22.2.17

Ancient Greek Astronomy

The Antikythera Mechanism was an analog computer from 150–100 BC designed to calculate the positions of astronomical objects.

Greek astronomy is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as Hellenistic astronomy, while the pre-Hellenistic phase is known as Classical Greek astronomy. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt.



The development of astronomy by the Greek and Hellenistic astronomers is considered by historians to be a major phase in the history of astronomy. Greek astronomy is characterized from the start by seeking a rational, physical explanation for celestial phenomena. Most of the constellations of the northern hemisphere derive from Greek astronomy, as are the names of many stars, asteroids, and planets. It was influenced by Egyptian and especially Babylonian astronomy; in turn, it influenced Indian, Arabic-Islamic and Western European astronomy.
Today the study of astronomy requires a deep understanding of mathematics and physics. It is important to realise that Greek astronomy (we are interested in the topic during the 1000 years between 700 BC and 300 AD) did not involve physics. Indeed, as Pannekoek points out in [7], a Greek astronomer aimed only to describe the heavens while a Greek physicist sought out physical truth. Mathematics provided the means of description, so astronomy during the 1000 years that interest us in this article was one of the branches of mathematics.

The Greeks began to think of philosophy from the time of Thales in about 600 BC. Thales himself, although famed for his prediction of an eclipse, probably had little knowledge of astronomy, yet he brought back from Egypt knowledge of mathematics into the Greek world and possibly also some knowledge of Babylonian astronomy. It is reasonable to begin by looking at what 'astronomy' was in Greece around this time. However we begin by looking further back than this to around 700 BC.

Basically at this time astronomy was all to do with time keeping. It is natural that astronomical events such as the day would make a natural period of time and likewise the periodic phases of the moon make the next natural time span. Indeed these provided the basic methods of time keeping around the period of 700 BC yet, of course, another important period of time, the year, was not easy to determine in terms of months. Yet a knowledge of the approximate length of the year was vital for food production and so schemes had to be devised. Farmers at this time would base their planting strategies on the rising and setting of the constellations, that is the times when certain constellations would first become visible before sunrise or were last visible after sunset.

Hesiod, one of the earliest Greek poets, often called the "father of Greek didactic poetry" wrote around 700 BC. Two of his complete epics have survived, the one relevant to us here is Works and Days describing peasant life. In this work Hesiod writes that (see [5], also [1] and [7]):-
... when the Pleiades rise it is time to use the sickle, but the plough when they are setting; 40 days they stay away from heaven; when Arcturus ascends from the sea and, rising in the evening, remain visible for the entire night, the grapes must be pruned; but when Orion and Sirius come in the middle of heaven and the rosy fingered Eos sees Arcturus, the grapes must be picked; when the Pleiades, the Hyades, and Orion are setting, then mind the plough; when the Pleiades, fleeing Orion, plunge into the dark sea, storms may be expected; 50 days after the sun's turning is the right time for man to navigate; when Orion appears, Demeter's gift has to be brought to the well-smoothed threshing floor.
For many hundreds of years astronomers would write works on such rising and setting of constellations indicating that the type of advice given by Hesiod continued to be used.



An early time scale based on 12 months of 30 days did not work well since the moon rapidly gets out of phase with a 30 day month. So by 600 BC this had been replaced by a year of 6 'full' months of 30 days and 6 'empty' months of 29 days. This improvement in keeping the moon in phase with the month had the unfortunate effect of taking the year even further out of phase with the period of the recurring seasons. About the same time as Thales was making the first steps in philosophy, Solon, a statesman in Athens who became known as one of the Seven Wise Men of Greece, introduced an improved calendar.

Solon's calendar was based on a two yearly cycle. There were 13 months of 30 days and 12 months of 29 days in each period of two years so this gave a year of about 369 days and a month of 291/2 days. However, the Greeks relied mainly on the moon as their time-keeper and frequent adjustments to the calendar were necessary to keep it in phase with the moon and the seasons. Astronomy was clearly a subject of major practical importance in sorting out the mess of these calendars and so observations began to be made to enable better schemes to be devised.

Pythagoras, around 500 BC, made a number of important advances in astronomy. He recognised that the earth was a sphere, probably more because he believed that a sphere was the most perfect shape than for genuine scientific reasons. He also recognised that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realise that Venus as an evening star was the same planet as Venus as a morning star. There is a pleasing appeal to observational evidence in these discoveries, but Pythagoras had a philosophy based on mathematical 'perfection' which tended to work against a proper scientific approach. On the other side there is an important idea in the Pythagorean philosophy which had a lasting impact, namely the idea that all complex phenomena must reduce to simple ones. One should not underestimate the importance of this idea which has proved so powerful throughout the development of science, being a fundamental driving force to the great scientists such as Newton and particularly Einstein.

