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103-506: The Sheffield Patent , dated January 1, 1623 ( Julian calendar ) is a land grant from Edmund Sheffield, 1st Earl of Mulgrave (Sheffeild in the original) of England to Robert Cushman and Edward Winslow (residents of Plymouth Colony ) and their associates. It granted them the use of Cape Ann (in present-day Massachusetts ) and the neighboring bay and islands, allocating 500 acres (2 km) for public buildings and 30 acres (120,000 m) for private use for each settler arriving within

206-405: A "tropical millennium" is decreasing by about 0.06 per millennium (neglecting the oscillatory changes in the real length of the tropical year). This means there should be fewer and fewer leap days as time goes on. A possible reform could omit the leap day in 3200, keep 3600 and 4000 as leap years, and thereafter make all centennial years common except 4500, 5000, 5500, 6000, etc. but the quantity ΔT

309-514: A common year and the 25th to 29th in a leap year). Hence he regarded the bissextum as the first half of the doubled day. All later writers, including Macrobius about 430, Bede in 725, and other medieval computists (calculators of Easter) followed this rule, as does the liturgical calendar of the Roman Catholic Church. However, Celsus' definition continued to be used for legal purposes. It was incorporated into Justinian's Digest , and in

412-480: A complete cycle of seasons, and its length is approximated in the long term by the civil (Gregorian) calendar. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds. An equivalent, more descriptive, definition is "The natural basis for computing passing tropical years is the mean longitude of the Sun reckoned from the precessionally moving equinox (the dynamical equinox or equinox of date). Whenever

515-507: A corruption of Winnimanoth "pasture-month"), Brachmanoth (" fallow -month"), Heuuimanoth ("hay month"), Aranmanoth (" reaping month"), Witumanoth ("wood month"), Windumemanoth ("vintage month"), Herbistmanoth ("harvest month"), and Heilagmanoth ("holy month"). The calendar month names used in western and northern Europe, in Byzantium, and by the Amazigh (Berbers) , were derived from

618-459: A day less than 365.25 days (365 days, 5 hours, 55 minutes, 12 seconds, or 365.24667 days). Hipparchus used this method because he was better able to detect the time of the equinoxes, compared to that of the solstices. Hipparchus also discovered that the equinoctial points moved along the ecliptic (plane of the Earth's orbit, or what Hipparchus would have thought of as the plane of the Sun's orbit about

721-484: A large number of festivals were decreed to celebrate events of dynastic importance, which caused the character of the associated dates to be changed to NP . However, this practice was discontinued around the reign of Claudius , and the practice of characterising days fell into disuse around the end of the first century AD: the Antonine jurist Gaius speaks of dies nefasti as a thing of the past. The old intercalary month

824-411: A number of progressively better tables were published that allowed computation of the positions of the Sun, Moon and planets relative to the fixed stars. An important application of these tables was the reform of the calendar . The Alfonsine Tables , published in 1252, were based on the theories of Ptolemy and were revised and updated after the original publication. The length of the tropical year

927-428: A technical fashion to refer to the earlier of the two days, which requires the inscription to refer to the whole 48-hour day as the bissextile. Some later historians share this view. Others, following Mommsen , take the view that Celsus was using the ordinary Latin (and English) meaning of "posterior". A third view is that neither half of the 48-hour "bis sextum" was originally formally designated as intercalated, but that

1030-525: A wise man called Acoreus during the feast, stating his intention to create a calendar more perfect than that of Eudoxus (Eudoxus was popularly credited with having determined the length of the year to be 365 + 1 ⁄ 4 days). But the war soon resumed and Caesar was attacked by the Egyptian army for several months until he achieved victory. He then enjoyed a long cruise on the Nile with Cleopatra before leaving

1133-581: Is a reformed version of the Julian calendar organized by the Catholic Church and enacted in 1582. By the time of the reform, the date of the vernal equinox had shifted about 10 days, from about March 21 at the time of the First Council of Nicaea in 325, to about March 11. The motivation for the change was the correct observance of Easter. The rules used to compute the date of Easter used a conventional date for

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1236-402: Is an international standard. It is a solar calendar that is designed to maintain synchrony with the mean tropical year. It has a cycle of 400 years (146,097 days). Each cycle repeats the months, dates, and weekdays. The average year length is 146,097/400 = 365 + 97 ⁄ 400 = 365.2425 days per year, a close approximation to the mean tropical year of 365.2422 days. The Gregorian calendar

1339-446: Is designed so as to resynchronise the calendar year with the solar year at regular intervals. The word "tropical" comes from the Greek tropikos meaning "turn". Thus, the tropics of Cancer and Capricorn mark the extreme north and south latitudes where the Sun can appear directly overhead, and where it appears to "turn" in its annual seasonal motion. Because of this connection between

