Astronomical year numbering

Astronomical year numbering is based on AD/CE year numbering, but follows normal decimal integer numbering more strictly. Thus, it has a year 0; the years before that are designated with negative numbers and the years after that are designated with positive numbers.[1] Astronomers use the Julian calendar for years before 1582, including the year 0, and the Gregorian calendar for years after 1582, as exemplified by Jacques Cassini (1740),[2] Simon Newcomb (1898)[3] and Fred Espenak (2007).[4]

The prefix AD and the suffixes CE, BC or BCE (Common Era, Before Christ or Before Common Era) are dropped.[1] The year 1 BC/BCE is numbered 0, the year 2 BC is numbered −1, and in general the year n BC/BCE is numbered "−(n − 1)"[1] (a negative number equal to 1 − n). The numbers of AD/CE years are not changed and are written with either no sign or a positive sign; thus in general n AD/CE is simply n or +n.[1] For normal calculation a number zero is often needed, here most notably when calculating the number of years in a period that spans the epoch; the end years need only be subtracted from each other.

The system is so named due to its use in astronomy. Few other disciplines outside history deal with the time before year 1, some exceptions being dendrochronology, archaeology and geology, the latter two of which use 'years before the present'. Although the absolute numerical values of astronomical and historical years only differ by one before year 1, this difference is critical when calculating astronomical events like eclipses or planetary conjunctions to determine when historical events which mention them occurred.

Year zero usage

In his Rudolphine Tables (1627), Johannes Kepler used a prototype of year zero which he labeled Christi (Christ's) between years labeled Ante Christum (Before Christ) and Post Christum (After Christ) on the mean motion tables for the Sun, Moon, Saturn, Jupiter, Mars, Venus and Mercury.[5] In 1702, the French astronomer Philippe de la Hire used a year he labeled Christum 0 at the end of years labeled ante Christum (BC), and immediately before years labeled post Christum (AD) on the mean motion pages in his Tabulæ Astronomicæ, thus adding the designation 0 to Kepler's Christi.[6] Finally, in 1740 the French astronomer Jacques Cassini (Cassini II), who is traditionally credited with the invention of year zero,[7][8][9] completed the transition in his Tables astronomiques, simply labeling this year 0, which he placed at the end of Julian years labeled avant Jesus-Christ (before Jesus Christ or BC), and immediately before Julian years labeled après Jesus-Christ (after Jesus Christ or AD).[2]

Cassini gave the following reasons for using a year 0:[10]

The year 0 is that in which one supposes that Jesus Christ was born, which several chronologists mark 1 before the birth of Jesus Christ and which we marked 0, so that the sum of the years before and after Jesus Christ gives the interval which is between these years, and where numbers divisible by 4 mark the leap years as so many before or after Jesus Christ.

— Jacques Cassini

Fred Espanak of NASA lists 50 phases of the moon within year 0, showing that it is a full year, not an instant in time.[4] Jean Meeus gives the following explanation:[11]

There is a disagreement between astronomers and historians about how to count the years preceding year 1. In [Astronomical Algorithms], the 'B.C.' years are counted astronomically. Thus, the year before the year +1 is the year zero, and the year preceding the latter is the year −1. The year which historians call 585 B.C. is actually the year −584. The astronomical counting of the negative years is the only one suitable for arithmetical purpose. For example, in the historical practice of counting, the rule of divisibility by 4 revealing Julian leap-years no longer exists; these years are, indeed, 1, 5, 9, 13, ... B.C. In the astronomical sequence, however, these leap-years are called 0, −4, −8, −12, ..., and the rule of divisibility by 4 subsists.