Around 450 BC Oenopides is said to have discovered the ecliptic made an angle of 24° with the equator, which was accepted in Greece until refined by Eratosthenes in around 250 BC. Some scholars accept that he discovered that the ecliptic was at an angle but doubt that he measured the angle. Whether he learnt of the 12 signs of the zodiac from scholars in Mesopotamia or whether his discoveries were independent Greek discoveries is unknown. Oenopides is also credited with suggesting a calendar involving a 59 year cycle with 730 months. Other schemes proposed were 8 year cycles, with extra months in three of the eight years and there is evidence that this scheme was adopted.

About the same time as Oenopides proposed his 59 year cycle, Philolaus who was a Pythagorean, also proposed a 59 year cycle based on 729 months. This seemed to owe more to the numerology of the Pythagoreans than to astronomy since 729 is 272, 27 being the Pythagorean number for the moon, while it is also 93, 9 being the Pythagorean number associated with the earth. Philolaus is also famed as the first person who we know to propose that the earth moves. He did not have it orbiting the sun, however, but rather all the heavenly bodies went in circles round a central fire which one could never see since there was a counter earth between the earth and the fire. This model, certainly not suggested by any observational evidence, is more likely to have been proposed so that there were 10 heavenly bodies, for 10 was the most perfect of all numbers to the Pythagoreans.

Meton, in 432 BC, introduced a calendar based on a 19 year cycle but again this is similar to one devised in Mesopotamia some years earlier. Meton worked in Athens with another astronomer Euctemon, and they made a series of observations of the solstices (the points at which the sun is at greatest distance from the equator) in order to determine the length of the tropical year. Again we do not know if the 19 year cycle was an independent discovery or whether Greek advances were still based on earlier advances in Mesopotamia. Meton's calendar never seems to have been adopted in practice but his observations proved extremely useful to later Greek astronomers such as Hipparchus and Ptolemy.

That Meton was famous and widely known is seen from the play Birds written by Aristopenes in about 414 BC. Two characters are speaking, one is Meton [see D Barrett (trs.), Aristophanes, Birds (London, 1978)]:-
Meton: I propose to survey the air for you: it will have to be marked out in acres.
Peisthetaerus: Good lord, who do you think you are?

Meton: Who am I? Why Meton. THE Meton. Famous throughout the Hellenic world - you must have heard of my hydraulic clock at Colonus? 
Meton and Euctemon are associated with another important astronomical invention of the time, namely a parapegma. A parapegma was a stone tablet with movable pegs and an inscription to indicate the approximate correspondence between, for example, the rising of a particular star and the civil date. Because the calendar had to be changed regularly to keep the civil calendar in phase with the astronomical one, the parapegma had movable pegs which could be adjusted as necessary. A parapegma soon also contained meteorological forecasts associated with the risings and settings of the stars and not only were stone parapegma constructed but also ones on papyri. Meton and Euctemon are usually acknowledged as the inventors of parapegmata and certainly many later astronomers compiled the data nessary for their construction.

There is evidence for other observational work being undertaken around this time, for Vitruvius claims that Democritus of Abdera, famed for his atomic theory, devised a star catalogue. We have no knowledge of the form this catalogue took but Democritus may well have described the major constellations in some way.

The beginning of the 4th century BC was the time that Plato began his teachings and his writing was to have a major influence of Greek thought. As far as astronomy is concerned Plato had a negative effect, for although he mentions the topic many times, no dialogue is devoted to astronomy. Worse still, Plato did not believe in astronomy as a practical subject, and condemned as lowering the spirit the actual observation of the heavenly bodies. Plato only believed in astronomy to the extent that it encouraged the study of mathematics and suggested beautiful geometrical theories.

Perhaps we should digress for a moment to think about how the ideas of philosophy which were being developed by Plato and others affected the development of astronomy. Neugebauer [6] feels that philosophy had a detrimental affect:-
I see no need for considering Greek philosophy as an early stage in the development of science ... One need only read the gibberish of Proclus's introduction to his huge commentary on Book I of Euclid's Elements to get a vivid picture of what would have become of science in the hands of philosophers. The real "Greek miracle" is the fact that a scientific methodology was developed, and survived, in spite of a widely admired dogmatic philosophy.
Although there is some truth in what Neugebauer writes here, I [EFR] feel that he has overstated his case. It is true that philosophers came up with ideas about the universe which were not based on what we would call today the scientific method. However, the very fact that theories were proposed which could be shown to be false by making observations, must have provided a climate where the scientific approach could show its strength. Also the fact the philosophy taught that one should question all things, even "obvious" truths, was highly beneficial. Another important philosophical idea which had important consequences from the time of Pythagoras, and was emphasised by Plato, was that complex phenomena must be consequences of basic simple phenomena. As Theon of Smyrna expressed it, writing in the first century AD:-
The changing aspects of the revolution of the planets is because, being fixed in their own circles or in their own shperes whose movements they follow, they are carried across the zodiac, just as Pythagoras had first understood it, by a regulated simple and equal revolution but which results by combination in a movement that appears variable and unequal.
This led Theon to write:-
It is natural and necessary that all the heavenly bodies have a uniform and regular movement.
Perhaps the most telling argument against the above claim by Neugebauer is that our present idea of space-time, as developed from Einstein's theory of relativity, was suggested more by the basic philosophy of simplicity than by experimental evidence.
The advances made not long after the time of Plato by Eudoxus, incorporating the idea of basic simplicity as expressed in Pythagorean and Platonic philosophy, were made by an outstanding mathematician and astronomer. In fact Eudoxus marks the beginning of a new phase in Greek astronomy and must figure as one of a small number of remarkable innovators in astronomical thought. Eudoxus was the first to propose a model whereby the apparently complex motions of the heavenly bodies did indeed result from simple circular motion. He built an observatory on Cnidus and from there he observed the star Canopus. 