1442-404: Is given the symbol ♎︎ (because it used to be toward Libra ). Because of the precession of the equinoxes and nutation these directions change, compared to the direction of distant stars and galaxies, whose directions have no measurable motion due to their great distance (see International Celestial Reference Frame ). The ecliptic longitude of the Sun is the angle between ♈︎ and

1545-409: Is longer: that tropical year is comparatively short. The "mean tropical year" is based on the mean sun , and is not exactly equal to any of the times taken to go from an equinox to the next or from a solstice to the next. The following values of time intervals between equinoxes and solstices were provided by Meeus and Savoie for the years 0 and 2000. These are smoothed values which take account of

1648-407: Is more than the actual solar year value of approximately 365.2422 days (the current value, which varies), which means the Julian calendar gains one day every 129 years. In other words, the Julian calendar gains 3.1 days every 400 years. Gregory's calendar reform modified the Julian rule, to reduce the average length of the calendar year from 365.25 days to 365.2425 days and thus corrected

1751-507: Is no basis for the statement sometimes seen that they were called " Undecimber " and " Duodecimber ", terms that arose in the 18th century over a millennium after the Roman Empire's collapse. Their individual lengths are unknown, as is the position of the Nones and Ides within them. Because 46 BC was the last of a series of irregular years, this extra-long year was, and is, referred to as

1854-554: Is still used as a religious calendar in parts of the Eastern Orthodox Church and in parts of Oriental Orthodoxy as well as by the Amazigh people (also known as the Berbers). The Julian calendar was proposed in 46 BC by (and takes its name from) Julius Caesar , as a reform of the earlier Roman calendar , which was largely a lunisolar one. It took effect on 1 January 45 BC , by his edict . Caesar's calendar became

1957-620: The Persian calendar by introduction of the Persian Zoroastrian (i. e. Young Avestan) calendar in 503 BC and afterwards, the first day of the year (1 Farvardin= Nowruz ) slipped against the vernal equinox at the rate of approximately one day every four years. Likewise in the Egyptian calendar , a fixed year of 365 days was in use, drifting by one day against the sun in four years. An unsuccessful attempt to add an extra day every fourth year

2060-585: The Prutenic Tables in 1551, and gave a tropical year length of 365 solar days, 5 hours, 55 minutes, 58 seconds (365.24720 days), based on the length of a sidereal year and the presumed rate of precession. This was actually less accurate than the earlier value of the Alfonsine Tables. Major advances in the 17th century were made by Johannes Kepler and Isaac Newton . In 1609 and 1619 Kepler published his three laws of planetary motion. In 1627, Kepler used

2163-427: The month names reflected Ottoman tradition. Tropical year The tropical year is one type of astronomical year and particular orbital period . Another type is the sidereal year (or sidereal orbital period), which is the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars , resulting in a duration of 20 minutes longer than the tropical year, because of

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2266-487: The precession of the equinoxes . Since antiquity, astronomers have progressively refined the definition of the tropical year. The entry for "year, tropical" in the Astronomical Almanac Online Glossary states: the period of time for the ecliptic longitude of the Sun to increase 360 degrees . Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises

2369-411: The "last year of confusion". The new calendar began operation after the realignment had been completed, in 45 BC. The Julian months were formed by adding ten days to a regular pre-Julian Roman year of 355 days, creating a regular Julian year of 365 days. Two extra days were added to January, Sextilis (August) and December, and one extra day was added to April, June, September, and November. February

2472-410: The 1970s. A key development in understanding the tropical year over long periods of time is the discovery that the rate of rotation of the earth, or equivalently, the length of the mean solar day , is not constant. William Ferrel in 1864 and Charles-Eugène Delaunay in 1865 predicted that the rotation of the Earth is being retarded by tides. This could be verified by observation only in the 1920s with

2575-425: The 7-day week in the first century AD, and dominical letters began to appear alongside nundinal letters in the fasti. The Julian calendar has two types of year: "normal" years of 365 days and "leap" years of 366 days. There is a simple cycle of three "normal" years followed by a leap year and this pattern repeats forever without exception. The Julian year is, therefore, on average 365.25 days long. Consequently,

2678-632: The Balkans and parts of Palestine, most notably in Judea. The Asian calendar was an adaptation of the Ancient Macedonian calendar used in the Roman province of Asia and, with minor variations, in nearby cities and provinces. It is known in detail through the survival of decrees promulgating it issued in 8   BC by the proconsul Paullus Fabius Maximus . It renamed the first month Dios as Kaisar , and arranged

