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Home , Tropical year, Year zero

Year and Subdivisions A. AD, BC, CE, and BCE · AD: : After the birth of Christ: BC: Before Christ; CE: Common or Christian ; and BCE: Before Common or Christian Era (to avoid Christ in terms of his birth) · Adoption of birth of Christ as (initial, start) 6th scholar Dionysius Exiguus compiled table of values for Easter. · Dionysius chose to number the since the birth of Christ, rather than honor the persecutor (284-305) · Dionysius (wrongly) fixed ' birth with respect to Diocletian's reign in such a manner that it falls on 25 December 753 AUC (, i.e. since the founding of Rome), thus making the current era start with C.E. 1 on 1 January 754 AUC. · There is no zero, thus 1 BC to 1 AD; also Jesus was really probably born 7BCE (?) · Easter: celebration of death and resurrection in C.E. 30; first Sunday after the first full after vernal . · Astronomers: Instead of 1 B.C.E. they use 0, instead of 2 B.C.E. they use -1, instead of 3 B.C.E. they use -2, etc.

B. “Our Year”: based on the 's motion around . The from one fixed point to the next is called a tropical year (mean interval between vernal ), length is currently 365.242190 days, but it varies. Around 1900 its length was 365.242196 days, and around 2100 it will be 365.242184 days · Solar : based on tropical year, sidereal · : synodic : from one new moon to the next, varies: in 1900: 29.5305886 days, 2100 it will be 29.5305891 days, synodic · : tries to have tropical year coincide with lunar ; length of the tropical year is not a multiple of the length of the synodic month. Means addition of months and/or days, 19 tropical years is 234.997 synodic months · : first millennium started in 1 AD – 1000AD, is 1001 – 2000 millennium, third is 2001-3000 · : 970 leap years for every 4000 years by

C. Julian Period · The Julian period (and the Julian number) must not be confused with the (7980 years) · Joseph Justus Scaliger (1540-1609): interested in assigning every year a positive value without worrying about BCE/CE; invented what is today known as the Julian Period. o Starts on 1 January 4713 B.C.E. (Julian calendar) and lasts for 7980 years. C.E. 2000 is thus year 6713 in the Julian period. After 7980 years the number starts from 1 again. o In 4713 B.C.E. the Indiction, the Golden Number, and the Solar Number were all 1. The next this happens is 15 x 19 x 28 = 7980 years later, in C.E. 3268 · Indiction Number: [(Y+2) mod15] + 1 (first used by Constantine the Great on 1 September 312AD) used in the to specify the position of a year in a 15 year taxation cycle by emperor, ceased to be used in 1806. Had nothing to do with · Golden Number: [Y mod 19 + 1 = 5] · Solar Number: [(Y + 8) mod 28 + 1 = 20]

