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Julian Calendar

Julian calendar

The Julian calendar was introduced in 46 BC by Julius Caesar and took force in 45 BC (709 ab urbe condita). It was chosen after consultation with the Alexandrian astronomer Sosigenes and was probably designed to approximate the tropical year, known at least since Hipparchus. It has a regular year of 365 days divided into 12 months, and a leap day is added to February every four years. Hence the Julian year is on average 365.25 days long. The Julian calendar remained in use into the 20th century in some countries and is still used by many national Orthodox churches. However, too many leap days are added with respect to the astronomical seasons on this scheme. On average, the astronomical solstices and the equinoxes advance by about 11 minutes per year against the Julian year, causing the calendar to gain a day about every 134 years. While Hipparchus and presumably Sosigenes were aware of the discrepancy, although not of its correct value, it was evidently felt to be of little importance. However, it accumulated significantly over time, and eventually led to the reform of 1582, which replaced the Julian calendar with the more accurate Gregorian calendar. The notation "Old Style" (OS) is sometimes used to indicate a date in the Julian calendar, as opposed to "New Style", which indicates a date in the Gregorian Calendar. This notation is used when there might otherwise be confusion about which date is found in a text.

From Roman to Julian

The ordinary year in the previous Roman calendar consisted of 12 months, for a total of 355 days. In addition, an intercalary month, the Mensis Intercalaris, was sometimes inserted between February and March. This intercalary month was formed by inserting 22 days before the last five days of February, creating a 27-day month. It began after a truncated February having 23 or 24 days, so that it had the effect of adding 22 or 23 days to the year, forming an intercalary year of 377 or 378 days. According to the later writers Censorinus and Macrobius, the ideal intercalary cycle consisted of ordinary years of 355 days alternating with intercalary years, which were alternately 377 and 378 days long. On this system, the average Roman year would have had 366¼ days over four years, giving it an average drift of one day per year relative to any solstice or equinox. Macrobius describes a further refinement wherein, for 8 years out of 24, there were only three intercalary years each of 377 days. This refinement averages the length of the year to 365¼ days over 24 years. In practice, intercalations did not occur schematically according to these ideal systems, but were determined by the pontifices. So far as can be determined from the historical evidence, they were much less regular than these ideal schemes suggest. They usually occurred every second or third year, but were sometimes omitted for much longer, and occasionally occurred in two consecutive years. If managed correctly this system allowed the Roman year, on average, to stay roughly aligned to a tropical year. However, if too many intercalations were omitted, as happened after the Second Punic War and during the Civil Wars, the calendar would drift rapidly out of alignment with the tropical year. Moreover, since intercalations were often determined quite late, the average Roman citizen often did not know the date, particularly if he were some distance from the city. For these reasons, the last years of the pre-Julian calendar were later known as years of confusion. The problems became particularly acute during Julius Caesar's pontificate, 63 BC to 46 BC, when there were only five intercalary months, whereas there should have been eight, and none at all during the five Roman years before 46 BC. The Julian reform was intended to correct this problem permanently. Before it took effect, the missed intercalations during Julius Caesar's pontificate were made up by inserting 67 days (22+23+22) between November and December of 46 BC in the form of two months, in addition to 23 days which had already been added to February. Thus 90 days were added to this last year of the Roman Republican calendar, giving it 445 days. Because it was the last of a series of irregular years, this extra-long year was, and is, referred to as the last year of confusion. The first year of operation of the new calendar was 45 BC.

Leap years error

Despite the new calendar being much simpler than the Roman calendar, the pontifices apparently misunderstood the algorithm. They added a leap day every three years, instead of every four years. According to Macrobius, the error was the result of counting inclusively, so that the four year cycle was considered as including both the first and fourth years. This resulted in too many leap days. Caesar Augustus remedied this discrepancy by restoring the correct frequency after 36 years of this mistake. He also skipped several leap days in order to realign the year. The historic sequence of leap years (i.e. years with a leap day) in this period is not given explicitly by any ancient source, although the existence of the triennial leap year cycle is confirmed by an inscription that dates from 9 or 8 BC. The chronologist Joseph Scaliger established in 1583 that the Augustan reform was instituted in 8 BC, and inferred that the sequence of leap years was 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9 BC, AD 8, 12 etc. This proposal is still the most widely accepted solution. It has also sometimes been suggested that 45 BC was a leap year. Other solutions have been proposed from time to time. Kepler proposed in 1614 that the correct sequence of leap years was 43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10 BC, AD 8, 12 etc. In 1883 the German chronologist Matzat proposed 44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11 BC, AD 4, 8, 12 etc., based on a passage in Dio Cassius that mentions a leap day in 41 BC that was said to be contrary to (Caesar's) rule. In the 1960s Radke argued the reform was actually instituted when Augustus became pontifex maximus in 12 BC, suggesting the sequence 45, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12 BC, AD 4, 8, 12 etc. In 1999, an Egyptian papyrus was published which gives an ephemeris table for 24 BC with both Roman and Egyptian dates. From this it can be shown that the most likely sequence was in fact 44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8 BC, AD 4, 8, 12 etc, very close to that proposed by Matzat. This sequence shows that the standard Julian leap year sequence began in AD 4, the twelfth year of the Augustan reform. Also, under this sequence the actual Roman year coincided with the proleptic Julian year between 32 and 26 BC. This suggests that one aim of the realignment portion of the Augustan reform was to ensure that key dates of his career, notably the fall of Alexandria on 1 August 30 BC, were unaffected by his correction. Roman dates before 32 BC were typically a day or two before the day with the same Julian date, so 1 January in the Roman calendar of the first year of the Julian reform actually fell on 31 December 46 BC (Julian date). A curious effect of this is that Caesar's assassination on the Ides (15th day) of March in 44 BC fell on 14 March 44 BC in the Julian calendar.

Naming of the months

Immediately after the Julian reform, the twelve months of the Roman calendar were named Ianuarius, Februarius, Martius, Aprilis, Maius, Iunius, Quintilis, Sextilis, September, October, November, and December, just as they were before the reform. Their lengths were set to their modern values. The old intercalary month, the Mensis Intercalaris, was abolished and replaced with an single intercalary day at the same point (i.e. five days before the end of Februarius). The first month of the year continued to be Ianuarius, as it had been since 153 BC. The Romans later renamed months after Caesar and Augustus, renaming Quintilis (originally, "the Fifth month", with March = month 1) as Iulius (July) in 44 BC and Sextilis ("Sixth month") as Augustus (August) in 8 BC. (Note that the letter J was not invented until the 17th century). Quintilis was renamed to honour Caesar because it was the month of his birth. According to a senatusconsultum quoted by Macrobius, Sextilis was renamed to honour Augustus because several of the most significant events in his rise to power, culminating in the fall of Alexandria, fell in that month. Other months were renamed by other emperors, but apparently none of the later changes survived their deaths. Caligula renamed September ("Seventh month") as Germanicus; Nero renamed Aprilis (April) as Neroneus, Maius (May) as Claudius and Iunius (June) as Germanicus; and Domitian renamed September as Germanicus and October ("Eighth month") as Domitianus. At other times, September was also renamed as Antoninus and Tacitus, and November ("Ninth month") was renamed Faustina and Romanus. Commodus was unique in renaming all twelve months after his own adopted names (January to December): Amazonius, Invictus, Felix, Pius, Lucius, Aelius, Aurelius, Commodus, Augustus, Herculeus, Romanus, and Exsuperatorius. Much more lasting than the ephemeral month names of the post-Augustan Roman emperors were the names introduced by Charlemagne. He renamed all of the months agriculturally into Old High German. They were used until the 15th century, and with some modifications until the late 18th century in Germany and in the Netherlands (January-December): Wintarmanoth (winter month), Hornung (spring), Lentzinmanoth (Lent month), Ostarmanoth (Easter month), Winnemanoth (grazing month), Brachmanoth (plowing month), Heuvimanoth (hay month), Aranmanoth (harvest month), Witumanoth (wood month), Windumemanoth (vintage month), Herbistmanoth (autumn/harvest month), and Heilagmanoth (holy month). Translations of these month names are still used to this day in some Slavic languages, such as Polish.

