The Moon and the Planets in Classical Greece and Rome
The Moon and the Planets in Classical Greece and Rome
- Robert HannahRobert HannahUniversity of Waikato
While the moon naturally featured in Mediterranean cultures from time immemorial, principally noted in the earliest literature as a marker of time, time-dependent constructs such as the calendar, and time-related activities, awareness and recognition of the five visible planets came relatively late to the Greeks and thence to the Romans.
The moon underlies the local calendars of the Greeks, with documentary and literary evidence from the Late Bronze Age through the Imperial Roman period, and there are signs that the earliest Roman calendar also paid homage to the moon in its divisions of the month. However, although Homer in the 8th century BCE knows of a Morning and an Evening Star, he shows no indication of realizing that these are one and the same, the planet Venus. That particular identification may have come in the 6th century BCE, and it appears to have been not until the 4th century BCE that the Greeks recognized the other four planets visible to the naked eye—Saturn, Jupiter, Mars, and Mercury. This awareness probably came via contact with Babylonian astronomy and astrology, where identification and observations of the planets had figured from the 2nd millennium BCE and served as a basis for astrological prognostications. But it is time, not astrology, that lies at the heart of Greek and Roman concerns with the moon and the planets. Indeed, the need to tell time accurately has been regarded as the fundamental motivation of Greek astronomy.
A major cultural issue that long engaged the Greeks was how to synchronize the incommensurate cycles of the moon and the sun for calendrical purposes. Given the apparent irregularities of their cycles, the planets might seem to offer no obvious help with regard to time measurement. Nonetheless they were included by Plato in the 4th century BCE in his cosmology, along with the sun and moon, as heavenly bodies created specifically to compute time. Astrology then provided a useful framework in which the sun, moon, planets, and stars all combined to enable the interpretation and forecasting of life events. It became necessary for the Greeks, and their successors the Romans, to be able to calculate as accurately as possible the positions of the heavenly bodies in order to determine readings of the past, present, and future.
Greek astronomy had always had a speculative aspect, as philosophers strove to make sense of the visible cosmos. A deep-seated assumption held by Greek astronomers, that the heavenly bodies moved in uniform, circular orbits, lead to a desire over the centuries to account for or explain away the observed irregularities of planetary motions with their stations and retrogradations. This intention “to save the phenomena,”— that is, to preserve the fundamental circularity—was said to have originated with Plato. While arithmetical schemes had sufficed in Babylonia for such calculation, it was a Greek innovation to devise increasingly complex geometric theories of circular motions (eccentrics and epicycles) in an effort to understand how the sun, moon, and planets moved, so as to place them more precisely in time and space.
- History of Ideas about Planets and Planetary Systems
Time and time-keeping lie at the heart of Greek and Roman concerns with the moon and the planets; indeed, the need to tell time accurately has been regarded as the fundamental motivation of Greek astronomy (Dicks, 1966, p. 39). This necessity governed human activities on land and sea, and it caused the Greeks and Romans to look to the heavenly bodies to provide signals for when to sow and harvest on the farm, when to set sail or avoid voyages by sea, when to hold their religious festivals, when to conduct regular political activities, when to undertake significant ventures, and other daily activities (Hannah, 2005; Michels, 1967; Pritchett, 2001; Stern, 2012). This is not to say that farmers and sailors, priests and politicians were completely dependent upon these astronomical signals before undertaking any enterprise, but the celestial bodies provided an adjunct set of warnings for when activities should take place (Grenfell & Hunt, 1906; Reiche, 1989).
The need to comprehend the motions of the sun and moon for calendric purposes overrode for a long period any detailed study of the motions of the other planets—the word planet (πλάνης) means “wanderer” in Greek and the sun and moon were counted also as planets, since they wandered, in contrast to the “fixed” stars that form the backdrop to the night sky (see Gregory, 2000, pp. 105–109 on the distinction between this use of the word πλάνης, which in other contexts means “disorderly” and which is not an attribute of the cosmos from the Greek perspective). From the 4th century BCE onward, however, the Greeks gave increasing attention to the motions of the planets, particularly to finding geometric ways not only to calculate and predict their positions for practical purposes, but also to explain their apparent diversions from uniform, circular motion in a philosophical quest to “save the phenomena.” Older arithmetical methods of calculating planetary positions, borrowed from the Babylonians, combined with geometrical models, enabled the Greeks to produce geared mechanisms and tables of planetary positions that were, for their time and purposes, remarkably accurate.
Three developments warrant special mention in the long period of development of the topics under discussion. The first relates to the study of ancient astronomy under the influence of the “Brown School of the History of Science.” Otto Neugebauer (b. 1899–d. 1990) is regarded as the founder of this loosely constituted school (not all were members of Brown University, where Neugebauer was based), and its hallmarks were a focus on mathematical astronomy and on the translation and analytical study of Egyptian, Babylonian, Greco-Roman, Indian, and Islamic mathematical texts through to the Renaissance. Neugebauer’s crowning publication was the magisterial and still highly influential A History of Ancient Mathematical Astronomy (Neugebauer, 1975), but also fundamental to any study of ancient astronomy are his seminal editions and analyses of Babylonian and Egyptian texts and documents (Neugebauer, 1941–1943, 1955 Neugebauer & Parker, 1969; Neugebauer & Sachs, 1945). Building on the work of early 20th-century scholars, such as Franz Xaver Kugler, S. J., who pioneered the decipherment of Babylonian cuneiform texts for their scientific content (e.g., Kugler, 1907–1935), Neugebauer firmly established the existence of the exact sciences of mathematics and astronomy in the Near Eastern and Greco-Roman worlds. Others who worked with or alongside Neugebauer included Richard Parker, Abraham Sachs, Gerald Toomer, and David Pingree. In a recent reflection on the “Brown School,” Francesca Rochberg has usefully discerned a distinction between the science of Neugebauer (the founder) and Pingree (the last holder of the Chair of the History of Mathematics at Brown) (Rochberg, 2016). She noted that these two scholars did much to shift 20th century perceptions of science from a practice seen simply as a heritage of a purely Greek way of thinking, achieving this shift through their extension of our knowledge of Western and South Asian ways of thinking about the world of knowledge. Nonetheless, she showed, they differed in their appreciation of what science is: Neugebauer saw it as a unity irrespective of any cultural contexts, while Pingree saw its geographical disunity and its cultural constructedness. Much work since Neugebauer has indeed expanded our awareness of the cultural context of ancient scientific endeavours. It is not that Neugebauer was ignorant of this cultural context, particularly with regard to Greek and Babylonian astronomy and astrology (he wrote knowledgably on the latter as well: Neugebauer & van Hoesen, 1959), but at times he seems to have had a blind spot with regard to some cultural demonstrations of astronomical knowledge, particularly in his approach to Egyptian astronomy. Recent works (e.g., Belmonte, Shaltout, & Fekri, 2008; Magli, 2013; Quack, 2016) represent a welcome antidote to Neugebauer’s famous dismissal of Egyptian mathematical astronomy in a handful of pages (Neugebauer, 1975, pp. 559–565). That its astronomy was not so bound to mathematics as Babylonian and eventually Greek astronomies were may be true, but an increased number of papyri and new data on the astronomical orientations of pyramids and temples in Egypt are now available to indicate the complexity and sophistication of Egyptian astronomy and the need to understand its scientific character within its own cultural setting.