The star Canopus played an important role in early astronomy, for it is seen to set and rise in Cnidus yet one does no have to go much further north from there before it can never be seen. The observations made at Eudoxus's observatory in Cnidus, as well as those made at an observatory near Heliopolis, formed the basis of a book concerning the rising and setting of the constellations. Eudoxus, another who followed Pythagorean doctrines, proposed a beautiful mathematical theory of concentric spheres to describe the motion of the heavenly bodies. It is clear that Eudoxus thought of this as a mathematical theory, and did not believe in the spheres as physical objects.

Although a beautiful mathematical theory, Eudoxus's model would not have stood the test of the simplest of observational data. Callippus, who was a pupil of Polemarchus himself a pupil of Eudoxus, refined this system as presented by Eudoxus. The reason that we have so much information about the spheres of Eudoxus and Callippus is that Aristotle accepted the theory, not not as a mathematical model as originally proposed, but rather as spheres which have physical reality. He discussed the interactions of one sphere on another, but there is no way that he could have had enough understanding of physics to get anywhere near describing the effects of such an interaction. Although in many areas Aristotle advocated a modern scientific approach and he collected data in a scientific way, this was unfortunately not the case in astronomy. As Berry writes [2]:-

There are also in Aristotle's writings a number of astronomical speculations, founded on no solid evidence and of little value ... his original contributions are not comparable with his contributions to the mental and moral sciences, but are inferior in value to his work in other natural sciences ...
As Berry goes on to say, this was very unfortunate for astronomy since the influence of the writings of Aristotle had an authority for many centuries which meant that astronomers had a harder battle than they might otherwise have had in getting the truth accepted.

The next development which was absolutely necessary for progress in astronomy took place in geometry. Spherical geometry was developed by a number of mathematicians with an important text being written by Autolycus in Athens around 330 BC. Some claim that Autolycus based his work on spherical geometry On the Moving Sphere on an earlier work by Eudoxus. Whether or not this is the case there is no doubt that Autolycus was strongly influenced by the views of Eudoxus on astronomy. Like so many astronomers, Autolycus wrote a work On Risings and Settings which is a book on observational astronomy.

After Autolycus the main place for major developments in astronomy seemed to move to Alexandria. There Euclid worked and wrote on geometry in general but also making an important contribution to spherical geometry. Euclid also wrote Phaenomena which is an elementary introduction to mathematical astronomy and gives results on the times stars in certain positions will rise and set.

Aristarchus, Timocharis and Aristyllus were three astronomers who all worked at Alexandria and their lives certainly overlapped. Aristyllus was a pupil of Timocharis and in Maeyama [23] analyses 18 of their observations and shows that Timocharis observed around 290 BC while Aristyllus observed a generation later around 260 BC. He also reports an astounding accuracy of 5' for Aristyllus' observations. Maeyama writes [23]:-
The order of accuracy is an essential measure for the development of natural sciences. accuracy is in fact more than the mere operation of measuring. Accuracy increases only by virtue of active measuring. There cannot exist a high order of observational accuracy which is not connected with a high order of observations. Hence my assumption is that there must have been abundant accurate observations of the fixed stars made at least at the epochs 300 BC - 250 BC in Alexandria. They must have disappeared in the fires which frequently raged there.

Maeyama also points out that this is the period when the coordinate systems for giving stellar positions originated. Both the equatorial and the ecliptic systems appear at this time. But why were these observations being made? This is a difficult question to answer for on the face of it there seems little point in the astronomers of Alexandria striving for observational accuracy at this time. In [34] van der Waerden makes an interesting suggestion related to the other important astronomer who worked in Alexandria around this time, namely Aristarchus.

