Year

A year is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons are generally recognized: spring, summer, autumn and winter. In tropical and subtropical regions, several geographical sectors do not present defined seasons; but in the seasonal tropics, the annual wet and dry seasons are recognized and tracked.

An analemma illustrates the changing position of the Sun over the course of a year, as seen at a fixed time of day.

A calendar year is an approximation of the number of days of the Earth's orbital period, as counted in a given calendar. The Gregorian calendar, or modern calendar, presents its calendar year to be either a common year of 365 days or a leap year of 366 days, as do the Julian calendars; see below. For the Gregorian calendar, the average length of the calendar year (the mean year) across the complete leap cycle of 400 years is 365.2425 days. The ISO standard ISO 80000-3, Annex C, supports the symbol a (for Latin annus) to represent a year of either 365 or 366 days. In English, the abbreviations y and yr are commonly used.

In astronomy, the Julian year is a unit of time; it is defined as 365.25 days of exactly 86,400 seconds (SI base unit), totalling exactly 31,557,600 seconds in the Julian astronomical year.[1]

The word year is also used for periods loosely associated with, but not identical to, the calendar or astronomical year, such as the seasonal year, the fiscal year, the academic year, etc. Similarly, year can mean the orbital period of any planet; for example, a Martian year and a Venusian year are examples of the time a planet takes to transit one complete orbit. The term can also be used in reference to any long period or cycle, such as the Great Year.[2]

Etymology

English year (via West Saxon ġēar (/jɛar/), Anglian ġēr) continues Proto-Germanic *jǣran (*jē₁ran). Cognates are German Jahr, Old High German jār, Old Norse ár and Gothic jer, from the Proto-Indo-European noun *yeh₁r-om "year, season". Cognates also descended from the same Proto-Indo-European noun (with variation in suffix ablaut) are Avestan yārǝ "year", Greek ὥρα (hṓra) "year, season, period of time" (whence "hour"), Old Church Slavonic jarŭ, and Latin hornus "of this year".

Latin annus (a 2nd declension masculine noun; annum is the accusative singular; annī is genitive singular and nominative plural; annō the dative and ablative singular) is from a PIE noun *h₂et-no-, which also yielded Gothic aþn "year" (only the dative plural aþnam is attested).

Although most languages treat the word as thematic *yeh₁r-o-, there is evidence for an original derivation with an *-r/n suffix, *yeh₁-ro-. Both Indo-European words for year, *yeh₁-ro- and *h₂et-no-, would then be derived from verbal roots meaning "to go, move", *h₁ey- and *h₂et-, respectively (compare Vedic Sanskrit éti "goes", atasi "thou goest, wanderest"). A number of English words are derived from Latin annus, such as annual, annuity, anniversary, etc.; per annum means "each year", annō Dominī means "in the year of the Lord".

The Greek word for "year", ἔτος, is cognate with Latin vetus "old", from the PIE word *wetos- "year", also preserved in this meaning in Sanskrit vat-sa-ras "year" and vat-sa- "yearling (calf)", the latter also reflected in Latin vitulus "bull calf", English wether "ram" (Old English weðer, Gothic wiþrus "lamb").

In some languages, it is common to count years by referencing to one season, as in "summers", or "winters", or "harvests". Examples include Chinese 年 "year", originally 秂, an ideographic compound of a person carrying a bundle of wheat denoting "harvest". Slavic besides godŭ "time period; year" uses lěto "summer; year".

Intercalation

Astronomical years do not have an integer number of days or lunar months. Any calendar that follows an astronomical year must have a system of intercalation such as leap years.

Julian calendar

In the Julian calendar, the average (mean) length of a year is 365.25 days. In a non-leap year, there are 365 days, in a leap year there are 366 days. A leap year occurs every fourth year, or leap year, during which a leap day is intercalated into the month of February. The name "Leap Day" is applied to the added day.

The Revised Julian calendar, proposed in 1923 and used in some Eastern Orthodox Churches, has 218 leap years every 900 years, for the average (mean) year length of 365.2422222 days, close to the length of the mean tropical year, 365.24219 days (relative error of 9·10−8). In the year 2800 CE, the Gregorian and Revised Julian calendars will begin to differ by one calendar day.[3]

Gregorian calendar

The Gregorian calendar attempts to cause the northward equinox to fall on or shortly before March 21 and hence it follows the northward equinox year, or tropical year.[4] Because 97 out of 400 years are leap years, the mean length of the Gregorian calendar year is 365.2425 days; with a relative error below one ppm (8·10−7) relative to the current length of the mean tropical year (365.24219 days) and even closer to the current March equinox year of 365.242374 days that it aims to match. It is estimated that by the year 4000 CE, the northward equinox will fall back by one day in the Gregorian calendar, not because of this difference, but due to the slowing of the Earth's rotation and the associated lengthening of the day.

