the ancient world, the colors assigned to stars weren’t necessarily a literal physical color as we would use it today, but were oftentimes representative of an astrological character. So certain stars were sometimes described as black even though that would be physically impossible if for no other reason than the star just couldn’t be observed.

Well there are a few other bits and bobs in the Almagest, Ptolemy goes through a measurement of the distance to the Sun, but it’s fairly similar to the technique that Hipparchus used, just a lot more complicated so it’s not really worth going into. The whole book is several hundred pages long and very dense, so I’ve had to just pick out the highlights from it. Although it never went out of print, so to speak, it is a difficult enough text that it was one of those books that fell into the category of being more admired than read. Everyone had heard of it, but it was only deeply understood by a very few.

There is one other work of Ptolemy’s that is worth commenting on, and this is the Tetrabiblos, written at the end of his life. Tetrabiblos literally means “four books,” which as a title doesn’t really tell you very much, except, I guess, to keep going after you finish the first one. But, to be fair, after writing a book that literally ended up with the title “the greatest,” anything after that was going to be a bit of a let down.

The Tetrabiblos is the companion text to the Almagest. The Almagest was a complete treatise of known astronomy at the time, and the Tetrabiblos was a complete treatise of known astrology of the time. At this point I think it’s worth pausing and getting up to speed a little bit on the state of astrology in late antiquity. Back in the early episodes I spent a fair amount of time talking about Babylonian astrology. Their approach to astrology was rather different than how we think of astrology today. To the Babylonians, the gods would place signs in the sky which the wise could read to understand what was happening in the world. The gods, of course, were only concerned with the grandest of human affairs — astrological omens would portend wars, famines, the death of a king and so forth. The gods weren’t going to bother putting up a sign in the heavens for a peasant like you.

Now, over the course of the Hellenistic Era, there was increasing cultural contact between the Greeks and the Babylonians, though by this point they are often called the Chaldeans. One of the results of this was that astrology started to play an increased role in Greek society. But there was a problem with the Babylonian philosophy of astrology. To them, the gods would place a sign in the heavens as an omen of an upcoming event. These signs were usually lunar or solar eclipses, a planet going retrograde in a particular constellation, or a planetary conjunction. But by this point, Greek astronomers had more or less figured all these things out. They had models of lunar and solar eclipses and models of planetary motions. These couldn’t be a sign that the gods placed in the skies because the gods weren’t really choosing to do anything at all — the planets obeyed regular laws that astronomers knew about. So the interpretation of astrology shifted. Rather than events in the heavens being a sign from the gods, the heavens themselves came to have a causal impact on life here on Earth. And this interpretation had a democratizing consequence because the heavens hang above us all equally. The Babylonian gods could only be bothered to put up signs for the rich and famous. But if a planet’s position in the sky was having some causal influence on us here on Earth, it would have that influence on all of us just the same, prince or pauper. So, as astrology permeated into Greek culture, it began to develop a more individualistic flavor.

Ptolemy’s Tetrabiblos reflects both these approaches to astrology. His first book is in essence a defense of the practice of astrology and an exposition of the basic principles that motivate it. One of the principle criticisms of astrology today is that astrologers have a pretty poor track record of actually predicting anything. But this argument isn’t exactly modern. Ancient astrologers also had a pretty poor track record of predicting anything and their failures to predict anything didn’t go unnoticed. Ptolemy nevertheless defends the practice essentially by saying that life is messy and complicated. The heavens can provide a subtle influence, but this can be overwhelmed by random, unrelated circumstances. We can predict, for example that on average June will be warmer than May, but that doesn’t rule out the possibility of a cold spell in June. Similarly, we should be able to predict certain general patterns on an individual’s temperament based on the influence of the heavens at the time of their birth, but this doesn’t rule out deviations from this pattern due to random events in their life.

