Hipparchic cycle
Encyclopedia
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 Chaldea
n astronomer Kidinnu
, so as to closely match an integer number of synodic months (4267), anomalistic months (4573), years (345), and days (126007 + about 1 hour); it is also close to a half-integer number of draconic months (4630.53...), so it is an eclipse cycle
. By comparing his own eclipse observations with Babylonian records from 345 years earlier, he could verify the accuracy of the various periods that the Chaldean astronomers used.
The second is a calendar cycle: Hipparchus proposed a correction to the Calippic cycle (of 76 years), which itself was proposed as a correction to the Metonic cycle
(of 19 years). He may have published it in the book Peri eniausíou megéthous ("On the Length of the Year"), which is lost. From solstice observations, Hipparchus found that the tropical year
is about 1/300 of a day shorter than the 365 + 1/4 days that Calippus used (see Almagest III.1). So he proposed to make a 1-day correction after 4 Calippic cycles, such that 304 years = 3760 lunations = 111035 days. This is a very decent approximation for an integer number of lunations in an integer number of days (error only 0.014 days). But it is in fact 1.37 days longer than 304 tropical years: the mean tropical year is actually about 1/128 day (11 minutes 15 seconds) shorter than the Julian calendar year of 365.25 days. These differences cannot be corrected with any cycle that is a multiple of the 19-year cycle of 235 lunations: it is an accumulation of the mismatch between years and months in the basic Metonic cycle, and the lunar months need to be shifted systematically by a day with respect to the solar year (i.e. the Metonic cycle itself needs to be corrected) after every 228 years.
Hipparchus
Hipparchus, the common Latinization of the Greek Hipparkhos, can mean:* Hipparchus, the ancient Greek astronomer** Hipparchic cycle, an astronomical cycle he created** Hipparchus , a lunar crater named in his honour...
introduced two cycles that have been named after him in later literature.
The first is described in Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
's Almagest IV.2. Hipparchus constructed a cycle by multiplying by 17 a cycle due to the Chaldea
Chaldea
Chaldea or Chaldaea , from Greek , Chaldaia; Akkadian ; Hebrew כשדים, Kaśdim; Aramaic: ܟܐܠܕܘ, Kaldo) was a marshy land located in modern-day southern Iraq which came to briefly rule Babylon...
n astronomer Kidinnu
Kidinnu
Kidinnu was a Chaldean astronomer and mathematician. Strabo of Amaseia called him Kidenas, Pliny the Elder Cidenas, and Vettius Valens Kidynas....
, so as to closely match an integer number of synodic months (4267), anomalistic months (4573), years (345), and days (126007 + about 1 hour); it is also close to a half-integer number of draconic months (4630.53...), so it is an eclipse cycle
Eclipse cycle
Eclipses may occur repeatedly, separated by certain intervals of time: these intervals are called eclipse cycles. The series of eclipses separated by a repeat of one of these intervals is called an eclipse series.- Eclipse conditions :...
. By comparing his own eclipse observations with Babylonian records from 345 years earlier, he could verify the accuracy of the various periods that the Chaldean astronomers used.
The second is a calendar cycle: Hipparchus proposed a correction to the Calippic cycle (of 76 years), which itself was proposed as a correction to the Metonic cycle
Metonic cycle
In astronomy and calendar studies, the Metonic cycle or Enneadecaeteris is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the solar year and the synodic month...
(of 19 years). He may have published it in the book Peri eniausíou megéthous ("On the Length of the Year"), which is lost. From solstice observations, Hipparchus found that the tropical year
Tropical year
A tropical year , for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice...
is about 1/300 of a day shorter than the 365 + 1/4 days that Calippus used (see Almagest III.1). So he proposed to make a 1-day correction after 4 Calippic cycles, such that 304 years = 3760 lunations = 111035 days. This is a very decent approximation for an integer number of lunations in an integer number of days (error only 0.014 days). But it is in fact 1.37 days longer than 304 tropical years: the mean tropical year is actually about 1/128 day (11 minutes 15 seconds) shorter than the Julian calendar year of 365.25 days. These differences cannot be corrected with any cycle that is a multiple of the 19-year cycle of 235 lunations: it is an accumulation of the mismatch between years and months in the basic Metonic cycle, and the lunar months need to be shifted systematically by a day with respect to the solar year (i.e. the Metonic cycle itself needs to be corrected) after every 228 years.