We know that Aristarchus measured the ratio of the distances to the moon and to the sun and, although his methods could never yield accurate results, they did show that the sun was much further from the earth than was the moon. His results also showed that the sun was much larger than the earth, although again his measurements were very inaccurate. Some historians believe that this knowledge that the sun was the largest of the three bodies, earth, moon and sun, led him to propose his heliocentric theory. Certainly it is for this theory, as reported by Archimedes, that Aristarchus has achieved fame. His sun-centred universe found little favour with the Greeks, however, who continued to develop more and more sophisticated models based on an earth centred universe.

Now Goldstein and Bowen in [16] attempt to answer the question of why Timocharis and Aristyllus made their accurate observations. These authors do not find a clear purpose for the observations, such as the marking of a globe. However van der Waerden in [34] suggests that the observations were made to determine the constants in the heliocentric theory of Aristarchus. Although this theory has strong attractions, and makes one want to believe in it, all the evidence suggests that Timocharis certainly began his observations some time before Aristarchus proposed his heliocentric universe.

Goldstein and Bowen in [16] make other interesting suggestions. They believe that the observations of Timocharis and Aristyllus recorded the distance from the pole, and the distances between stars. They argued that the observations were made by means of an instrument similar to Heron's dioptra. These are interesting observations since the work of Timocharis and Aristyllus strongly influenced the most important of all of the Greek astronomers, namely Hipparchus, who made his major contribution about 100 years later. During these 100 years, however, there were a number of advances. Archimedes measured the apparent diameter of the sun and also is said to have designed a planetarium. Eratosthenes made important measurements of the size of the earth, accurately measured the angle of the ecliptic and improved the calendar. Apollonius used his geometric skills to mathematically develop the epicycle theory which would reach its full importance in the work of Ptolemy.

The contributions of Hipparchus are the most important of all the ancient astronomers and it is fair to say that he made the most important contribution before that of Copernicus in the early sixteenth century. As Berry writes in [2]:-
An immense advance in astronomy was made by Hipparchus, whom all competent critics have agreed to rank far above any other astronomers of the ancient world, and who must stand side by side with the greatest astronomers of all time.

It is Hipparchus's approach to science that ranks him far above other ancient astronomers. His approach, based on data from accurate observations, is essentially modern in that he collected his data and then formed his theories to fit the observed facts. Most telling regarding his understanding of the scientific method is the fact that he proposed a theory of the motion of the sun and the moon yet he was not prepared to propose such a theory for the planets. He realised that his data was not sufficiently good or sufficiently plentiful to allow him to base a theory on it. However, he made observations to help his successors to develop such a theory. Delambre, in his famous work on the history of astronomy, writes:-

When we consider all that Hipparchus invented or perfected, and reflect upon the number of his works and the mass of calculations which they imply, we must regard him as one of the most astonishing men of antiquity, and as the greatest of all in the sciences which are not purely speculative, and which require a combination of geometrical knowledge with a knowledge of phenomena, to be observed only by diligent attention and refined instruments.
Although a great innovator, Hipparchus gained important understanding from the Babylonians. As Jones writes in [21]:-

For Hipparchus, the availability of the Babylonian predictive methods was a boon.
We will not describe the contributions of Hipparchus and Ptolemy in detail in this article since these are given fully in their biographies in our archive. Suffice to end this article with a quotation from [6]:-
Alexandria in the second century AD saw the publication of Ptolemy's remarkable works, the 'Almagest' and the 'Handy Tables', the 'Geography', the 'Tetrabiblos', the 'Optics', the 'Harmonics', treatises on logic, on sundials, on stereographic projection, all masterfully written, products of one of the greatest scientific minds of all times. The eminence of these works, in particular the 'Almagest', had been evident already to Ptolemy's contemporaries. this caused an almost total obliteration of the prehistory of the Ptolemaic astronomy. Ptolemy had no successor.

Eudoxan astronomy
In classical Greece, astronomy was a branch of mathematics; astronomers sought to create geometrical models that could imitate the appearances of celestial motions. This tradition began with the Pythagoreans, who placed astronomy among the four mathematical arts (along with arithmetic, geometry, and music). The study of number comprising the four arts was later called the Quadrivium.

Although he was not a creative mathematician, Plato (427–347 BC) included the quadrivium as the basis for philosophical education in the Republic. He encouraged a younger mathematician, Eudoxus of Cnidus (c. 410 BC–c. 347 BC), to develop a system of Greek astronomy. According to a modern historian of science, David Lindberg:


"In their work we find a shift from stellar to planetary concerns,  the creation of a geometrical model, the "two-sphere model," for the representation of stellar and planetary phenomena, and the establishment of criteria governing theories designed to account for planetary observations".

The two-sphere model is a geocentric model that divides the cosmos into two regions, a spherical Earth, central and motionless (the sublunary sphere) and a spherical heavenly realm centered on the Earth, which may contain multiple rotating spheres made of aether.