The second noteworthy historiographical development concerns advances in the study of ancient calendars. The Opus de Emendatione Temporum of Joseph Justus Scaliger (1629) established new standards in the study of ancient chronology. Such study in itself was not new, nor was the methodology of combining astronomical studies with philology and adding ancient Near Eastern history to the conventional study of Greece and Rome. Rather, what was significant was the extreme care that he took over the compilation of the ancient calendars, which laid the basis for the current understanding of the relationship between the various ethnic calendars of the ancient world; the establishment of an independent epoch in the form of the Julian Period, which is still used in astronomy; and the formulation of a rigorous method of source criticism, which set aside well-established forgeries that had formed the foundation of previous chronologies (Grafton, 1975). On this foundation much later scholars like Ideler and Ginzel built their substantial works on ancient chronologies and calendars (Ginzel, 1906–1914; Ideler, 1825–1826). Ginzel’s tables in particular were excerpted (although not always accurately) by Bickerman (1980). From general studies like these, scholars developed more regionally focused studies, such as those of Samuel (1972), on Greek and Roman chronology, and Trümpy (1997) on Greek calendars. Trümpy in particular demonstrates the increasing tendency of the later 20th century to analyze calendars as products of the highly localized cultural environments that constituted ancient Greek city states. Mikalson (1975) was a very precise case in point, devoted solely to the sacred calendar of Athens. Chronography has long been the preserve of experts—Scaliger had the reputation of not suffering fools or the ignorant—but there are now works that seek to open up the study to a wider public by explaining the astronomy and the documentary evidence that underpin the results (Hannah, 2005; Samuel, 1972).
The final development worth noting relates to the increased knowledge that we now have of mechanical representations of the cosmos as a result of research into the Antikythera Mechanism. Discovered by chance in 1900, in the underwater wreckage of an ancient ship off the coast of the island of Antikythera, south of the Greek mainland, the fragments of this complex mechanical instrument—now 82 in total, of variable size and preservation—continue to tell us much about Greek astronomical science and mechanical engineering in the 2nd century BCE.
In 1972, X-rays were taken of the Mechanism by radiographer Charalambos Karakalos for the physicist Derek de Solla Price. These showed that it originally comprised over 30 interlocking, toothed gears, and several plates that were interrelated by their capacity to mark time in various ways—an Egyptian calendar, a zodiac dial, and a star calendar (parapegma). These discoveries led Price to attempt a reconstruction and ultimately to publish his findings in a monograph (Price, 1974). For him, the instrument was a type of calendar computer, a loose term nowadays since it was not programmable, but adequate for his time.
In the 1990s, Michael Wright, initially collaborating with Allan Bromley and researching as an individual since Bromley’s untimely death, has manufactured the most detailed physical reconstructions of the Mechanism and worked toward explaining its underlying astronomical theory and outputs in a long series of publications (e.g., Wright, 2007). In its time, Mogi Vicentini’s virtual reconstruction in 2009 of Wright’s model version 2 provided a brilliant opportunity to imagine the device as a whole and also to appreciate the extraordinary engineering skill that lies behind its construction (see The Antikythera Mechanism).
The most recent investigators of the device are the members of the Antikythera Mechanism Research Project (AMRP), originally led by Tony Freeth and Mike Edmunds and comprising three teams from the United Kingdom, Greece, and North America; and the UCL Antikythera Research Team, of which Freeth is a member and which is based at University College London. Indeed, two videos by Freeth provide the most immediate visual introductions to the Mechanism, one being a remarkable lecture given at the Stanford Humanities Center in 2016, the other a more recent update by the UCL Team, which shows a radically different reconstruction of the gearing (Figure 1). X-ray computed tomography and Polynomial Texture Mapping, developed by Hewlett Packard, have been particularly useful for the AMRP to provide much more data capable of interpretation than had been visible under standard X-ray. These investigations have clarified the interconnections of the gearing and enabled more and more precise reconstructions of the device, and they have provided detailed images of the minute inscriptions from the fragments that enable us to understand better what the instrument was used for (Figure 1). The Mechanism’s complex train of more than 30 gears, moving at different speeds, were arranged so as to coordinate otherwise discordant time-scales. It managed to correlate the motions of the sun and the moon, via the 19-year Metonic Cycle, and of the five planets known to antiquity in epicyclic motion through the zodiac. The device could also be used to compute eclipses, and it had a dial to signal the two- and four-yearly games festivals at Olympia, Isthmia (near Corinth), Delphi, Nemea, Dodona, and possibly Rhodes. A parapēgma, or star calendar, also coordinated with dials giving the zodiacal year, the Egyptian calendar and even a civil calendar, which was probably the Epirote variation of the Corinthian calendar (Iversen, 2017). The explanation of a number of these features appear in this article. That in itself is illustrative of how integrative of many aspects of contemporary Greek astronomy the Mechanism was.
The Moon and Time
The moon, along with the sun and the stars, defined major aspects of time-keeping. The apparent motion of the sun marked out the seasons and the course of the agricultural year; the rising or setting of stars at dawn or dusk also signaled the change of seasons, as well as providing signals for human activity on land and sea; and the moon, with its recurring phases from new to full and back to new moon, measured the length of the months in both the religious and the political spheres, and also prompted or warned off farming activity.
While the sun marks out short time by way of the day (and may also mark out the hours, for instance by means of cast shadows of people or sundials: Hannah, 2009, pp. 68–95), as well as long time through the seasonal year, the moon provides a clear demarcation of intermediate time within the year through the regular periods of the month from one new moon to the next. The earliest translatable written evidence from the Greek world, the Linear B tablets from the so-called Mycenaean period in the Late Bronze Age (ca. 1400–1200 BCE), includes references to months at Knossos in Crete and at Pylos in mainland Greece. These months are usually allied with the word me-no, which is the Mycenaean Greek form of the later historical Greek word for “month,” men. Both words are related to mene, an early Greek word for “moon.” This also suggests that the Mycenaean calendar was at least initially lunar or partly so. The month-names themselves in the tablets appear to derive from gods’ names or local place names, and, typical also of later Greek practice, the months from Knossos and Pylos suggest that each site had a different set of names for the months (Hannah, 2005, pp. 16–17).
In the 8th and 7th centuries bce, the Homeric poems, the Iliad and the Odyssey (ca. 750–700 BCE) and the later Homeric Hymns—so-called from their supposed derivation from Homer—use the waning and waxing of the moon as a means for timing, for instance Odysseus’ return to Ithaka (Odyssey 19.307), or the length of a pregnancy (Iliad 19.117; compare Homeric Hymn to Hermes 11, ca. 630–600 BCE). Overall, however, the Homeric year was a seasonal and agricultural one, and therefore solar rather than lunar. Hesiod (ca. 700–650 BCE), in his didactic poem about the farmer’s life, Works and Days, timed activities on the land via reference to the sun’s turning at the solstices and to the rising and setting of a handful of prominent stars.
The full moon was associated by Greek poets, and later by Roman ones too, with love-making (Kidd, 1974), as was also the Evening Star (Venus). The Greek poet Pindar, in the 5th century BCE, for instance, talks of the goddess Thetis lying in love with the mortal Peleus on an evening of the mid-month, and therefore of the full moon, conceiving the great Greek hero Achilles (Pindar, Isthmian Ode 8. 44). The Roman poet Plautus, ca. 200 BCE, has the god Jupiter bed the mortal Alcumena to produce the hero Hercules on a night made propitious and fertile by the presence of both the Evening Star and the full moon (Plautus, Amphitruo 273–276; see Hannah, 1993, 2009, pp. 23–26). Even much later in the 2nd century ce, we hear of a belief that the best time for a couple to conceive a child was when the moon was waxing: this is mentioned, although not accepted, by the medical writer Soranos (1.41), who ascribes the belief simply to “some of the ancients.”
