Astronomical year numbering

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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]

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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.

Usage of the year zero

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 the year zero

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 (1890-1967) used negative years (identified by a minus sign, −) to label BC years and unsigned positive years to label AD years in a table. He may have done so to save space and he 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]

Related Research Articles

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".

Common Era (CE) is one of the year notations used for the Gregorian calendar, the world's most widely used calendar era. Before the Common Era (BCE) is the era before CE. BCE and CE are alternatives to the Dionysian BC and AD notations, respectively. The Dionysian era distinguishes eras using the notations BC and AD. The two notation systems are numerically equivalent: "2021 CE" and "AD 2021" each describe the current year; "400 BCE" and "400 BC" are each the same year. The Gregorian calendar is used throughout the world today, and is an international standard for civil calendars.

The Julian calendar, proposed by Julius Caesar in AUC 708, was a reform of the Roman calendar. It took effect on 1 January AUC 709 , by edict. It was designed with the aid of Greek mathematicians and astronomers such as Sosigenes of Alexandria.

A leap year is a calendar year that contains an additional day added to keep the calendar year synchronized with the astronomical year or seasonal year. Because astronomical events and seasons do not repeat in a whole number of days, calendars that have a constant number of days in each year will unavoidably drift over time with respect to the event that the year is supposed to track, such as seasons. By inserting an additional day or month into some years, the drift between a civilization's dating system and the physical properties of the solar system can be corrected. A year that is not a leap year is a common year.

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.

The Julian day is the continuous count of days since the beginning of the Julian period, and is used primarily by astronomers, and in software for easily calculating elapsed days between two events.

Chronology is the science of arranging events in their order of occurrence in time. Consider, for example, the use of a timeline or sequence of events. It is also "the determination of the actual temporal sequence of past events".

Dionysius Exiguus was a 6th-century monk born in Scythia Minor. He was a member of a community of Scythian monks concentrated in Tomis, the major city of Scythia Minor. Dionysius is best known as the inventor of Anno Domini (AD) dating, which is used to number the years of both the Gregorian calendar and the (Christianised) Julian calendar. Almost all churches adopted his computus for the dates of Easter.

In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a celestial body, as they are subject to perturbations and vary with time. These time-varying astronomical quantities might include, for example, the mean longitude or mean anomaly of a body, the node of its orbit relative to a reference plane, the direction of the apogee or aphelion of its orbit, or the size of the major axis of its orbit.

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The term ante Christum natum, usually abbreviated to a. Chr. n., a.Ch.n., a.C.n., A.C.N., or ACN, denotes the years before the birth of Jesus Christ. It is a Latin equivalent to the English "BC". The phrase ante Christum natum is also seen shortened to ante Christum, similarly abbreviated to a. Chr., A. C. or AC. A related phrase, p. Chr. n., p. Ch. n., or post Christum natum complements a. Ch. n. and is equivalent to "Anno Domini" (AD).

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The year zero does not exist in the Anno Domini (AD) system commonly 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 and in ISO 8601:2004, as well as in most Buddhist and Hindu calendars.

The Mesoamerican Long Count calendar is a non-repeating, vigesimal (base 20) and octodecimal (base 18) calendar used by several pre-Columbian Mesoamerican cultures, most notably the Maya. For this reason, it is often known as the MayaLong Count calendar. Using a modified vigesimal tally, the Long Count calendar identifies a day by counting the number of days passed since a mythical creation date that corresponds to August 11, 3114 BCE in the Proleptic Gregorian calendar. The Long Count calendar was widely used on monuments.

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References

1. Espenak, Fred. "Year Dating Conventions". NASA Eclipse Web Site. NASA. Archived from the original on 8 February 2009. Retrieved 19 February 2009.
2. 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. 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 , 1740, Explication et Usage p. 5, translated by Wikipedia from the French:
"L'année 0 est celle dans laquelle on suppose qu'est né Jesus-Christ & 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 divisibles par 4 marquent les années bissextiles tant avant qu'après Jesus-Christ."
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.