Plato's main books on cosmology are the Timaeus and the Republic. In them he described the two-sphere model and said there were eight circles or spheres carrying the seven planets and the fixed stars. According to the "Myth of Er" in the Republic, the cosmos is the Spindle of Necessity, attended by Sirens and spun by the three daughters of the Goddess Necessity known collectively as the Moirai or Fates.

According to a story reported by Simplicius of Cilicia (6th century), Plato posed a question for the Greek mathematicians of his day: "By the assumption of what uniform and orderly motions can the apparent motions of the planets be accounted for?" (quoted in Lloyd 1970, p. 84). Plato proposed that the seemingly chaotic wandering motions of the planets could be explained by combinations of uniform circular motions centered on a spherical Earth, apparently a novel idea in the 4th century.

Eudoxus rose to the challenge by assigning to each planet a set of concentric spheres. By tilting the axes of the spheres, and by assigning each a different period of revolution, he was able to approximate the celestial "appearances." Thus, he was the first to attempt a mathematical description of the motions of the planets. A general idea of the content of On Speeds, his book on the planets, can be gleaned from Aristotle's Metaphysics XII, 8, and a commentary by Simplicius on De caelo, another work by Aristotle. Since all his own works are lost, our knowledge of Eudoxus is obtained from secondary sources. Aratus's poem on astronomy is based on a work of Eudoxus, and possibly also Theodosius of Bithynia's Sphaerics. They give us an indication of his work in spherical astronomy as well as planetary motions.
Renaissance woodcut illustrating the two-sphere model.

Callippus, a Greek astronomer of the 4th century, added seven spheres to Eudoxus' original 27 (in addition to the planetary spheres, Eudoxus included a sphere for the fixed stars). Aristotle described both systems, but insisted on adding "unrolling" spheres between each set of spheres to cancel the motions of the outer set. Aristotle was concerned about the physical nature of the system; without unrollers, the outer motions would be transferred to the inner planets.

Archaic Greek astronomy
References to identifiable stars and constellations appear in the writings of Homer and Hesiod, the earliest surviving examples of Greek literature. In the Iliad and the Odyssey, Homer refers to the following celestial objects:

the constellation Boötes
the star cluster Hyades
the constellation Orion
the star cluster Pleiades
Sirius, the Dog Star
the constellation Ursa Major

Hesiod, who wrote in the early 7th century BC, adds the star Arcturus to this list in his poetic calendar Works and Days. Though neither Homer nor Hesiod set out to write a scientific work, they hint at a rudimentary cosmology of a flat earth surrounded by an "Ocean River." Some stars rise and set (disappear into the ocean, from the viewpoint of the Greeks); others are ever-visible. At certain times of the year, certain stars will rise or set at sunrise or sunset.
Anaximander, Detailansicht aus "Die Schule von Athen", Raphael Santi, 1510/11, Stanzen des Vatikans, Rom.

Speculation about the cosmos was common in Pre-Socratic philosophy in the 6th and 5th centuries BC. Anaximander (c. 610 BC–c. 546 BC) described a cylindrical earth suspended in the center of the cosmos, surrounded by rings of fire. Philolaus (c. 480 BC–c. 405 BC) the Pythagorean described a cosmos with the stars, planets, Sun, Moon, Earth, and a counter-Earth (Antichthon)—ten bodies in all—circling an unseen central fire. Such reports show that Greeks of the 6th and 5th centuries BC were aware of the planets and speculated about the structure of the cosmos. Also, a more detailed description about the cosmos, Stars, Sun, Moon and the Earth can be found in the Orphism, which dates back to the end of the 5th century BC, and it is probably even older. Within the lyrics of the Orphic poems we can find remarkable information such as that the Earth is round, it has an axis and it moves around it in one day, it has three climate zones and that the Sun magnetizes the Stars and planets.

The planets in early Greek astronomy
The name "planet" comes from the Greek term πλανήτης (planētēs), meaning "wanderer", as ancient astronomers noted how certain lights moved across the sky in relation to the other stars. Five planets can be seen with the naked eye: Mercury, Venus, Mars, Jupiter, and Saturn, the Greek names being Hermes, Aphrodite, Ares, Zeus and Cronus. Sometimes the luminaries, the Sun and Moon, are added to the list of naked eye planets to make a total of seven. Since the planets disappear from time to time when they approach the Sun, careful attention is required to identify all five. Observations of Venus are not straightforward. Early Greeks thought that the evening and morning appearances of Venus represented two different objects, calling it Hesperus ("evening star") when it appeared in the western evening sky and Phosphorus ("light-bringer") when it appeared in the eastern morning sky. They eventually came to recognize that both objects were the same planet. Pythagoras is given credit for this realization.