The Moon and Greek Calendars
The moon, with its cycle from one new moon to another, formed the basis of all Greek calendars, a feature noted by Geminus in his Introduction to Astronomy (8. 7–14; Evans & Berggren, 2006, pp. 176–177). He also points out how the Greeks counted the days of each month from the new moon, and yet sought to maintain their sacrifices to the gods in the same seasons of the year from one year to the next. The years themselves were governed by the sun, whose annual cycle does not correspond in length to that of the moon.
A seasonal/solar year, measuring the return of the sun to the same point in its apparent circuit (solstice to solstice, or equinox to equinox), comprises approximately 365.25 days. A lunar month consists of 29.53059 days on average, or approximately 29.5 days, so a solar year consists of more than twelve whole lunar months but less than thirteen. Therefore a solar year cannot be expressed as an integral number of lunar months, and yet a calendar must seek to do this for practical purposes. A major issue that long engaged people in antiquity was how to synchronize these incommensurate cycles of the moon and the sun for calendrical purposes, so that the moon-based festivals of the gods could be held at the seasonally appropriate times of the solar year (Hannah, 2005; Samuel, 1972). That the festivals sometimes fell out of sync with the seasons is illustrated in Athens by the well-known complaint by the Moon herself in the play, Clouds, staged by Aristophanes in 423 BCE: she says she is threatened by the gods because they miss out on the meals that should be theirs from sacrifices, but those sacrifices have not been held on the correct days; at times the calendar is so out of kilter with the moon that the Athenians are celebrating when the gods are in mourning, or the people are in the lawcourts when they should be sacrificing to the gods (Aristophanes, Clouds 615–626).
That one city’s calendar could also easily be out of sync with another, despite both using the same moon as the basis of their months, is shown by an instance provided by the writer Plutarch (ca. 50–120 ce ) in his Life of Aristides, an Athenian leader in the 5th century BCE. At one point of the biography he notes that the battle of Plataea was on the fourth day of the month Boedromion, according to the Athenian calendar, but on the 27th day of the month Panemos, according to the Boiotian calendar. He adds, “the discrepancy between the days should not cause wonder, since even now when people are more exacting in astronomy, different peoples have different beginnings and endings for their months.” (Plutarch, Life ofAristides 19, p. 7). Other cases abound. While the cause has traditionally been seen as a matter of civic officials haphazardly inserting days or months, it is just as likely that in many cases two states might well observe the same new moon on different days and so start their months on different dates (Dunn, 1999).
Another aspect of the story from Plutarch is that the two political entities, the city-state of Athens and the Boiotian League, had different names for months lying in the same point of the year. This was the norm in Greece, with each state preserving its own independent calendar, which kept not only differently named months—although some might be in common, especially between ethnically or politically related states—but could also start the year at different points of the solar year. Athens began its year at the first new moon following the summer solstice, while Boiotia began its sixth months away at the winter solstice. Even politically related states, like Athens and Delos, could differ, with the latter starting its year also after the winter solstice, even though they shared four month names in common. The civic calendar deciphered on the Antikythera Mechanism is different again, beginning the year after the autumn equinox. So too did the Macedonian calendar, which, following the conquests of Alexander the Great in the late 4th century BCE, became the most wide-spread Greek calendar in the eastern Mediterranean and Near East. Some of these calendars survived well beyond the time of the introduction of the Roman Julian calendar in the 1st century BCE, preserving local cultural identities.
Synchronizing the Moon and Sun
To stabilize the lunar calendar within the solar year, various forms of lunisolar cycles were used by the Greeks. The aim of these cycles was to find as nearly as possible a whole number of lunar months that corresponded to a whole number of solar years, so that over the period of the cycle the lunar calendar would align, with some flexibility, with the sun, and at the start of a new cycle the moon and sun would be in the same relative positions as they were at the start of the previous cycle. We know of cycles in Greece that ran over periods of 2, 8, 11, and 16 years, but it is the 19-year cycle that proved the most reliable and accurate in practical terms. Indeed, forms of this cycle still underpin the Hebrew calendar and the calculation of Christian Easter.
The first signs of a 19-year cycle occur, however, in Babylonia. From early in the 2nd millennium BCE onward, documents show that an extra month was intercalated by an ad hoc royal decree (e.g., we know this was done in the reign of Hammurabi, king of Babylon 1848–1806 BCE), usually by means of doubling the sixth or twelfth month (Britton & Walker, 1996, p. 45). The king was still the one who issued such instructions in the time of Nabunaid (556–539 BCE), the last of the kings of Babylon before the Persian Achaemenid dynasty took power. Under the latter, the instructions for intercalation came from the priests in Babylon. From at least the second half of the 6th century bce, a cycle of seven intercalations of an extra month over 19 years was used, and systematically governed intercalations from 475 BCE (Ossendrijver, 2018). By this means it could be ensured that the sun and moon had returned to the same positions that they held 19 years earlier, and would do so again every 19 years hence. This is because 19 solar years equal 235 whole months, each amounting to 6,940 days in round terms. The impetus for this fixing of the intercalary cycle has been seen in the need to coordinate administration over the vast distances of the Persian Empire (Stern, 2012, pp. 121–123).
Such a 19-year cycle is usually named Metonic, after the known discoverer in the Greek world, the astronomer Meton of Athens, who lived in the late 5th century BCE. It is now accepted, however, that the cycle was known in Babylonia long before his time. The political centralization of Mesopotamia, through various empires and dynasties, over hundreds of years enabled consistent record-keeping of observations and encouraged the passing on of this knowledge through the generations (Evans, 1998, p. 298). It is easier to imagine the discovery of a long-term cycle for coordinating the lunar and solar cycles in this context than it is in the relatively uncoordinated world of the Greek city-states.
Geminus (Introduction to Astronomy 8.50–58: Evans & Berggren, 2006, pp. 183–184) tells us that the astronomers of the time of Euctemon, Philippus, and Callippus (thus covering the century from the late 5th century BCE) observed that over a period of 19 years there were 6,940 days or 235 months, including seven intercalary months. Of the 235 months, they made 110 “hollow” (i.e., of 29 days each), and the remaining 125 “full” (i.e., of 30 days each). The imbalance between “full” and “hollow” months means that they cannot alternate throughout the cycle, but sometimes there would be two “full” months in succession. Geminus then explains how the devisers of the cycle arrived at 110 “hollow” months: all 235 months are initially assigned 30 days each, which gives a total of 7,050 days to the 19-year period. This overshoots the sum of 6,940 days of 235 lunar months by 110 days, so 110 months must each have one day omitted through the cycle, and they become 29-day months. To ensure as even a distribution of this omission as possible, he says that the Greeks divided the 6,940 days by 110 to get a quotient of 63, so that the 110 days were removed at intervals of 63 days. If the 19-year cycle is left to run unchanged, in four cycles (76 years) it gains a day against a solar calendar of 3651/4 days. Geminus (Introduction to Astronomy 8.59–60; Evans & Berggren, 2006, pp. 184–185) tells us that Callippus therefore refined the 19-year cycle by running it over four periods and removing the extra day that had accumulated over that period. The first Metonic cycle began in 432 BCE, while the first Callippic cycle began in 330 BCE.
