Information about Callippic Cycle
In 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 in 330 BC. It is a period of 76 years, as an improvement on the 19-year Metonic cycle.
A century before Callippus, Meton invented the cycle of 19 years that counted 6,940 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 length of 6940/19 = 365 + 1/4 + 1/76 days = 365 d 6 h 18 min 56 s. But Callippus knew that the length of the year was more closely 365 + 1/4 day (= 365d 6h 00m 00s), so he multiplied the 19-year cycle by 4 to reach an integer number of days, and then dropped 1 day from the last 19-year cycle. Thus he constructed a cycle of 76 years that contains 940 lunations and 27,759 days, and has been called the Callippic after him.
Although the cycle's error has been calculated as one full day in 553 years, or 4.95 parts per million.[1], 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 taken as 940 lunations less one day then the Callippic mean year will be shortened by 1/76 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 short 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 in the 47th year of the first Callippic cycle (283 BC), when on the eighth of Anthesterion, the Pleiades were occulted by the Moon.[2]
The Callippic calendar originally used the names of months from the Attic calendar, although later astronomers, such as Hipparchus, preferred other calendars, including the 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 in the month of Athyr, in year 465 of Nabonassar. However, the original, complete form of the Callippic calendar is no longer known.[2]
An occultation
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A century before Callippus, Meton invented the cycle of 19 years that counted 6,940 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 length of 6940/19 = 365 + 1/4 + 1/76 days = 365 d 6 h 18 min 56 s. But Callippus knew that the length of the year was more closely 365 + 1/4 day (= 365d 6h 00m 00s), so he multiplied the 19-year cycle by 4 to reach an integer number of days, and then dropped 1 day from the last 19-year cycle. Thus he constructed a cycle of 76 years that contains 940 lunations and 27,759 days, and has been called the Callippic after him.
Although the cycle's error has been calculated as one full day in 553 years, or 4.95 parts per million.[1], 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 taken as 940 lunations less one day then the Callippic mean year will be shortened by 1/76 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 short 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 in the 47th year of the first Callippic cycle (283 BC), when on the eighth of Anthesterion, the Pleiades were occulted by the Moon.[2]
The Callippic calendar originally used the names of months from the Attic calendar, although later astronomers, such as Hipparchus, preferred other calendars, including the 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 in the month of Athyr, in year 465 of Nabonassar. However, the original, complete form of the Callippic calendar is no longer known.[2]
See also
References
1. ^ This article incorporates content from the 1728 Cyclopaedia, a publication in the public domain.
2. ^ Evans, James. "The Callippic Cycle." The History & Practice of Ancient Astronomy. Oxford University Press US. 1998. ISBN 0-19-509539-1. 186–7.
2. ^ Evans, James. "The Callippic Cycle." The History & Practice of Ancient Astronomy. Oxford University Press US. 1998. ISBN 0-19-509539-1. 186–7.
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calendar is a system for naming periods of time, typically days. These names are known as calendar dates. Cycles in a calendar are often synchronised with the perceived motion of astronomical objects.
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A calendar is also a physical device (often paper).
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In arithmetic and number theory, the least common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b.
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A year (from Old English gēr) is the time between two recurrences of an event related to the orbit of the Earth around the Sun. By extension, this can be applied to any planet: for example, a "Martian year" is the time in which Mars completes its own orbit.
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Callippus or Calippus (Greek: Κάλλιπος; ca. 370 BC–ca. 300 BC) was a Greek astronomer and mathematician.
He was born at Cyzicus, and studied under Eudoxus of Cnidus at the Academy of Plato.
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He was born at Cyzicus, and studied under Eudoxus of Cnidus at the Academy of Plato.
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The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the year (specifically, the seasonal i.e. tropical year) and the synodic month.
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Meton of Athens (Greek: Μέτων ὁ Ἀθηναῖος) was a Greek mathematician, astronomer, geometer, and engineer who lived in Athens in the 5th century BCE.
