Ancient Greek astronomy

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.[1] Most of the constellations of the northern hemisphere derive from Greek astronomy,[2] 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.

NAMA Machine d'Anticythère 1
The Antikythera Mechanism was an analog computer from 150–100 BC designed to calculate the positions of astronomical objects.

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 oldest European texts, the Iliad and the Odyssey, Homer has several astronomical phenomena including solar eclipses. Eclipses that can even permit the dating of these events as the place is known and the calculation of the time is possible, especially if other celestial phenomena are described at the same time.

In the Iliad and the Odyssey, Homer refers to the following celestial objects:

Anaximander
Anaximander

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.

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 cyclical 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.[3]

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.

Development of Ancient Greek Astronomy

Development of Ancient Greek Astronomy

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 (1) a shift from stellar to planetary concerns, (2) the creation of a geometrical model, the "two-sphere model," for the representation of stellar and planetary phenomena, and (3) the establishment of criteria governing theories designed to account for planetary observations".[4]

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.

Ptolemaicsystem-small
Renaissance woodcut illustrating the two-sphere model.

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.

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.

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 Greek fero φέρω "to carry"and 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

Aristarchus working
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

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 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:

  1. Moon
  2. Mercury
  3. Venus
  4. Sun
  5. Mars
  6. Jupiter
  7. Saturn
  8. 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.

Claudius Ptolemy of Alexandria performed a deep examination of the shape and motion of the Earth and celestial bodies. He worked at the museum, or instructional center, school and library of manuscripts in Alexandria. Ptolemy is responsible for a lot of concepts, but one of his most famous works summarizing these concepts is the Almagest, a series of 13 books where he presented his astronomical theories. Ptolemy discussed the idea of epicycles and center of the world. The epicycle center moves at a constant rate in a counter clockwise direction. Once other celestial bodies, such as the planets, were introduced into this system, it became more complex. The models for Jupiter, Saturn, and Mars included the center of the circle, the equant point, the epicycle, and an observer from earth to give perspective. The discovery of this model was that the center of the Mercury and Venus epicycles must always be colinear with the Sun. This assures of bounded elongation. (Bowler, 2010, 48) Bounded elongation is the angular distance of celestial bodies from the center of the universe. Ptolemy's model of the cosmos and his studies landed him an important place in history in the development of modern-day science. The cosmos was a concept further developed by Ptolemy that included equant circles, however Copernicus model of the universe was simpler. In the Ptolemaic system, the Earth was at the center of the universe with the Moon, the Sun, and five planets circling it. The circle of fixed stars marked the outermost sphere of the universe and beyond that would be the philosophical “aether” realm. The Earth was at the exact center of the cosmos, most likely because people at the time believed the Earth had to be at the center of the universe because of the deductions made by observers in the system. The sphere carrying the Moon is described as the boundary between the corruptible and changing sublunary world and the incorruptible and unchanging heavens above it (Bowler, 2010, 26). The heavens were defined as incorruptible and unchanging based on theology and mythology of the past. The Almagest introduced the idea of the sphericity of heavens. The assumption is that the sizes and mutual distances of the stars must appear to vary however one supposes the earth to be positioned, yet no such variation occurred (Bowler, 2010, 55), The aether is the area that describes the universe above the terrestrial sphere. This component of the atmosphere is unknown and named by philosophers, though many do not know what lies beyond the realm of what has been seen by human beings. The aether is used to affirm the sphericity of the heavens and this is confirmed by the belief that different shapes have an equal boundary and those with more angles are greater, the circle is greater than all other surfaces, and a sphere greater than all other solids. Therefore, through physical considerations, and heavenly philosophy, there is an assumption that the heavens must be spherical. The Almagest also suggested that the earth was spherical because of similar philosophy. The differences in the hours across the globe are proportional to the distances between the spaces at which they are being observed. Therefore, it can be deduced that the Earth is spherical because of the evenly curving surface and the differences in time that was constant and proportional. In other words, the Earth must be spherical because they change in time-zones across the world occur in a uniform fashion, as with the rotation of a sphere. The observation of eclipses further confirmed these findings because everyone on Earth could see a lunar eclipse, for example, but it would be at different hours. The Almagest also suggest that the Earth is at the center of the universe. The basis on which this is found is in the fact that six zodiac signs can be seen above Earth, while at the same time the other signs are not visible (Bowler, 2010, 57). The way that we observe the increase and decrease of daylight would be different if the Earth was not at the center of the universe. Though this view later proofed to be invalid, this was a good proponent to the discussion of the design of the universe. Ideas on the universe were later developed and advanced through the works of other philosophers such as Copernicus, who built on ideas through his knowledge of the world and God.