Scholars have been divided as to whether to take Geminus seriously about the awkward omission of days in Meton’s cycle—the prospect of omitting a different day of a month every 63 days seemed impractical (Neugebauer, 1975, pp. 617–618)—and even about his account of the cycle as a whole (Toomer, 1984, pp. 12–13, thought Geminos’ description was “fiction,” and was pessimistic about all attempts to reconstruct the cycle). But recent studies of the Antikythera Mechanism (2nd century BCE) show that at least in its case a procedure very like Geminus,’ this time of omitting a day every 64 days over a period of 235 months, was practiced with this instrument (Allen, Ambrisco, Anastasiou, Bate, Bitsakis, Crawley, Edmunds, Gelb, Hadland, Hockley, Jones, Malzbender, Moussas, Ramsey, Seiradakis, Steele, Tselikas, and Zafeiropoulou, 2016, pp. 169–171). On the basis of the deciphered fragmentary remains of the Mechanism different proposals have been published recently for the insertion of the intercalary month: months 1, 4, 7, 10, 12, 15, and 18 of the cycle in one version (Allen et al., 2016, pp. 169–171), but months 1, 3, 6, 9, 11, 14, 17 in another (Iversen, 2017, p. 184, Table 6; Freeth, Jones, Steele, & Bitsakis, 2008, Supplementary Notes, 12).
Much work has been done in recent years to suggest that the Athenians did in fact avail themselves of the 19-year Metonic cycle in their civil calendar. An initial cycle of 19 years between 432 and 413 bc appears to have encountered difficulties, with the intercalation perhaps applied inconsistently. Thereafter, down to 331 BCE, an “ideal” cycle has been discerned, incorporating a regular pattern of intercalary years in years 2, 5, 8, 10, 13, 16, and 18 (Hannah, 2009, p. 37, where the initial cycle was inadvertently assigned to 432–419 BCE; Osborne, 2003, 2000, updating Dinsmoor, 1931/1966, pp. 419–440).
If these two cases, the Antikythera Mechanism (in one version or the other) and the Athenian civic cycle, are correct, it would suggest that astronomers and civic authorities availed themselves of the Metonic cycle, but in different formations in different times and places.
The Moon, the Sun and the Roman Calendar
Our present-day month names, from January to December, are derived from the Roman Republican calendar. The Romans attributed the creation of their calendar to Numa, the legendary second king of Rome. He was said to have divided the year into months, and the months into days, each day being designated a “festival day” (dedicated to the gods), a “working day” (available for public and private business), or “a half-festival day” (shared between sacred and secular business). There were further subdivisions of these days, so that, for example, working days included “lawcourt days” (fasti), “assembly days” (comitiales), “adjournment days,” “appointed days,” and “battle days” (Brind’Amour, 1983; Hannah, 2005, pp. 98–102; Michels, 1967; Rüpke, 1995, 2011).
According to Macrobius (Saturnalia 1.13), Numa was credited with making the calendar lunar, by increasing the Roman year first to 354 days and then to 355, and dividing the year into twelve months by adding January and February at the beginning. The length of the year was increased to 354 days to accord with the time “in which twelve circuits of the moon are completed,” and then to ensure it kept in step with the sun an extra intercalary month of 22 or 23 days (called “Mercedinus” or “Mercedonius”) was inserted after 23 February every second year (354 × 2 + 22 = 730, and 730 ÷ 2 = 365, approximately a solar year).
However, Numa was also said to have added an extra day to the year “in honor of the odd number,” bringing the length of the year to 355 days. His curious obsession with odd numbers extended to the lengths that he gave to the months: each month, except February, contained an odd number of days—29 for January, April, June, Sextilis, September, November, December, and 31 for March, May, Quintilis, and October; February had 28 days. (In 44 BCE, before Julius Caesar’s assassination, the Roman Senate decreed that the month Quintilis should be called Iulius after him, because he was born in that month (Cassius Dio 44.5.2). The month Sextilis was named Augustus, in the lifetime of the emperor of that name, because it was the month in which he gained his most significant political honors (Suetonius, Life of Augustus 31).)
The resulting number of days per month disguises what must have been an originally moon-based calendar. There are clues to this character. The months were divided into three parts, at day 1 (kalendae), and then, depending on the actual month, at day 5 or 7 (nonae), and day 13 or 15 (idus). A fourth dividing point may originally have existed around days 23 and 24 of the month: the vestiges of this last marker may be found in the calendars at the point of the festivals of the Tubilustrium on 23 March/May and of the day marked QRCF (Quando Rex Comitiavit Fas—“when the king goes into the Assembly, it is lawful”) on 24 March/May. This would provide four “weeks” in the month, which matched lunar periods from new moon, to first quarter, to full moon, and finally last quarter (Rüpke, 1995, pp. 209–225). The names given to the first three of these divisions further suggest a lunar aspect: kalendae derives from the proclaiming of the new crescent by the priest; nonae simply signifies eight days—nine by Roman inclusive reckoning—before the next division; and idus may stem from a Greek word for the full moon.
In 46 bce, Julius Caesar ordered a wholesale revision of the calendar to the point of adopting a solar year of 3651/4 days, with the quarter-day to be absorbed into an extra single whole day added every fourth “leap” year. Significantly, Caesar had the services of the Greek astronomer Sosigenes, who came from Alexandria in Egypt. There, according to the Canopus Decree of 238 BCE, Ptolemy III had sought to correct the error of the “wandering” 365-day Egyptian year by inserting a leap day every fourth year. Because it lacked a “leap day” of any kind, the Egyptian 365-day year fell out of sync at the rate of one day every four years against the sun and seasons, and so over a long period of time the religious festivals also fell in the wrong seasons. The Greek astronomer Geminus, writing in the 1st century BCE, commented on the reluctance of the Egyptians to correct this slippage, noting that “they want the sacrifices to the gods to occur not at the same moment of the year but to pass through all seasons of the year, and the summer festival to occur in winter and autumn and spring as well” (Geminus, Introduction to Astronomy, 8.16–19). In this way, the whole year was sacralized by the festivals, as they slowly drifted through all the seasons in a cycle of 1461 Egyptian years. The same effect occurs in the modern Islamic religious calendar. Ptolemy’s III’s attempt to make the correction failed, however, except for a short time in Alexandria, and the civil calendar of Egypt continued to wander slowly, slipping a day against the sun every four years, until the time of the Romans (Bennett, 2011).
Ninety days were now added to 46 BCE, making it 445 days long in order to begin the new calendar at the proper season. From January 1, 45 bce, a year of 365 days was instituted, with months of the same length as they are nowadays in the Western calendar. It is indicative of the fundamentally religious character of the calendar that the extra ten days, by which the new Julian year exceeded the old Republican year of 355 days, were fixed at the end of different months in order that the usual dates for religious festivals could be maintained. Also characteristic of the religious undertow is the fact that maintaining the calendar remained the preserve of the pontifices, under the Pontifex Maximus, and in a period of continuing instability, the priests initially inserted the extra “leap” day by mistake every three years, rather than every four. The error was corrected under the first emperor, Augustus, in his role as Pontifex Maximus, and the Julian year began to function properly only from 8 ce. In Egypt, a leap-year system was finally imposed in 26 BCE by Augustus, when he added a sixth “epagomenal” day to the Egyptian calendar every fourth year. This established the so-called “Alexandrian calendar,” which has a very long history from then on (Bennett, 2003; Stern, 2012, pp. 262–269).
