Gregorian calendar

Bula Inter Gravissimas (1582)

Gregory XIII

German Jesuit Christopher Clavius. Along with Galileo, he was the most outstanding and important member of the implementation of the calendar. One of the biggest craters on the moon is named.

The Gregorian calendar is a calendar originating in Europe, currently used officially in almost the entire world, named after its promoter, Pope Gregory XIII, who promulgated its use through the Bull Inter Gravissimas. Starting in 1582, it gradually replaced the Julian calendar in different countries, used since Julius Caesar established it in the year 46 BC. C. The Julian calendar was basically the Egyptian calendar, the first known solar calendar that established the length of the year at 365.25 days.

The Gregorian calendar originated from a first study carried out in 1515 by scientists from the University of Salamanca, and a second in 1578. The first was ignored and the second, finally, emerged the current world calendar, although credit was attributed to other characters.

The first countries to adopt the current calendar were those dependent on the Spanish Monarchy of King Philip II, that is, Spain and its viceroyalties in America, the Philippine islands, the states of the Italian peninsula (now Italy) and Portugal, then also under the Spanish Crown, and in addition the Italian states dependent on the Holy See in 1582. However, the Kingdom of Great Britain and its American colonies did not do so until 1752.

History

The Gregorian reform arose from the need to put into practice one of the agreements of the Council of Trent, which was to adjust the calendar to eliminate the gap produced since the first Council of Nicaea, held in 325, in which the astral moment in which Easter should be celebrated and, in relation to it, the other mobile religious festivals had been fixed. What mattered, then, was the regularity of the liturgical calendar, for which it was necessary to introduce certain corrections in the civil calendar. Basically, it was about adapting the civil calendar to the tropical year.

The Council of Nicea determined that Easter should be commemorated on the Sunday following the full moon after the spring equinox in the northern hemisphere (autumn equinox in the southern hemisphere). That year 325 the equinox had occurred on March 21, but with the passage of time the date of the event had been brought forward to the point that in 1582, the lag was already 10 days, and the equinox that same year of 1582 was dated March 11.

The lag came from an inaccurate calculation of the number of days in the tropical year; according to the Julian calendar that instituted a leap year every four, he considered that the tropical year was made up of 365.25 days, while the correct figure is 365.2422, or what is the same, 365 days, 5 hours, 48 minutes and 45.10 seconds. Those more than 11 minutes counted in addition to each year had supposed an accumulated error of approximately 10 days in the 1257 years between 325 and 1582.

The "Calendar Commission" was established, in which astronomers Cristóbal Clavio and Luis Lilio stood out. Clavio, who belonged to the Jesuit order, was a renowned mathematician and astronomer whom Galileo Galilei required as scientific endorsement of his telescopic observations. As for Lilio, we know that he was the main author of the calendar reform. He died in 1576 without seeing the process completed. In the Alphonse Tables, carried out at the initiative of King Alfonso X of Castilla, a value of 365 days 5 hours 49 minutes and 16 seconds was assigned to the tropical year, which was taken as correct by the Calendar Commission. Pedro Chacón, a Spanish mathematician, wrote the Compendium with the opinion of Lilio, supported by Clavio, and the reform was approved on September 14, 1580, to be put into practice in October 1582.

Thursday (Julian) October 4, 1582 was succeeded by Friday (Gregorian) October 15, 1582. Thus, ten days disappeared because they had already been overcounted in the Julian calendar.

The calendar was immediately adopted in countries where the Catholic Church had influence. However, in non-Catholic countries, such as Protestants, Anglicans, Orthodox, and others, this calendar was not implemented until several years (or centuries) later, and in some, it is still called the Julian calendar, so as not to recognize the authority of the Pope of Rome at his implantation. Despite the fact that the Gregorian calendar is the official one in their countries, the Orthodox churches (except Finland) continue to use the Julian calendar (or modifications of it, other than the Gregorian calendar). However, apart from the maintenance of a different ecclesiastical calendar in some countries, the Gregorian calendar is the one that is considered as the basis for the establishment of the civil year throughout the world, including countries with a different ecclesiastical or religious year than the one established. in the Gregorian reform of the XVI century.