D. Month · Length and how many days relate to type of calendar and civilization · Origins of current Gregorian months: (Mostly derived from ) o January (Januarius): god Janus; February (Februarius): Februa (purification festival); March (Martius): god ; April (Aprilis) after Aphrodite or latin word aperire (to open), May (Maius): goddess Maia; June (Junius): goddess Juno; July (Julius): after in 44 BCE; prior name was Quintilius from quintus meaning 5 in old , August (Augustus) after emperor Augustus in 8 BCE, prior name was Sextilis from sextus meaning 6 in old Roman Calendar; September: septum (7th month in old Roman calendar), October: octo (8 in old Roman calendar ). November: Novem (9th in old roman calendar); December: decem (10th in old Roman calendar) · /month not based on each other: is not a 28 day cycle and 29.5306 days cannot be neatly subdivided into weekly blocks of complete days, 12 months is about 11 days shorter than tropical year) E. Week: Jewish cosmology vs. ancient astrology · Jewish: seven days of creation; Hebrew word for week shavu’a interchangeable with shabbath which came from verb sh-b-th which means to cease from labor; practice of working 6 days and resting on seventh “practiced by God when creating universe” but probably most likely a product of Exile period in Jewish (586 BC) · Need for continuous week for “settled” life and social organization continuity could not be interrupted by such natural phenomena as the lunar cycle; the break from relying of a multiple of a day as opposed to a approximation of a lunar month was a huge step; the first to do so was ancient Egyptians; · Seven of ancient astronomy: Saturn, Sun, Moon, Mars, , Jupiter, and ; moved regularly across sky o Greek verb “planasthai” to wander o Original Babylonian/Mesopotamia reason to develop astronomy tables was to design horoscopes, but there were no “day of Moon” o Astronomical week came after Alexander the Great’s conquest of western Asia (2nd century BC) o Astronomical practice to arrange in order: Saturn-Jupiter-Mars-Sun-Venus-Mercury-Moon, mathematical practice to subdivide daily cycle into 24 integrated, order due to geocentric distances (Saturn and Moon being farthest and nearest, incorrect), sequence of planetary days consists on planetary leaps (skipping two planets each time) · Spread of seven day week: growing popularity of astrology, church integrated Jewish and astrological together o Sunday first day of week, “Lord’s day”, Early Christians were Jewish and observed both Sunday and Saturday until identity as both Christian and Jew was difficult to maintain, at this times social contrasts within became established, however, chose to keep seven day week even though could have used Roman’s Eight day week o Islam spread seven day cycle to east coast of Africa, Sudan, Central Asia, North and West Africa, Mohammed’s choice of Friday for public worship may have been to separate from Jewish Saturday and Christian Sunday · Ancient Greek split month into 3-10 day weeks, Romans had market week of 8 days with 1 day of rest and celebration, French: 10 days in a week, Maya have 13 and 20 day weeks · USSR: tried a five day week (1929) and a six day week (1932), restored to seven day by 1940 F. Day · Subdivision of 24 hours was Egyptian mathematical practice · First did not have hands, minute was not important until Industrial revolution · Daylight Saving (NOT savings) Time o Save energy, enjoy light later on summer evenings o USA 1925(most): begins at 2 am on the first Sunday in April, ends at 2 am on last Sunday in October change from 1:59 AM to 3:00 AM, EU (1996) begins at 1am according the () last Sunday in March and ends last Sunday in October, first conceived by Benjamin Franklin in 1784, seriously considered in 1907 by William Willett by advancing clocks 20 four Sunday in April and turning them back by 20 minutes four Sundays in October to take advantage of the daylight, he lobbied for a year and died before it changed Major Calendars A. Early Greek (between 700 BC - 300 AD) · Astronomy: did not include physics, only sought to describe the heavens with mathematics, · Many Calendars: the day was first natural period of time, also periodic phases of the moon, but approximate length of year was necessary for agriculture o 12 months of 30 days, moon rapidly gets out of phase o By 600 BC: a year was 6 full months of 30 days and 6 empty months