Particularly from the Romans we learn of activities that were encouraged or discouraged according to the moon. In the Greek tradition, Hesiod had listed days of good or bad omen in the lunar months, though without explicitly tying them to the moon’s influence. After him, however, Greek literature is reticent on this issue. In contrast, among the Romans there was a rich folkloric tradition about the moon’s influence on farming activity. According to this lore, for instance, crops should be planted generally just before the moon begins to wax, or during the waxing period: as the moon grows, so too will the plants. Conversely, harvesting should take place during the waning moon. Variations are allowed, depending on the nature of the end-product: grapes, for instance, may be picked under the waning moon if they are to be dried, but under the waxing moon if they are meant for making wine (Taverner, 1918).
Recognition of the five visible planets came relatively late to the Greeks, and hence to the Romans. Tablets from Babylonia attest to an awareness of the planets from the mid-2nd millennium BCE: the so-called “Venus Tablet” from the reign of Ammiṣaduqa, ca. 1646–1626 BCE, demonstrates close observation of this planet very early on (North, 1994, pp. 28–30; London, British Museum K.160). However, evidence of similar identifications in the Greek world before the late 5th or 4th century BCE is very limited and contested. Homer knows of Heosphoros (“bringer of morning”: Iliad 23.226) and Hesperos (“of the evening”: Iliad 22.317). This is what will later be called Venus, but the poet betrays no awareness that they are the same celestial body. The identification of the two as one and the same body is credited by later Greek sources to Pythagoras or Parmenides in the 6th century BCE (Evans & Berggren, 2006, p. 119, n.20).
Late sources also credit the 6th century BCE philosophers, Anaximander and Anaximenes, with some knowledge of the planets. To the former is attributed an investigation into the order of the planets, their sizes and their distances (Simplicius, On Aristotle, On the Heavens 471.1), while to the latter is ascribed the notion that “the stars execute their turnings in consequence of their being driven out of their course by condensed air which resists their free motion” (Aetius, 2.23.1: see translation in Heath, 1913, p. 42). This passage was taken by Heath to suggest that the planets, not the fixed stars, were meant, but Dicks found Heath “unconvincing” (Dicks, 1966, p. 30), and more recently Gregory has read these “stars” simply as the fixed stars, which along with the sun and moon “make their turnings by being pushed by enclosed and rigid air” (translation Gregory, 2007a, p. 50). In other words Anaximenes is probably referring only to the diurnal movement of the fixed stars, as well as of the sun and moon, across the heavens, rather than the irregular movement of the five planets, which are not fixed to the sphere of stars.
For the 5th century bce, we have the figure of Anaxagoras (ca. 500–428 BCE), a philosopher from Clazomenae on the southwestern coast of Turkey but active in Athens, at a time of its greatest development politically. His works are mentioned as available for sale in Plato’s dialogue, Apology, in which Socrates speaks in defense of his own beliefs. Socrates disclaims the charge of atheism, and in so doing distinguishes himself from Anaxagoras, who is characterized as teaching that the sun and moon are not gods, which everyone else believes they are, but that the one is a stone and the other earth, a view that Socrates calls “absurd” (or just “extraordinary,” depending on one’s translation of the word ἄτοπα) (Plato, Apology 26d–e). Both sides of this assertion are noteworthy: on the one hand, we see the attribution of divinity to the sun and moon was generally acceptable in Greece at the time, but on the other hand there was a counter-belief that they were instead simply physical entities. Quotations from Anaxagoras’s works come to us from a variety of later sources, which suggest that the philosopher wrote in prose, unlike his predecessors in the previous century who tended to write in poetic verse. As Dicks pointed out, the use of prose may well have made Anaxagoras’ work more accessible and comprehensible to a wider public (Dicks, 1970, p. 56).
One piece of Anaxagoras’ thought worth noting for its accuracy is in relation to the moon: he believed that the moon does not have its own light, but gets it from the sun (Graham, 2010, pp. 296–297, fragment 38.8; pp. 300–301, fragment 44). More precisely, though, he distinguished between the light that the moon gained from the sun, and its own light, “which is the colour of coal, as the eclipse shows us” (Graham, 2010, pp. 300–301, fragment 46). Of particular interest for our present purposes, however, is his positing Mind (nous) as responsible for initiating the rotation of the whole cosmos, generating not only all the objects of the sensible world, but also the rotations of the sun, moon, and stars (Graham, 2010, pp. 292–295, fragments 32, 33, 37, 38). The metaphysical nature of the prime cause of celestial motion—nous—is very Greek, and indeed quite Platonic in the long term. The term for “rotation” is perichoresis (περιχώρησις), which implies circular motion (as for a Greek chorus dancing, or the stars wheeling around in the night sky) (Graham, 2010, pp. 292–293, fragment 33). Circularity and the cyclic nature of things also feature prominently in the fragments associated with Anaxagoras’s contemporary, the Sicilian Greek, Empedocles (ca. 492–432 BCE; Dicks, 1970, p. 53; see, for example, Graham, 2010, pp. 350–355, fragment 41; 358–359 fragment 50). This notion of circular motion will be very long-lasting and fundamental to Greek astronomical thinking about celestial motions (see the section “Saving the Phenomena”).
An influential, but quite shadowy figure in Greek philosophy was Pythagoras, a native of the island of Samos, where he was born in the mid-6th century BCE, who moved to South Italy around 530 BCE, where he died. His philosophy is difficult to unpick from the stories and legends that accrued around him, but from his pupil, Philolaus (ca. 470–390 BCE), we have something more concrete to deal with, which is relevant to us. Philolaus was the first to make the earth a planet. Instead of having the earth as the center of the sphere, Philolaus says there is a central fire. Aristotle (On the Heavens, 293a21–24: Graham, 2010, pp. 498–499, fragment 24) mentions this central feature of the “fire” as Pythagorean, and says the Pythagoreans regarded the earth as one of the stars, and further postulated the existence of a “counter-earth” (antichthon, ἀντίχθων). Aetius, writing later in the 1st or 2nd century ce , elaborates on this model, telling us that the “sphere” (of the cosmos) comprised “ten bodies,” namely (working from the outermost inwards) the planets, the sun, the moon, the earth, and the “counter-earth,” with the “hearth” in the center (for a diagram, see Gregory, 2007b, p. 6, 2016, p. 100, Figure 6.3). From this we deduce there were five planets recognized by the Pythagoreans, but none is named, nor is their order specified.
A book, On the Planets, is attributed to Democritus in the late 5th century BCE (Graham, 2010, pp. 522–523, fragment 7; Diogenes Laertius, Lives of Eminent Philosophers 9. 46). The term in Greek, planetes (πλάνητης), when used for the planets, seems first to occur directly in the works of Plato, written in the 4th century BCE. He refers to “the sun, moon, and five others stars which are called planets and which came into existence for the definition and safeguarding of the numbers of time” (Plato, Timaeus 38c). He also hints at the planets in his Republic (Plato, Republic 616d–617b). However, of the five proper planets he names only “the bringer of morning” (Heosphoros), like Homer, and “the one called sacred to Hermes,” meaning Mercury (Plato, Timaeus 38d).