Lengths of the months

According to the 13th century scholar Sacrobosco, the original scheme for the months in the Julian Calendar was very regular, alternately long and short. From January through December, the month lengths according to Sacrobosco for the Roman Republican calendar were: :30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, and 29, totaling 354 days. He then thought that Julius Caesar added one day to every month except February, a total of 11 more days, giving the year 365 days. A leap day could now be added to the extra short February: :31, 29 (30), 31, 30, 31, 30, 31, 30, 31, 30, 31, and 30 He then said Augustus changed this to: :31, 28 (29), 31, 30, 31, 30, 31, 31, 30, 31, 30, and 31 giving us the irregular month lengths which we still use today, so that the length of Augustus would not be shorter than (and therefore inferior to) the length of Iulius. Although this theory is still widely repeated, it is certainly wrong. First, a wall painting of a Roman Republican calendar has survived [http://www.personal.psu.edu/users/w/x/wxk116/RomanCalendar/Fasti4.gif] which confirms the literary accounts that the months were already irregular before Julius Caesar reformed it: :29, 28, 31, 29, 31, 29, 31, 29, 29, 31, 29, and 29 Also, the Julian reform did not change the dates of the Nones and Ides. In particular, the Ides are late (on the 15th rather than 13th) in March, May, July and October, showing that these months always had 31 days in the Roman calendar, whereas Sacrobosco's theory requires that the length of October was changed. Further, Sacrobosco's theory is explicitly contradicted by the third and fifth century authors Censorinus and Macrobius, and, finally, it is inconsistent with seasonal lengths given by Varro, writing in 37 BC, before the Augustan reform, with the 31-day Sextilis given by the new Egyptian papyrus from 24 BC, and with the 28-day February shown in the Fasti Caeretani, which is dated before 12 BC.

Year numbering

The dominant method that the Romans used to identify a year for dating purposes was to name it after the two consuls who took office in it. Since 153 BC, they had taken office on 1 January, and Julius Caesar did not change the beginning of the year. Thus this consular year was an eponymous or named year. Roman years were named this way until the last consul was appointed in 541. Only rarely did the Romans number the year from the founding of the city (of Rome), ab urbe condita (AUC). This method was used by Roman historians to determine the number of years from one event to another, not to date a year. Different historians had several different dates for the founding. The Fasti Capitolini, an inscription containing an official list of the consuls which was published by Augustus, used an epoch of 752 BC. The epoch used by Varro, 753 BC, has been adopted by modern historians. Indeed, Renaissance editors often added it to the manuscripts that they published, giving the false impression that the Romans numbered their years. Most modern historians tacitly assume that it began on the day the consuls took office, and ancient documents such as the Fasti Capitolini which use other AUC systems do so in the same way. However, the Varronian AUC year did not formally begin on 1 January, but on Founder's Day, 21 April. This prevented the early Roman church from celebrating Easter after 21 April because the festivities associated with Founder's Day conflicted with the solemnity of Lent, which was observed until the Saturday before Easter Sunday. In addition to consular years, the Romans sometimes used the regnal year of the emperor. Anno Diocletiani, named after Diocletian, was often used by the Alexandrian Christians to number their Easters during the fourth and fifth centuries. In AD 537, Justinian required that henceforth the date must include the name of the emperor, in addition to the indiction and the consul (the latter ending only four years later). The indiction caused the Byzantine year to begin on 1 September, which is still used in the Eastern Orthodox Church for the beginning of the liturgical year. In AD 525 Dionysius Exiguus proposed the system of anno Domini, which gradually spread through the western Christian world, once the system was adopted by Bede. Years were numbered from the supposed date of the incarnation or annunciation of Jesus on 25 March, although this soon changed to Christmas, then back to Annunciation Day in Britain, and the numbered year even began on Easter in France.

From Julian to Gregorian

The Julian calendar was in general use in Europe from the times of the Roman Empire until 1582, when Pope Gregory XIII promulgated the Gregorian Calendar, which was soon adopted by most Catholic countries. The Protestant countries followed later, and the countries of Eastern Europe even later. Great Britain had Thursday 14 September 1752 follow Wednesday 2 September 1752. Sweden adopted the new style calendar in 1753, but also for a twelve-year period starting in 1700 used a modified Julian Calendar. Russia remained on the Julian calendar until after the Russian Revolution (which is thus called the 'October Revolution' but occurred in November according to the Gregorian calendar), in 1917, while Greece continued to use it until 1923. Although all Eastern European countries had adopted the Gregorian calendar on or before 1923, their national Eastern Orthodox churches had not. A revised Julian calendar was proposed during a synod in Constantinople in May of 1923, consisting of a solar part which was and will be identical to the Gregorian calendar until the year 2800, and a lunar part which calculated Easter astronomically at Jerusalem. All Orthodox churches refused to accept the lunar part, so almost all Orthodox churches continue to celebrate Easter according to the Julian calendar (the Finnish Orthodox Church uses the Gregorian Easter). The solar part was only accepted by some Orthodox churches, those of Constantinople, Alexandria, Antioch, Greece, Cyprus, Romania, Poland, Bulgaria (in 1963), and the Orthodox Church in America (although some OCA parishes are permitted to use the Julian calendar). Thus, these churches celebrate the Nativity on the same day that Western Christians do, 25 December Gregorian until 2800. The Orthodox churches of Jerusalem, Russia, Serbia, Georgia, Ukraine, and the Greek Old Calendarists continue to use the Julian calendar for their fixed dates, thus they celebrate the Nativity on 25 December Julian (7 January Gregorian until 2100).

External links

- [http://aa.usno.navy.mil/data/docs/JulianDate.html Julian-Gregorian Converter]
- [http://webexhibits.org/calendars/index.html Calendars through the ages] on WebExhibits.
- [http://www.tyndale.cam.ac.uk/Egypt/ptolemies/chron/roman/chron_rom_cal.htm Roman Dates]
- [http://penelope.uchicago.edu/~grout/encyclopaedia_romana/calendar/romancalendar.html The Roman Calendar]
- [http://5ko.free.fr/jul-greg.php?e=en Synoptical Julian-Gregorian Calendar] - compare the Julian and Gregorian calendars for any date between 1582 and 2100 using this side-by-side reference. Category:Ancient Rome Category:Specific calendars als:Julianischer Kalender ko:율리우스력 ja:ユリウス暦 simple:Julian calendar th:ปฏิทินจูเลียน

46 BC

Events

- February 6 – Julius Caesar defeats the combined army of Pompeian followers and Numidians under Metellus Scipio and Juba at Thapsus.
- April 20 – Cicero, in Rome, writes to Varro "If our voices are no longer heard in the Senate and in the Forum, let us follow the example of the ancient sages and serve our country through our writings, concentrating on questions of ethics and constitutional law."
- November – Caesar leaves for Farther Hispania to deal with a fresh outbreak of resistance.
- Caesar is "elected" Pontifex Maximus for life, and reforms the Roman calendar to create the Julian calendar. The transitional year is extended to 445 days to synchronize the new calendar and the seasonal cycle. The Julian Calendar would remain the standard in the western world for over 1600 years, until superceeded by the Gregorian Calendar in 1582.
- Caesar gets drunk and hits a member of the Roman Senate.
- Caesar appoints his nephew Octavian his heir.