— Jean Meeus, Astronomical Algorithms

Signed years without year 0

Although he used the usual French terms "avant J.-C." (before Jesus Christ) and "après J.-C." (after Jesus Christ) to label years elsewhere in his book, the Byzantine historian Venance Grumel used negative years (identified by a minus sign, −) to label BC years and unsigned positive years to label AD years in a table. He did so possibly to save space and put no year 0 between them.[12]

Version 1.0 of the XML Schema language, often used to describe data interchanged between computers in XML, includes built-in primitive datatypes date and dateTime. Although these are defined in terms of ISO 8601 which uses the proleptic Gregorian calendar and therefore should include a year 0, the XML Schema specification states that there is no year zero. Version 1.1 of the defining recommendation realigned the specification with ISO 8601 by including a year zero, despite the problems arising from the lack of backward compatibility.[13]

See also


  1. ^ a b c d Espenak, Fred. "Year Dating Conventions". NASA Eclipse Web Site. NASA. Archived from the original on 8 February 2009. Retrieved 19 February 2009.
  2. ^ a b Jacques Cassini, Tables Astronomiques (1740), Explication et Usage pp. 5 (PA5), 7 (PA7), Tables pp. 10 (RA1-PA10), 22 (RA1-PA22), 63 (RA1-PA63), 77 (RA1-PA77), 91 (RA1-PA91), 105 (RA1-PA105), 119 (RA1-PA119). (in French)
  3. ^ Simon Newcomb, "Tables of the Motion of the Earth on its Axis and Around the Sun" in Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac, Volume VI: Tables of the Four Inner Planets, (United States Naval Observatory, 1898), pp. 27 & 34–35.
  4. ^ a b Fred Espenak, Phases of the Moon: −99 to 0 (100 to 1 BCE) Archived 5 June 2009 at the Wayback Machine NASA Eclipse web site
  5. ^ Johannes Kepler, Tabulae Rudolphinae (1627) Pars secunda, 42 (Zu Seite 191), 48 (197), 54 (203), 60 (209), 66 (215), 72 (221), 78 (227). (Latin)
  6. ^ Tabulae Astronomicae - Philippo de la Hire (1702), Tabulæ 15, 21, 39, 47, 55, 63, 71; Usus tabularum 4. (Latin)
  7. ^ Robert Kaplan, The nothing that is (Oxford: Oxford University Press, 2000) 103.
  8. ^ Dick Teresi, "Zero", The Atlantic, July 1997 (see under Calendars and the Cosmos).
  9. ^ L. E. Doggett, "Calendars" Archived 10 February 2012 at the Wayback Machine, Explanatory Supplement to the Astronomical Almanac, ed. P. Kenneth Seidelmann, (Sausalito, California: University Science Books, 1992/2005) 579.
  10. ^ Jacques Cassini, Tables Astronomiques, Explication et Usage 5, translated by Wikipedia from the French:
    "L'année 0 est celle dans laquelle on suppose qu'est né J. C. que plusieurs Chronologistes marquent 1 avant la naissance de J. C. & que nous avons marquée 0, afin que la somme des années avant & après J. C. donne l'intervalle qui est entre ces années, & que les nombres disibles par 4 marquent les années bissextiles tant avant qu'après J. C."
  11. ^ Jean Meeus, Astronomical Algorithms (Richmod, Virginia: Willmann-Bell, 1991) 60.
  12. ^ V. Grumel, La chronologie (Paris: Presses Universitaires de France, 1958) 30. (in French)
  13. ^ Biron, P.V. & Malhotra, A. (Eds.). (28 October 2004). XML Schema Part 2: Datatypes (2nd ed.). World Wide Web Consortium.
1st century BC

The 1st century BC, also known as the last century BC, started on the first day of 100 BC and ended on the last day of 1 BC. The AD/BC notation does not use a year zero; however, astronomical year numbering does use a zero, as well as a minus sign, so "2 BC" is equal to "year –1". This is the 100th century in the Holocene calendar; it spans the years 9,901 to 10,000. 1st century AD (Anno Domini) follows.

In the course of the century all the remaining independent lands surrounding the Mediterranean were steadily brought under Roman control, being ruled either directly under governors or through puppet kings appointed by Rome. The Roman state itself was plunged into civil war several times, finally resulting in the marginalization of its 500-year-old republic, and the embodiment of total state power in a single man—the emperor.