The rest of the gods’ names given to the planets by the Greeks appear from the 4th century BCE. All five are named in the dialogue, Epinomis, which came out of Plato’s School (Epinomis 987b–c), and Aristotle, in his Metaphysics 12.1073b, names all but Mars, but that is mentioned in his On the Heavens 292a.5, and in his Meteorology 343b.30, he mentions Zeus (i.e., Jupiter) alone. These names look to be derived from their Babylonian equivalents. In Babylon the planet Mercury was the star of Nabu, Venus that of Ishtar, Mars that of Nergal, Jupiter that of Marduk, and Saturn that of Ninib. Each of these Babylonian gods found his or her more or less appropriate equivalent in the Greek pantheon: Nabu—Hermes; Ishtar—Aphrodite; Nergal—Ares; Marduk—Zeus; and Ninib—Kronos (Cumont, 1935, p. 7). Each of these Greek gods, in turn, have their Roman equivalents, who lend their names to the planets as we have them now. It is clear from the Epinomis that these divine names also signify a degree of divinity being ascribed to the planets, as the author talks of the planets being almost of Aphrodite, Hermes, etc., but it is in Greco-Roman astrology that we see a fuller transference to the planets of the characters of the eponymous gods.
These divine and other names of the five visible planets are given in a treatise, On the Cosmos, that was once attributed to Aristotle himself but is now seen as the work of a follower who lived any time from Aristotle’s period in the mid-4th century BCE to the end of the 1st century BCE (Thom, 2014, pp. 3–7, who opts for the late 1st century BCE, while Sider, 2015 still argues for Aristotle’s time). This source organizes the planets in nested circles from the outermost circle of the cosmos, that of the fixed stars, inwards to the innermost circle, that of the moon. The planets are named: Phainon (“the Shining One”), which is also known as Kronos (i.e., Saturn); Phaëthon (“the Radiant One”), which is also Zeus (Jupiter); Pyroeis (“the Fiery One”), which is named after Heracles as well as Ares (Mars); Stilbon (“the Glittering One”), which is sacred to Hermes (Mercury), but also for some to Apollo; and Phosphoros (“the Light-Bringer”), which is named after Aphrodite (Venus), or sometimes after Hera. Then come the circles of the sun and finally the moon. The light-oriented names—Phainon, Phaëthon, Pyroeis, Stilbon and Phosphoros—would seem to be derived from a desire to distinguish the planets through their physical appearance, specifically in terms of their brightness. Cumont took this to be a sign that these names were given by astronomers, qua scientists, so as to distance themselves from the multifarious religions of the Eastern and Greek worlds (Cumont, 1935, pp. 18–19). Otherwise, we simply do not know the origins of these “names of light” (Thom, 2014, p. 59 n.24). The first datable use of such names occurs in 265 and 262 BCE, associated with an astronomer called Dionysios, whose observations of Stilbon (Mercury) are recorded by Ptolemy in the 2nd century CE (Ptolemy, Almagest 9.7.5 and 9.10: Toomer, 1984, pp. 450, 464). The ancient symbols still used today for these planets—♄ (Saturn), ♃ (Jupiter), ♂ (Mars), ♀ (Venus), and ☿(Mercury)—and usually seen in astrological charts are much more recent, deriving from manuscripts of the Byzantine period.
The Babylonians, through long, careful observation and recording, had identified the five visible planets—Jupiter, Saturn, Mars, Venus, and Mercury—by the 8th century BCE. Mathematical schemes were developed to account for and to enable prediction of their motions, important in Babylonian culture because the planets formed an integral element of astrology. In this sense astronomy was the child of astrology. Both were defined much later by Ptolemy (Tetrabiblos 1.1) as predictive endeavors making use of the celestial bodies, astronomy for the positions of the celestial bodies, astrology for the configurations of those bodies to indicate their influence on human affairs (Barton, 1994; Beck, 2007; Koch-Westenholz, 1995; Rochberg, 2004).
In the wake of the conquest of the Persian Empire by Alexander the Great, in the late 4th century, Babylonian astronomy/astrology was absorbed by the Greeks. Data on the planets may have been part of that inheritance (Dicks, 1970, p. 167)—Aristotle, On the Heavens 292a.7–9 notes the transference of celestial observations from Babylonia to Greece. The Greeks sought to understand and predict the motions of the sun, moon, and five visible planets in increasingly detailed fashion, attempting to find ways of enabling observations and predictions to match. To some extent, we may understand these attempts as a means to predict more accurately the motions of the planets in the service of astrology, which became more and more personalized, particularly in Alexandria, the scientific center of the Hellenistic world. But we can also see Greek interest in the planets in the context of a problem in natural philosophy that was identified by Plato and his followers. Alongside the old Babylonian observational data and mathematical schemes, a distinctively Greek conception of the cosmos as a geometric structure developed. Something of this can already be seen in Plato’s description of the circles of the Same and Different in his Timaeus. (Plato, Timaeus 36b–d. Here he has the creative force, personified as a craftsman (demiurge), structuring the cosmos as a sphere, because this is a perfect and uniform shape. The cosmos is caused to revolve uniformly around itself. The demiurge then forms a long band, marked off according to arithmetical and harmonic intervals, which is then split lengthways to create two strips. These in turn are bent round to form two circles, with one placed inside the other to form the dynamic structure of the universe. In astronomical terms, these bands correspond to the sidereal equator and the ecliptic. The demiurge made the equatorial band move to the right and named it the circle of the Same, while he set the ecliptic diagonally against the circle of the Same and named it the circle of the Different. The circle of the Same corresponds to the primary movement of the entire universe. The demiurge split the circle of the Different in six places into seven unequal circles. These correspond to the orbits of the seven known planets.
This description can be viewed as emanating from a mechanical view of the cosmos, as if Plato were describing a celestial globe or even an armillary sphere. We shall see that a plausible connection between mechanics and astronomy has been proposed for later in the Hellenistic period.
Different methods of predicting celestial events existed side-by-side in Babylonia, and were carried on throughout the Hellenistic period. Observational records survive from the 7th century to the 1st century BCE in the form of the so-called Astronomical Diaries; the practice of observing and recording is known to be older still. Another set of records, whose data were probably derived from the Diaries, comprise the Goal-Year Texts. These contain material for the prediction of planetary and lunar phenomena for a given year, the “goal-year.” The predictions rely on the regular recurrence of planetary phenomena after a certain number of years. A third category of texts is the Almanacs, which provide forecasts of phenomena for each month in a Babylonian year. While many data are derived from observation, some, such as solstices and equinoxes, are the result of computation according to various schemes. In addition, non-astronomical phenomena are included in the Diaries, such as meteorological conditions, changes in the level of the river Euphrates, and even the prices of basic commodities. A principal goal of Babylonian astronomy was the establishment of period-relations for predictive purposes, based on planetary phenomena. In other words, the astronomical data served as the basis for omens predicting future events or activities (Hunger, 2020).
From early in the 4th century to the 1st century BCE in Babylonia, mathematical astronomy existed alongside the Diaries and their off-shoots. Fundamental to this was the use of the zodiacal circle as a coordinate system for computing celestial positions. This circle was introduced around 400 BCE, and mathematical astronomy developed quickly thereafter. Data were derived via a variety of algorithms to provide a number of different types of tables. Predominant in the archaeological record are the synodic tables (synodic referred originally to a “meeting,” i.e., conjunction, with the sun, but came to refer to more general relations to the sun and its position plotted against the zodiac). These synodic tables provide data relating to various planetary phenomena with respect to the sun, such as a planet’s first or last appearances, its rising or setting in opposition to the sun, and (for the outer planets) the stations marking its period of retrogradation, when a planet appears to backtrack its way across the stars for a time before resuming its normal direction (cf. Neugebauer, 1975, pp. 380–381; Ossendrijver, 2020; Sidoli, 2020).