Calendar problems

The Gregorian calendar adjusts this gap by changing the general rule of leap every four years, and makes an exception for years that are multiples of 100, an exception that in turn had another exception, that of years that are multiples of 400, which were leap years The new rule for leap years was formulated as follows: the basic length of the year is 365 days; but those years that are divisible by 4 will be leap years (that is, they will have 366 days), except for multiples of 100 (1700, 1800, 1900..., which will not be leap years), from which those that are also divisible are excepted. by 400 (1600, 2000, 2400..., which will be leap years). The Gregorian calendar adjusts the duration of the year to 365.2425 days, which leaves a difference of 0.0003 days per year of error, that is, it advances about 1/2 minute each year (approx. 26 s/year), which means that adjustment of one day is required every 3323 years. This difference comes from the fact that the translation of the Earth around the Sun does not coincide with an exact number of days of rotation of the Earth around its axis. When the center of the Earth has made one complete revolution around the Sun and has returned to the same "relative position" in which it was the previous year, 365 days have been completed and a little less than a quarter of a day (0, 2422 to be more exact). To match the year to an integer number of days requires periodic adjustments every few years.

However, trying to create a rule to correct this error of one day every 3323 years is complex. In such a long time the Earth slows down in its rotation speed (and the translation movement also slows down) and this creates a new difference that it is necessary to correct. The Moon exerts a retarding effect on this rate of spin due to the eccentricity created by the tides. The decrease in spin speed created by that eccentricity is similar to what occurs when we spin a frisbee by putting some wet sand on one side of the bottom edge: when the saucer is spun, its spin speed is much slower. to the one it has when there is no such eccentricity. This effect is still being analyzed and measured by the scientific world and, additionally, there are other effects that make it difficult to define rules with such precision. This error is only one part per million. The most practical thing will be that when the difference is significant, that is, when it reaches one day, it is declared that the next leap year is not. In any case, there are almost two thousand years of analysis and discussion left before this adjustment is needed.

Another different problem, as has already been pointed out, is the decrease in the speed of the Earth's rotation (and also of the Earth's translation), which can be measured with great precision with an atomic clock. It is a different problem because it has nothing to do with calculating the calendar and, therefore, with the adjustments that have to be made to the calendar. It is rather the opposite: it is the atomic clock that has to adjust to the movements of the Earth, that is, to the duration of the solar day and the terrestrial year. The atomic clock measures uniform time, which therefore does not exist in nature, where the movements of the physical world are uniformly varied.

Despite being the most widely used, the Gregorian calendar has several deficiencies. The first, already mentioned, is its difference with the tropical year, but it is not important for practical purposes. Of greater importance is the difference in the length of the months (28, 29, 30, or 31 days) and the fact that the week, which is almost universally used as a labor unit of time, is not integrated into the months, so so that the number of working days in a month can vary between 24 and 27. Furthermore, in Christian countries, the fact that Easter is governed by a lunisolar rule (according to the Council of Nicaea such a holiday should be celebrated on the Sunday following the first full moon after the spring equinox, set for March 21 for the northern hemisphere) causes alterations in various activities (for example in education, tourism, etc.).

The day, the week and the month

• Day: is the fundamental time unit of the Gregorian calendar. One day it is approximately 86 400 seconds from International Atomic Time (ITA).
• Week: period of 7 days.
• Month: each of the twelve periods of time, from 28 to 31 days, in which the year is divided. The duration of one month was established in such a way that the months of 30 and 31 days, with the exception of February, retained its original duration of 28 days for religious reasons, except for the sixteen years, in which the month is 29 days.

Timeline

Year 1582

• Italy, Portugal, Spain (European and Canary Islands) and the Catholic area of Poland: after Thursday, October 4, 1582 came on Friday, October 15.
• France, Lorraine (Lorraine) and the Mississippi Valley (United States): after Sunday, December 9, 1582 came on Monday, December 20.
• The Netherlands (Brabant, Zeland and the Staten Generaal): after Monday, December 17, 1582 came on Tuesday, December 28.
• Belgium (Limburgh and Southern Provinces): after Thursday, 20 December, 1582 came on Friday, 31 December.