The internal turbulence that plagued Rome at this time can be seen as the death throes of the Roman Republic, as it finally gave way to the autocratic ambitions of powerful men like Sulla, Julius Caesar, Mark Antony and Octavian. Octavian's ascension to total power as the emperor Augustus is considered to mark the point in history where the Roman Republic ends and the Roman Empire begins. Some scholars refer to this event as the Roman Revolution. It is believed that the birth of Jesus, the central figure of Christianity took place at the close of this century.

In the eastern mainland, the Han Dynasty began to decline and the court of China was in chaos in the latter half of this century. Trapped in a difficult situation, the Xiongnu had to begin emigration to the west or attach themselves to the Han.

Anno Domini

The terms anno Domini (AD) and before Christ (BC) are used to label or number years in the Julian and Gregorian calendars. The term anno Domini is Medieval Latin and means "in the year of the Lord", but is often presented using "our Lord" instead of "the Lord", taken from the full original phrase "anno Domini nostri Jesu Christi", which translates to "in the year of our Lord Jesus Christ".

This calendar era is based on the traditionally reckoned year of the conception or birth of Jesus of Nazareth, with AD counting years from the start of this epoch, and BC denoting years before the start of the era. There is no year zero in this scheme, so the year AD 1 immediately follows the year 1 BC. This dating system was devised in 525 by Dionysius Exiguus of Scythia Minor, but was not widely used until after 800.The Gregorian calendar is the most widely used calendar in the world today. For decades, it has been the unofficial global standard, adopted in the pragmatic interests of international communication, transportation, and commercial integration, and recognized by international institutions such as the United Nations.Traditionally, English followed Latin usage by placing the "AD" abbreviation before the year number. However, BC is placed after the year number (for example: AD 2019, but 68 BC), which also preserves syntactic order. The abbreviation is also widely used after the number of a century or millennium, as in "fourth century AD" or "second millennium AD" (although conservative usage formerly rejected such expressions). Because BC is the English abbreviation for Before Christ, it is sometimes incorrectly concluded that AD means After Death, i.e., after the death of Jesus. However, this would mean that the approximate 33 years commonly associated with the life of Jesus would neither be included in the BC nor the AD time scales.Terminology that is viewed by some as being more neutral and inclusive of non-Christian people is to call this the Current or Common Era (abbreviated as CE), with the preceding years referred to as Before the Common or Current Era (BCE). Astronomical year numbering and ISO 8601 avoid words or abbreviations related to Christianity, but use the same numbers for AD years.


A century (from the Latin centum, meaning one hundred; abbreviated c.) is a period of 100 years. Centuries are numbered ordinally in English and many other languages.

A centenary is a hundredth anniversary, or a celebration of this, typically the remembrance of an event which took place a hundred years earlier.


Chronostratigraphy is the branch of stratigraphy that studies the age of rock strata in relation to time.

The ultimate aim of chronostratigraphy is to arrange the sequence of deposition and the time of deposition of all rocks within a geological region, and eventually, the entire geologic record of the Earth.

The standard stratigraphic nomenclature is a chronostratigraphic system based on palaeontological intervals of time defined by recognised fossil assemblages (biostratigraphy). The aim of chronostratigraphy is to give a meaningful age date to these fossil assemblage intervals and interfaces.


Circa (from Latin, meaning 'around, about') – frequently abbreviated c., ca. or ca and less frequently circ. or cca. – signifies "approximately" in several European languages and as a loanword in English, usually in reference to a date. Circa is widely used in historical writing when the dates of events are not accurately known.

When used in date ranges, circa is applied before each approximate date, while dates without circa immediately preceding them are generally assumed to be known with certainty.


1732–1799: Both years are known precisely.

c. 1732 – 1799: The beginning year is approximate; the end year is known precisely.

1732 – c. 1799: The beginning year is known precisely ; the end year is approximate.

c. 1732 – c. 1799: Both years are approximate.

Conversion between Julian and Gregorian calendars

The tables below list equivalent dates in the Julian and Gregorian calendars. Years are given in astronomical year numbering.