Other calendars
Further information: Lunisolar calendar

Historically, lunisolar calendars intercalated entire leap months on an observational basis. Lunisolar calendars have mostly fallen out of use except for liturgical reasons (Hebrew calendar, various Hindu calendars).

A modern adaptation of the historical Jalali calendar, known as the Solar Hijri calendar (1925), is a purely solar calendar with an irregular pattern of leap days based on observation (or astronomical computation), aiming to place new year (Nowruz) on the day of vernal equinox (for the time zone of Tehran), as opposed to using an algorithmic system of leap years.

Year numbering

A calendar era assigns a cardinal number to each sequential year, using a reference point in the past as the beginning of the era.

The worldwide standard is the Anno Domini, although some prefer the term Common Era because it has no explicit reference to Christianity. It was introduced in the 6th century and was intended to count years from the nativity of Jesus.[5]

The Anno Domini era is given the Latin abbreviation AD (for Anno Domini "in the year of the Lord"), or alternatively CE for "Common Era". Years before AD 1 are abbreviated BC for Before Christ or alternatively BCE for Before the Common Era. Year numbers are based on inclusive counting, so that there is no "year zero". In the modern alternative reckoning of Astronomical year numbering, positive numbers indicate years AD, the number 0 designates 1 BC, −1 designates 2 BC, and so on.

Pragmatic divisions

Financial and scientific calculations often use a 365-day calendar to simplify daily rates.

Fiscal year

A fiscal year or financial year is a 12-month period used for calculating annual financial statements in businesses and other organizations. In many jurisdictions, regulations regarding accounting require such reports once per twelve months, but do not require that the twelve months constitute a calendar year.

For example, in Canada and India the fiscal year runs from April 1; in the United Kingdom it runs from April 1 for purposes of corporation tax and government financial statements, but from April 6 for purposes of personal taxation and payment of state benefits; in Australia it runs from July 1; while in the United States the fiscal year of the federal government runs from October 1.

Academic year
Main article: Academic year

An academic year is the annual period during which a student attends an educational institution. The academic year may be divided into academic terms, such as semesters or quarters. The school year in many countries starts in August or September and ends in May, June or July. In Israel the academic year begins around October or November, aligned with the second month of the Hebrew calendar.

Some schools in the UK, Canada and the United States divide the academic year into three roughly equal-length terms (called trimesters or quarters in the United States), roughly coinciding with autumn, winter, and spring. At some, a shortened summer session, sometimes considered part of the regular academic year, is attended by students on a voluntary or elective basis. Other schools break the year into two main semesters, a first (typically August through December) and a second semester (January through May). Each of these main semesters may be split in half by mid-term exams, and each of the halves is referred to as a quarter (or term in some countries). There may also be a voluntary summer session and/or a short January session.

Some other schools, including some in the United States, have four marking periods. Some schools in the United States, notably Boston Latin School, may divide the year into five or more marking periods. Some state in defense of this that there is perhaps a positive correlation between report frequency and academic achievement.

There are typically 180 days of teaching each year in schools in the US, excluding weekends and breaks, while there are 190 days for pupils in state schools in Canada, New Zealand and the United Kingdom, and 200 for pupils in Australia.

In India the academic year normally starts from June 1 and ends on May 31. Though schools start closing from mid-March, the actual academic closure is on May 31 and in Nepal it starts from July 15.

Schools and universities in Australia typically have academic years that roughly align with the calendar year (i.e., starting in February or March and ending in October to December), as the southern hemisphere experiences summer from December to February.

Astronomical years
See also: Astronomical month

Julian year
Main article: Julian year (astronomy)

The Julian year, as used in astronomy and other sciences, is a time unit defined as exactly 365.25 days. This is the normal meaning of the unit "year" used in various scientific contexts. The Julian century of 36525 days and the Julian millennium of 365250 days are used in astronomical calculations. Fundamentally, expressing a time interval in Julian years is a way to precisely specify how many days (not how many "real" years), for long time intervals where stating the number of days would be unwieldy and unintuitive. By convention, the Julian year is used in the computation of the distance covered by a light-year.