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"parts-per" notations are used to denote low concentrations of chemical elements. Also known as mixing ratios, they are often used to denote the relative abundance of trace elements in the Earth's crust, trace elements in forensics or other analyses, dissolved minerals in water, or
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The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the year (specifically, the seasonal i.e. tropical year) and the synodic month.
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solstice occurs twice a year, whenever Earth's axis tilts the most toward or away from the Sun, causing the Sun to be farthest north or south at noon. The name is derived from Latin sol (sun) and sistere
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June 28 is the 1st day of the year (2nd in leap years) in the Gregorian calendar. There are 0 days remaining.
In common years it is always in ISO week 26.
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In common years it is always in ISO week 26.
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The proleptic Julian calendar is produced by extending the Julian calendar to dates preceding AD 4 when its quadrennial leap year stabilized. The leap years actually observed between its official implementation in 45 BC and AD 4 were erratic, see the Julian calendar article for
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Claudius Ptolemaeus (Greek: Κλαύδιος Πτολεμαῖος; after 83 – 161 AD), known in English as Ptolemy, was a Greek[1] or Egyptian
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Almagest is the Latin form of the Arabic name (al-kitabu-l-mijisti, i.e. "The Great Book") of a mathematical and astronomical treatise proposing the complex motions of the stars and planetary paths, originally written in Greek as
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Timocharis of Alexandria (ca. 320 BC - 260 BC) was a Greek astronomer and philosopher. Likely born in Alexandria, he was a contemporary of Euclid.
In approximately 3rd century BC, with the help of Aristillus, he created the first star catalogue in the Western world.
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In approximately 3rd century BC, with the help of Aristillus, he created the first star catalogue in the Western world.
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The Attic calendar is the calendar that was in use in ancient Attica, the ancestral territory of the Athenian polis. This article focuses on the 5th and 4th centuries BC, the classical period that produced some of the most significant works of ancient Greek literature.
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Pleiades
A Hubble Space Telescope (HST) image of the Pleiades .
Credit: HST/NASA/ESA.
Observation data: J2000 epoch
Constellation: Taurus
Right ascension: 3h 47m 24s[1]
Declination:
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A Hubble Space Telescope (HST) image of the Pleiades .
Credit: HST/NASA/ESA.
Observation data: J2000 epoch
Constellation: Taurus
Right ascension: 3h 47m 24s[1]
Declination:
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- In twelver Shi'ism the occultation is the name given to the disappearance of the Twelfth Imam. See also occult (disambiguation).
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The Moon as seen by an observer on Earth
Orbital characteristics
Periapsis: 363,104 km
0.0024 AU
Apoapsis: 405,696 km
0.0027 AU
Semi-major axis: 384,399 km
0.
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The Attic calendar is the calendar that was in use in ancient Attica, the ancestral territory of the Athenian polis. This article focuses on the 5th and 4th centuries BC, the classical period that produced some of the most significant works of ancient Greek literature.
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The ancient civil Egyptian calendar had a year that was 365 days long and was divided into 12 months of 30 days each, plus 5 extra days (epagomenes) at the end of the year. The months were divided into 3 "weeks" of ten days each.
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The Greek astronomer Hipparchus introduced two cycles that have been named after him in later literature.
The first is described in Ptolemy's Almagest IV.2. Hipparchus constructed a cycle by multiplying by 17 a cycle due to the Chaldean astronomer Kidinnu, so as to closely
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The first is described in Ptolemy's Almagest IV.2. Hipparchus constructed a cycle by multiplying by 17 a cycle due to the Chaldean astronomer Kidinnu, so as to closely
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Hathor also known as Hatour (Coptic: ) is the third month of the Coptic calendar. It lies between November 11 and December 9 of the Gregorian calendar. The month of Hathor is also the third month of the Season of 'Akhet
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Callippus or Calippus (Greek: Κάλλιπος; ca. 370 BC–ca. 300 BC) was a Greek astronomer and mathematician.
He was born at Cyzicus, and studied under Eudoxus of Cnidus at the Academy of Plato.
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He was born at Cyzicus, and studied under Eudoxus of Cnidus at the Academy of Plato.
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