Era (geology)

A geologic era is a subdivision of geologic time that divides an eon into smaller units of time. The Phanerozoic Eon is divided into three such time frames: the Paleozoic, Mesozoic, and Cenozoic (meaning "old life", "middle life" and "recent life") that represent the major stages in the macroscopic fossil record. These eras are separated by catastrophic extinction boundaries, the P-T boundary between the Paleozoic and the Mesozoic and the K-Pg boundary between the Mesozoic and the Cenozoic. There is evidence that catastrophic meteorite impacts played a role in demarcating the differences between the eras.

The Hadean, Archean and Proterozoic eons were as a whole formerly called the Precambrian. This covered the four billion years of Earth history prior to the appearance of hard-shelled animals. More recently, however, the Archean and Proterozoic eons have been subdivided into eras of their own.

Geologic eras are further subdivided into geologic periods, although the Archean eras have yet to be subdivided in this way.


Floruit (UK: , US: ), abbreviated fl. (or occasionally flor.), Latin for "he/she flourished", denotes a date or period during which a person was known to have been alive or active. In English, the word may also be used as a noun indicating the time when someone flourished.

Fluorine absorption dating

Fluorine absorption dating is a method used to determine the amount of time an object has been underground.

Fluorine absorption dating can be carried out based on the fact that groundwater contains fluoride ions. Items such as bone that are in the soil will absorb fluoride from the groundwater over time. From the amount of absorbed fluoride in the item, the time that the item has been in the soil can be estimated.

Many instances of this dating method compare the amount of fluorine and uranium in the bones to nitrogen dating to create more accurate estimation of date. Older bones have more fluorine and uranium and less nitrogen. But because decomposition happens at different speeds in different places, it's not possible to compare bones from different sites.

As not all objects absorb fluorine at the same rate, this also undermines the accuracy of such a dating technique. Although this can be compensated for by accommodating for the rate of absorption in calculations, such an accommodation tends to have a rather large margin of error.

In 1953 this test was used to easily identify that the 'Piltdown Man' was forged, almost 50 years after it was originally 'unearthed'.

Geologic Calendar

The Geologic Calendar is a scale in which the geological lifetime of the earth is mapped onto a calendrical year; that is to say, the day one of the earth took place on a geologic January 1 at precisely midnight, and today's date and time is December 31 at midnight. On this calendar, the inferred appearance of the first living single-celled organisms, prokaryotes, occurred on a geologic February 25 around 12:30pm to 1:07pm, dinosaurs first appeared on December 13, the first flower plants on December 22 and the first primates on December 28 at about 9:43pm. The first Anatomically modern humans did not arrive until around 11:48 p.m. on New Year's Eve, and all of human history since the end of the last ice-age occurred in the last 82.2 seconds before midnight of the new year.

Geological period

A geological period is one of the several subdivisions of geologic time enabling cross-referencing of rocks and geologic events from place to place.

These periods form elements of a hierarchy of divisions into which geologists have split the Earth's history.

Eons and eras are larger subdivisions than periods while periods themselves may be divided into epochs and ages.

The rocks formed during a period belong to a stratigraphic unit called a system.


The Haabʼ (Mayan pronunciation: [haːɓ]) is part of the Maya calendric system. It was a 365-day calendar used by many of the pre-Columbian cultures of Mesoamerica.


Limmu was an Assyrian eponym. At the beginning of the reign of an Assyrian king, the limmu, an appointed royal official, would preside over the New Year festival at the capital. Each year a new limmu would be chosen. Although picked by lot, there was most likely a limited group, such as the men of the most prominent families or perhaps members of the city assembly. The Assyrians used the name of the limmu for that year to designate the year on official documents. Lists of limmus have been found accounting for every year between 892 BC and 648 BC.

During the Old Assyrian period, the king himself was never the limmum, as it was called in their language. In the Middle Assyrian and Neo-Assyrian periods, however, the king could take this office.

