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102-660: Revolution Day or the Day of the Revolution refers to public holidays or remembrance days in various country held in commemoration of an important event in the country's history, usually the starting point or a turning point in a revolution that led to significant political change. The leap day in the French Republican Calendar , in use for several years after the French Revolution , added after

204-510: A chaser ("lacking") year, the month of Kislev is reduced to 29 days. In a malei ("filled") year, the month of Marcheshvan is increased to 30 days. 13-month years follow the same pattern, with the addition of the 30-day Adar Alef, giving them between 383 and 385 days. The observed and calculated versions of the lunar Islamic calendar do not have regular leap days, even though both have lunar months containing 29 or 30 days, generally in alternating order. However,

306-476: A Roman superstition that even numbers were unlucky. When Caesar changed the calendar to follow the solar year closely, he made all months have 30 or 31 days, leaving February unchanged except in leap years. In the Gregorian calendar, the standard calendar in most of the world, almost every fourth year is a leap year. Each leap year, the month of February has 29 days instead of 28. Adding one extra day in

408-475: A franciade , is also known as "Revolution Day" ( Jour de la Révolution or Fête de la Révolution in French). See Sansculottides for details. Leap year An astronomical year lasts slightly less than 365 ⁠ 1 / 4 ⁠  days. The historic Julian calendar has three common years of 365 days followed by a leap year of 366 days, by extending February to 29 days rather than

510-405: 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

612-575: A 13th month. Tropical year A tropical year or solar year (or tropical period ) is the time that the Sun takes to return to the same position in the sky – as viewed from the Earth or another celestial body of the Solar System – thus completing a full cycle of astronomical seasons . For example, it is the time from vernal equinox to the next vernal equinox, or from summer solstice to

714-424: A Wednesday in 2028. The length of a day is also occasionally corrected by inserting a leap second into Coordinated Universal Time (UTC) because of variations in Earth's rotation period . Unlike leap days, leap seconds are not introduced on a regular schedule because variations in the length of the day are not entirely predictable. Leap years can present a problem in computing, known as the leap year bug , when

816-411: 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

918-406: A leap day every 4 years amounts to about 3 extra days. The Gregorian calendar therefore omits 3 leap days every 400 years, which is the length of its leap cycle . This is done by omitting 29 February in the 3 century years (multiples of 100) that are not multiples of 400. The years 2000 and 2400 are leap years, but not 1700, 1800, 1900, 2100, 2200, and 2300. By this rule, an entire leap cycle

1020-412: A marriage proposal was refused by the man; compensation was deemed to be a pair of leather gloves, a single rose, £1, and a kiss. In some places the tradition was tightened to restricting female proposals to the modern leap day, 29 February, or to the medieval (bissextile) leap day, 24 February. According to Felten: "A play from the turn of the 17th century, 'The Maydes Metamorphosis,' has it that 'this

1122-411: 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

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1224-452: A satirical newspaper titled La Bougie du Sapeur is published only on leap year, on 29 February. In Greece, marriage in a leap year is considered unlucky. One in five engaged couples in Greece will plan to avoid getting married in a leap year. In February 1988 the town of Anthony, Texas , declared itself the "leap year capital of the world", and an international leapling birthday club

1326-421: A year is not correctly identified as a leap year or when 29 February is not handled correctly in logic that accepts or manipulates dates. On 1 January 45 BC , by edict, Julius Caesar reformed the historic Roman calendar to make it a consistent solar calendar (rather than one which was neither strictly lunar nor strictly solar), thus removing the need for frequent intercalary months . His rule for leap years

1428-454: Is bound to serve the pirates until his 21st birthday (that is, when he turns 88 years old, since 1900 was not a leap year) rather than until his 21st year . For legal purposes, legal birthdays depend on how local laws count time intervals. The Civil Code of Taiwan since 10 October 1929, implies that the legal birthday of a leapling is 28 February in common years: If a period fixed by weeks, months, and years does not commence from

1530-435: Is 400 years which total 146,097 days, and the average number of days per year is 365 +  1 ⁄ 4  −  1 ⁄ 100  +  1 ⁄ 400  = 365 + 97 ⁄ 400  = 365.2425. This rule could be applied to years before the Gregorian reform to create a proleptic Gregorian calendar , though the result would not match any historical records. The Gregorian calendar