2781-448: The Earth's orbit being elliptical, using well-known procedures (including solving Kepler's equation ). They do not take into account periodic variations due to factors such as the gravitational force of the orbiting Moon and gravitational forces from the other planets. Such perturbations are minor compared to the positional difference resulting from the orbit being elliptical rather than circular. The mean tropical year on January 1, 2000,

2884-507: The Earth) in a direction opposite that of the movement of the Sun, a phenomenon that came to be named "precession of the equinoxes". He reckoned the value as 1° per century, a value that was not improved upon until about 1000 years later, by Islamic astronomers . Since this discovery a distinction has been made between the tropical year and the sidereal year. During the Middle Ages and Renaissance

2987-473: The English Statute De Anno et Die Bissextili of 1236, which was not formally repealed until 1879. The effect of the bissextile day on the nundinal cycle is not discussed in the sources. According to Dio Cassius, a leap day was inserted in 41 BC to ensure that the first market day of 40 BC did not fall on 1 January, which implies that the old 8-day cycle was not immediately affected by

3090-526: The Gregorian calendar would be 3 days, 17 min, 33 s behind the Sun after 10,000 years. Aggravating this error, the length of the tropical year (measured in Terrestrial Time) is decreasing at a rate of approximately 0.53 s per century and the mean solar day is getting longer at a rate of about 1.5 ms per century. These effects will cause the calendar to be nearly a day behind in 3200. The number of solar days in

3193-423: The Gregorian calendar. The low-precision extrapolations are computed with an expression provided by Morrison and Stephenson: where t is measured in Julian centuries from 1820. The extrapolation is provided only to show Δ T is not negligible when evaluating the calendar for long periods; Borkowski cautions that "many researchers have attempted to fit a parabola to the measured Δ T values in order to determine

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3296-434: The Julian calendar's drift against the solar year : the Gregorian calendar gains just 0.1 day over 400 years. For any given event during the years from 1901 through 2099, its date according to the Julian calendar is 13 days behind its corresponding Gregorian date (for instance Julian 1 January falls on Gregorian 14 January). Most Catholic countries adopted the new calendar immediately; Protestant countries did so slowly in

3399-549: The Julian reform. However, he also reports that in AD ;44, and on some previous occasions, the market day was changed to avoid a conflict with a religious festival. This may indicate that a single nundinal letter was assigned to both halves of the 48-hour bissextile day by this time, so that the Regifugium and the market day might fall on the same date but on different days. In any case, the 8-day nundinal cycle began to be displaced by

3502-432: The Julian year drifts over time with respect to the tropical (solar) year (365.24217 days). Although Greek astronomers had known, at least since Hipparchus , a century before the Julian reform, that the tropical year was slightly shorter than 365.25 days, the calendar did not compensate for this difference. As a result, the calendar year gains about three days every four centuries compared to observed equinox times and

3605-563: The Latin names. However, in eastern Europe older seasonal month names continued to be used into the 19th century, and in some cases are still in use, in many languages, including: Belarusian , Bulgarian , Croatian , Czech , Finnish, Georgian , Lithuanian , Macedonian , Polish , Romanian , Slovene , Ukrainian . When the Ottoman Empire adopted the Julian calendar, in the form of the Rumi calendar,

3708-544: The SI second. As a result, the time scales of TT and UT1 build up a growing difference: the amount that TT is ahead of UT1 is known as Δ T , or Delta T . As of 5 July 2022, TT is ahead of UT1 by 69.28 seconds. As a consequence, the tropical year following the seasons on Earth as counted in solar days of UT is increasingly out of sync with expressions for equinoxes in ephemerides in TT. As explained below, long-term estimates of

3811-462: The Sun as a function of Terrestrial Time, and this angular speed is used to compute how long it would take for the Sun to move 360°. The above formulae give the length of the tropical year in ephemeris days (equal to 86,400 SI seconds), not solar days . It is the number of solar days in a tropical year that is important for keeping the calendar in synch with the seasons (see below). The Gregorian calendar , as used for civil and scientific purposes,

3914-469: The Sun, measured eastward along the ecliptic. This creates a relative and not an absolute measurement, because as the Sun is moving, the direction the angle is measured from is also moving. It is convenient to have a fixed (with respect to distant stars) direction to measure from; the direction of ♈︎ at noon January 1, 2000 fills this role and is given the symbol ♈︎ 0 . There was an equinox on March 20, 2009, 11:44:43.6 TT. The 2010 March equinox

4017-592: The Terminalia (23 February). If managed correctly this system could have allowed the Roman year to stay roughly aligned to a tropical year . However, since the pontifices were often politicians, and because a Roman magistrate's term of office corresponded with a calendar year, this power was prone to abuse: a pontifex could lengthen a year in which he or one of his political allies was in office, or refuse to lengthen one in which his opponents were in power. Caesar's reform