Nitrogen dating

Nitrogen dating is a form of relative dating which relies on the reliable breakdown and release of amino acids from bone samples to estimate the age of the object. For human bones, the assumption of about 5% nitrogen in the bone, mostly in the form of collogen, allows fairly consistent dating techniques.Compared to other dating techniques, Nitrogen dating can be unreliable because leaching from bone is dependent on temperature, soil pH, ground water, and the presence of microorganism that digest nitrogen rich elements, like collagen. Some studies compare nitrogen dating results with dating results from methods like fluorine absorption dating to create more accurate estimates. Though some situations, like thin porous bones might more rapidly change the dating created by multiple methods.

Proleptic Gregorian calendar

The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to dates preceding its official introduction in 1582. In countries that adopted the Gregorian calendar later, dates occurring in the interim (between 1582 and the local adoption) are sometimes "Gregorianized" as well. For example, George Washington was born on February 11, 1731 (Old Style), as Great Britain and its possessions were using the Julian calendar with English years starting on March 25 until September 1752. After the switch, that day became February 22, 1732, which is the date commonly given as Washington's birthday.

Proleptic Julian calendar

The proleptic Julian calendar is produced by extending the Julian calendar backwards to dates preceding AD 8 when the quadrennial leap year stabilized. The leap years that were actually observed between the implementation of the Julian calendar in 45 BC and AD 8 were erratic: see the Julian calendar article for details.

A calendar obtained by extension earlier in time than its invention or implementation is called the "proleptic" version of the calendar. Likewise, the proleptic Gregorian calendar is occasionally used to specify dates before the introduction of the Gregorian calendar in 1582. Because the Julian calendar was used before that time, one must explicitly state that a given quoted date is based on the proleptic Gregorian calendar if that is the case.

Note that the Julian calendar itself was introduced by Julius Caesar, and as such is older than the introduction of the Anno Domini era (or the "Common Era", counting years since the birth of Christ as calculated by Dionysus Exiguus in the 6th century, and widely used in medieval European annals since about the 8th century, notably by Bede). The proleptic Julian calendar uses Anno Domini throughout, including for dates of Late Antiquity when the Julian calendar was in use but Anno Domini wasn't, and for times predating the introduction of the Julian calendar.

Years are given cardinal numbers, using inclusive counting (AD 1 is the first year of the Anno Domini era, immediately preceded by 1 BC, the first year preceding the Anno Domini era, there is no "zeroth" year).

Thus, the year 1 BC of the proleptic Julian calendar is a leap year.

This is to be distinguished from the "astronomical year numbering", introduced in 1740 by French astronomer Jacques Cassini, which considers each New Year an integer on a time axis, with year 0 corresponding to 1 BC, and "year −1" corresponding to 2 BC, so that in this system, Julian leap years have a number divisible by four.

The determination of leap years in the proleptic Julian calendar (in either numbering) is distinct from the question of which years were historically considered leap years during the Roman era, due to the leap year error: Between 45 BC and AD 8, the leap day was somewhat unsystematic. Thus there is no simple way to find an equivalent in the proleptic Julian calendar of a date quoted using either the Roman pre-Julian calendar or the Julian calendar before AD 8. The year 46 BC itself is a special case, because of the historical introduction of the Julian calendar in that year, it was allotted 445 days. Before then, the Roman Republican calendar used a system of intercalary months rather than leap days.

Solar calendar

A solar calendar is a calendar whose dates indicate the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as standard in the world, is an example of a solar calendar.

The main other type of calendar is a lunar calendar, whose months correspond to cycles of Moon phases. The months of the Gregorian calendar do not correspond to cycles of Moon phase.


A stratotype or type section is a geological term that names the physical location or outcrop of a particular reference exposure of a stratigraphic sequence or stratigraphic boundary. If the stratigraphic unit is layered, it is called a stratotype, whereas the standard of reference for unlayered rocks is the type locality.

Year zero

Year zero does not exist in the anno Domini system usually used to number years in the Gregorian calendar and in its predecessor, the Julian calendar. In this system, the year 1 BC is followed by AD 1. However, there is a year zero in astronomical year numbering (where it coincides with the Julian year 1 BC) and in ISO 8601:2004 (where it coincides with the Gregorian year 1 BC) as well as in all Buddhist and Hindu calendars.

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