Births

Deaths

- Marcus Porcius Cato, the younger commits suicide after the battle of Thapsus
- Metellus Scipio (Quintus Caecilius Metellus Pius Cornelianus Scipio Nasica) killed at the battle of Thapsus while his forces attempt to surrender.
- Vercingetorix, Gaul leader Category:46 BC ko:기원전 46년 simple:46 BC

45 BC

Events

Rome :
- January 1 - Julian calendar goes into effect :
- March 17 - In his last victory, Julius Caesar defeats the Pompeian forces of Titus Labienus and Pompey the younger in the Battle of Munda. Pompey the younger was excuted, and Labienus died in battle, but Sextus Pompey escaped to take command of the remnants of the Pompeian fleet. :
- The veterans of Julius Caesar's Legions Legio XIII Gemina and Legio X Equestris dembobilized. The veterans of the 10th legion would be settled in Narbo, while those of the 13th would be given somewhat better lands in Italia it'self. :
- Julius Caesar is named dictator for life :
- Caesar probably writes the Commentaries in this year.
- Possible first year of the Azes I Era

Births

- Iullus Antonius - son of Mark Antony and Fulvia; consul 10 BC
- Wang Mang - "usurper" of the Han Dynasty and Emperor of the Xin Dynasty

Deaths

- February - Tullia, daughter of Cicero
- March 17 - Titus Labienus, killed in the battle of Munda
- March 17 - Gnaeus Pompeius, son of Pompey the Great, executed after the battle of Munda Category:45 BC ko:기원전 45년

Ab urbe condita

:For the book Ab Urbe Condita see Ab Urbe Condita (book). Ab urbe condita (AUC or a.u.c.) is Latin for "from the founding of the city" (of Rome), supposed to have happened in 753 BC. It was one of several methods used for dating years in the Roman era, when the Roman calendar and the Julian calendar were in use. It appears to have been widely replaced by the anno Diocletiani (A.D.) system which in turn was gradually superseded by the anno Domini (A.D.) system of Dionysius Exiguus. Some modern historians claim that an era ab urbe condita (from the founding of the city of Rome) did not, in reality, exist in the ancient world, and the use of reckoning the years in this way is modern.

Significance

Dionysius Exiguus From emperor Claudius onwards Varro's calculation (see below) superseded other contemporary calculations. Celebrating the anniversary of the city became part of imperial propaganda. Claudius was the first to hold magnificent celebrations in honor of the city's anniversary, in 47 AD, eight hundred years after the supposed founding of the city. In 147/8 Antoninus Pius held similar celebrations, and in 248 Philip the Arab celebrated Rome's first millennium, together with Ludi saeculares for Rome's alleged tenth saeculum. Coins from his reign commemorate the celebrations. A coin by a contender for the imperial throne, Pacatianus, explicitely states '1001', which is an indication that the citizens of the Empire had a sense of the beginning of a new era, a Saeculum Novum. When the Roman Empire turned Christian in the following century, this imagery came to be used in a more metaphysical sense.

Calculation by Varro

The traditional date for the founding of Rome of April 21, 753 BC was initiated by Varro. In practice the Romans typically dated events from the reign year of the current ruler (during the republic a consul had a term of a single year). Varro may have used the consular list with its mistakes, and called the year of the first consuls "245 ab urbe condita" (a.u.c.), accepting the 244-year interval from Dionysius of Halicarnassus for the kings after the foundation of Rome. The correctness of Varro's calculation has not been proved scientifically but is still used worldwide.

Alternative calculations

According to Velleius Paterculus (VIII, 5) The foundation of Rome took place 437 years after the capture of Troy (1182 BC), It took place shortly before an eclipse of the Sun that was observed at Rome on June 25, 745 BC and had a magnitude of 50.3%. Its beginning occurred at 16:38, its middle at 17:28, and its end at 18:16. However, according to Lucius Tarrutius of Firmum Romulus and Remus were conceived in the womb on the 23rd day of the Egyptian month Choiac, at the time of a total eclipse of the Sun. (This eclipse occurred on June 15, 763 BC, with a magnitude of 62.5% at Rome. Its beginning took place at 6:49, its middle at 7:47 and its end at 8:51.) He was born on the 21st day of the month Thoth. The first day of Thoth fell on March 2 in that year (Prof. E.J. Bickerman, 1980: 115). It means that Rhea Silvia's pregnancy lasted for 281 days. Rome was founded on the ninth day of the month Pharmuthi, which was the 21st of April, as universally agreed. The Romans add that about the time Romulus started to build the city, an eclipse of the Sun was observed by Antimachus, the Teian poet, on the 30th day of the lunar month. This eclipse on June 25, 745 BC (see above) had a magnitude of 54.6% at Teos, Asia Minor. It started at 17:49 it was still eclipsed at sunset, at 19:20. Romulus vanished in the 54th year of his life, on the Nones of Quintilis (July), on a day when the Sun was darkened. The day turned into night, which sudden darkness was believed to be an eclipse of the Sun. It occurred on July 17, 709 BC, with a magnitude of 93.7%, beginning at 5:04 and ending at 6:57. (All these eclipse data have been calculated by Prof. Aurél Ponori-Thewrewk, retired director of the Planetarium of Budapest.) Plutarch placed it in the 37th year from the foundation of Rome, on the fifth of our July, then called Quintilis, on "Caprotine Nones," Livy (I, 21) also states that Romulus ruled for 37 years. He was slain by the senate or disappeared in the 38th year of his reign. Most of these have been recorded by Plutarch (Lives of Romulus, Numa Pompilius and Camillus), Florus (Book I, I), Cicero (The Republic VI, 22: Scipio's Dream), Dio (Dion) Cassius and Dionysius of Halicarnassus (L. 2). Dio in his Roman History (Book I) confirms our data by telling that Romulus was in his 18th year of age whan he had founded Rome. Therefore, three eclipse records prove that Romulus reigned from 746 BC to 709 BC, and Rome was founded in 745 BC. Q. Fabius Pictor (c. 250 BC) tells that Roman consuls started for the first time 239 years after Rome's foundation (Enciclopedia Italiana, XIV, 1951: 173). Livy (I, 60) gives almost the same, 240 years for that interval. Polybius, The Histories (III, 22. 1-2) tells that 28 years after the expulsion of the last Roman king (or, in the 28th year, we believe), Xerxes crossed over to Greece, and that event is fixed to 478 BC by two solar eclipses. According to all these, the a.u.c. system should be handled accordingly, with due precaution.

Sosigenes

There were several historical figures called Sosigenes:
- Sosigenes of Alexandria, an astronomer consulted by Julius Caesar for the design of the Julian calendar.
- Sosigenes the Peripatetic, who was a peripatetic philosopher living at the end of the 2nd century A.D. and the tutor of Alexander of Aphrodisias. See also: Sosigenes (crater)

Hipparchus (astronomer)

Hipparchus (Greek Ἳππαρχος) (ca. 190 BC – ca. 120 BC) was a Greek astronomer, geographer, and mathematician. Hipparchus was born in Nicaea (now Iznik, Turkey) and probably died on the island of Rhodes. He is known to have been active at least from 147 BC to 127 BC. Hipparchus is considered the greatest astronomical observer, and by some the greatest astronomer of antiquity. He was the first Greek to develop quantitative and accurate models for the motion of the Sun and Moon. For this he made use of the observations and knowledge accumulated over centuries by the Chaldeans from Babylonia. He was also the first to compile a trigonometric table, which allowed him to solve any triangle. With his solar and lunar theories and his numerical trigonometry, he was probably the first to develop a reliable method to predict solar eclipses. His other achievements include the discovery of precession, the compilation of the first star catalogue, and probably the invention of the astrolabe. Claudius Ptolemaeus, three centuries later depended much on Hipparchus. However, his synthesis of astronomy superseded Hipparchus's work: although Hipparchus wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus has been preserved by later copyists. As a consequence, we know comparatively little about Hipparchus. Aratus