4120-713: The accuracy of the mean tropical year. Many new observing instruments became available, including The complexity of the model used for the Solar System must be limited to the available computation facilities. In the 1920s punched card equipment came into use by L. J. Comrie in Britain. For the American Ephemeris an electromagnetic computer, the IBM Selective Sequence Electronic Calculator was used since 1948. When modern computers became available, it

4223-445: The apparent speed of the Sun) varies in its elliptical orbit: faster in the perihelion , slower in the aphelion . The equinox moves with respect to the perihelion (and both move with respect to the fixed sidereal frame). From one equinox passage to the next, or from one solstice passage to the next, the Sun completes not quite a full elliptic orbit. The time saved depends on where it starts in

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4326-501: The apparent velocity of the Sun as the Earth revolves in its orbit. The most important such time scale is Universal Time , which is the mean solar time at 0 degrees longitude (the IERS Reference Meridian ). Civil time is based on UT (actually UTC ), and civil calendars count mean solar days. However the rotation of the Earth itself is irregular and is slowing down, with respect to more stable time indicators: specifically,

4429-487: The astronomical almanac published by Caesar to facilitate the reform. Eventually, it was decided to establish a calendar that would be a combination between the old Roman months, the fixed length of the Egyptian calendar, and the 365 + 1 ⁄ 4 days of Greek astronomy. According to Macrobius, Caesar was assisted in this by a certain Marcus Flavius. Caesar's reform only applied to the Roman calendar . However, in

4532-422: The beginning of the fifth. This error continued for thirty-six years by which time twelve intercalary days had been inserted instead of the number actually due, namely nine. But when this error was at length recognised, it too was corrected, by an order of Augustus, that twelve years should be allowed to pass without an intercalary day, since the sequence of twelve such years would account for the three days which, in

4635-586: The correct Julian calendar. Due to the confusion about this period, we cannot be sure exactly what day (e.g. Julian day number ) any particular Roman date refers to before March of 8 BC, except for those used in Egypt in 24   BC which are secured by astronomy. An inscription has been discovered which orders a new calendar to be used in the Province of Asia to replace the previous Greek lunar calendar. According to one translation Intercalation shall commence on

4738-452: The country in June 47 BC. Caesar returned to Rome in 46 BC and, according to Plutarch , called in the best philosophers and mathematicians of his time to solve the problem of the calendar. Pliny says that Caesar was aided in his reform by the astronomer Sosigenes of Alexandria who is generally considered the principal designer of the reform. Sosigenes may also have been the author of

4841-530: The course of the following two centuries or so; most Orthodox countries retain the Julian calendar for religious purposes but adopted the Gregorian as their civil calendar in the early part of the twentieth century. The ordinary year in the previous Roman calendar consisted of 12 months, for a total of 355 days. In addition, a 27- or 28-day intercalary month , the Mensis Intercalaris , was sometimes inserted between February and March. This intercalary month

4944-459: The course of thirty-six years, had been introduced by the premature actions of the priests. So, according to Macrobius, Some people have had different ideas as to how the leap years went. The above scheme is that of Scaliger (1583) in the table below. He established that the Augustan reform was instituted in 8 BC. The table below shows for each reconstruction the implied proleptic Julian date for

5047-463: The date in both calendars was the same. The dates in the Alexandrian and Julian calendars are in one-to-one correspondence except for the period from 29 August in the year preceding a Julian leap year to the following 24 February. From a comparison of the astronomical data with the Egyptian and Roman dates, Alexander Jones concluded that the Egyptian astronomers (as opposed to travellers from Rome) used

5150-408: The day after 14 Peritius [a.d. IX Kal. Feb, which would have been 15 Peritius] as it is currently constituted in the third year following promulgation of the decree. Xanthicus shall have 32 days in this intercalary year. This is historically correct. It was decreed by the proconsul that the first day of the year in the new calendar shall be Augustus' birthday, a.d. IX Kal. Oct. Every month begins on

5253-407: The early Julian calendar. The earliest direct evidence is a statement of the 2nd century jurist Celsus , who states that there were two-halves of a 48-hour day, and that the intercalated day was the "posterior" half. An inscription from AD 168 states that a.d. V Kal. Mart. was the day after the bissextile day. The 19th century chronologist Ideler argued that Celsus used the term "posterior" in

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5356-715: The ephemeral month names of the post-Augustan Roman emperors were the Old High German names introduced by Charlemagne . According to his biographer, Einhard, Charlemagne renamed all of the months agriculturally in German. These names were used until the 15th century, over 700 years after his rule, and continued, with some modifications, to be used as "traditional" month names until the late 18th century. The names (January to December) were: Wintarmanoth ("winter month"), Hornung , Lentzinmanoth ("spring month", " Lent month"), Ostarmanoth (" Easter month"), Wonnemanoth (" joy -month",