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

AiKhanoumSunDial
Greek equatorial sun dial, Ai-Khanoum, Afghanistan 3rd-2nd century BC.

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.[5] 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.[6]

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."[7]

Later in the 6th century, the Romaka Siddhanta ("Doctrine of the Romans"), and the Paulisa Siddhanta (sometimes attributed as the "Doctrine of Paul" or in general the Doctrine of Paulisa muni) were considered as two of the five main astrological treatises, which were compiled by Varahamihira in his Pañca-siddhāntikā ("Five Treatises").[8] 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."[9]

Sources for Greek astronomy

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).

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.

See also

Notes

  1. ^ Krafft, Fritz (2009). "Astronomy". In Cancik, Hubert; Schneider, Helmuth (eds.). Brill's New Pauly.
  2. ^ Thurston, H., Early Astronomy. Springer, 1994. p.2
  3. ^ I. Passas, K. Hasapis, Ορφικά. Encyclopedia Helios, 1984
  4. ^ David C. Lindberg (2010). The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, Prehistory to A.D. 1450 (Second ed.). University of Chicago Press. p. 86. ISBN 978-0-226-48204-0.
  5. ^ "Afghanistan, les trésors retrouvés", p269
  6. ^ "Les influences de l'astronomie grecques sur l'astronomie indienne auraient pu commencer de se manifester plus tot qu'on ne le pensait, des l'epoque Hellenistique en fait, par l'intermediaire des colonies grecques des Greco-Bactriens et Indo-Grecs" (French) Afghanistan, les trésors retrouvés", p269. Translation: "The influence of Greek astronomy on Indian astronomy may have taken place earlier than thought, as soon as the Hellenistic period, through the agency of the Greek colonies of the Greco-Bactrians and the Indo-Greeks.
  7. ^ Pingree, David (1963). "Astronomy and Astrology in India and Iran". Isis. 54 (2): 229–246. doi:10.1086/349703. JSTOR 228540.
  8. ^ "the Pañca-siddhāntikā ("Five Treatises"), a compendium of Greek, Egyptian, Roman and Indian astronomy. Varāhamihira's knowledge of Western astronomy was thorough. In 5 sections, his monumental work progresses through native Indian astronomy and culminates in 2 treatises on Western astronomy, showing calculations based on Greek and Alexandrian reckoning and even giving complete Ptolemaic mathematical charts and tables. Encyclopædia Britannica Source
  9. ^ ":Mleccha hi yavanah tesu samyak shastram idam sthitam
    Rsivat te api pujyante kim punar daivavid dvijah
    -(Brhatsamhita 2.15)

References

  • Aaboe, Asger H. (2001). Episodes from the Early History of Astronomy. New York: Springer. ISBN 978-0-387-95136-2.
  • Dreyer, John L. E. (1953). A History of Astronomy from Thales to Kepler (2nd ed.). New York: Dover Publications. ISBN 978-0-486-60079-6.
  • Evans, James (1998). The History and Practice of Ancient Astronomy. New York: Oxford University Press. ISBN 978-0-19-509539-5.
  • Heath, Thomas L. (1913). Aristarchus of Samos. Oxford: Clarendon Press.
  • Lindberg, David C. (2010). The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 B.C. to A.D. 1450 (2 ed.). Chicago: University of Chicago Press. ISBN 978-0-226-48204-0.
  • Lloyd, Geoffrey E. R. (1970). Early Greek Science: Thales to Aristotle. New York: W. W. Norton & Co.
  • Neugebauer, Otto E. (1975). A History of Ancient Mathematical Astronomy. Berlin: Springer. ISBN 978-0-387-06995-1.
  • Newton, Robert R. (1977). The Crime of Claudius Ptolemy. Baltimore: Johns Hopkins University Press. ISBN 978-0-8018-1990-2.
  • Pedersen, Olaf (1993). Early Physics and Astronomy: A Historical Introduction (2nd ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-40340-5.
  • Revello, Manuela (2013). "Sole, luna ed eclissi in Omero", in TECHNAI 4. Pisa-Roma: Fabrizio Serra editore. pp. 13–32.
  • Toomer, Gerald J. (1998). Ptolemy's Almagest. Princeton: Princeton University Press. ISBN 978-0-691-00260-6.
  • Bowler, Peter J., and Iwan Rhys Morus. Making Modern Science: A Historical Survey. Chicago, IL: Univ. of Chicago Press, 2010.