1632-599: 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

1734-525: Is added seven times every 19 years to the twelve lunar months in its common years to keep its calendar year from drifting through the seasons. In the Solar Hijri and Bahá'í calendars , a leap day is added when needed to ensure that the following year begins on the March equinox . The term leap year probably comes from the fact that a fixed date in the Gregorian calendar normally advances one day of

1836-402: 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

1938-424: Is an observational calendar that starts on the spring equinox (Northern Hemisphere) and adds a single intercalated day to the last month (Esfand) once every 4 or 5 years; the first leap year occurs as the fifth year of the typical 33-year cycle and the remaining leap years occur every 4 years through the remainder of the 33-year cycle. This system has less periodic deviation or jitter from its mean year than

2040-483: Is called leap day and is created by adding an extra day to February. This day is added to the calendar in leap years as a corrective measure because the Earth does not orbit the Sun in precisely 365 days. Since about the 15th century, this extra day has been 29 February, but when the Julian calendar was introduced, the leap day was handled differently in two respects. First, leap day fell within February and not at

2142-759: Is celebrated in August, so leap years do not affect his commemoration, and, while the feast of the First and Second Findings of the Head of John the Baptist is celebrated on 24 February, the Orthodox church calculates days from the beginning of the current month, rather than counting down days to the Kalends of the following month, this is not affected. Thus, only the feast of St. John Cassian and any movable feasts associated with

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2244-450: 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

2346-574: Is done seven times every nineteen years (specifically, in years 3, 6, 8, 11, 14, 17, and 19). This is to ensure that Passover ( Pesah ) is always in the spring as required by the Torah (Pentateuch) in many verses relating to Passover. In addition, the Hebrew calendar has postponement rules that postpone the start of the year by one or two days. These postponement rules reduce the number of different combinations of year length and starting days of

2448-404: 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

2550-401: Is leape year/women wear breeches.' A few hundred years later, breeches wouldn't do at all: Women looking to take advantage of their opportunity to pitch woo were expected to wear a scarlet petticoat  – fair warning, if you will." In Finland, the tradition is that if a man refuses a woman's proposal on leap day, he should buy her the fabrics for a skirt. In France, since 1980,

2652-409: 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

2754-492: Is not accounted. Replacement (by 29 February) of the awkward practice of having two days with the same date appears to have evolved by custom and practice; the etymological origin of the term "bissextile" seems to have been lost. In England in the fifteenth century, "29 February" appears increasingly often in legal documents – although the records of the proceedings of the House of Commons of England continued to use

2856-512: The Kalends . This bis sextum ("twice sixth") was rendered in later languages as " bissextile ": the "bissextile day" is the leap day, and a "bissextile year" is a year which includes a leap day. This second instance of the sixth day before the Kalends of March was inserted in calendars between the "normal" fifth and sixth days. By legal fiction, the Romans treated both the first "sixth day" and

2958-518: The March Equinox and 21 March, as explained at Gregorian calendar , below. Prior to Caesar's creation of what would be the Julian calendar, February was already the shortest month of the year for Romans. In the Roman calendar (after the reform of Numa Pompilius that added January and February), all months except February had an odd number of days – 29 or 31. This was because of

3060-600: 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

3162-532: The tabular Islamic calendar used by Islamic astronomers during the Middle Ages and still used by some Muslims does have a regular leap day added to the last month of the lunar year in 11 years of a 30-year cycle. This additional day is found at the end of the last month, Dhu al-Hijjah , which is also the month of the Hajj . [REDACTED] The Solar Hijri calendar is the modern Iranian calendar . It

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3264-547: The vernal equinox . This is calculated and known years in advance. The Revised Bengali Calendar of Bangladesh and the Indian National Calendar organise their leap years so that every leap day is close to 29 February in the Gregorian calendar and vice versa. This makes it easy to convert dates to or from Gregorian. The Thai solar calendar uses the Buddhist Era (BE) but has been synchronised with

3366-410: 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

3468-448: 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,

3570-457: 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

3672-679: The Feasts do not apply to the years from the Creation to the deliverance of the Hebrews from Egypt under Moses. It was at that time (cf. Exodus 13) that the God of Abraham, Isaac and Jacob gave the Hebrews their "Law" including the days to be kept holy and the feast days and Sabbaths. Years consisting of 12 months have between 353 and 355 days. In a k'sidra ("in order") 354-day year, months have alternating 30 and 29 day lengths. In