Life and work

Most of what is known about Hipparchus comes from Ptolemy's (2nd century) Almagest ("the great treatise"; ed. [Toomer 1981]), with additional references to him by Pappus of Alexandria and Theon of Alexandria (4th century) in their commentaries on the Almagest; from Strabo's Geographia ("Geography"), and from Pliny the Elder's Naturalis historia ("Natural history") (1st century). There is a strong tradition that Hipparchus was born in Nicaea (Greek Νικαία), in the ancient district of Bithynia (modern-day İznik in province Bursa), in what today is Turkey. The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him from 147 BC to 127 BC; earlier observations since 162 BC might also be made by him. The date of his birth (ca. 190 BC) was calculated by Delambre based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his latest observations. Hipparchus obtained information from Alexandria as well as Babylon, but it is not known if and when he visited these places. It is not known what Hipparchus' economic means were and how he supported his scientific activities. Also, his appearance is unknown: there are no contemporary portraits.In the 2nd and 3rd centuries coins were made in his honour in Bithynia that bear his name and show him with a globe; this confirms the tradition that he was born there. Hipparchus is believed to have died on the island of Rhodes, where he spent most of his later life — Ptolemy attributes observations to him from Rhodes in the period from 141 BC to 127 BC. Hipparchus's main original works are lost. His only preserved work is Toon Aratou kai Eudoxou Fainomenoon exegesis ("Commentary on the Phaenomena of Eudoxus and Aratus"). This is a critical commentary in two books on a popular poem by Aratus based on the work by Eudoxus. It was published by Karl Manitius (In Arati et Eudoxi Phaenomena, Leipzig, 1894). Hipparchus also made a list of his major works, which apparently mentioned about fourteen books, but which is only known from references by later authors. His famous star catalogue probably was incorporated into the one by Ptolemy, but cannot be reliably reconstructed. We know he made a celestial globe; a copy of a copy may have been preserved in the oldest surviving celestial globe accurately depicting the constellations: the globe carried by the Farnese Atlas [Schaefer 2005]. Hipparchus is recognized as the originator and father of scientific astronomy. He is believed to be the greatest Greek astronomical observer, and many regard him as the greatest astronomer of ancient times, although Cicero gave preferences to Aristarchus of Samos. Some put in this place also Ptolemy of Alexandria. Hipparchus' writings had been mostly superseded by those of Ptolemy, so later copyists have not preserved them for posterity. Also see the biographical articles by [Toomer 1978] and [Jones 2001].

Babylonian sources

Many of the works of Greek scientists - mathematicians, astronomers, geographers - have been preserved up to the present time, or some aspects of their work and thought are still known through later references. However, achievements in these fields by Middle Eastern civilizations, notably those in Babylonia, had been forgotten. After the discovery of the archaeological sites in the 19th century, many writings on clay tablets have been found, some of them related to astronomy. Most known astronomical tablets have been described by A. Sachs, and later published by Otto Neugebauer in "Astronomical Cuneiform Texts" (3 vol.; Princeton and London, 1955). Since the rediscovery of the Babylonian civilization, it has become apparent that Greek astronomers, and in particular Hipparchus, borrowed a lot from the Chaldeans. F.X. Kugler demonstrated in his book Die Babylonische Mondrechnung ("The Babylonian lunar computation", Freiburg im Breisgau, 1900) the following: Ptolemy had stated in his Almagest IV.2 that Hipparchus improved the values for the Moon's periods known to him from "even more ancient astronomers" by comparing eclipse observations made earlier by "the Chaldeans", and by himself. However Kugler found that the periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu). Apparently Hipparchus only confirmed the validity of the periods he learned from the Chaldeans by his newer observations. It is clear that Hipparchus (and Ptolemy after him) had an essentially complete list of eclipse observations covering many centuries. Most likely these had been compiled from the "diary" tablets: these are clay tablets recording all relevant observations that the Chaldeans routinely made. Preserved examples date from 652 BC to AD 130, but probably the records went back as far as the reign of the Babylonian king Nabonassar: Ptolemy starts his chronology with the first day in the Egyptian calendar of the first year of Nabonassar, i.e., 26 February 747 BC. This raw material by itself must have been hard to use, and no doubt the Chaldeans themselves compiled extracts of e.g., all observed eclipses (some tablets with a list of all eclipses in a period of time covering a saros have been found). This allowed them to recognise periodic recurrences of events. Among others they used in System B (cf. Almagest IV.2):
- 223 (synodic) months = 239 returns in anomaly (anomalistic month) = 242 returns in latitude (draconic month). This is now known as the saros period which is very useful for predicting eclipses.
- 251 (synodic) months = 269 returns in anomaly
- 5458 (synodic) months = 5923 returns in latitude
- 1 synodic month = 29;31:50:08:20 days (sexagesimal; 29.53059413... days in decimals = 29 days 12 hours 44 min 3⅓ s) The Babylonians expressed all periods in synodic months, probably because they used a lunisolar calendar. Various relations with yearly phenomena led to different values for the length of the year. Similarly various relations between the periods of the planets were known. The relations that Ptolemy attributes to Hipparchus in Almagest IX.3 had all already been used in predictions found on Babylonian clay tablets. All this knowledge was transferred to the Greeks probably shortly after the conquest by Alexander the Great (331 BC). According to the late classical philosopher Simplicius (early 6th century AD), Alexander ordered the translation of the historical astronomical records under supervision of his chronicler Callisthenes of Olynthus, who sent it to his uncle Aristotle. It is worth mentioning here that although Simplicius is a very late source, his account may be reliable. He spent some time in exile at the Sassanid (Persian) court, and may have accessed sources otherwise lost in the West. It is striking that he mentions the title tèresis (Greek: guard) which is an odd name for a historical work, but is in fact an adequate translation of the Babylonian title massartu meaning "guarding" but also "observing". Anyway, Aristotle's pupil Callippus of Cyzicus introduced his 76-year cycle, which improved upon the 19-year Metonic cycle, about that time. He had the first year of his first cycle start at the summer solstice of 28 June 330 BC (Julian proleptic date), but later he seems to have counted lunar months from the first month after Alexander's decisive battle at Gaugamela in fall 331 BC. So Callippus may have obtained his data from Babylonian sources and his calendar may have been anticipated by Kidinnu. Also it is known that the Babylonian priest known as Berossus wrote around 281 BC a book in Greek on the (rather mythological) history of Babylonia, the Babyloniaca, for the new ruler Antiochus I; it is said that later he founded a school of astrology on the Greek island of Kos. Another candidate for teaching the Greeks about Babylonian astronomy/astrology was Sudines who was at the court of Attalus I Soter late in the 3rd century BC. In any case, the translation of the astronomical records required profound knowledge of the cuneiform script, the language, and the procedures, so it seems likely that it was done by some unidentified Chaldeans. Now, the Babylonians dated their observations in their lunisolar calendar, in which months and years have varying lengths (29 or 30 days; 12 or 13 months respectively). At the time they did not use a regular calendar (such as based on the Metonic cycle like they did later), but started a new month based on observations of the New Moon. This made it very tedious to compute the time interval between events. What Hipparchus may have done is transform these records to the Egyptian calendar, which uses a fixed year of always 365 days (consisting of 12 months of 30 days and 5 extra days): this makes computing time intervals much easier. Ptolemy dated all observations in this calendar. He also writes that "All that he (=Hipparchus) did was to make a compilation of the planetary observations arranged in a more useful way" (Almagest IX.2). Pliny states (Naturalis Historia II.IX(53)) on eclipse predictions: "After their time (=Thales) the courses of both stars (=Sun and Moon) for 600 years were prophecied by Hipparchus, ...". This seems to imply that Hipparchus predicted eclipses for a period of 600 years, but considering the enormous amount of computation required, this is very unlikely. Rather, Hipparchus would have made a list of all eclipses from Nabonasser's time to his own. Other traces of Babylonian practice in Hipparchus' work are:
- first Greek known to divide the circle in 360 degrees of 60 arc minutes.
- first consistent use of the sexagesimal number system.
- the use of the unit pechus ("cubit") of about 2° or 2½°.
- use of a short period of 248 days = 9 anomalistic months. Also see G.J. Toomer (1981?): Hipparchus and Babylonian Astronomy.