In the Unified Code for Units of Measure, the symbol a (without subscript) always refers to the Julian year, aj, of exactly 31557600 seconds.

365.25 d × 86400 s = 1 a = 1 aj = 31.5576 Ms

The SI multiplier prefixes may be applied to it to form ka (kiloannus), Ma (megaannus), etc.

Sidereal, tropical, and anomalistic years
The relations among these are considered more fully in Axial precession (astronomy).

Each of these three years can be loosely called an astronomical year.

The sidereal year is the time taken for the Earth to complete one revolution of its orbit, as measured against a fixed frame of reference (such as the fixed stars, Latin sidera, singular sidus). Its average duration is 365.256363004 days (365 d 6 h 9 min 9.76 s) (at the epoch J2000.0 = January 1, 2000, 12:00:00 TT).[6]

Today the mean tropical year is defined as the period of time for the mean ecliptic longitude of the Sun to increase by 360 degrees.[7] Since the Sun's ecliptic longitude is measured with respect to the equinox,[8] the tropical year comprises a complete cycle of the seasons; because of the biological and socio-economic importance of the seasons, the tropical year is the basis of most calendars. The modern definition of mean tropical year differs from the actual time between passages of, e.g., the northward equinox for several reasons explained below. Because of the Earth's axial precession, this year is about 20 minutes shorter than the sidereal year. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds, using the modern definition[9] ( = 365.24219 d × 86 400 s).

The anomalistic year is the time taken for the Earth to complete one revolution with respect to its apsides. The orbit of the Earth is elliptical; the extreme points, called apsides, are the perihelion, where the Earth is closest to the Sun (January 5, 07:48 UT in 2020), and the aphelion, where the Earth is farthest from the Sun (July 4, 11:35 UT in 2020). The anomalistic year is usually defined as the time between perihelion passages. Its average duration is 365.259636 days (365 d 6 h 13 min 52.6 s) (at the epoch J2011.0).[10]

Draconic year
Further information: Draconic period

The draconic year, draconitic year, eclipse year, or ecliptic year is the time taken for the Sun (as seen from the Earth) to complete one revolution with respect to the same lunar node (a point where the Moon's orbit intersects the ecliptic). The year is associated with eclipses: these occur only when both the Sun and the Moon are near these nodes; so eclipses occur within about a month of every half eclipse year. Hence there are two eclipse seasons every eclipse year. The average duration of the eclipse year is

346.620075883 days (346 d 14 h 52 min 54 s) (at the epoch J2000.0).

This term is sometimes erroneously used for the draconic or nodal period of lunar precession, that is the period of a complete revolution of the Moon's ascending node around the ecliptic: 18.612815932 Julian years (6798.331019 days; at the epoch J2000.0).

Full moon cycle

The full moon cycle is the time for the Sun (as seen from the Earth) to complete one revolution with respect to the perigee of the Moon's orbit. This period is associated with the apparent size of the full moon, and also with the varying duration of the synodic month. The duration of one full moon cycle is:

411.78443029 days (411 days 18 hours 49 minutes 35 seconds) (at the epoch J2000.0).

Lunar year

The lunar year comprises twelve full cycles of the phases of the Moon, as seen from Earth. It has a duration of approximately 354.37 days. Muslims use this for celebrating their Eids and for marking the start of the fasting month of Ramadan. A Muslim calendar year is based on the lunar cycle.

Vague year

The vague year, from annus vagus or wandering year, is an integral approximation to the year equaling 365 days, which wanders in relation to more exact years. Typically the vague year is divided into 12 schematic months of 30 days each plus 5 epagomenal days. The vague year was used in the calendars of Ethiopia, Ancient Egypt, Iran, Armenia and in Mesoamerica among the Aztecs and Maya.[11] It is still used by many Zoroastrian communities.

Heliacal year

A heliacal year is the interval between the heliacal risings of a star. It differs from the sidereal year for stars away from the ecliptic due mainly to the precession of the equinoxes.

Sothic year

The Sothic year is the interval between heliacal risings of the star Sirius. It is currently less than the sidereal year and its duration is very close to the Julian year of 365.25 days.

Gaussian year

The Gaussian year is the sidereal year for a planet of negligible mass (relative to the Sun) and unperturbed by other planets that is governed by the Gaussian gravitational constant. Such a planet would be slightly closer to the Sun than Earth's mean distance. Its length is:

365.2568983 days (365 d 6 h 9 min 56 s).