Year 1583

Pramatic of the Philip II Calendar (Pragmatic about the ten days of the year(14 May 1583, reprinted in Lima on 14 July 1584)

• In the Netherlands (Holland, Flanders, Hennegan and some southern provinces), on Saturday, January 1, 1583 came after Friday, December 21, 1582, so there were no Christmas holidays or New Year's Eve.
• Germany (Catholic zones): originally on Monday, February 21, 1583, should happen on Sunday, February 10, but the people did not make any case. It was then decided that on Sunday, October 16, 1583, it would continue on Saturday, October 5.
• Austria (Tirol, Salzburg and Brescia): Sunday, 16 October 1583, followed Saturday, 5 October.
• Austria (Carintia-Kärnten and Estiria-Steiermark): Sunday, December 25, 1583, would follow Saturday, December 14.
• In the Spanish possessions in Asia and America, such as the Viceroyalty of New Spain (Today Mexico, Cuba and southern U.S.A.) in North and Central America; the Spanish South America (Virreinato del Perú) and the Philippine General Office), on Saturday, October 15, 1583 came after Friday, October 4. Due to the distance with the metropolis and the difficulty of arriving the order of change in time to all places in the year of 1582, the Spanish monarch Felipe II, dictated a Pragmatic on 14 May 1583, establishing that year (1583) for the change of calendar in the western and eastern Indies.
• Netherlands (Groninga): Monday, 21 February 1583, came after 10 February. They returned to the Julianus in July-August 1594. Finally on Wednesday, January 12, 1701 came after Tuesday, December 31, 1700.

Year 1584

• Bohemia (Bohemia, Moravia and Lusace): on Tuesday, January 17, 1584 came after Monday, January 6.
• Switzerland (most Catholic cantons): Sunday, January 22, came after January 11.
• Silesia (Slask): Monday, January 23, came after Sunday, January 12.

Year 1587

• Hungary: Sunday, November 1, 1587 came after Saturday, October 21.

Year 1590

• Transylvania (Siebenbürgen-Ardeal-Erdély): on Tuesday, December 25, 1590 came after Monday, December 14.

Year 1605

• Canada (New Scotland): from 1605 to 13 October 1710, they used the Gregorian calendar. Then they used the Julianus from October 2, 1710 until Wednesday, September 2, 1752, which was followed by Thursday, September 14. Since then they used the Gregorian.

The rest of Canada had been using the Gregorian calendar since its original implantation.

Year 1610

• Germany (Prussia): Thursday, September 2, 1610 came after Wednesday, August 22.

Year 1682

• France (Strasbourg): February 1682.

Year 1700

• Protestant Germany, Denmark and Norway: on Monday, March 1, 1700 came after February 18.
• Netherlands (Güeldres-Gelderland, Netherlands Protestant area): Monday, July 12, 1700 came after June 30.
• Netherlands (Utrecht and Overijssel): Sunday, December 12, 1700 came after Saturday, November 30.

Year 1701

• The Netherlands (Frisia and again Groningen) and Switzerland (Zúrich, Bern, Basel, Schaffhausen, Gent, Mühlhausen and Biel): Wednesday, January 12, 1701 came after Tuesday, December 31, 1700.
• Netherlands (Drenthe): Thursday, 12 May 1701 came after Wednesday, 30 April.

Year 1752

• England and its colonies (Terranova and the coast of Hudson Bay in Canada; Atlantic coast of the United States, Washington and Oregon; Scotland, Ireland, India): Thursday, September 14, 1752 came after Wednesday, September 2.

This is the reason why it is said that writers Miguel de Cervantes Saavedra and William Shakespeare both died on April 23, 1616, actually the latter died 10 days later (May 3, of the current European calendar).

In England, the days on the Julian calendar that occurred before the introduction of the Gregorian calendar in 1752 are called OS (OS).Old Style or 'old style'). Initial NS (New Style or 'new style') indicate the Gregorian calendar.

Year 1753

• Sweden and Finland (which when it was conquered by Russia had to adopt to some degree the Julian calendar): in the year 1700 it was decided to cancel the biased days for forty years, which would result in the accumulation of the missing 10 days. That year it was fulfilled, but not in the 1704 and 1708 bisies (it is not known why). Therefore in that decade their dates did not coincide with any other country (whether it had Gregorian or Julian calendar). Later, in 1712 they decided that they would return to the Julian calendar by adding a day ("30 February") to the 1712 bisister year. Forty years later they decided to make the normal drastic change: on Thursday, March 1, 1753 came after Wednesday, February 17.

Year 1867

• Alaska: October 1867, when it became a U.S. federal entity.

Year 1873

• Japan: a lunar calendar was used before.

Year 1875

• Egypt.