One of the main ways that Ptolemy’s astrology worked, which persisted into the middle ages, at least in its general approach, was by collecting pairs of opposing attributes and assigning those attributes to the different planets. So Mars is associated with the attribute of dryness, which leads to a destructive, evil influence, whereas Jupiter is associated with the attribute of moistness, which is conducive to growth.

The second book of the Tetrabiblos is more in the line of the traditional Babylonian style of astrology and is called “mundane astrology.” Here Ptolemy examines the influence of the heavens on entire groups of people. Some of this is more or less accurate. Ptolemy says that people who live at lower latitudes have darker skin and thick curly hair to protect them from greater heat, and those at higher latitudes have fairer skin and thinner hair. But he also divides the world into four quarters, each of which are ruled by varying degrees by different planets. In the northwest, which for Ptolemy included Spain and Britain, the dominant planets were Jupiter and Mars, both of which were masculine and domineering. As a consequence Ptolemy claimed that these people were independent and martial and the men had a low regard for relationships with women.

The third book gets into the more individualistic Greek style of astrology and covers what you think of when you imagine astrology today. Given the date, time, and location of an individual’s birth, how do you construct a horoscope to predict qualities of the individual’s personality and what the nature of their life will be — will they live a long time, have good fortune, so so forth.

The last book has to do with what we would maybe call “Advanced Topics.” For example, how do you combine the horoscopes from two different individuals to see whether or not a man and woman will be a good match? At the end of the book, Ptolemy then describes how the influence of the planets changes over the course of one’s life. According to Ptolemy, a person’s life can be divided into seven stages, each of which is associated with a particular planet, starting with the closest one, the Moon, and ending with the most distant, Saturn. So at the beginning of one’s life is the period of infancy, which is associated with the Moon. Just as the body rapidly grows in infancy, of all the celestial objects the Moon is the one that most rapidly grows and wanes. Following infancy is the period of childhood which is associated with the planet Mercury. Mercury was seen as the lightest and flightiest of the planets, since it is relatively faint and seen to flit back and forth between either side of the Sun. In the same way, children run around and are at one moment concerned with one thing and in the next forget about it and move on to something else. Around puberty, one enters the period of youth and the dominant influence becomes the planet Venus. Consequently, for the first time one’s thoughts turn to love. After coming of age, one enters the period of young adulthood where the dominant influence is the Sun. Now one’s life is characterized by vigor, work, and people start to take you seriously. After a period of about 20 years, one then enters into late adulthood where the dominant planet shifts to Mars. Now, one’s demeanor becomes more severe. One has certain goals one wants to accomplish in life and realizes that there is not as much time to accomplish them as one would like. Around one’s mid 50s one enters into maturity, characterized by Jupiter with the attributes of gravitas and respect, one has achieved a position of authority in the community. And finally, by one’s late 60s, one enters into old age, characterized by Saturn, the god of time, and grows slower and weaker.

So with that, we have the zenith of Greek astronomy in the works of Ptolemy. Greek intellectual life trundles on through the Roman Era for another couple of centuries before the Western Empire falls, but there are no more Greek astronomers anywhere close to the stature of a Ptolemy or Apollonius, let alone a Hipparchus. Of course, astronomers still existed through this period, there was Porphyry of Tyre and Martianus Capella, and, in fact, many of the authors of the surviving sources on early Greek astronomy lived during late antiquity. And I can’t end this episode without at least mentioning the astronomer Hypatia who edited part of the Almagest and was murdered by a Christian mob. But given that we’ve spent this episode on the best that Greek astronomy achieved, I want to end this episode on a high note, so the sad story of Hypatia will have to wait for a future episode.

But now that after 17 episodes we have finished with Greek astronomy, where will this podcast go next? In the next month I would like to swing back and catch up with a culture which has rudely butted into the story on Greek astronomy from time to time, namely the Romans. I hope you’ll join me then. Until the next full moon, good night and clear skies.

Additional references

• Freeman, Philip, The Philosopher and the Druids