Geometry and trigonometry

Hipparchus is recognised as the first mathematician who compiled a trigonometry table, which he needed when computing the eccentricity of the orbits of the Moon and Sun. He tabulated values for the chord function, which gives the length of the chord for each angle. He did this for a circle with a circumference of 21,600 and a radius of (rounded) 3438 units: this has a unit length of 1 arc minute along its perimeter. He tabulated the chords for angles with increments of 7.5°. In modern terms, the chord of an angle equals twice the sine of half of the angle, i.e.: : chord(A) = 2 sin(A/2). He described it in a work (now lost), called Toon en kuklooi eutheioon (Of Lines Inside a Circle) by Theon of Alexandria (4th century) in his commentary on the Almagest I.10; his table seems to have survived in astronomical treatises in India, for instance the Surya Sidhanta. This was a significant innovation, because it allowed Greek astronomers to solve any triangle, and made it possible to make quantitative astronomical models and predictions using their preferred geometric techniques. See [Toomer 1973]. For his chord table Hipparchus must have used a better approximation for π than the one from Archimedes (between 3 + 1/7 and 3 + 10/71); maybe the one later used by Ptolemy: 3;8:30 (sexagesimal) (Almagest VI.7); but it is not known if he computed an improved value himself. Hipparchus could construct his chord table using the Pythagorean theorem and a theorem known to Archimedes. He also might have developed and used the theorem in plane geometry called Ptolemy's theorem, because it was proved by Ptolemy in his Almagest (I.10) (later elaborated on by Carnot). Hipparchus was the first to show that the stereographic projection is conformal, and that it transforms circles on the sphere that do not pass through the center of projection to circles on the plane. This was the basis for the astrolabe. Besides geometry, Hipparchus also used arithmetic techniques from the Chaldeans. He was one of the first Greek mathematicians to do this, and in this way expanded the techniques available to astronomers and geographers. There is no indication that Hipparchus knew spherical trigonometry, which was first developed by Menelaus of Alexandria in the 1st century. Ptolemy later used the new technique for computing things like the rising and setting points of the ecliptic, or to take account of the lunar parallax. Hipparchus may have used a globe for this (to read values off the coordinate grids drawn on it), as well as approximations from planar geometry, or arithmetical approximations developed by the Chaldeans.

Lunar and solar theory

Motion of the moon

Hipparchus also studied the motion of the Moon and confirmed the accurate values for some periods of its motion that Chaldean astronomers had obtained before him. The traditional value (from Babylonian System B) for the mean synodic month is 29 days;31,50,8,20 (sexagesimal) = 29.5305941... d. Expressed as 29 days + 12 hours + 793/1080 hours this value has been used later in the Hebrew calendar (possibly from Babylonian sources). The Chaldeans also knew that 251 synodic months = 269 anomalistic months. Hipparchus extended this period by a factor of 17, because after that interval the Moon also would have a similar latitude, and it is close to an integer number of years (345). Therefore, eclipses would reappear under almost identical circumstances. The period is 126007 days 1 hour (rounded). Hipparchus could confirm his computations by comparing eclipses from his own time (presumably 27 January 141 BC and 26 November 139 BC according to [Toomer 1980]), with eclipses from Babylonian records 345 years earlier (Almagest IV.2; [Jones 2001]). Already al-Biruni (Qanun VII.2.II) and Copernicus (de revolutionibus IV.4) noted that the period of 4,267 lunations is actually about 5 minutes longer than the value for the eclipse period that Ptolemy attributes to Hipparchus. However, the best clocks and timing methods of the age had an accuracy of no better than 8 minutes. Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than try to derive an improved value from his own observations. From modern ephemerides [Chapront et al. 2002] and taking account of the change in the length of the day (see ΔT) we estimate that the error in the assumed length of the synodic month was less than 0.2 s in the 4th century BC and less than 0.1 s in Hipparchus' time.

Orbit of the Moon

It had been known for a long time that the motion of the Moon is not uniform: its speed varies. This is called its anomaly, and it repeats with its own period; the anomalistic month. The Chaldeans took account of this arithmetically, and used a table giving the daily motion of the Moon according to the date within a long period. The Greeks however preferred to think in geometrical models of the sky. Apollonius of Perga had at the end of the 3rd century BC proposed two models for lunar and planetary motion: # In the first, the Moon would move uniformly along a circle, but the Earth would be eccentric, i.e., at some distance of the center of the circle. So the apparent angular speed of the Moon (and its distance) would vary. # The Moon itself would move uniformly (with some mean motion in anomaly) on a secondary circular orbit, called an epicycle, that itself would move uniformly (with some mean motion in longitude) over the main circular orbit around the Earth, called deferent; see deferent and epicycle. Apollonius demonstrated that these two models were in fact mathematically equivalent. However, all this was theory and had not been put to practice. Hipparchus was the first to attempt to determine the relative proportions and actual sizes of these orbits. Hipparchus devised a geometrical method to find the parameters from three positions of the Moon, at particular phases of its anomaly. In fact, he did this separately for the eccentric and the epicycle model. Ptolemy describes the details in the Almagest IV.11. Hipparchus used two sets of three lunar eclipse observations, which he carefully selected to satisfy the requirements. The eccentric model he fitted to these eclipses from his Babylonian eclipse list: 22/23 December 383 BC, 18/19 June 382 BC, and 12/13 December 382 BC. The epicycle model he fitted to lunar eclipse observations made in Alexandria at 22 September 201 BC, 19 March 200 BC, and 11 September 200 BC.
- For the eccentric model, Hipparchus found for the ratio between the radius of the eccenter and the distance between the center of the eccenter and the center of the ecliptic (i.e., the observer on Earth): 3144 : 327+2/3 ;
- and for the epicycle model, the ratio between the radius of the deferent and the epicycle: 3122+1/2 : 247+1/2 . The somewhat weird numbers are due to the cumbersome unit he used in his chord table. The results are distinctly different. This is partly due to some sloppy rounding and calculation errors, for which Ptolemy criticised him (he himself made rounding errors too). Anyway, Hipparchus found inconsistent results; he later used the ratio of the epicycle model (3122+1/2 : 247+1/2), which is too small (60 : 4;45 hexadecimal): Ptolemy established a ratio of 60 : 5+1/4 . See [Toomer 1967].