Year 1912 or 1929

• China: I had a lunar calendar before. The authors do not agree whether the change occurred in 1912 or 1929. Until a few years ago in Hong Kong the people used the lunar calendar (which is very difficult to translate into the Gregorian calendar, which is strictly solar).
• Albania: December 1912.

Year 1914 or 1926

• Turkey: until 1 January 1914 (according to other authors until 1926 by the Western reforms of Mustafa Kemal Atatürk) Turkey worked with the Islamic calendar.

Year 1916

• Bulgaria: on 14 April 1916 it came after 31 March.

Year 1918

• Russia and Estonia: Thursday, February 14, 1918 came after Wednesday, January 31. Other eastern areas of the Soviet Union changed it two years later.

Year 1919

• Romania: Monday, April 14, 1919 came after Sunday, March 31.
• Yugoslavia.

Year 1923

• Greece: Thursday, March 1, 1923 came after February 15.

Length of the Gregorian year

The Gregorian calendar distinguishes between:

• Common year: 365 days
• Year bisies: 366 days
• Secular year: the finished in "00" — a minimum of 100—

An leap year is a multiple of 4, with the exception of secular years. Regarding these, the secular year multiple of 400 is a leap year.

In this way, the Gregorian calendar is made up of 400-year cycles:

• In 400 years there are (400/4)-4 secular = 96 bisy years
• Of the 4 secular years, only one is bisiest (maximum of 400)
• In the 400-year cycle we have 96 + 1 = 97 bisy years, and 400 – 97 = 303 common years

Doing the calculation in days:

• 97 × 366 days = 35 502 days
• 303 × 365 = 110 595 days

This makes a total of 146,097 days in the 400 years, so the average length of the Gregorian year is 365.2425 days.

In the 400-year cycle of the Gregorian calendar, these 146,097 days, which are 20,871 × 7 days, there are an integer number of weeks 20,871, such that in each 400-year cycle not only exactly the same cycle of common and leap years, but that the weekly cycle is also exact, this congruence gives rise to the fact that taking a group of 400 years in a row, the following cycle of 400 years is exactly the same.

The first week of the year, number 1, is the one that contains the first Thursday of January. The weeks of a year run from 1 to 52, unless the year ends on Thursday, or on Thursday or Friday if it is a leap year, in which case add one more week: 53.

• Month: period of 30 or 31 days, except for February that has 28 days in a common year, and 29 days in a bisister year.

The nemotecnia of the knuckles

A mnemonic is to make two fists and bring them together with the knuckles up. The protruding knuckles will represent the months of 31 days, and the gaps between the knuckles the months of less than 31 days. The first knuckle (that of the little finger) represents January (and because it is outstanding, it is equivalent to 31 days). The next hole (between the knuckles of the little finger and the ring finger) represents February (and because it is a hole it has less than 31 days, in this case 29 or 28 days). The second knuckle (of the ring finger) represents March (and because it is outstanding, it is equivalent to 31 days) and so on until reaching July, represented by the knuckle of the index finger (which, because it is outstanding, is equivalent to 31 days). Then it is passed to the other hand and it is counted from the knuckle of the index finger, which, like the previous one, will represent August (and because it is outstanding, it will be equivalent to 31 days). The count continues until reaching December, represented by the knuckle of the ring finger (which, because it is outstanding, says that December has 31 days).

Another way to visualize the above mnemonic is as follows: With the closed fist of either hand, place your index finger of the other hand on the knuckle of your fist's index finger; that knuckle indicates the month of January. Move your index finger to the gap between the knuckles of the index and middle fingers of your fist, that gap represents February, move your index finger to the next knuckle (middle finger) "March" and so on, considering each knuckle and interstice until reaching the knuckle of the little finger that represents July, once here bring your index finger back to the knuckle of the index finger of the fist that will now indicate the month of August and continue the count again until the ring knuckle which will be december Each knuckle month is 31 days and each interstice month is 30 days with the exception of February.

Origin of the Christian Era

The Romans counted time with different computations. One of them consisted of starting to count from the year of the foundation of Rome, that is, ab urbe condita, abbreviated a.u.c. Another modality It was the consular system. In addition, there are the so-called provincial eras, such as the Era of Diocletian, the Caesarean Era of Antioch or the Hispanic Era that began in 38 BC.