of 29 days o Solon (600 BC) based on two year cycle 13 months of 30 days and 12 months of 29 days (378 days/2 = 369 days) · Pythagoreans (500 BC): earth was a sphere, orbit of moon inclined to equator of earth, venues as evening star was same as morning star o Oenopides (450 BC) discovered made a 24 angle with equator (refined by Eratosthenes 250 BC); 59 year calendar cycle with 730 months o Philolaus: 59 year cycle of 729 months: 729 = 27squared, 27 was number for moon and 9cubed since 9 was number for moon · Meton (432 BC) calendar based on 19 year cycle (similar to one we will talk about from Babylonian), also made observations of to determine length of tropical year · Spherical geomtry (Autoycus) was next major development to aid in astronomy (330 BC) · Euclid worked on and wrote Phaenomena: elementary astronomy and times when stars in certain positions rise and set · 260 BC Alexandria: accuracy increases with acitve measuring, equatorial and ecliptic systems originate · Aristarchus (310BC – 230BC): ratio of distances to the moon and sun showed sun much further away , sun much larger than earth which may have led to the heliocentric theory (found little favor with Greeks) · Archimedes (287 BC-212 BC): designed planetarium. Measured diameter of sun · Eratosthenes (276 BC-194 BC): size of earth , accurately measured ecliptic, improved calendar B. Egyptian · Because of difficulties to align and lunar calendar – Egyptians used three · First strictly lunar calendar, but this failed to predict flooding of Nile accurately: regulated lunar calendar by means of the guidance of a sidereal calendar. · ‘Discovered’ “Dog Star” whose “rising” corresponded to true solar year, only 12 minutes shorter, brightest “fixed” star · 8th century B.C.E., the Egyptian pharaoh’s primary advisor, the Vizier was to report when Sirius was absent from sky for approximately two weeks. This first appearance of Sirius in the pre-dawn sky was used to start the so-called Egyptian "lunar" , this calendar was then not only based on a astronomical , but a geophysical event as well · Second Calendar was based on a civil year of 365 days, three each with four months of 30 days each, five intercalary days were added at its end, served government and administration o Three seasons: Inundation, when the Nile flooded; Going Forth, planting when Nile was normal bed; and Deficiency, time of low water and harvest, months number in order of (first month of harvest) · Discrepancies between the two calendars; since first lunar was based on rising of Sirius, seasons were at same time every year, the civil calendar would fall ¼ of a day each year and be behind one day in four years (after 1460 years it would realign, 4*365), led to a second lunar calendar based on civil, not on sighting of Sirius, used to determine religious celebrations and duties, every time a lunar year started before a civil year, a month was added (every 25 years), original lunar calendar still maintained for agriculture and original civil calendar maintained for business · Hours were unequal, daylight being divided into 12 parts, and the night likewise; the of these parts varied with the seasons. Both water clocks and were constructed with notations to indicate the hours for the different months and seasons of the year. C. Babylonian · 29, 30 day months, extra month to accommodate three time every eight years at irregular intervals, if need of further adjustment king would periodically order the insertion of an additional extra month into the calendar. (why the adjustment: try to keep lunar /solar year aligned) · 300 BC began more reliable calendar under Persian Kings, 19 years and 235 months: month added during years 3, 6, 8, 11, 14, 17, and 19 of the cycle. (19*12 = 228 + 7 =235) · Month names were Nisanu, Ayaru, Simanu, Du'uzu, Abu, Ululu, Tashritu, Arakhsamna, Kislimu, Tebetu, Shabatu, Adaru. The month Adaru II was intercalated six times within the 19-year cycle but never in the year that was 17th of the cycle, when Ululu II was inserted, new months began when new moon was visible · Day began at sunset, used water clocks and sundials counting hours · Influenced Jewish Calendar (Babylonian exile in 6th century BCE) D. Mayan: traced back to 1000 BC, classical period 300-900 AD different than Asian or Europe approach · Three dating systems: long count, tzolkin, haab; Typical : 12.18.16.2.6, 3 Cimi 4 Zotz · 