5459-476: The first day of Caesar's reformed calendar and the first Julian date on which the Roman calendar date matches the Julian calendar after the completion of Augustus' reform. By the systems of Scaliger, Ideler and Bünting, the leap years prior to the suspension happen to be BC years that are divisible by 3, just as, after leap year resumption, they are the AD years divisible by 4. Pierre Brind'Amour argued that "only one day

5562-451: The following decades many of the local civic and provincial calendars of the empire and neighbouring client kingdoms were aligned to the Julian calendar by transforming them into calendars with years of 365 days with an extra day intercalated every four years. The reformed calendars typically retained many features of the unreformed calendars. In many cases, the New Year was not on 1 January,

5665-401: The gradual mean motion. They could express the mean longitude of the Sun in a polynomial such as: where T is the time in Julian centuries. The derivative of this formula is an expression of the mean angular velocity, and the inverse of this gives an expression for the length of the tropical year as a linear function of T . Two equations are given in the table. Both equations estimate that

5768-509: The insertion of a regular intercalary month in February. When Caesar decreed the reform, probably shortly after his return from the African campaign in late Quintilis (July), he added 67 more days by inserting two extraordinary intercalary months between November and December. These months are called Intercalaris Prior and Intercalaris Posterior in letters of Cicero written at the time; there

5871-466: The leap day was not on the traditional bissextile day , the old month names were retained, the lengths of the reformed months did not match the lengths of Julian months, and, even if they did, their first days did not match the first day of the corresponding Julian month. Nevertheless, since the reformed calendars had fixed relationships to each other and to the Julian calendar, the process of converting dates between them became quite straightforward, through

5974-404: The length of the tropical year is to first find an expression for the Sun's mean longitude (with respect to ♈︎), such as Newcomb's expression given above, or Laskar's expression. When viewed over a one-year period, the mean longitude is very nearly a linear function of Terrestrial Time. To find the length of the tropical year, the mean longitude is differentiated, to give the angular speed of

6077-413: The length of the tropical year was found by comparing equinox dates that were separated by many years; this approach yielded the mean tropical year. If a different starting longitude for the Sun is chosen than 0° ( i.e. ♈︎), then the duration for the Sun to return to the same longitude will be different. This is a second-order effect of the circumstance that the speed of the Earth (and conversely

6180-469: The length of the tropical year were used in connection with the reform of the Julian calendar , which resulted in the Gregorian calendar. Participants in that reform were unaware of the non-uniform rotation of the Earth, but now this can be taken into account to some degree. The table below gives Morrison and Stephenson's estimates and standard errors ( σ ) for ΔT at dates significant in the process of developing

6283-465: The longitude reaches a multiple of 360 degrees the mean Sun crosses the vernal equinox and a new tropical year begins". The mean tropical year in 2000 was 365.24219 ephemeris days , each ephemeris day lasting 86,400 SI seconds. This is 365.24217 mean solar days . For this reason, the calendar year is an approximation of the solar year: the Gregorian calendar (with its rules for catch-up leap days )

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6386-450: The magnitude of the deceleration of the Earth's rotation. The results, when taken together, are rather discouraging." One definition of the tropical year would be the time required for the Sun, beginning at a chosen ecliptic longitude, to make one complete cycle of the seasons and return to the same ecliptic longitude. Before considering an example, the equinox must be examined. There are two important planes in solar system calculations:

6489-460: The months such that each month started on the ninth day before the kalends of the corresponding Roman month; thus the year began on 23 September, Augustus's birthday. The first step of the reform was to realign the start of the calendar year (1 January) to the tropical year by making 46 BC 445 days long, compensating for the intercalations which had been missed during Caesar's pontificate. This year had already been extended from 355 to 378 days by

6592-457: The months. Macrobius states that the extra days were added immediately before the last day of each month to avoid disturbing the position of the established religious ceremonies relative to the Nones and Ides of the month. The inserted days were all initially characterised as dies fasti ( F – see Roman calendar ). The character of a few festival days was changed. In the early Julio-Claudian period

6695-448: The motion of planets, and atomic clocks. Ephemeris time (ET) is the independent variable in the equations of motion of the Solar System, in particular, the equations from Newcomb's work, and this ET was in use from 1960 to 1984. These ephemerides were based on observations made in solar time over a period of several centuries, and as a consequence represent the mean solar second over that period. The SI second , defined in atomic time,

6798-453: The need to do so arose as the concept of a 48-hour day became obsolete. There is no doubt that the bissextile day eventually became the earlier of the two days for most purposes. In 238 Censorinus stated that it was inserted after the Terminalia (23 February) and was followed by the last five days of February, i.e., a.d. VI, V, IV, III and prid. Kal. Mart. (which would be 24 to 28 February in