The Greeks inherited this Babylonian astronomical tradition. Both Hipparchus in the 2nd century BCE and Ptolemy in the 2nd century ce had access to and made use of Babylonian records, and they and others added their own detailed observations (Toomer, 1984, pp. 166, 176, 322).
The Planetary Week
The sun, moon, and five visible planets gave their names to the seven weekdays of the Roman calendar. This seven-day week was a relatively late innovation in the Roman calendar, introduced probably in the time of Augustus, and it was used alongside the original eight-day market week (nundinae) of the Republic. The Augustan poet Tibullus (1.3.18) refers to “Saturn’s holy day,” meaning what we call Saturday. A number of inscriptions and graffiti from Pompeii (therefore, pre-79 ce) refer to the days of week by their planetary names. One graffito, for instance, presents all seven days in sequence in a column headed by the word “day” (dies): [of] Saturn, Sun, Moon, Mars, Mercury, Jupiter, Venus (CIL IV.8863:). By around 200 ce, the historian Cassius Dio can note the relatively recent adoption of the planetary week—it was unknown to the Greeks, he says—and can report that it is now known throughout the Roman world (Cassius Dio 37.18.1).
The sequence of the weekday names is arrived at by assigning each planet in the order of their supposed distance from the earth, from furthest away to closest—Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon—in sequence to each hour of the 24-hour day and then continuously to each of the 168 hours of a seven-day period. By this means, starting with Saturn’s day (Saturday), it will be found that the first hour of each day thereafter starts with a planetary god in the order that became the seven-day week: Saturn, Sun, Moon, Mars, Mercury, Jupiter, Venus (see Hannah, 2005, pp. 141–143; also Beck, 1988, p. 1–11 for illustrative tables). Most of these names are still recognizable in the Romance languages—Italian has Lunedì, Martedì, Mercoledì, Giovedì, Venerdì (Saturday and Sunday have been subsequently Christianized). In English, Saturday, Sunday, and Monday preserve the Latin names, while the rest have been taken over by Norse gods’ names.
Zerubavel has argued that the seven-day week was derived from a dual influence, one strand being the Jewish week based on the regular observance of the Sabbath, the other being astrology based on its use of the seven “planets” (i.e., the sun, moon, and five visible planets), with both strands in turn originating in Babylonia (Zerubavel, 1985, pp. 5–26). Nonetheless, the Jewish week ends with the Sabbath on Saturday, while the Roman seven-day week starts with Saturday, which undoubtedly derives from an astrological origin, so astrology as the single source of influence seems more likely. This week probably came to Rome via Alexandria, the source of influence also for the Julian calendar (Bultrighini, 2018, p. 63 n.6). Macrobius (Dream of Scipio 1.19.1–2) calls the sequence of the planets that forms the basis of the week “Chaldaean,” a likely sign that Babylonian astrology lay at its base.
Within astrology, each hour was assigned to one of the planets following the sequence from Saturn to the Moon as just noted. This double rulership, of the day and of the hour, was supposed to offer success or failure to any enterprise via the benefic or malefic character of the given planets—Jupiter and Venus were accounted benefic, Saturn and Mars malefic, and the Sun, Moon, and Mercury were ambivalent. Beyond this time-rulership, the planets (as gods, or instruments of gods) were thought to affect outcomes through their locations on the zodiac at a given time, and through their angular relationships (termed aspects) to other planets on the circle of the zodiac—that is, opposition (half of the zodiacal circle), trine (a third), quartile (a quarter), and sextile (a sixth)—some of which are generally favorable and so enhance a planet’s power, while others are unfavorable and so diminish power (Beck, 1988, 2007).
“Saving the Phenomena”
As we have seen, the Greeks were inheritors to a very long empirical and mathematical tradition in astronomy from the Persian Empire and its predecessors. Their own tradition had been more of a philosophical nature (Dicks, 1970). This speculative cosmology remained a persistent strand in Greek thought, and had a remarkable longevity in rural folklore (cf. du Boulay, 2009, pp. 32–33, 47–48, for the survival of beliefs into the 20th century). But from the 4th century bce, another strand appeared that gave a new character to Greek astronomical theory. It seems to have been generated in the Platonic school and centered around the problem of how to account for the motions of the planets. The end-result was a geometricization and a mechanization of the cosmos, which proved to have a long-lasting effect on Western theories of the universe.
At the heart of this very Greek way of thinking lay a call, attributed by later sources to Plato himself, to seek the means by which the apparent, irregular orbits of the planets could be explained by geometrical models within a paradigm that required uniform, circular motion of the celestial bodies. The call was summed up in the catchphrase σώζειν τὰ φαίνομενα (“to save the phenomena”), which subordinated empirical observations to a dominant model of circular motions around the earth. As Simplicius, in the 6th century ce, reports it:
Plato, as Sosigenes says, set the following problem for those engaged in such studies: “By what hypotheses of regular and ordered motions are the apparent motions of the planets to be saved?”Simplicius, On Aristotle, On the Heavens, 488.21–24
The catchphrase itself, however, appears in the extant literature only from the late 2nd century BCE, and its attribution to Plato has therefore been seen as an anachronism from a much later period (Bowen, 2013, pp. 251–259). When Geminus (Introduction to Astronomy 1.19–22; Evans & Berggren, 2006, pp. 117–118) states that “the Pythagoreans” proposed that the motions of sun, the moon, and the five planets are circular and uniform and that they sought to “explain” the phenomena, it is not clear which “Pythagoreans” he means—the early ones of the 6th and 5th centuries BCE, or the revived Pythagorean movement of his own time in the 1st century BCE—nor is their aim strictly to “save” the phenomena in the face of a discordance between theory (regular, circular motion) and observation (stations and retrogradations among the planets), but to “explain” them. Nonetheless, others are still happy to take the call to save the phenomena as Platonic in origin (Gregory, 2016, p. 104). After all, on the basis of the maxim that “absence of evidence is not evidence of absence,” the fact that the extant literature does not provide us now with evidence that Plato issued this call to “save the phenomena” does not mean he, or a close follower in the 4th century BCE, did not do so.
Eudoxus, in the first half of the 4th century BCE, is credited as the first to provide a model that seeks to preserve uniform circular motion despite the non-uniform paths of the planets (Dicks, 1970, pp. 175–188). His system comprises a set of concentric spheres, each centered on earth and each home to a planet. Each sphere rotates on its own axis, with its own uniform motion but at different speeds and moving in opposite directions. The motions of the spheres were thought to be such that a planet appeared to describe a figure-of-eight path, called a hippopede from the Greek for a “horse-fetter,” which it resembled (Figure 2). Babylonian influence has been presumed as underlying the system, but it lacked rigor in detail: for instance, it failed to account for the visible variations in size and brightness of bodies like the moon and Venus.
Increasingly accurate, but also ever more cumbersome, models were developed by Callippus and Aristotle later in the 4th century. Where Eudoxus had proposed 27 separate spheres, Callippus suggested 34, and Aristotle increased them further, in confusing fashion (the number of spheres is ultimately unclear), including spheres with retroactive motion in order to prevent the rotation of one planet’s spheres from influencing another’s; only the moon lacks such retroactive spheres, as it is situated nearest the earth, at the center of the model (Gregory, 2016, pp. 104–107; see also Mendell, 1998; Yavetz, 1998, 2001).