Apparent motion of the Sun

Before Hipparchus, Meton, Euktemon, and their pupils at Athens had made a solstice observation (i.e., timed the moment of the summer solstice) on June 27, 432 BC (proleptic Julian calendar). Aristarchus is said to have done so in 280 BC, and Hipparchus also had an observation by Archimedes. Hipparchus himself observed the summer solstice in 135 BC, but he found observations of the moment of equinox more accurate, and he made many during his lifetime. Ptolemy gives an extensive discussion of Hipparchus' work on the length of the year in the Almagest III.1, and quotes many observations that Hipparchus made or used, spanning 162 BC to 128 BC. Ptolemy quotes an equinox timing by Hipparchus (at 24 March 146 BC at dawn) that differs from the observation made on that day in Alexandria (at 5h after sunrise): Hipparchus may have visited Alexandria but he did not make his equinox observations there; presumably he was on Rhodes (at the same geographical longitude). He may have used his own armillary sphere or an equatorial ring for these observations. Hipparchus (and Ptolemy) knew that observations with these instruments are sensitive to a precise alignment with the equator. The real problem however is that atmospheric refraction lifts the Sun significantly above the horizon: so its apparent declination is too high, which changes the observed time when the Sun crosses the equator. Worse, the refraction decreases as the Sun rises, so it may appear to move in the wrong direction with respect to the equator in the course of the day - as Ptolemy mentions; however, Ptolemy and Hipparchus apparently did not realize that refraction is the cause. At the end of his career, Hipparchus wrote a book called Peri eniausíou megéthous ("On the Length of the Year") about his results. The established value for the tropical year, introduced by Callippus in or before 330 BC (possibly from Babylonian sources, see above), was 365 + 1/4 days. Hipparchus' equinox observations gave varying results, but he himself points out (quoted in Almagest III.1(H195)) that the observation errors by himself and his predecessors may have been as large as 1/4 day. So he used the old solstice observations, and determined a difference of about one day in about 300 years. So he set the length of the tropical year to 365 + 1/4 - 1/300 days (= 365.24666... days = 365 days 5 hours 55 min, which differs from the actual value (modern estimate) of 365.24219... days = 365 days 5 hours 48 min 45 s by only about 6 min). Between the solstice observation of Meton and his own, there were 297 years spanning 108,478 days. This implies a tropical year of 365.24579... days = 365 days;14,44,51 (sexagesimal; = 365 days + 14/60 + 44/60² + 51/60³), and this value has been found on a Babylonian clay tablet [A. Jones, 2001]. This is an indication that Hipparchus' work was known to Chaldeans. Another value for the year that is attributed to Hipparchus (by the astrologer Vettius Valens in the 1st century) is 365 + 1/4 + 1/288 days (= 365.25347... days = 365 days 6 hours 5 min), but this may be a corruption of another value attributed to a Babylonian source: 365 + 1/4 + 1/144 days (= 365.25694... days = 365 days 6 hours 10 min). It is not clear if this would be a value for the sidereal year (actual value at his time (modern estimate) ca. 365.2565 days), but the difference with Hipparchus' value for the tropical year is consistent with his rate of precession (see below).

Orbit of the Sun

Before Hipparchus the Chaldean astronomers knew that the lengths of the seasons are not equal. Hipparchus made equinox and solstice observations, and according to Ptolemy (Almagest III.4) determined that spring (from spring equinox to summer solstice) lasted 94 + 1/2 days, and summer (from summer solstice to autumn equinox) 92 + 1/2 days. This is an unexpected result given a premise of the Sun moving around the Earth in a circle at uniform speed. Hipparchus' solution was to place the Earth not at the center of the Sun's motion, but at some distance from the center. This model described the apparent motion of the Sun fairly well (of course today we know that the planets like the Earth move in ellipses around the Sun, but this was not discovered until Johannes Kepler published his first two laws of planetary motion in 1609). The value for the eccentricity attributed to Hipparchus by Ptolemy is that the offset is 1/24 of the radius of the orbit (which is too large), and the direction of the apogee would be at longitude 65.5° from the vernal equinox. Hipparchus may also have used another set of observations (94 + 1/4 and 92 + 3/4 days), which would lead to different values. The question remains if Hipparchus is really the author of the values provided by Ptolemy, who found no change three centuries later, and added lengths for the autumn and winter seasons.

Calendar

"To be written"

Distance, parallax, size of the Moon and Sun

Hipparchus also undertook to find the distances and sizes of the Sun and the Moon. He published his results in a work of two books called Peri megethoon kai 'apostèmátoon ("On Sizes and Distances") by Pappus in his commentary on the Almagest V.11; Theon of Smyrna (2nd century) mentions the work with the addition "of the Sun and Moon". Hipparchus measured the apparent diameters of the Sun and Moon with his diopter. Like others before and after him, he found that the Moon's size varies as it moves on its (eccentric) orbit, but he found no perceptible variation in the apparent diameter of the Sun. He found that at the mean distance of the Moon, the Sun and Moon had the same apparent diameter; at that distance, the Moon's diameter fits 650 times into the circle, i.e., the mean apparent diameters are 360/650 = 0°33'14". Like others before and after him, he also noticed that the Moon has a noticeable parallax, i.e., that it appears displaced from its calculated position (compared to the Sun or stars), and the difference is greater when closer to the horizon. He knew that this is because the Moon circles the center of the Earth, but the observer is at the surface - Moon, Earth and observer form a triangle with a sharp angle that changes all the time. From the size of this parallax, the distance of the Moon as measured in Earth radii can be determined. For the Sun however, there was no observable parallax (we now know that it is about 8.8", more than ten times smaller than the resolution of the unaided eye). In the first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. He then analyzed a solar eclipse, presumably that of 14 March 190 BC. It was total in the region of the Hellespont (and in fact in his birth place Nicaea); at the time the Romans were preparing for war with Antiochus III in the area, and the eclipse is mentioned by Livy in his Ab Urbe Condita VIII.2. It was also observed in Alexandria, where the Sun was reported to be obscured for 4/5 by the Moon. Alexandria and Nicaea are on the same meridian. Alexandria is at about 31° North, and the region of the Hellespont at about 41° North; authors like Strabo and Ptolemy had fairly decent values for these geographical positions, and presumably Hipparchus knew them too. So Hipparchus could draw a triangle formed by the two places and the Moon, and from simple geometry was able to establish a distance of the Moon, expressed in Earth radii. Because the eclipse occurred in the morning, the Moon was not in the meridian, and as a consequence the distance found by Hipparchus was a lower limit. In any case, according to Pappus, Hipparchus found that the least distance is 71 (from this eclipse), and the greatest 81 Earth radii. In the second book, Hipparchus starts from the opposite extreme assumption: he assigns a (minimum) distance to the Sun of 470 Earth radii. This would correspond to a parallax of 7', which is apparently the greatest parallax that Hipparchus thought would not be noticed (for comparison: the typical resolution of the human eye is about 2'; Tycho Brahe made naked eye observation with an accuracy down to 1'). In this case, the shadow of the Earth is a cone rather than a cylinder as under the first assumption. Hipparchus observed (at lunar eclipses) that at the mean distance of the Moon, the diameter of the shadow cone is 2+½ lunar diameters. That apparent diameter is, as he had observed, 360/650 degrees. With these values and simple geometry, Hipparchus could determine the mean distance; because it was computed for a minumum distance of the Sun, it is the maximum mean distance possible for the Moon. With his value for the eccentricity of the orbit, he could compute the least and greatest distances of the Moon too. According to Pappus, he found a least distance of 62, a mean of 67+1/3, and consequently a greatest distance of 72+2/3 Earth radii. With this method, as the parallax of the Sun decreases (i.e., its distance increases), the minimum limit for the mean distance is 59 Earth radii - exactly the mean distance that Ptolemy later derived. Hipparchus thus had the problematic result that his minimum distance (from book 1) was greater than his maximum mean distance (from book 2). He was intellectually honest about this discrepancy, and probably realized that especially the first method is very sensitive to the accuracy of the observations and parameters (in fact, modern calculations show that the size of the solar eclipse at Alexandria must have been closer to 9/10 than to the reported 4/5). Ptolemy later measured the lunar parallax directly (Almagest V.13), and used the second method of Hipparchus' with lunar eclipses to compute the distance of the Sun (Almagest V.15). He criticizes Hipparchus for making contradictory assumptions, and obtaining conflicting results (Almagest V.11): but apparently he failed to understand Hipparchus' strategy to establish limits consistent with the observations, rather than a single value for the distance. His results were the best so far: the actual mean distance of the Moon is 60.3 Earth radii, within his limits from book 2. Theon of Smyrna wrote that according to Hipparchus, the Sun is 1,880 times the size of the Earth, and the Earth twenty-seven times the size of the Moon; apparently this refers to volumes, not diameters. From the geometry of book 2 it follows that the Sun is at 2,550 Earth radii, and the mean distance of the Moon is 60½ radii. Similarly, Cleomedes quotes Hipparchus for the sizes of the Sun and Earth as 1050:1; this leads to a mean lunar distance of 61 radii. Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses. See [Toomer 1974] for a more detailed discussion.