3774-489: The Gregorian calendar and operates on the simple rule that New Year's Day must fall in the 24 hours of the vernal equinox. The 33-year period is not completely regular; every so often the 33-year cycle will be broken by a cycle of 29 years. The Hijri-Shamsi calendar, also adopted by the Ahmadiyya Community, is based on solar calculations and is similar to the Gregorian calendar in its structure with

3876-496: The Gregorian calendar will be 2800, because it will be a leap year in the Gregorian calendar but not in the Revised Julian calendar. This rule gives an average year length of 365.242222 days. This is a very good approximation to the mean tropical year, but because the vernal equinox year is slightly longer, the Revised Julian calendar, for the time being, does not do as good a job as the Gregorian calendar at keeping

3978-482: 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

4080-411: The Gregorian calendar. For legal purposes, the two days of the bis sextum were considered to be a single day, with the second sixth being intercalated; but in common practice by the year 238, when Censorinus wrote, the intercalary day was followed by the last five days of February, a. d. VI , V , IV , III , and pridie Kal. Mart. (the days numbered 24, 25, 26, 27, and 28 from

4182-423: 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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4284-542: The Gregorian since AD  1941. The Chinese calendar is lunisolar , so a leap year has an extra month, often called an embolismic month after the Greek word for it. In the Chinese calendar, the leap month is added according to a rule which ensures that month 11 is always the month that contains the northern winter solstice . The intercalary month takes the same number as the preceding month; for example, if it follows

4386-584: The Lenten or Pre-Lenten cycles are affected. In Ireland and Britain, it is a tradition that women may propose marriage only in leap years. While it has been claimed that the tradition was initiated by Saint Patrick or Brigid of Kildare in 5th century Ireland, this is dubious, as the tradition has not been attested before the 19th century. Supposedly, a 1288 law by Queen Margaret of Scotland (then age five and living in Norway), required that fines be levied if

4488-550: 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

4590-462: 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,

4692-469: 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

4794-475: The UK 1 March is considered to be a leapling's legal birthday. The Revised Julian calendar adds an extra day to February in years that are multiples of four, except for years that are multiples of 100 that do not leave a remainder of 200 or 600 when divided by 900. This rule agrees with the rule for the Gregorian calendar until 2799. The first year that dates in the Revised Julian calendar will not agree with those in

4896-749: 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

4998-422: The additional "sixth day" before the Kalends of March as one day. Thus a child born on either of those days in a leap year would have its first birthday on the following sixth day before the Kalends of March. In a leap year in the original Julian calendar, there were indeed two days both numbered 24 February. This practice continued for another fifteen to seventeen centuries, even after most countries had adopted

5100-448: 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

5202-511: 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,

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5304-400: The beginning of February in a common year), so that the intercalated day was the first of the doubled pair. Thus the intercalated day was effectively inserted between the 23rd and 24th days of February. All later writers, including Macrobius about 430, Bede in 725, and other medieval computists (calculators of Easter), continued to state that the bissextum (bissextile day) occurred before

5406-429: The beginning of a week, month, or year, it ends with the ending of the day which precedes the day of the last week, month, or year which corresponds to that on which it began to commence. But if there is no corresponding day in the last month, the period ends with the ending of the last day of the last month. Since 1990 non-retroactively, Hong Kong considers the legal birthday of a leapling 1 March in common years: In

5508-538: The calendar every 4 years compensates for the fact that a period of 365 days is shorter than a tropical year by almost 6 hours. However, this correction is excessive and the Gregorian reform modified the Julian calendar's scheme of leap years as follows: Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example,

5610-402: The common 28. The Gregorian calendar , the world's most widely used civil calendar, makes a further adjustment for the small error in the Julian algorithm. Each leap year has 366 days instead of 365. This extra leap day occurs in each year that is a multiple of 4, except for years evenly divisible by 100 but not by 400. In the lunisolar Hebrew calendar , Adar Aleph , a 13th lunar month ,

5712-513: The days were numbered from the beginning of the month, it was named 24 February in common years, but the presence of the bissextum in a bissextile year immediately before a. d. VI Kal. Mart. shifted the latter day to 25 February in leap years, with the Vigil of St. Matthias shifting from 23 February to the leap day of 24 February. This shift did not take place in pre-Reformation Norway and Iceland; Pope Alexander III ruled that either practice