6901-449: The new calendar was much simpler than the pre-Julian calendar, the pontifices initially added a leap day every three years, instead of every four. There are accounts of this in Solinus, Pliny, Ammianus, Suetonius, and Censorinus. Macrobius gives the following account of the introduction of the Julian calendar: Caesar's regulation of the civil year to accord with his revised measurement

7004-479: The new one as 24 January, a.d. IX Kal. Feb 5 BC in the Julian calendar, which was a leap year. Thus from inception the dates of the reformed Asian calendar are in one-to-one correspondence with the Julian. Another translation of this inscription is Intercalation shall commence on the day after the fourteenth day in the current month of Peritius [a.d. IX Kal. Feb], occurring every third year. Xanthicus shall have 32 days in this intercalary year. This would move

7107-571: The next 70 years. Cape Ann was subsequently settled by members of the Dorchester Company , which was later absorbed into the Massachusetts Bay Company . This Massachusetts -related article is a stub . You can help Misplaced Pages by expanding it . Julian calendar The Julian calendar is a solar calendar of 365 days in every year with an additional leap day every fourth year (without exception). The Julian calendar

7210-405: The ninth day before the kalends. The date of introduction, the day after 14 Peritius, was 1 Dystrus, the next month. The month after that was Xanthicus. Thus Xanthicus began on a.d. IX Kal. Mart., and normally contained 31 days. In leap year, however, it contained an extra "Sebaste day", the Roman leap day, and thus had 32 days. From the lunar nature of the old calendar we can fix the starting date of

7313-550: The observations of Tycho Brahe and Waltherus to produce the most accurate tables up to that time, the Rudolphine Tables . He evaluated the mean tropical year as 365 solar days, 5 hours, 48 minutes, 45 seconds (365.24219 days). Newton's three laws of dynamics and theory of gravity were published in his Philosophiæ Naturalis Principia Mathematica in 1687. Newton's theoretical and mathematical advances influenced tables by Edmond Halley published in 1693 and 1749 and provided

7416-458: The orbit. If the starting point is close to the perihelion (such as the December solstice), then the speed is higher than average, and the apparent Sun saves little time for not having to cover a full circle: the "tropical year" is comparatively long. If the starting point is near aphelion, then the speed is lower and the time saved for not having to run the same small arc that the equinox has precessed

7519-425: The plane of the ecliptic (the Earth's orbit around the Sun), and the plane of the celestial equator (the Earth's equator projected into space). These two planes intersect in a line. One direction points to the so-called vernal, northward, or March equinox which is given the symbol ♈︎ (the symbol looks like the horns of a ram because it used to be toward the constellation Aries ). The opposite direction

7622-513: The predominant calendar in the Roman Empire and subsequently most of the Western world for more than 1,600 years, until 1582 when Pope Gregory XIII promulgated a revised calendar. The Julian calendar has two types of years: a normal year of 365 days and a leap year of 366 days. They follow a simple cycle of three normal years and one leap year, giving an average year that is 365.25 days long. That

7725-411: The provincial calendars that were aligned to the Julian calendar. Other name changes were proposed but were never implemented. Tiberius rejected a senatorial proposal to rename September as "Tiberius" and October as "Livius", after his mother Livia. Antoninus Pius rejected a senatorial decree renaming September as "Antoninus" and November as "Faustina", after his empress . Much more lasting than

7828-436: The seasons. This discrepancy was largely corrected by the Gregorian reform of 1582. The Gregorian calendar has the same months and month lengths as the Julian calendar, but, in the Gregorian calendar, year numbers evenly divisible by 100 are not leap years, except that those evenly divisible by 400 remain leap years (even then, the Gregorian calendar diverges from astronomical observations by one day in 3,030 years). Although

7931-422: The starting date back three years to 8 BC, and from the lunar synchronism back to 26 January (Julian). But since the corresponding Roman date in the inscription is 24 January, this must be according to the incorrect calendar which in 8 BC Augustus had ordered to be corrected by the omission of leap days. As the authors of the previous paper point out, with the correct four-year cycle being used in Egypt and

8034-480: The sun entered the 8th degree of Capricorn on that date, this stability had become an ordinary fact of life. Although the approximation of 365 + 1 ⁄ 4 days for the tropical year had been known for a long time, ancient solar calendars had used less precise periods, resulting in gradual misalignment of the calendar with the seasons. The octaeteris , a cycle of eight lunar years popularised by Cleostratus (and also commonly attributed to Eudoxus ) which