The so-called Christian era arose in 607, during the pontificate of Boniface IV, and here the start of the scale became the date of the birth of Christ, which was not known exactly at first. A Romanian monk, Dionysius the Meager, a mathematician, based on the Bible and other historical sources, between the years 526 and 530, had dated the birth of Christ on December 25, 753 a.u.c. The following year 754 a.u.c. it became the year 1 A.D., Anno Domini, year 1 of the Lord, but previous years continued to be counted as a.u.c. years. Finally in the 17th century the years prior to 1 A.D. were counted. as years before Christ, a. C., and the later ones are years after Christ, d. C.. As a curiosity, there is currently a consensus in placing the birth of Christ from five to seven years before the date set by the Meager; but there is a lack of data to propose any exact new date, and in any case it is unrealistic to even think of correcting the error.

When the counting of the Christian era began, there was no mathematical concept of zero, and the years were counted in order (ie: first year, second, etc.). The beginning of the Gregorian calendar is, therefore, January 1 of the first year (year 1 AD), which begins the first decade, the first century (1st century) and the first millennium. The first year before Christ (year 1 BC) corresponds to the same year 753 a.u.c. (since Christ was born almost at the end, on December 25). Thus, there is no year 0. Established in this way the origin of the calendar, the first millennium (first 1000 years) elapsed between January 1 of the year 1 and December 31 of the year 1000. In the same way, the first century elapsed between January 1 of year 1 and December 31 of year 100.

Precision

The Gregorian calendar, by skipping three leap days every 400 years, improves on the approximation made by the Julian calendar, giving an average year of 365.2425 mean solar days. This approximation is in error by approximately one day in 3030 years with respect to the current value of the mean tropical year. However, due to the precession of the equinoxes, which is not constant, and the movement of the perihelion (which affects the orbital speed of the Earth) the error with respect to the astronomical vernal equinox is variable; If an approximate average interval between spring equinoxes is considered with a duration of 365.24237 days in cycles of 2000 years, this implies an error close to 1 day every 7700 years. In any case, the Gregorian calendar is substantially more accurate than the Julian calendar (which, with an average year of 365.25 days, incurs 1 day of error every 128 years).

In the 19th century, Sir John Herschel proposed a modification to the Gregorian calendar with 969 leap days every 4000 years, in instead of the 970 leap days that the Gregorian calendar would insert into the same period. This would reduce the average year to 365.24225 days. Herschel's proposal would make the year 4000, and its multiples, common instead of leap years. Although this modification has been proposed several times already, it has never been officially adopted.

On time scales of thousands of years, the Gregorian calendar lags behind the astronomical seasons due to the slowing down of the Earth's rotation, which makes each day a little longer over time (see acceleration of the tides and leap second), while the year maintains a more uniform duration.

Seasonal calendar error

The image shows the difference between the Gregorian calendar and the astronomical seasons.

The vertical axis is the date in June and the horizontal axis is the years in the Gregorian calendar.

Each dot is the date and time of the June solstice of that particular year. The error drifts about a quarter of a day per year. Centuries are ordinary years, unless they are divisible by 400, in which case they are included in leap years. This causes a correction in the years 1700, 1800, 1900, 2100, 2200, and 2300.

For example, these corrections cause December 23, 1903 to be the latest solstice in a December month, while December 20, 2096 is the earliest December solstice, with -2.25 days away. difference from the theoretical date of the seasonal event.

ISO standard

ISO 8601 standard for writing dates and times.

• Date: it is the year, month and day, written in that order, separated by a script or not. The year will consist of 4 figures, and the month and day of two figures each -the first being a zero-. For example, on 4 November 2007 it will be written as 20071104 or 2007-11-04.
• Date of the week: alternative to the previous one, add the corresponding number to the week preceded by the letter W -initial of weekWeek, English. So, 2005-W07-5 indicates the fifth day of the seventh week of 2005.
• Time: two figures for the hours, minutes and seconds, in that order, being the Midnight the 00:00:00. The time scale goes from 0 to 24 hours. So, the 5th and 4th of the afternoon will be 17:15:00.
• Date and time: the date and time as explained above are indicated, separating them by one T -initial of timeTime or time, in English. For example: 2 and a half of the morning of 30 December 2005 indicates: 2005-12-30T02:30.

In addition, the Royal Spanish Academy recommends writing dates in the following terms: December 30 of 2005, or December 30 of the year 2005, although this recommendation does not imply that it is considered incorrect to use the article in these cases: December 30 of 2005. Obviously, in the latter case, the term year is understood.