Hellenistic astronomy
Planetary models and observational astronomy
The Eudoxan system had several critical flaws. One was its inability to predict motions exactly. Callippus' work may have been an attempt to correct this flaw. A related problem is the inability of his models to explain why planets appear to change speed. A third flaw is its inability to explain changes in the brightness of planets as seen from Earth. Because the spheres are concentric, planets will always remain at the same distance from Earth. This problem was pointed out in Antiquity by Autolycus of Pitane (c. 310 BC).
Apollonius of Perga (c. 262 BC–c. 190 BC) responded by introducing two new mechanisms that allowed a planet to vary its distance and speed: the eccentric deferent and the deferent and epicycle. The deferent is a circle carrying the planet around the Earth. (The word deferent comes from the Latin ferro, ferre, meaning "to carry.") An eccentric deferent is slightly off-center from Earth. In a deferent and epicycle model, the deferent carries a small circle, the epicycle, which carries the planet. The deferent-and-epicycle model can mimic the eccentric model, as shown by Apollonius' theorem. It can also explain retrogradation, which happens when planets appear to reverse their motion through the zodiac for a short time. Modern historians of astronomy have determined that Eudoxus' models could only have approximated retrogradation crudely for some planets, and not at all for others.

In the 2nd century BC, Hipparchus, aware of the extraordinary accuracy with which Babylonian astronomers could predict the planets' motions, insisted that Greek astronomers achieve similar levels of accuracy. Somehow he had access to Babylonian observations or predictions, and used them to create better geometrical models. For the Sun, he used a simple eccentric model, based on observations of the equinoxes, which explained both changes in the speed of the Sun and differences in the lengths of the seasons. For the Moon, he used a deferent and epicycle model. He could not create accurate models for the remaining planets, and criticized other Greek astronomers for creating inaccurate models.
Hipparchus also compiled a star catalogue. According to Pliny the Elder, he observed a nova (new star). So that later generations could tell whether other stars came to be, perished, moved, or changed in brightness, he recorded the position and brightness of the stars. Ptolemy mentioned the catalogue in connection with Hipparchus' discovery of precession. (Precession of the equinoxes is a slow motion of the place of the equinoxes through the zodiac, caused by the shifting of the Earth's axis). Hipparchus thought it was caused by the motion of the sphere of fixed stars.

Heliocentrism and cosmic scales
In the 3rd century BC, Aristarchus of Samos proposed an alternate cosmology (arrangement of the universe): a heliocentric model of the solar system, placing the Sun, not the Earth, at the center of the known universe (hence he is sometimes known as the "Greek Copernicus"). His astronomical ideas were not well-received, however, and only a few brief references to them are preserved. We know the name of one follower of Aristarchus: Seleucus of Seleucia.
Aristarchus's 3rd-century BCE calculations on the relative sizes of (from left) the Sun, Earth and Moon, from a 10th-century CE Greek copy

Aristarchus also wrote a book On the Sizes and Distances of the Sun and Moon, which is his only work to have survived. In this work, he calculated the sizes of the Sun and Moon, as well as their distances from the Earth in Earth radii. Shortly afterwards, Eratosthenes calculated the size of the Earth, providing a value for the Earth radii which could be plugged into Aristarchus' calculations. Hipparchus wrote another book On the Sizes and Distances of the Sun and Moon, which has not survived. Both Aristarchus and Hipparchus drastically underestimated the distance of the Sun from the Earth.

Astronomy in the Greco-Roman and Late Antique eras
Hipparchus is considered to have been among the most important Greek astronomers, because he introduced the concept of exact prediction into astronomy. He was also the last innovative astronomer before Claudius Ptolemy, a mathematician who worked at Alexandria in Roman Egypt in the 2nd century. Ptolemy's works on astronomy and astrology include the Almagest, the Planetary Hypotheses, and the Tetrabiblos, as well as the Handy Tables, the Canobic Inscription, and other minor works.

Ptolemaic astronomy
The Almagest is one of the most influential books in the history of Western astronomy. In this book, Ptolemy explained how to predict the behavior of the planets, as Hipparchus could not, with the introduction of a new mathematical tool, the equant. The Almagest gave a comprehensive treatment of astronomy, incorporating theorems, models, and observations from many previous mathematicians. This fact may explain its survival, in contrast to more specialized works that were neglected and lost. Ptolemy placed the planets in the order that would remain standard until it was displaced by the heliocentric system and the Tychonic system:

Moon
Mercury
Venus
Sun
Mars
Jupiter
Saturn
Fixed stars
The extent of Ptolemy's reliance on the work of other mathematicians, in particular his use of Hipparchus' star catalogue, has been debated since the 19th century. A controversial claim was made by Robert R. Newton in the 1970s. in The Crime of Claudius Ptolemy, he argued that Ptolemy faked his observations and falsely claimed the catalogue of Hipparchus as his own work. Newton's theories have not been adopted by most historians of astronomy.