Insofar as simplicity, not complexity, was considered appropriate to the heavenly and divine realms, these models were challenged by new models, which were developed around 200 BCE (Evans, 2020; Evans & Carmen, 2014). The new systems were based on variations of eccentrics and epicycles. In the theory of eccentrics, each planet orbited the earth in a circle, whose center was slightly displaced from the earth (hence eccentric). For the sun (Figure 3), this model allows for the difference in the lengths of the four astronomical seasons from the spring/vernal equinox, to the summer solstice, to the autumn equinox, and on to the winter solstice. Spring is the longest season, and it exceeds autumn, the shortest, by six days according to Hipparchus and Ptolemy (Evans, 1998, pp. 211–212, 2020, p. 94).
An alternative model allowed for the sun and planets each to move in a smaller circle, called an epicycle, whose center ran counterclockwise along a larger circle, called the deferent, at whose center was the earth. The sun or planet ran clockwise around its circle, at the same rate as the epicyle ran around the deferent (Figure 4) (see Evans, 1998, p. 212).
Geometrically the eccentric and the epicycle-plus-concentric-deferent systems are equivalent systems (see Evans, 1998, pp. 212–213, with Figure 5.9), and this was recognized as such in antiquity—certainly by Theon of Smyrna and Ptolemy, and perhaps much earlier by Apollonius of Perge. Hipparchus is said by Theon to have preferred the epicycle-plus-concentric-deferent as representing reality better, while Ptolemy preferred the simpler eccentric system (Evans, 2020, p. 95).
While these geometric models accounted for much of the irregularity observable in the planetary orbits, they did not account for all, and so other more complex systems arose, such as Ptolemy’s displacement of the center of uniform motion away from both the center of the deferent circle and the earth, thus creating what was later called the equant point. Around this point, the planet, still on its epicycle, circled uniformly but eccentrically from both the deferent circle and the earth.
With the equant system, it became possible to predict planetary phenomena accurately using a geometrical theory, rather than a mathematical one as the Babylonians had done (Evans, 2020, p. 98). However, the complexity of the older theory of concentric spheres had now been replaced by a complexity of circles, so it is perhaps not surprising to find a call to return to simpler, even purer, ideas. In the 5th century ce, the Neoplatonist philosopher, Proclus, himself a practicing astronomer, disputed the value of the eccentrics and epicycles, seeing them as potentially mathematical inventions divorced from reality:
Those skilled in astronomy, who are eager to show that the movements of the heavenly bodies are regular, have unwittingly shown their very nature to be irregular and full of changes. For what are we to say about the eccentrics and the epicycles which they always babble on about? Are these only to be imagined or are they to have substance in their spheres, in which they have been bound? For if these are only to be imagined, they [the astronomers] have unwittingly shifted from physical bodies to mathematical inventions and have drawn the causes of physical movements from things which do not exist in nature.
Proclus, Exposition of Astronomical Hypotheses 7.50.3–53.1
Proclus recognized that the planetary movements were in reality irregular, yet he noted that this irregularity occurred on a regular basis as the planets moved through their periodic orbits. He therefore called for an acceptance of this “regular irregularity” of the planets, with the overall progress of the planet still preserving uniform, circular motion (Pedersen & Hannah, 2002).
The impetus for viewing the workings of the cosmos through epicycles and eccentrics has recently been discerned in the development, earlier by about half a century, of geared mechanisms (Evans & Carmen, 2014). Gears appeared in the middle of the 3rd century BCE, with the publication of the Aristotelian Mechanical Problems and the works of Ctesibius and Archimedes marking something of the road to this point. However, mathematical interest in epicycles and eccentrics is not evinced until the time of Apollonius of Perge, arguably at the end of the same century. Some sense of the possibilities that could arise from the integration of mechanical gearing and astronomical theories of planetary motion might be seen in the gearing mechanisms used in the later Anitkythera Mechanism (Figure 1). Here engineering solutions were found, notably in the pin-and-slot mechanism, that enable the device to produce outputs that replicate the effects of the regularly irregular motions of the moon and planets (Evans & Carmen, 2014).
This connection between astronomy and engineering may find some echo much later in Proclus’s own disgruntlement with the eccentric-epicyclic hypothesis and similar ideas, which he says “assume the movement of the heavenly bodies as if by a theatrical machine” (Proclus, Commentary on the Timaeus of Plato 3.56.30–31, in Taylor, 2005, p. 775).
Time, it might fairly be said, was of the essence in endeavors around the moon and five known planets in antiquity. The moon’s cycle was key to all civil calendars in Greece, providing the start of the month with its first crescent, and offering a recurrent cycle of moons as the basis for the annual calendar. However, the incommensurability of the lunar year and the solar/seasonal year meant that, if there was a desire to maintain a close relationship between the seasons and their related festivals, then some synchronization of the moon’s and the sun’s cycles was necessary to establish a workable calendar. Different cycles lead eventually to the formation in the late 5th century BCE of the 19-year “Metonic” cycle, which was probably imported from Babylon, where it had been created previously. It remains a matter of debate to what extent this cycle was put into public use, but evidence has been adduced to indicate it may have been in Hellenistic Athens, and the Antikythera Mechanism certainly illustrates its use in a high-status, bespoke mechanical instrument of the same period.
The Republican Roman calendar also arguably evinces lunar influence in the divisions of the month into four parts and in the names of three of those parts, but this lunar aspect was quickly lost in the lengths of the months and in the biennial process of intercalation. Civil strife in the first century BCE led to the disengagement of this calendar from the seasonal year, and scientific influence from Alexandria in Egypt steered Julius Caesar towards the adoption of a truly solar calendar in 46 BCE. After the correction of an initial misunderstanding about the proper placement of the four-yearly leap day, this calendar became the norm for the Roman world and lasted through to the Early Modern period before requiring slight adjustment through the Gregorian calendar. Through this development the sun, rather than the moon or the sun and moon together, directed the calendar.
To judge from literary evidence, Greek recognition of the five visible planets came relatively late: in the 6th century BCE for Venus—although Homer knows it as a Morning and an Evening Star in the 8th century, without realizing it is the same entity—and in the 5th-to-4th centuries BCE for Saturn, Jupiter, Mars, and Mercury. With the gods’ names for the planets came also some degree of divinity for them, and this would be further developed through the burgeoning system of astrology, borrowed by the Greeks, and later the Romans, from Babylonia.
Mechanics may also have been an influence in the development of theories that arose in order to explain the regularly irregular motions of the planets through their synodic periods. A call was attributed to Plato to seek hypotheses of uniform, circular motions that would allow the observed phenomena of the planetary orbits to be “saved.” Early theories posited by Eudoxus, Callipus, and Aristotle imagined the planets moving in nested spheres. These were replaced by hypotheses built around circles in the form of eccentrics, epicycles, and equants, motions whose effects geared instruments could replicate as outputs, as is shown in the Antikythera Mechanism. Future work could usefully engage more in the proposed relationship between mechanics and astronomical theory.
The interest in establishing these planetary hypotheses was also fed by the desire to have a secure and precise means of timing and predicting planetary behavior, to bolster the practice of astrology from the Hellenistic period onwards. There was no fundamental distinction in antiquity between astronomy and astrology, but instead they were regarded as closely related predictive endeavors that made use of the celestial bodies, the one for positioning those bodies, the other for their configurations to indicate their influence on human affairs. New research is already being undertaken on the study of temporal precision, important to both astrology and astronomy, with the hour serving as the focus of a number of projects, whose results are awaited with interest (Miller & Symons, 2020).
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