8137-645: The three-year cycle abolished in Rome, it is unlikely that Augustus would have ordered the three-year cycle to be introduced in Asia. The Julian reform did not immediately cause the names of any months to be changed. The old intercalary month was abolished and replaced with a single intercalary day at the same point (i.e., five days before the end of February). The Romans later renamed months after Julius Caesar and Augustus, renaming Quintilis as "Iulius" (July) in 44 BC and Sextilis as "Augustus" (August) in 8 BC. Quintilis

8240-459: The time between equinoxes (and prevent them from confounding efforts to measure long-term variations) requires precise observations and an elaborate theory of the apparent motion of the Sun. The necessary theories and mathematical tools came together in the 18th century due to the work of Pierre-Simon de Laplace , Joseph Louis Lagrange , and other specialists in celestial mechanics . They were able to compute periodic variations and separate them from

8343-403: The tropical year gets roughly a half second shorter each century. Newcomb's tables were sufficiently accurate that they were used by the joint American-British Astronomical Almanac for the Sun, Mercury , Venus , and Mars through 1983. The length of the mean tropical year is derived from a model of the Solar System, so any advance that improves the solar system model potentially improves

8446-448: The tropical year is 20 min. shorter than the sidereal year. When tropical year measurements from several successive years are compared, variations are found which are due to the perturbations by the Moon and planets acting on the Earth, and to nutation. Meeus and Savoie provided the following examples of intervals between March (northward) equinoxes: Until the beginning of the 19th century,

8549-413: The tropics and the seasonal cycle of the apparent position of the Sun, the word "tropical" was lent to the period of the seasonal cycle . The early Chinese, Hindus, Greeks, and others made approximate measures of the tropical year. In the 2nd century BC Hipparchus measured the time required for the Sun to travel from an equinox to the same equinox again. He reckoned the length of the year to be 1/300 of

8652-512: The underpinnings of all solar system models until Albert Einstein 's theory of General relativity in the 20th century. From the time of Hipparchus and Ptolemy, the year was based on two equinoxes (or two solstices) a number of years apart, to average out both observational errors and periodic variations (caused by the gravitational pull of the planets, and the small effect of nutation on the equinox). These effects did not begin to be understood until Newton's time. To model short-term variations of

8755-649: The use of conversion tables known as "hemerologia". The three most important of these calendars are the Alexandrian calendar and the Ancient Macedonian calendar ─which had two forms: the Syro-Macedonian and the 'Asian' calendars. Other reformed calendars are known from Cappadocia , Cyprus and the cities of (Roman) Syria and Palestine. Unreformed calendars continued to be used in Gaul (the Coligny calendar ), Greece, Macedon,

8858-463: The vernal equinox (March 21), and it was considered important to keep March 21 close to the actual equinox. If society in the future still attaches importance to the synchronization between the civil calendar and the seasons, another reform of the calendar will eventually be necessary. According to Blackburn and Holford-Strevens (who used Newcomb's value for the tropical year) if the tropical year remained at its 1900 value of 365.242 198 781 25 days

8961-424: The very accurate Shortt-Synchronome clock and later in the 1930s when quartz clocks began to replace pendulum clocks as time standards. Apparent solar time is the time indicated by a sundial , and is determined by the apparent motion of the Sun caused by the rotation of the Earth around its axis as well as the revolution of the Earth around the Sun. Mean solar time is corrected for the periodic variations in

9064-525: Was 365.242 189 7 or 365 ephemeris days , 5 hours, 48 minutes, 45.19 seconds. This changes slowly; an expression suitable for calculating the length of a tropical year in ephemeris days, between 8000 BC and 12000 AD is where T is in Julian centuries of 36,525 days of 86,400 SI seconds measured from noon January 1, 2000 TT. Modern astronomers define the tropical year as time for the Sun's mean longitude to increase by 360°. The process for finding an expression for

9167-401: Was March 20, 17:33:18.1 TT, which gives an interval - and a duration of the tropical year - of 365 days 5 hours 48 minutes 34.5 seconds. While the Sun moves, ♈︎ moves in the opposite direction. When the Sun and ♈︎ met at the 2010 March equinox, the Sun had moved east 359°59'09" while ♈︎ had moved west 51" for a total of 360° (all with respect to ♈︎ 0 ). This is why

9270-500: Was abolished. The new leap day was dated as ante diem bis sextum Kalendas Martias ('the sixth doubled day before the Kalends of March'), usually abbreviated as a.d. bis VI Kal. Mart. ; hence it is called in English the bissextile day. The year in which it occurred was termed annus bissextus , in English the bissextile year. There is debate about the exact position of the bissextile day in

9373-405: Was formed by inserting 22 or 23 days after the first 23 days of February; the last five days of February, which counted down toward the start of March, became the last five days of Intercalaris. The net effect was to add 22 or 23 days to the year, forming an intercalary year of 377 or 378 days. Some say the mensis intercalaris always had 27 days and began on either the first or the second day after