Besselian year

The Besselian year is a tropical year that starts when the (fictitious) mean Sun reaches an ecliptic longitude of 280°. This is currently on or close to January 1. It is named after the 19th-century German astronomer and mathematician Friedrich Bessel. The following equation can be used to compute the current Besselian epoch (in years):[12]

B = 1900.0 + (Julian dateTT − 2415020.31352) / 365.242198781

The TT subscript indicates that for this formula, the Julian date should use the Terrestrial Time scale, or its predecessor, ephemeris time.

Variation in the length of the year and the day
Further information: Length of day (astronometry)

The exact length of an astronomical year changes over time.

  • The positions of the equinox and solstice points with respect to the apsides of Earth's orbit change: the equinoxes and solstices move westward relative to the stars because of precession, and the apsides move in the other direction because of the long-term effects of gravitational pull by the other planets. Since the speed of the Earth varies according to its position in its orbit as measured from its perihelion, Earth's speed when in a solstice or equinox point changes over time: if such a point moves toward perihelion, the interval between two passages decreases a little from year to year; if the point moves towards aphelion, that period increases a little from year to year. So a "tropical year" measured from one passage of the northward ("vernal") equinox to the next, differs from the one measured between passages of the southward ("autumnal") equinox. The average over the full orbit does not change because of this, so the length of the average tropical year does not change because of this second-order effect.
  • Each planet's movement is perturbed by the gravity of every other planet. This leads to short-term fluctuations in its speed, and therefore its period from year to year. Moreover, it causes long-term changes in its orbit, and therefore also long-term changes in these periods.
  • Tidal drag between the Earth and the Moon and Sun increases the length of the day and of the month (by transferring angular momentum from the rotation of the Earth to the revolution of the Moon); since the apparent mean solar day is the unit with which we measure the length of the year in civil life, the length of the year appears to decrease. The rotation rate of the Earth is also changed by factors such as post-glacial rebound and sea level rise.
Numerical value of year variation

Mean year lengths in this section are calculated for 2000, and differences in year lengths, compared to 2000, are given for past and future years. In the tables a day is 86,400 SI seconds long.[13][14][15][16]

Mean year lengths for 2000
Type of yearDaysHoursMinutesSeconds
Tropical36554845
Sidereal3656910
Anomalistic36561353
Eclipse346145255
Year length difference from 2000
(seconds; positive when length for tabulated year is greater than length in 2000)
YearTropicalSiderealAnomalisticEclipse
−4000−8−45−15−174
−20004−19−11−116
07−4−5−57
20000000
4000−14−3554
6000−35−1210104

Summary
Days Year type
346.62Draconic, also called eclipse.
354.37Lunar.
365Vague, and a common year in many solar calendars.
365.24219Tropical, also called solar, averaged and then rounded for epoch J2000.0.
365.2425Gregorian, on average.
365.25Julian.
365.25636Sidereal, for epoch J2000.0.
365.259636Anomalistic, averaged and then rounded for epoch J2011.0.
366Leap in many solar calendars.

An average Gregorian year is 365.2425 days (52.1775 weeks, 8765.82 hours, 525949.2 minutes or 31556952 seconds). For this calendar, a common year is 365 days (8760 hours, 525600 minutes or 31536000 seconds), and a leap year is 366 days (8784 hours, 527040 minutes or 31622400 seconds). The 400-year cycle of the Gregorian calendar has 146097 days and hence exactly 20871 weeks.

"Greater" astronomical years

Equinoctial cycle

The Great Year, or equinoctial cycle, corresponds to a complete revolution of the equinoxes around the ecliptic. Its length is about 25,700 years.

Galactic year

The Galactic year is the time it takes Earth's Solar System to revolve once around the galactic center. It comprises roughly 230 million Earth years.[17]

Seasonal year
Main article: Seasonal year
Further information: Effect of sun angle on climate

A seasonal year is the time between successive recurrences of a seasonal event such as the flooding of a river, the migration of a species of bird, the flowering of a species of plant, the first frost, or the first scheduled game of a certain sport. All of these events can have wide variations of more than a month from year to year.