5814-498: The end: 24 February was doubled to create, strangely to modern eyes, two days both dated 24 February. Second, the leap day was simply not counted so that a leap year still had 365 days. The early Roman calendar was a lunisolar one that 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 into February, at

5916-475: The equinox, the tropical year comprises 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

6018-569: The exception that its epoch is the Hijra . The Coptic calendar has 13 months, 12 of 30 days each, and one at the end of the year of 5 days, or 6 days in leap years. The Coptic Leap Year follows the same rules as the Julian Calendar so that the extra month always has 6 days in the year before a Julian Leap Year. The Ethiopian calendar has 12 months of 30 days plus 5 or 6 epagomenal days , which comprise

6120-414: The first day of Passover is never Monday, Wednesday, or Friday. This rule is known in Hebrew as " lo badu Pesah " ( לא בד״ו פסח ), which has a double meaning — "Passover is not a legend", but also "Passover is not Monday, Wednesday, or Friday" (as the Hebrew word badu is written by three Hebrew letters signifying Monday, Wednesday, and Friday). One reason for this rule is that Yom Kippur ,

6222-500: The first or second day after the Terminalia a. d. VII Kal. Mar. (23 February), to resynchronise the lunar and solar cycles. The remaining days of Februarius were discarded. This intercalary month, named Intercalaris or Mercedonius , contained 27 days. The religious festivals that were normally celebrated in the last 5 days of February were moved to the last 5 days of Intercalaris. The lunisolar calendar

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6324-401: 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

6426-404: The holiest day in the Hebrew calendar and the tenth day of the Hebrew year, now must never be adjacent to the weekly Sabbath (which is Saturday), i.e., it must never fall on Friday or Sunday, in order not to have two adjacent Sabbath days. However, Yom Kippur can still be on Saturday. A second reason is that Hoshana Rabbah , the 21st day of the Hebrew year, will never be on Saturday. These rules for

6528-507: The last five days of February. In England, the Church and civil society continued the Roman practice whereby the leap day was simply not counted, so that a leap year was only reckoned as 365 days. Henry III 's 1236 Statute De Anno et Die Bissextili instructed magistrates to treat the leap day and the day before as one day. The practical application of the rule is obscure. It

6630-486: The leap day – to be inserted every fourth year, and this too was done after 23 February. To create the intercalary day, the existing ante diem sextum Kalendas Martias (sixth day (inclusive: i.e. what we would call the fifth day before) before the Kalends (first day) of March, i.e. what we would call 24 February) was doubled, producing ante diem bis sextum Kalendas Martias [a second sixth day before

6732-404: 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

6834-413: 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

6936-473: 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

7038-414: 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 )

7140-450: 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:

7242-448: 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,

7344-413: The next summer solstice. It is the type of year used by tropical solar calendars . 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

7446-558: 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

7548-630: The old system until the middle of the sixteenth century. It was not until the passage of the Calendar (New Style) Act 1750 that 29 February was formally recognised in British law. In the liturgical calendar of the Christian churches, the placement of the leap day is significant because of the date of the feast of Saint Matthias , which is defined as the sixth day before 1 March (counting inclusively). The Church of England's Book of Common Prayer

7650-463: 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

7752-425: 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

7854-459: The second month (二月) then it is simply called "leap second month" i.e. simplified Chinese : 闰二月 ; traditional Chinese : 閏二月 ; pinyin : rùn'èryuè . The Hebrew calendar is lunisolar with an embolismic month . This extra month is called Adar Rishon ( first Adar ) and is added before Adar , which then becomes Adar Sheini ( second Adar ). According to the Metonic cycle , this

7956-459: 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

8058-403: 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

8160-452: 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,

8262-490: The tropical year, because of 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

8364-413: 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

8466-512: 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

8568-463: 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

8670-424: The vernal equinox on or close to 21 March. The Baháʼí calendar is a solar calendar composed of 19 months of 19 days each (361 days). Years begin at Naw-Rúz, on the vernal equinox , on or about 21 March. A period of "Intercalary Days", called Ayyam-i-Ha , is inserted before the 19th month. This period normally has 4 days, but an extra day is added when needed to ensure that the following year starts on