Eclipses

Pliny (Naturalis Historia II.X) tells us that Hipparchus demonstrated that lunar eclipses can occur five months apart, and solar eclipses seven months (instead of the usual six months); and the Sun can be hidden twice in thirty days, but as seen by different nations. Ptolemy discussed this a century later at length in Almagest VI.6. The geometry, and the limits of the positions of Sun and Moon when a solar or lunar eclipse is possible, are explained in Almagest VI.5. Hipparchus apparently made similar calculations. The result that two solar eclipses can occur one month apart is important, because this can not be based on observations: one is visible on the northern and the other on the southern hemisphere - as Pliny indicates -, and the latter was inaccessible to the Greek. Prediction of a solar eclipse, i.e., exactly when and where it will be visible, requires a solid lunar theory and proper treatment of the lunar parallax. Hipparchus must have been the first to be able to do this. A rigorous treatment requires spherical trigonometry, but Hipparchus may have made do with planar approximations. He may have discussed these things in Peri tes kata platos meniaias tes selenes kineseoos ("On the monthly motion of the Moon in latitude"), a work mentioned in the Suda. Pliny also remarks that "he also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the moon was eclipsed in the west while both luminaries were visible above the earth." (translation H. Rackham (1938), Loeb Classical Library 330 p.207). Toomer (1980) argued that this must refer to the large total lunar eclipse of 26 November 139 BC, when over a clean sea horizon as seen from the citadel of Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast. This would be the second eclipse of the 345-year interval that Hipparchus used to verify the traditional Babylonian periods: this puts a late date to the development of Hipparchus' lunar theory. We do not know what "exact reason" Hipparchus found for seeing the Moon eclipsed while apparently it was not in exact opposition to the Sun. Parallax lowers the altitude of the luminaries; refraction raises them, and from a high point of view the horizon is lowered.

Astronomical instruments and astrometry

Hipparchus is credited with the invention or improvement of several astronomical instruments, which were used for a long time for naked-eye observations. According to Synesius of Ptolemais (4th century) he made the first astrolabion: this may have been an armillary sphere (which Ptolemy however says he constructed, in Almagest V.1); or the predecessor of the planar instrument called astrolabe (also mentioned by Theon of Alexandria). With an astrolabe Hipparchus was the first to be able to measure the geographical latitude and time by observing stars. Previously this was done at daytime by measuring the shadow cast by a gnomon, or with the portable instrument known as scaphion. Ptolemy mentions (Almagest V.14) that he used a similar instrument as Hipparchus, called dioptra, to measure the apparent diameter of the Sun and Moon. Pappus of Alexandria described it (in his commentary on the Almagest of that chapter), as did Proclus (Hypotyposis IV). It was a 4-foot rod with a scale, a sighting hole at one end, and a wedge that could be moved along the rod to exactly obscure the disk of Sun or Moon. Hipparchus also observed solar equinoxes, which may be done with an equatorial ring: its shadow falls on itself when the Sun is on the equator (i.e., in one of the equinoctial points on the ecliptic), but the shadow falls above or below the opposite side of the ring when the Sun is south or north of the equator. Ptolemy quotes (in Almagest III.1 (H195)) a description by Hipparchus of an equatorial ring in Alexandria; a little further he describes two such instruments present in Alexandria in his own time.

Geography

Hipparchus applied his knowledge of spherical angles to the problem of denoting locations on the Earth's surface. Before him a grid system had been used by Dicaearchus of Messana, but Hipparchus was the first to apply mathematical rigor to the determination of the latitude and longitude of places on the Earth. Hipparchus wrote a critique in three books on the work of the geographer Eratosthenes of Cyrene (3rd century BC), called Pròs tèn 'Eratosthénous geografían ("Against the Geography of Eratosthenes"). It is known to us from Strabo of Amaseia, who in his turn criticised Hipparchus in his own Geografia. Hipparchus apparently made many detailed corrections to the locations and distances mentioned by Eratosthenes. It seems he did not introduce many improvements in methods, but he did propose a means to determine the geographical longitudes of different cities at lunar eclipses (Strabo Geografia 7). A lunar eclipse is visible simultaneously on half of the Earth, and the difference in longitude between places can be computed from the difference in local time when the eclipse is observed. His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical.

Star catalogue

After that, in 135 BC, enthusiastic about a nova in the constellation of Scorpius, he measured with an equatorial armillary sphere ecliptical coordinates of about 1,000 stars (the exact number is not known) for his star catalogue. He also knew the work Phainomena (Phenomena). That poem, known as Phaenomena or Arateia, describes the constellations and the stars that form them. Hipparchus' commentary contains many measurements of stellar position and times for rising, culmination, and setting of the constellations treated in the Phaenomena, and these are likely to have been based on measurements of stellar positions— and he knew the Enoptron (Mirror of Nature) of Eudoxus of Cnidus, who had his school near Cyzicus on the southern coast of the Sea of Marmara and through the Phenomena Eudoxus' sphere, which was made from metal or stone and where there were marked constellations, brightest stars, the tropic of Cancer and the tropic of Capricorn. These comparisons embarrassed him because he could not put together Eudoxus' detailed statements with his own observations and observations of that time. From all this he found that coordinates of the stars and the Sun had systematically changed. Their ecliptic latitudes β remained unchanged, but their ecliptic longitudes λ had increased, at a rate which he estimated to be at least one degree per century. This catalog served him to find any changes on the sky but unfortunately it is not preserved today. However, a 2005 analysis of an ancient statue of Atlas shows stars at positions that appear to have been determined using Hipparchus' data. [http://www.phys.lsu.edu/farnese/] His star map was thoroughly modified as late as 1,000 years later in 964 by Al Sufi and 1,500 years later (1437) by Ulugh Beg. Later, Halley would use his star catalogue to discover proper motions as well. The system of celestial coordinates used in Hipparchus's star catalog is not known. Since Ptolemy's copy in the Almagest is given in ecliptical coordinates, that system would seem the most likely; although there is evidence that both ecliptic coordinates and equatorial coordinates were used in the original observations.

Celestial bodies

Hipparchus in 130 BC wrote about an open cluster, the M44 Praesepe (NGC 2632) as a "Little Cloud" or "Cloudy Star". Before him the object was known to Aratus ca. 260 BC, who wrote about it as a "Little Mist". Hipparchus also included this object in his famous star catalogue. The cluster was also known to Chinese astronomers. [Moore 1994], [10] : ...to be extended ...

Celestial coordinate systems

Delambre in his Histoire de l'Astronomie Ancienne (1817) concluded that Hipparchus knew and used a real (celestial) equatorial coordinate system, directly with the right ascension and declination (or with its complement, polar distance). Later Otto Neugebauer in his A History of Ancient Mathematical Astronomy (1975) rejected Delambre's claims.