9476-437: Was given as 365 solar days 5 hours 49 minutes 16 seconds (≈ 365.24255 days). This length was used in devising the Gregorian calendar of 1582. In Uzbekistan , Ulugh Beg 's Zij-i Sultani was published in 1437 and gave an estimate of 365 solar days 5 hours 49 minutes 15 seconds (365.242535 days). In the 16th century Copernicus put forward a heliocentric cosmology . Erasmus Reinhold used Copernicus' theory to compute

9579-447: Was intended to agree with the ephemeris second based on Newcomb's work, which in turn makes it agree with the mean solar second of the mid-19th century. ET as counted by atomic clocks was given a new name, Terrestrial Time (TT), and for most purposes ET = TT = International Atomic Time + 32.184 SI seconds. Since the era of the observations, the rotation of the Earth has slowed down and the mean solar second has grown somewhat longer than

9682-429: Was intended to solve this problem permanently, by creating a calendar that remained aligned to the sun without any human intervention. This proved useful very soon after the new calendar came into effect. Varro used it in 37 BC to fix calendar dates for the start of the four seasons, which would have been impossible only 8 years earlier. A century later, when Pliny dated the winter solstice to 25 December because

9785-411: Was intercalated between 1/1/45 and 1/1/40 (disregarding a momentary 'fiddling' in December of 41) to avoid the nundinum falling on Kal. Ian." Alexander Jones says that the correct Julian calendar was in use in Egypt in 24 BC, implying that the first day of the reform in both Egypt and Rome, 1 January 45 BC , was the Julian date 1 January if 45 BC was a leap year and 2 January if it

9888-578: Was made in 238 BC ( Decree of Canopus ). Caesar probably experienced this "wandering" or "vague" calendar in that country. He landed in the Nile delta in October 48 BC and soon became embroiled in the Ptolemaic dynastic war, especially after Cleopatra managed to be "introduced" to him in Alexandria . Caesar imposed a peace, and a banquet was held to celebrate the event. Lucan depicted Caesar talking to

9991-434: Was not changed in ordinary years, and so continued to be the traditional 28 days. Thus, the ordinary (i.e., non-leap year) lengths of all of the months were set by the Julian calendar to the same values they still hold today. The Julian reform did not change the method used to account days of the month in the pre-Julian calendar , based on the Kalends, Nones and Ides, nor did it change the positions of these three dates within

10094-476: Was not. This necessitates fourteen leap days up to and including AD 8 if 45 BC was a leap year and thirteen if it was not. In 1999, a papyrus was discovered which gives the dates of astronomical phenomena in 24 BC in both the Egyptian and Roman calendars. From 30 August 26 BC (Julian) , Egypt had two calendars: the old Egyptian in which every year had 365 days and the new Alexandrian in which every fourth year had 366 days. Up to 28 August 22 BC (Julian)

10197-480: Was possible to compute ephemerides using numerical integration rather than general theories; numerical integration came into use in 1984 for the joint US-UK almanacs. Albert Einstein 's General Theory of Relativity provided a more accurate theory, but the accuracy of theories and observations did not require the refinement provided by this theory (except for the advance of the perihelion of Mercury) until 1984. Time scales incorporated general relativity beginning in

10300-428: Was proclaimed publicly by edict, and the arrangement might have continued to stand had not the correction itself of the calendar led the priests to introduce a new error of their own; for they proceeded to insert the intercalary day, which represented the four quarter-days, at the beginning of each fourth year instead of at its end, although the intercalation ought to have been made at the end of each fourth year and before

10403-693: Was renamed to honour Caesar because it was the month of his birth. According to a senatus consultum 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, occurred in that month. Other months were renamed by other emperors, but apparently none of the later changes survived their deaths. In AD 37, Caligula renamed September as "Germanicus" after his father ; in AD 65, Nero renamed April as "Neroneus", May as "Claudius" and June as "Germanicus"; and in AD 84 Domitian renamed September as "Germanicus" and October as "Domitianus". Commodus

10506-496: 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". The emperor Tacitus is said to have ordered that September, the month of his birth and accession, be renamed after him, but the story is doubtful since he did not become emperor before November 275. Similar honorific month names were implemented in many of

10609-499: Was used in some early Greek calendars, notably in Athens , is 1.53 days longer than eight mean Julian years . The length of nineteen years in the cycle of Meton was 6,940 days, six hours longer than the mean Julian year. The mean Julian year was the basis of the 76-year cycle devised by Callippus (a student under Eudoxus) to improve the Metonic cycle. In Persia (Iran) after the reform in

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