12.18.16.2.6: Long count: mixed base 20/base 18 representation of a number representing the number of days since the start of the Mayan era dating back to August 12, 3013 BC (start of Mayan era) based on cycles of 360 days (18x20 =360). Basic unit is kin (day) which is the last component in date: 20 kin = 1 uinal; 360 days = 18 uinal = 1 tun (1 year); 20 tun = 1 katun (20 years); 120 katun = 1 baktun (394 years), etc. The alatun = 23,040,000,000 days (63 million years) is longest named time period in any calendar; · First day written as 13.0.0.0.0 since batun (first component) are numbered 1-13 ~3114BC may have been Mayan idea of creation of world and depending equivalence to our calendar the 13.0.0.0.0 will occur on either 21 or 23 December, 2012 (or 2273) · 3 Cimi: Tzolkin date: divine calendar, 260 day cycle: related to the Venus, considered to be the sacred calendar (13*20); combination of two “week” lengths; numbered week of 13 days numbered 1-13, The named days (0-19) is a cycle of divinities, the named week and the basic unit in long count (kin) corresponds; however the 13.0.0.0.0 corresponds to 4 Ahau and the years of Tzolkin calendar are not counted · Zotz: Haab component; civil calendar, 18 months of 20 days each plus five extra days (known as Uayeb; the five days which were also represented by a hieroglyph meaning chaos; bad luck days “days without names”, “days without souls”, unlucky to be born during these days of prayer and mourning, extinguished fires, didn’t eat hot foods; the years of Haab are not counted, 13.0.0.0.0 corresponds to 58 Cumku · Calendar Round: 18,980 days before the Tzolkin and Haab year repeat same day · Mayan astronomers claimed 149 lunar months equal 4400 days, estimation of 29.5302 days compared to today’s accepted value of 29.53059 days; were able to make accurate predictions without trigonometry or fractions (that we are aware of) For example: month names associated with seasons; Yaxkin means new or strong sun and at the beginning of Long count, 1 Yaxkin was the day after the winter (when sun starts to shine longer and higher) · Adopted by Aztecs E. Islamic · Lunar calendar based on the Qur'an and its proper observance is a sacred duty for Muslims, official calendar in countries around the Gulf; other Muslim countries use Gregorian calendar for civil use and Islamic for religious purposes · Twelve months which start when lunar crescent is first seen by human eye after a new moon; new can be predicted but visibility of crescent is hard to predict (weather, atmosphere, location of observer), also some rely on local sighting and others rely on sighting by authorities somewhere in Muslim world · Calendars are printed for planning purposes, but based on estimates of the visibility of the lunar crescent, actual month may start a day earlier or later than predicted in the printed calendar · Some sources say odd numbered months have 30 days and even have 29 days with an extra day added in leap years, which gives a month average of 29.53056 which is close to synodic month of 29.53059 · Mohammed’s emigration to Medina in AD 622, AH 1 (Anno Hegirae); 2003 AD = 1424 AH; 2003-622=1381 years in Christian calendar, 1423 years have passed in · (Since 1999) Suadi Arabia bases calendar on astronomical moon; if on the 29th, the sun sets before the moon – next day will be new month, but if moon sets first – it will be the 30th of the current month F. Jewish (today’s originating CE 359 by Sanhedrin president Hillil II), taken from Babylonian · Used for religious proposes by Jews all over world, official calendar of Israel · lunisolar calendar, addition of month to 19 year cycle to compensate · Ordinary year with 12 months has 353 (deficient), 354 (regular), or 355 (complete) days, leap year has 13 months; months start on the day of a new moon (approximate when first crescent is visible); leap years occur if year mod 19 = 0, 3, 6, 8, 11, 14, or 17 · Years are counted since creation of world, 3761 BCE, AM 1 (), AM 1 calculated by adding up ages of people in the Bible, New Year’s Day comes from one of four days of which only 1 Tishari (Rosh HaShanah) and 15 Shevat are celebrated today o First day of Calendary Year: 1 Tishri determines type of year by using five rules o The New Year starts on the day of the new moon that occurs about 354 days (or 384 days if the previous year was a leap year) after 1 Tishri of the previous year.