Brightness of stars

Hipparchus had in 134 BC ranked stars in six magnitude classes according to their brightness: he assigned the value of 1 to the twenty brightest stars, to weaker ones a value of 2, and so forth to the stars with a class of 6, which can be barely seen with the naked eye. This scheme was later adopted by Ptolemy and a similar system is still in use today. (See Apparent magnitude).

Precession of the equinoxes (146 BC-130 BC)

Hipparchus is perhaps most famous for having been the first to measure the precession of the equinoxes. There is some suggestion that the Babylonians may have known about precession, but it appears that Hipparchus was the first to really understand it and measure it. According to al-Battani, Chaldean astronomers had distinguished the tropical and sidereal year. He stated that they had, around 330 BC, an estimation for the length of the sidereal year to be S_K = 365 days 6 hours 11 min (= 365.258 days) with an error of (about) 2 min. This phenomenon was probably also known to Kidinnu around 314 BC. Yu Xi (fourth century) was the first Chinese astronomer to mention precession. Hipparchus and his predecessors mostly used simple instruments for astronomical calculations, such as the gnomon, astrolabe, armillary sphere, etc. Additionally, as the first in history to correctly explain this with retrogradical movement of vernal point γ over the ecliptic for about 45", 46" or 47" (36" or 3/4' according to Ptolemy) per annum (today's value is 50.29"), he showed the Earth's axis is not fixed in space. By comparing his own measurements of the position of the equinoxes to the star Spica during a lunar eclipse at the time of equinox with those of Euclid's contemporaries (Timocharis of Alexandria (ca. 320 BC–260 BC), Aristyllus 150 years earlier, the records of Chaldean astronomers (especially Kidinnu's records), and observations of a temple in Thebes, Egypt, that was built around 2000 BC) he still later observed that the equinox had moved 2° relative to Spica. He also noticed this motion in other stars. He obtained a value of not less than 1° in a century. The modern value is 1° in 72 years. After him many Greek and Arab astronomers had confirmed this phenomenon. Ptolemy compared his catalogue with those of Aristyllus, Timocharis, Hipparchus and the observations of Agrippa and Menelaus of Alexandria from the early 1st century and he finally confirmed Hipparchus' empirical fact that the poles of the celestial equator in one Platonic year (approximately 25,777 sidereal years) encircle the ecliptical pole. The diameter of this circle is equal to the inclination of ecliptic relative to the celestial equator. The equinoctial points in this time traverse the whole ecliptic and they move 1° in a century. This velocity is equal to that calculated by Hipparchus. Because of these accordances, Delambre, P. Tannery and other French historians of astronomy had wrongly jumped to conclusions that Ptolemy recorded his star catalogue from Hipparchus' with an ordinary extrapolation. It was not known until 1898 when Marcel Boll and others had found that Ptolemy's catalogue differs from Hipparchus' not only in the number of stars but in other respects. This phenomenon was named by Ptolemy just because the vernal point γ leads the Sun. In Latin praecesse means "to overtake" or "to outpass", and today also means to twist or to turn. Its own name shows this phenomenon was discovered before its theoretical explanation, otherwise it would have been given a better term. Many later astronomers, physicists and mathematicians had occupied themselves with this problem, practically and theoretically. The phenomenon itself had opened many new promising solutions in several branches of celestial mechanics: Thabit ibn Qurra's theory of trepidation and oscillation of equinoctial points, Isaac Newton's general gravitational law (which had explained it in full), Leonhard Euler's kinematic equations and Joseph Lagrange's equations of motion, Jean d'Alembert's dynamical theory of the movement of a rigid body, some algebraic solutions for special cases of precession, John Flamsteed's and James Bradley's difficulties in the making of precise telescopic star catalogues, Friedrich Bessel's and Simon Newcomb's measurements of precession, and finally the precession of perihelion in Albert Einstein's general theory of relativity.

Hipparchus and astrology

In addition to his other writings dealing with astronomical topics, the work of Hipparchus dealing with the calculation and prediction of celestial positions would have been very useful to those engaged in astrology. Astrology developed in the Greco-Roman world during the Hellenistic period, borrowing many elements from Babylonian astronomy; some historians have suggested that Hipparchus played a key role in this. Remarks made by Pliny the Elder (who died 79 AD during the eruption of the volcano Mount Vesuvius), in his Natural History Book 2.24, suggest that some ancient authors did regard Hipparchus as an important figure in the history of astrology. Pliny claimed that Hipparchus "can never be sufficiently praised, no one having done more to prove that man is related to the stars and that our souls are a part of heaven."

Named after Hipparchus

The ESA's Hipparcos Space Astrometry Mission was named after him, as are the Hipparchus lunar crater and the asteroid 4000 Hipparchus.

Literature

- Edition and translation: Karl Manitius: In Arati et Eudoxi Phaenomena, Leipzig, 1894.
- G.J. Toomer (1967): The Size of the Lunar Epicycle According to Hipparchus. Centaurus 12(3), 145..150.
- G.J. Toomer (1973): The Chord Table of Hipparchus and the Early History of Greek Trigonometry. Centaurus 18, 6..28.
- G.J. Toomer (1974): Hipparchus on the Distances of the Sun and Moon. Arch.Hist.Exact Sci. 14, 126..142.
- G.J. Toomer (1978): Hipparchus in "Dictionary of Scientific Biography" 15, 207..224.
- G.J. Toomer (1980): Hipparchus' Empirical Basis for his Lunar Mean Motions, Centaurus 24, 97..109.
- G.J. Toomer (1981?): Hipparchus and Babylonian Astronomy, (?)
- Patrick Moore (1994): Atlas of the Universe, Octopus Publishing Group LTD (Slovene translation and completion by Tomaž Zwitter and Savina Zwitter (1999): Atlas vesolja), 225.
- A. Jones: Hipparchus in "Encyclopedia of Astrono

February

February is the second month of the year in the Gregorian Calendar. It is the shortest Gregorian month and the only month with the length of 28 or 29 days. The month has 29 days in leap years, when the year number is divisible by four (except for years that are divisible by 100 and not by 400). In other years the month has 28 days. February begins, astronomically speaking, with the sun in the constellation of Capricornus and ends with the sun in the constellation of Aquarius. Astrologically speaking, February begins with the sun in the sign of Aquarius and ends in the sign of Pisces. February was named for the Roman god Februus, the god of purification. January and February were the last two months to be added to the Roman calendar, since the Romans originally considered winter a monthless period. This change was made by Numa Pompilius about 700 BC in order to bring the calendar in line with a standard lunar year. Numa's Februarius contained 29 days (30 in a leap year). Augustus is alleged to have removed one day from February and added it to August, (renamed from Sextilis to honor himself), so that Julius Caesar's July would not contain more days. However there is little historical evidence to support this claim. July February was nominally the last month of the Roman calendar, as the year originally began in March. At certain intervals Roman priests inserted an intercalary month, Mercedonius, after February to realign the year with the seasons. Historical names for February include the Anglo-Saxon terms Solmoneth (mud month) and Kale-monath (named for cabbage) as well as Charlemagne's designation Hornung. In old Japanese calendar, the month is called Kisaragi (如月, 絹更月 or 衣更月). It is sometimes also called Mumetsuki (梅見月) or Konometsuki (木目月). In Finnish, the month is called helmikuu, meaning "month of the pearl". "February" is pronounced without the first r, as "Febuary", by many speakers. This is probably dissimilation, or an analogical change influenced by "January".

External links

- [http://www.straightdope.com/classics/a2_160.html The Straight Dope: How come February has only 28 days?] Category:Months ko:2월 ms:Februari ja:2月 simple:February th:กุมภาพันธ์