External links

Astrolabe

An astrolabe (Ancient Greek: ἀστρολάβος astrolabos; Arabic: ٱلأَسْطُرلاب‎ al-Asturlāb; Persian: اِستاره یاب‎ Astaara yab) is an elaborate inclinometer, historically used by astronomers and navigators to measure the altitude above the horizon of a celestial body, day or night. It can be used to identify stars or planets, to determine local latitude given local time (and vice versa), to survey, or to triangulate. It was used in classical antiquity, the Islamic Golden Age, the European Middle Ages and the Age of Discovery for all these purposes.

The astrolabe's importance not only comes from the early development of astronomy, but is also effective for determining latitude on land or calm seas. Although it is less reliable on the heaving deck of a ship in rough seas, the mariner's astrolabe was developed to solve that problem.

Callippic cycle

For astronomy and calendar studies, the Callippic cycle (or Calippic) is a particular approximate common multiple of the year (specifically the tropical year) and the synodic month, that was proposed by Callippus during 330 BC. It is a period of 76 years, as an improvement of the 19-year Metonic cycle.

A century before Callippus, Meton had discovered the cycle in which 19 years equals 235 lunations. If we assume a year is about ​365 1⁄4 days, 19 years total about 6940 days, which exceeds 235 lunations by almost a third of a day, and 19 tropical years by four tenths of a day. It implicitly gave the solar year a duration of ​6940⁄19 = 365 + ​5⁄19 = 365 + ​1⁄4 + ​1⁄76 days = 365 d 6 h 18 min 56 s. Callippus accepted the 19-year cycle, but held that the duration of the year was more closely ​365 1⁄4 days (= 365 d 6 h), so he multiplied the 19-year cycle by 4 to obtain an integer number of days, and then omitted 1 day from the last 19-year cycle. Thus, he computed a cycle of 76 years that consists of 940 lunations and 27,759 days, which has been named the Callippic cycle after him.Although the cycle's error has been computed as one full day in 553 years, or 4.95 parts per million, in actuality 27,759 days in 76 years has a mean year of exactly ​365 1⁄4 days, which relative to the mean northward equinoctial year is about 11 minutes too long per year, in other words the cycle drifts another day late per ​130 10⁄11 years, which is considerably worse than the drift of the unrounded Metonic cycle. If the Callippic cycle is considered as closer to its unrounded length of ​27,758 3⁄4 days (based on 940 lunations) then its accuracy is essentially the same as the unrounded Metonic cycle (within a few seconds per year). If it is considered as 940 lunations less one day then the Callippic mean year will be shortened by ​1⁄76 of a day (18 minutes 57 seconds), making it grossly too short, and it will also grossly drift ahead with respect to the mean lunar cycle at the rate of ​1⁄940 of a day (1 minute 31 seconds) per lunar month. If the cycle length is truncated to 27,758 days then the mean year is 365 days 5 hours 41 minutes 3 seconds, or almost 8 minutes too brief per year, and it will drift ahead of the mean lunar cycle by about ​(​3⁄4)⁄940 day (1 minute 9 seconds) per lunar month. Altogether, the purported accuracy of this cycle is not impressive, but it is of historical interest.The first year of the first Callippic cycle began at the summer solstice of 330 BC (28 June in the proleptic Julian calendar), and was subsequently used by later astronomers. In Ptolemy's Almagest, for example, he cites (Almagest VII 3, H25) observations by Timocharis during the 47th year of the first Callippic cycle (283 BC), when on the eighth of Anthesterion, the Pleiades star cluster was occulted by the Moon.The Callippic calendar originally used the names of months from the Attic calendar. Later astronomers, such as Hipparchus, preferred other calendars, including the ancient Egyptian calendar. Also Hipparchus invented his own Hipparchic calendar cycle as an improvement upon the Callippic cycle. Ptolemy's Almagest provided some conversions between the Callippic and Egyptian calendars, such as that Anthesterion 8, 47th year of the first Callippic period was equivalent to day 29 of the month of Athyr, during year 465 of Nabonassar. However, the original, complete form of the Callippic calendar is no longer known.It corresponds to:

940 synodic months

1020.084 draconic months

80.084 eclipse years (160 eclipse seasons)

1007.411 anomalistic monthsThe 80 eclipse years means that if there is a solar eclipse (or lunar eclipse), then after one callippic cycle a New Moon (resp. Full Moon) will take place at the same node of the orbit of the Moon, and under these circumstances another eclipse can occur.

Celestial Matters

Celestial Matters is a science fantasy novel by American writer Richard Garfinkle, set in an alternate universe with different laws of physics. Published by Tor Books in 1996, it is a work of alternate history and elaborated "alternate science", as the physics of this world and its surrounding cosmos are based on the physics of Aristotle and ancient Chinese Taoist alchemy.