A few mathematicians of Late Antiquity wrote commentaries on the Almagest, including Pappus of Alexandria as well as Theon of Alexandria and his daughter Hypatia. Ptolemaic astronomy became standard in medieval western European and Islamic astronomy until it was displaced by Maraghan, heliocentric and Tychonic systems by the 16th century. However, recently discovered manuscripts reveal that Greek astrologers of Antiquity continued using pre-Ptolemaic methods for their calculations (Aaboe, 2001).

Influence on Indian astronomy
Hellenistic astronomy is known to have been practiced near India in the Greco-Bactrian city of Ai-Khanoum from the 3rd century BC. Various sun-dials, including an equatorial sundial adjusted to the latitude of Ujjain have been found in archaeological excavations there. Numerous interactions with the Mauryan Empire, and the later expansion of the Indo-Greeks into India suggest that some transmission may have happened during that period.

Several Greco-Roman astrological treatises are also known to have been imported into India during the first few centuries of our era. The Yavanajataka ("Sayings of the Greeks") was translated from Greek to Sanskrit by Yavanesvara during the 2nd century, under the patronage of the Western Satrap Saka king Rudradaman I. Rudradaman's capital at Ujjain "became the Greenwich of Indian astronomers and the Arin of the Arabic and Latin astronomical treatises; for it was he and his successors who encouraged the introduction of Greek horoscopy and astronomy into India."

Later in the 6th century, the Romaka Siddhanta ("Doctrine of the Romans"), and the Paulisa Siddhanta ("Doctrine of Paul") were considered as two of the five main astrological treatises, which were compiled by Varahamihira in his Pañca-siddhāntikā ("Five Treatises"). Varahamihira wrote in the Brihat-Samhita: "For, the Greeks are foreigners. This science is well established among them. Although they are revered as sages, how much more so is a twice-born person who knows the astral science.Hellenistic astronomy is known to have been practiced near India in the Greco-Bactrian city of Ai-Khanoum from the 3rd century BC. Various sun-dials, including an equatorial sundial adjusted to the latitude of Ujjain have been found in archaeological excavations there. Numerous interactions with the Mauryan Empire, and the later expansion of the Indo-Greeks into India suggest that some transmission may have happened during that period.

Several Greco-Roman astrological treatises are also known to have been imported into India during the first few centuries of our era. The Yavanajataka ("Sayings of the Greeks") was translated from Greek to Sanskrit by Yavanesvara during the 2nd century, under the patronage of the Western Satrap Saka king Rudradaman I. Rudradaman's capital at Ujjain "became the Greenwich of Indian astronomers and the Arin of the Arabic and Latin astronomical treatises; for it was he and his successors who encouraged the introduction of Greek horoscopy and astronomy into India."

Later in the 6th century, the Romaka Siddhanta ("Doctrine of the Romans"), and the Paulisa Siddhanta ("Doctrine of Paul") were considered as two of the five main astrological treatises, which were compiled by Varahamihira in his Pañca-siddhāntikā ("Five Treatises"). Varahamihira wrote in the Brihat-Samhita: "For, the Greeks are foreigners. This science is well established among them. Although they are revered as sages, how much more so is a twice-born person who knows the astral science.

Famous astronomers of antiquity
In addition to the authors named in the article, the following list of people who worked on mathematical astronomy or cosmology may be of interest.

Anaxagoras
Archimedes
Archytas
Aristaeus
Aristillus
Conon of Samos
Democritus
Empedocles
Heraclides Ponticus
Hicetas
Hippocrates of Chios
Macrobius
Martianus Capella
Menelaus of Alexandria (Menelaus theorem)
Meton of Athens
Parmenides
Porphyry
Posidonius
Proclus
Thales
Theodosius of Bithynia