Symbols

A common symbol for the year as a unit of time is a, taken from the Latin word annus. In English, the abbreviations "y" or "yr" are more commonly used in non-scientific literature but also specifically in geology and paleontology, where "kyr, myr, byr" (thousands, millions, and billions of years, respectively) and similar abbreviations are used to denote intervals of time remote from the present.[18][19][20]

Symbol

NIST SP811[21] supports the symbol a as the unit of time for a year. In English, the abbreviations y and yr are also used.[18][19][20]

The Unified Code for Units of Measure[22] disambiguates the varying symbologies of ISO 1000, ISO 2955 and ANSI X3.50[23] by using:

at = 365.24219 days for the mean tropical year;
aj = 365.25 days for the mean Julian year;
ag = 365.2425 days for the mean Gregorian year;

where:

a, without a qualifier = 1 aj;
and ar, for are, is a unit of area.

The International Union of Pure and Applied Chemistry (IUPAC) and the International Union of Geological Sciences have jointly recommended defining the "annus," with symbol a, as the length of the tropical year in the year 2000:

a = 31556925.445 seconds (approximately 365.24219265 ephemeris days)

This differs from the above definition of 365.25 days by about 20 parts per million. The joint document says that definitions such as the Julian year "bear an inherent, pre-programmed obsolescence because of the variability of Earth’s orbital movement", but then proposes using the length of the tropical year as of 2000 AD (specified down to the millisecond), which suffers from the same problem.[24][25] (The tropical year oscillates with time by more than a minute.)

The notation has proved controversial as it conflicts with an earlier convention among geoscientists to use a specifically for years ago, and y or yr for a one-year time period.[25]

SI prefix multipliers

For the following, there are alternative forms that elide the consecutive vowels, such as kilannus, megannus, etc. The exponents and exponential notations are typically used for calculating and in displaying calculations, and for conserving space, as in tables of data.

  • ka (for kiloannum) – a unit of time equal to one thousand, or 103, years, or 1 E3 yr, also known as a millennium in anthropology and calendar uses. The prefix multiplier "ka" is typically used in geology, paleontology, and archaeology for the Holocene and Pleistocene periods, where a non−radiocarbon dating technique: e.g. ice core dating, dendrochronology, uranium-thorium dating, or varve analysis; is used as the primary dating method for age determination. If age is determined primarily by radiocarbon dating, then the age should be expressed in either radiocarbon or calendar (calibrated) years Before Present.
  • Ma (for megaannum) – a unit of time equal to one million, or 106, years, or 1 E6 yr. The suffix "Ma" is commonly used in scientific disciplines such as geology, paleontology, and celestial mechanics to signify very long time periods into the past or future. For example, the dinosaur species Tyrannosaurus rex was abundant approximately 66 Ma (66 million years) ago. The duration term "ago" may not always be indicated: if the quantity of a duration is specified while not explicitly mentioning a duration term, one can assume that "ago" is implied; the alternative unit "mya" does include "ago" explicitly. It is also written as "million years" (ago) in works for general public use. In astronomical applications, the year used is the Julian year of precisely 365.25 days. In geology and paleontology, the year is not so precise and varies depending on the author.
  • Ga (for gigaannum) – a unit of time equal to 109 years, or one billion years. "Ga" is commonly used in scientific disciplines such as cosmology and geology to signify extremely long time periods in the past.[26] For example, the formation of the Earth occurred approximately 4.54 Ga (4.54 billion years) ago and the age of the universe is approximately 13.8 Ga.
  • Ta (for teraannum) – a unit of time equal to 1012 years, or one trillion years. "Ta" is an extremely long unit of time, about 70 times as long as the age of the universe. It is the same order of magnitude as the expected life span of a small red dwarf.
  • Pa (for petaannum) – a unit of time equal to 1015 years, or one quadrillion years. The half-life of the nuclide cadmium-113 is about 8 Pa.[27] This symbol coincides with that for the pascal without a multiplier prefix, though both are infrequently used and context will normally be sufficient to distinguish time from pressure values.
  • Ea (for exaannum) – a unit of time equal to 1018 years, or one quintillion years. The half-life of tungsten-180 is 1.8 Ea.[28]

Abbreviations yr and ya

Further information: Before Present

In astronomy, geology, and paleontology, the abbreviation yr for years and ya for years ago are sometimes used, combined with prefixes for thousand, million, or billion.[19][29] They are not SI units, using y to abbreviate the English "year", but following ambiguous international recommendations, use either the standard English first letters as prefixes (t, m, and b) or metric prefixes (k, M, and G) or variations on metric prefixes (k, m, g). In archaeology, dealing with more recent periods, normally expressed dates, e.g. "22,000 years ago" may be used as a more accessible equivalent of a Before Present ("BP") date.