Celestial Matters won the 1997 Compton Crook Award for best first science fiction novel.

Celestial Sphere Woodrow Wilson Memorial

The grounds of the Palais des Nations (seat of the United Nations Office at Geneva) contain many fine objects donated by member states of the United Nations, private sponsors and artists. The Celestial Sphere (also known as the Armillary Sphere) in the Ariana Park of the Palais des Nations is the best-known of these. The huge - over four meter diameter - Celestial Sphere is the chef d'oeuvre of the American sculptor Paul Manship (1885–1966). It was donated in 1939 by the Woodrow Wilson Foundation to what was then the League of Nations building. Known also as the Woodrow Wilson Memorial Sphere of the Palais des Nations it is today a symbol of Geneva International and of Geneva as the centre of dialogue and peace.

Concentric spheres

The cosmological model of concentric or homocentric spheres, developed by Eudoxus, Callippus, and Aristotle, employed celestial spheres all centered on the Earth. In this respect, it differed from the epicyclic and eccentric models with multiple centers, which were used by Ptolemy and other mathematical astronomers until the time of Copernicus.

Counter-Earth

The Counter-Earth is a hypothetical body of the Solar System hypothesized by the pre-Socratic Greek philosopher Philolaus (c. 470 – c. 385 BC) to support his non-geocentric cosmology, in which all objects in the universe revolve around an unseen "Central Fire" (distinct from the Sun which also revolves around it). The Greek word Antichthon (Greek: Ἀντίχθων) means "Counter-Earth".

In modern times a hypothetical planet always on the other side of the Sun from Earth has been called a "Counter-Earth", and has been a recurring theme in UFO claims, as well as in fiction (particularly science fiction).

Dioptra

A dioptra (sometimes also named dioptre or diopter from Greek: διόπτρα) is a classical astronomical and surveying instrument, dating from the 3rd century BC. The dioptra was a sighting tube or, alternatively, a rod with a sight at both ends, attached to a stand. If fitted with protractors, it could be used to measure angles.

Equant

Equant (or punctum aequans) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is used to explain the observed speed change in planetary orbit during different stages of the orbit. This planetary concept allowed Ptolemy to keep the theory of uniform circular motion alive by stating that the path of heavenly bodies was uniform around one point and circular around another point.

Equatorial ring

An equatorial ring was an astronomical instrument used in the Hellenistic world to determine the exact moment of the spring and autumn equinoxes. Equatorial rings were placed before the temples in Alexandria, in Rhodes, and perhaps in other places, for calendar purposes.

The easiest way to understand the use of an equatorial ring is to imagine a ring placed vertically in the east-west plane at the Earth's equator. At the time of the equinoxes, the Sun will rise precisely in the east, move across the zenith, and set precisely in the west. Throughout the day, the bottom half of the ring will be in the shadow cast by the top half of the ring. On other days of the year, the Sun passes to the north or south of the ring, and will illuminate the bottom half. For latitudes away from the equator, the ring merely needs to be placed at the correct angle in the equatorial plane. At the Earth's poles, the ring would be horizontal.

The equatorial ring was about one to two cubits (45cm-90cm) in diameter. Because the Sun is not a point source of light, the width of the shadow on the bottom half of the ring is slightly less than the width of the ring. By waiting until the shadow was centered on the ring, the time of the equinox could be fixed to within an hour or so. If the equinox happened at night, or if the sky was cloudy, an interpolation could be made between two days' measurements.

The main disadvantage with the equatorial ring is that it needed to be aligned very precisely or false measurements could occur. Ptolemy mentions in the Almagest that one of the equatorial rings in use in Alexandria had shifted slightly, which meant that the instrument showed the equinox occurring twice on the same day. False readings can also be produced by atmospheric refraction of the Sun when it is close to the horizon.

Equatorial rings can also be found on armillary spheres and equatorial sundials.

Globe of Matelica

The Globe of Matelica (Globo of Matelica) is an ancient Roman sundial sculpted on a marble ball. The artifact was found during the 1985 reconstruction of the medieval Palazzo Pretorio, presently Museo Civico Archeologico, of Matelica in the region of Marche, Italy.

Gnomon

A gnomon ([ˈnoʊmɒn], from Greek γνώμων, gnōmōn, literally: "one that knows or examines") is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields.

Hipparchic cycle

The Greek astronomer Hipparchus introduced two cycles that have been named after him in later literature.