Source/Photography/Bibliography

Many Greek astronomical texts are known only by name, and perhaps by a description or quotations. Some elementary works have survived because they were largely non-mathematical and suitable for use in schools. Books in this class include the Phaenomena of Euclid and two works by Autolycus of Pitane. Three important textbooks, written shortly before Ptolemy's time, were written by Cleomedes, Geminus, and Theon of Smyrna. Books by Roman authors like Pliny the Elder and Vitruvius contain some information on Greek astronomy. The most important primary source is the Almagest, since Ptolemy refers to the work of many of his predecessors (Evans 1998, p. 24).
F Aveni, Empires of time : Calendars, clocks and cultures (New York, 1989).
Berry, A short history of astronomy (New York, 1961).
R Dicks, Early Greek Astronomy to Aristotle (London, 1970).
L E Dreyer, A history of astronomy from Thales to Kepler (New York, 1953).
Hetherington, A chronicle of pre-telescope astronomy (Chichester, 1996).
Neugebauer, A history of ancient mathematical astronomy (New York, 1975).
Pannekoek, A history of astronomy (New York, 1989).
H Thurston, Early astronomy (New York, 1994).
G Abraham, Mean sun and moon in ancient Greek and Indian astronomy, Indian J. Hist. Sci. 26 (4) (1991), 383-387.
J L Berggren, The relation of Greek spherics to early Greek astronomy, in Science and philosophy in classical Greece (New York, 1991), 227-248.
J L Berggren and R S D Thomas, Mathematical astronomy in the fourth century B.C. as found in Euclid's 'Phaenomena', Physis Riv. Internaz. Storia Sci. (N.S.) 29 (1) (1992), 7-33.
G L Geison, Did Conon of Samos transmit Babylonian observations, Isis (3) (193) 58 (1967), 398-401.
B R Goldstein, The obliquity of the ecliptic in ancient Greek astronomy, in Theory and observation in ancient and medieval astronomy (London, 1985), 12-23.
B R Goldstein, The obliquity of the ecliptic in ancient Greek astronomy, Arch. Internat. Hist. Sci. 33 (110) (1983), 3-14.
B R Goldstein and A C Bowen, A new view of early Greek astronomy, Isis 74 (273) (1983), 330-340.
B R Goldstein and A C Bowen, The introduction of dated observations and precise measurement in Greek astronomy, Arch. Hist. Exact Sci. 43 (2) (1991), 93-132.
G Hon, Is there a concept of experimental error in Greek astronomy?, British J. Hist. Sci. 22 (73 pt 2) (1989), 129-150.
Jones, A Greek Saturn table, Centaurus 27 (3-4) (1984), 311-317.
A Jones, Babylonian and Greek astronomy in a papyrus concerning Mars, Centaurus 33 (2-3) 1990), 97-114.
A Jones, On Babylonian astronomy and its Greek metamorphoses, in Tradition, transmission, transformation (Leiden, 1996), 139-155.
A Jones, The adaptation of Babylonian methods in Greek numerical astronomy, Isis 82 (313) (1991), 441-453.
Y Maeyama, The length of the synodic months : The main historical problem of the lunar motion, Arch. Internat. Hist. Sci. 29 (104) (1979), 68-94.
Y Maeyama, Ancient stellar observations : Timocharis, Aristyllus, Hipparchus, Ptolemy - the dates and accuracies, Centaurus 27 (3-4) (1984), 280-310.
R Mercier, Newly discovered mathematical relations between Greek and Indian astronomy, in Proceedings of the Symposium on the 1500th Birth Anniversary of Aryabhata I, Indian J. Hist. Sci. 12 (2) (1977), 120-126.
K P Moesgaard, The full moon serpent : A foundation stone of ancient astronomy?, Centaurus 24 (1980), 51-96.
E Nevill, The early eclipses of the sun and moon, Monthly Notices Roy. Ast. Soc. 67 (1906), 2-17.
D Pingree, The recovery of early Greek astronomy from India, J. Hist. Astronom. 7 (2) (1976), 109-123.
D Rawlins, Eratosthenes' geodest unraveled : was there a high-accuracy Hellenistic astronomy, Isis 73 (1982), 259-265.
C W Rufus, Greek astronomy - its birth, death, and immortality, J. Roy. Astr. Soc. 38 (1944), 143-153.
L Russo, The astronomy of Hipparchus and his time : a study based on pre-Ptolemaic sources, Vistas Astronom. 38 (2) (1994), 207-248.
B L van der Waerden, Greek astronomical calendars. IV. The parapegma of the Egyptians and their "perpetual tables", Arch. Hist. Exact Sci. 32 (2) (1985), 95-104.
B L van der Waerden, The Great Year in Greek, Persian and Hindu astronomy, Arch. Hist. Exact Sci. 18 (4) (1977/78), 359-383.
B L van der Waerden, The heliocentric system in Greek, Persian and Hindu astronomy, in From deferent to equant (New York, 1987), 525-545.
B L van der Waerden, The motion of Venus, Mercury and the Sun in early Greek astronomy, Arch. Hist. Exact Sci. 26 (2) (1982), 99-113.
B L van der Waerden, Greek astronomical calendars. III. The calendar of Dionysios, Arch. Hist. Exact Sci. 29 (2) (1984), 125-130.
L Wright, The astronomy of Eudoxus : geometry or physics?, Studies in Hist. and Philos. Sci. 4 (2) (1973/74), 165-172.
Close this window

Δεν υπάρχουν σχόλια:

Δημοσίευση σχολίου

loading...

Popular Posts Of The Week

Top best cpc cpm ppc ad network for publisher

Αναγνώστες

Translate

loading...
...
loading...
---------------------------------------------------------------------------