§ If the new moon occurs after noon on that day, delay the New Year by one day. (Because in that case the new crescent moon will not be visible until the next day.)

§ If this would cause the New Year to start on a Sunday, Wednesday, or Friday, delay it by one day.

§ If two consecutive years start 356 days apart (an illegal year length), delay the start of the first year by two days.

§ If two consecutive years start 382 days apart (an illegal year length), delay the start of the second year by one day.

§ These rules are such that religious observances do not interfere with each other

§ “First month” is Nissan, when Passover occurs

§ Day begins at sunset or when three medium stars should be visible depending on religious circumstances G. French (1792) · French tried to start a (Republican Year) that called for 10 day weeks, abandoned after Napoleon came into power (1806) o Each month divided into three “” of 10 days (unpopular: 9 work + 1 rest compared to Gregorian 6 work + 1 rest); days named: Primidi, Duodi, Tridi, Quartidi, Quintidi, Sextidi, Septidi, Octidi, Nonidi, Decadi. o 5 or six additional days followed that were celebration days o Each year was supposed to start on autumnal equinox, counted as one from 22 September, 1792 · New : day was ten hours of hundred minutes of hundred (100,00seconds per day)(84,600 seconds now so…?)

H. Chinese: origins in 14th century B.C.E. · Use Gregorian calendar for civil purposes · Uses a lunisolar calendar to determine festivals (similar to Jewish Calendar); ordinary year with 12 months and 353, 354, or 355 days and leap year with 383, 384, or 385 days, 60 year cycle · Determination of year o Determine dates for new moon (completely black) this is first day of new month, if there are 13 new moons between 11th month in one year to 11th month of next year, insert a leap month o Determine when sun’s is a multiple of 30 degrees (Principal Terms) 0 at Vernal Equinox, 90 at , 180 at Autumnal Equinox, 270 at Winter Solstice (between moon and sun) o Not counted in infinite sequence, years have names that are repeated 60 years (before 1911 revolution: counted since accession of emperor), two components; first is “celestial stem” (used for approximately 2000 years, since 2637 BCE); Current 60 year cycle started 2 Feb 1984 · Legend says: Emperor Huangdi invented the calendar in 2637 B.C.E · Early : Bureau of Astronomy made astronomical observations, surviving astronomical records inscribed in oracle bones date back to Shang Dynasty (14th century BCE); 19 year () and 76 year (Callipic cycle) cycles, beginning of year occurred at a new moon near winter solstice I. Indian · National Calendar of India is lunisolar calendar, coincides with Gregorian Calendar, Months named after traditional Indian months · Years counted from Saka Era; 1 Saka begins with with vernal equinox CE 79, reformed calendar began Saka Era 1879, Caitra 1 = CE 1957 March 22, years with 365 and leap years of 366 (intercalary day added to end of Caitra); leap year if 78 + Saka year is evenly divisible by 4 unless the sum is a multiple of 100. If is a multiple of 400, then it is a leap year · Indian religious calendar is lunisolar; o Solar months: Begins with Vaisakha where longitude of sun is 23 deg 15 min. Shortest is when earth is in perihelion , longest months during aphelion; o Coinciding lunar month with same name as solar month that lunar month begins, if two new moons in one solar month, both lunar months will bear name of the same solar month, but first will have prefix adhika (intercalary) and the year will have 13 lunar months which occur every two or three years o In a year where a short solar month doesn’t have a New Moon (near perihelion), the month is skipped (Ksaya) and a month in the first half will have two New Moons (happens anywhere between 19 and 141 years) · Before Reform, about 30 calendars used to set religious festivals for Hindus, Jainists, and Buddhists, and for civil use; based on common principles with local characteristics and customs · Ancient calendars used lunisolar calendar with intercalated months, five-year lunisolar calendar coordinated solar years and synodic and sidereal lunar months J. Current: Gregorian (or Christian) · Roman Calendar first · Mess: 1 March and consisted of only 304 days or 10 months (Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November, and December). Followed by an unnamed and unnumbered winter period. · Roman king Numa Pompilius (c. 715-673 B.C.E.) allegedly introduced February and January (in that order) between December and March, increasing the length of the year to 354 or 355 days. In 450 B.C.E., February was moved to its current position