8772-424: 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

8874-534: The week from 28 to 14, and regulate the location of certain religious holidays in relation to the Sabbath . In particular, the first day of the Hebrew year can never be Sunday, Wednesday, or Friday. This rule is known in Hebrew as " lo adu rosh " ( לא אד״ו ראש ), i.e., "Rosh [ha-Shanah, first day of the year] is not Sunday, Wednesday, or Friday" (as the Hebrew word adu is written by three Hebrew letters signifying Sunday, Wednesday, and Friday). Accordingly,

8976-420: The week from one year to the next, but the day of the week in the 12 months following the leap day (from 1 March through 28 February of the following year) will advance two days due to the extra day, thus leaping over one day in the week. For example, 1 March was on a Friday in 2024, then it will be on Saturday in 2025, Sunday in 2026, and Monday in 2027, but then will "leap" over Tuesday to fall on

9078-416: The years 1700, 1800, and 1900 are not leap years, but the years 1600 and 2000 are. Whereas the Julian calendar year incorrectly summarised Earth's tropical year as 365.25 days, the Gregorian calendar makes these exceptions to follow a calendar year of 365.2425 days. This more closely resembles a mean tropical year of 365.2422 days. Over a period of four centuries, the accumulated error of adding

9180-528: 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

9282-401: 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

9384-429: Was a simple one: add a leap day every 4 years. This algorithm is close to reality: a Julian year lasts 365.25 days, a mean tropical year about 365.2422 days. Consequently, even this Julian calendar drifts out of 'true' by about 3 days every 400 years. The Julian calendar continued in use unaltered for about 1600 years until the Catholic Church became concerned about the widening divergence between

9486-491: Was abandoned about 450 BC by the decemviri , who implemented the Roman Republican calendar , used until 46 BC. The days of these calendars were counted down (inclusively) to the next named day, so 24 February was ante diem sextum Kalendas Martias ["the sixth day before the calends of March"] often abbreviated a. d. VI Kal. Mart. The Romans counted days inclusively in their calendars, so this

9588-525: Was designed to keep the vernal equinox on or close to 21 March, so that the date of Easter (celebrated on the Sunday after the ecclesiastical full moon that falls on or after 21 March) remains close to the vernal equinox. The " Accuracy " section of the " Gregorian calendar " article discusses how well the Gregorian calendar achieves this design goal, and how well it approximates the tropical year . The intercalary day that usually occurs every 4 years

9690-437: 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

9792-447: 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

9894-549: Was lawful. Other feasts normally falling on 25–28 February in common years are also shifted to the following day in a leap year (although they would be on the same day according to the Roman notation). The practice is still observed by those who use the older calendars. In the Eastern Orthodox Church , the feast of St. John Cassian is celebrated on 29 February, but he is instead commemorated at Compline on 28 February in non-leap years. The feast of St. Matthias

9996-480: 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

10098-550: Was regarded as in force in the time of the famous lawyer Sir Edward Coke (1552–1634) because he cites it in his Institutes of the Lawes of England . However, Coke merely quotes the Act with a short translation and does not give practical examples. ... and by (b) the statute de anno bissextili , it is provided, quod computentur dies ille excrescens et dies proxime præcedens pro unico dii , so as in computation that day excrescent

10200-629: Was started. A person born on February 29 may be called a "leapling" or a "leaper". In common years, they celebrate their birthdays on 28 February or 1 March. Technically, a leapling will have fewer birthday anniversaries than their age in years. This phenomenon may be exploited for dramatic effect when a person is declared to be only a quarter of their actual age, by counting their leap-year birthday anniversaries only. For example, in Gilbert and Sullivan 's 1879 comic opera The Pirates of Penzance , Frederic (the pirate apprentice) discovers that he

10302-493: Was still using the "two days with the same date" system in its 1542 edition; it first included a calendar which used entirely consecutive day counting from 1662 and showed leap day as falling on 29 February. In the 1680s, the Church of England declared 25 February to be the feast of St Matthias. Until 1970, the Roman Catholic Church always celebrated the feast of Saint Matthias on a. d. VI Kal. Mart. , so if

10404-493: Was the fifth day before 1 March when counted in the modern exclusive manner (i.e., not including both the starting and ending day). Because only 22 or 23 days were effectively added, not a full lunation , the calends and ides of the Roman Republican calendar were no longer associated with the new moon and full moon. In Caesar's revised calendar, there was just one intercalary day – nowadays called

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