Metonic cycle

For astronomy and calendar studies, the Metonic cycle or Enneadecaeteris (from Ancient Greek: ἐννεακαιδεκαετηρίς, "nineteen years") is a period of very close to 19 years that is nearly a common multiple of the solar year and the synodic (lunar) month. The Greek astronomer Meton of Athens (fifth century BC) observed that a period of 19 years is almost exactly equal to 235 synodic months and, rounded to full days, counts 6,940 days. The difference between the two periods (of 19 solar years and 235 synodic months) is only a few hours, depending on the definition of the year.

Considering a year to be ​1⁄19 of this 6,940-day cycle gives a year length of 365 + ​1⁄4 + ​1⁄76 days (the unrounded cycle is much more accurate), which is about 11 days more than 12 synodic months. To keep a 12-month lunar year in pace with the solar year, an intercalary 13th month would have to be added on seven occasions during the nineteen-year period (235 = 19 × 12 + 7). When Meton introduced the cycle around 432 BC, it was already known by Babylonian astronomers. A mechanical computation of the cycle is built into the Antikythera mechanism.

The cycle was used in the Babylonian calendar, ancient Chinese calendar systems (the 'Rule Cycle' 章) and the medieval computus (i.e., the calculation of the date of Easter). It regulates the 19-year cycle of intercalary months of the modern Hebrew calendar. The start of the Metonic cycle depends on which of these systems is being used; for Easter, the first year of the current Metonic cycle is 2014.

Mural instrument

A mural instrument is an angle measuring device mounted on or built into a wall. For astronomical purposes, these walls were oriented so they lie precisely on the meridian. A mural instrument that measured angles from 0 to 90 degrees was called a mural quadrant. They were utilized as astronomical devices in ancient Egypt and ancient Greece. Edmond Halley, due to the lack of an assistant and only one vertical wire in his transit, confined himself to the use of a mural quadrant built by George Graham after its erection in 1725 at the Royal Observatory, Greenwich. Bradley's first observation with that quadrant was made on 15 June 1742.

Octaeteris

In astronomy, an octaeteris (plural: octaeterides) is the period of eight solar years after which the moon phase occurs on the same day of the year plus one or two days.

This period is also in a very good synchronicity with five Venusian visibility cycles (the Venusian synodic period) and thirteen Venusian revolutions around the sun (Venusian sidereal period). This means, that if Venus is visible beside the moon, after eight years the two will be again close together near the same date of the calendar.

The octaeteris, also known as oktaeteris, was noted by Cleostratus in ancient Greece as a 2923.5 day cycle. The 8 year short lunisolar cycle was probably known to many ancient cultures. The mathematical proportions of the octaeteris cycles were noted in Classic Vernal rock art in northeastern Utah by J. Q. Jacobs in 1990. The Three Kings panel also contains more accurate ratios, ratios related to other planets, and apparent astronomical symbolism.

The octaeteris is the calendar used for the Olympic games, every four years and the Greek use 50 months of one Olympiad, four-year cycle and 49 lunarmonths for the next Olympiad. This octaeteris calendar exist in the Antikythera Mechanism and is used for the Olympic dial of this ancient automaton, to determine the time of the Olympic games and other Greek festivities.

Sublunary sphere

In Aristotelian physics and Greek astronomy, the sublunary sphere is the region of the geocentric cosmos below the Moon, consisting of the four classical elements: earth, water, air, and fire.The sublunary sphere was the realm of changing nature. Beginning with the Moon, up to the limits of the universe, everything (to classical astronomy) was permanent, regular and unchanging – the region of aether where the planets and stars are located. Only in the sublunary sphere did the powers of physics hold sway.

The Sand Reckoner

The Sand Reckoner (Greek: Ψαμμίτης, Psammites) is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the Universe. In order to do this, he had to estimate the size of the universe according to the contemporary model, and invent a way to talk about extremely large numbers. The work, also known in Latin as Archimedis Syracusani Arenarius & Dimensio Circuli, which is about 8 pages long in translation, is addressed to the Syracusan king Gelo II (son of Hiero II), and is probably the most accessible work of Archimedes; in some sense, it is the first research-expository paper.

Triquetrum (astronomy)

The triquetrum (derived from the Latin tri- ["three"] and quetrum ["cornered"]) was the medieval name for an ancient astronomical instrument first described by Ptolemy (c. 90–c. 168) in the Almagest (V. 12). Also known as Parallactic Rulers, it was used for determining altitudes of heavenly bodies. Ptolemy calls it a "parallactic instrument" and seems to have used it to determine the zenith distance and parallax of the Moon.

Urania

Urania (; Ancient Greek: Οὐρανία, Ourania; meaning "heavenly" or "of heaven") was, in Greek mythology, the muse of astronomy.

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