between January and March. · To make up for the lack of days in a year, an extra month, Intercalaris or Mercedonius was introduced 8 year period the length of the years were: · 1: 12 months or 355 days 2: 13 months or 377 days 3: 12 months or 355 days 4: 13 months or 378 days 5: 12 months or 355 days 6: 13 months or 377 days 7: 12 months or 355 days 8: 13 months or 378 days · Total of 2930 days corresponding to a year of 366 1/4 days; too long, so 7 days were later dropped from the 8th year, yielding 365.375 days per year · Julian (45 B.C.E): Julius Cesar created to eliminate chaos · 45 BCE had 445 days and is called “year of confusion” · Julian calendar year consisted of 365.25 days, a little too long since the correct value for the tropical year is 365.242199 days · Error of 11 min. 14 sec. per year amounted to almost 1 ½ days in 20 years; 7 days in 1,000 years. The problem was placed before church councils, but no action was taken because the astronomers who were consulted didn't have enough precise information concerning the exact value of the tropical year. · Gregorian: switched to in 1582 when 10 day difference became intolerable. Pope Gregory XIII (hence Gregorian) decreed the day after October 4, 1582 would be October 15, 1582 (France, Spain, Portugal, and Italy complied, Various Catholic German countries, Belgium, the Netherlands, and Switzerland followed within a year or two, Hungary in 1587. rest of Europe didn’t follow suit for more than century · Mandated leap year every four years except those divisible by 100, but divisible by 400 4. Timekeeping A. Types of Clocks · Water clocks were the first timekeeping device that did not rely on celestial bodies o 1500 BCE oldest found in tomb of Amenhotep (Egyptian pharaoh) o 325 BCE Greek used stone vessels with sloping sides called clepsydras “water thieves”, markings showed passage of time, still in use in North Africa in 20th century o More complex in 100 BCE – 500 CE regulate pressure, fancier displays, rang bells gongs, etc. · Sun: Obelisks (350 BCE) a sort of that also showed the year’s longest and shortest days o (1500 BCE) Egyptian shadow clock or sundial: possibly the first portable timepiece, divided a sunlit day into 10 parts plus two "twilight hours" in the morning and evening. When the long stem with 5 variably spaced marks was oriented east and west in the morning, an elevated crossbar on the east end cast a moving shadow over the marks. At noon, the device was turned in the opposite direction to measure the afternoon "hours." · Pendulum: (1656 CE) , Dutch scientist, first that was regulated by a mechanism with a "natural" period of oscillation. (Galileo Galilei is credited with inventing the pendulum-clock concept, and he studied the motion of the pendulum as early as 1582. He even sketched out a design for a pendulum clock, but he never actually constructed one before his death in 1642.) Huygens' early pendulum clock had an error of less than 1 minute a day, the first time such accuracy had been achieved. His later refinements reduced his clock's error to less than 10 seconds a day. · Quartz (1920’s) generates an electric field · 1949 (NIST) first based on ammonia B. Sundials · Measure time as it is, noon is when sun is highest in sky “sun time” is from noon one day to noon the next day, may vary from 23 hr 59 min 40 sec (September) to 24 hr 20 seconds (December), Clock time is based 24 hours in a day · Sun casts a show which is interpreted. The shadow will differ since the sun is not always in the same place o Earth makes a full rotation every 23 hours 56 minutes 4 seconds o Path of sun in sky (ecliptic) 24hr 60min F 1I · : ´ ´G J°= 1min 360° 1hr H 4K C. Need for standard time · World time transmission started in 1852 · Greenwich Mean Time o Reputation and correctness of Greenwich Observatory’s publications of navigational data, benefit from single “prime” meridian, resolved in conference in Washington in 1884 o Zones: 24 hr day, 360 degrees of longitude, the sun travels roughly 15 degrees (longitudinally) in one o Official in U.S. by Act of Congress in March 1918

Sources: Calendars: http://webexhibits.org/calendars/calendar.html Sundials: http://www.sundials.co.uk/ Clocks/Time: http://physics.nist.gov/GenInt/Time/atomic.html Ancient Greek Astronomy: http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Greek_astronomy.html Zerubavel, Eviatar. “The Seven Day Circle: The history and Meaning of the Week” (Free Press) Mankiewicz, Richard. “The Story of Mathematics” (Princeton Press) Aveni, Anthony. “Empires of Time” (Univ. Press of Colorado) Greek Astronomy:

The development of the Calendar and Clock

Cassidy Schremser Spring, 2004 714