These abbreviations include:

Non-SI abbreviation Short for... SI-prefixed equivalent Comments and examples
kyr
kilo yearska
  • Thousand years
myr
Myr
million years
Mega years		Ma
  • Million years
byr
billion yearsGa
kya
kilo years agoka ago
mya
Mya
million years ago
Mega years ago		Ma ago
bya
Gya
billion years ago
giga years ago		Ga ago

Use of mya and bya is deprecated in modern geophysics, the recommended usage being Ma and Ga for dates Before Present, but "m.y." for the duration of epochs.[19][20] This ad hoc distinction between "absolute" time and time intervals is somewhat controversial amongst members of the Geological Society of America.[31]

Note that on graphs, using ya units on the horizontal axis time flows from right to left, which may seem counter-intuitive. If the ya units are on the vertical axis, time flows from top to bottom which is probably easier to understand than conventional notation.

See also

References

Notes
  1. "SI units". IAU. Retrieved February 18, 2010. (See Table 5 and Section 5.15.) Reprinted from: Wilkins, George A. (1989). "The IAU Style Manual" (PDF). IAU Transactions. XXB.
  2. OED, s.v. "year", entry 2.b.: "transf. Applied to a very long period or cycle (in chronology or mythology, or vaguely in poetic use)."
  3. Shields, Miriam Nancy (1924). "The new calendar of the eastern churches". Popular Astronomy. 32: 407. Bibcode:1924PA.....32..407S.
  4. Ziggelaar, A. (1983). "The Papal Bull of 1582 Promulgating a Reform of the Calendar". In G. V. Coyne; M. A. Hoskin; O. Pedersen (eds.). Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary. Vatican City: Pontifical Academy of Sciences. p. 223.
  5. Richards, E.G. (2013). "Calendars". In Urban, S.E.; Seidelmann, P.K. (eds.). Explanatory Supplement to the Astronomical Almanac (PDF) (3rd ed.). Mill Valley, CA: University Science Books. pp. 585, 590. ISBN 978-1-891389-85-6. Richards does not explicitly say that Anno Domini is the worldwide standard, but does say on page 585 that the Gregorian calendar is used throughout the world for secular purposes.
  6. International Earth Rotation and Reference System Service. (2010).IERS EOP PC Useful constants.
  7. Richards, E.G. (2013). Calendars. In S.E. Urban & P.K. Seidelmann (Eds.), Explanatory Supplement to the Astronomical Almanac (3rd ed.). Mill Valley, CA: University Science Books. p. 586.
  8. "longitude, ecliptic" and "dynamical equinox". (2018). In "Glossary", The Astronomical Almanac Online. United States Naval Observatory.
  9. Astronomical Almanac for the Year 2011. Washington and Taunton: U.S. Government Printing Office and the U.K. Hydrographic Office. 2009. p. M18 (Glossary).
  10. Astronomical Almanac for the Year 2011. Washington and Taunton: US Government Printing Office and the UK Hydrographic Office. 2009. pp. A1, C2.
  11. Calendar Description and Coordination Maya World Studies Center
  12. Astronomical Almanac for the Year 2010. Washington and Taunton: U.S. Government Printing Office and the U.K. Hydrographic Office. 2008. p. B3.
  13. U.S. Naval Observatory Nautical Almanac Office and Her Majesty's Nautical Almanac Office (2010). Astronomical Almanac for the year 2011. Washington: U.S. Government Printing Office. pp. C2, L8.
  14. Simon, J.L.; Bretagnon, P.; Chapront, J.; Chapront-Touzé, M.; Francou, G.; Laskar, J. (February 1994). "Numerical expressions for precession formulae and mean elements for the Moon and planets". Astronomy and Astrophysics. 282 (2): 663–683. Bibcode:1994A&A...282..663S.
  15. Taff, Lawrence G. (1985). Celestial Mechanics: A Computational Guide for the Practitioner. New York: John Wiley & Sons. p. 103. ISBN 978-0-471-89316-5. Values in tables agree closely for 2000, and depart by as much as 44 seconds for the years furthest in the past or future; the expressions are simpler than those recommended in the Astronomical Almanac for the Year 2011.
  16. Seidelmann, P. Kenneth (2013). Explanatory Supplement to the Astronomical Almanac. Sean E. Urban (ed.) (3 ed.). Univ Science Books. p. 587. ISBN 978-1-891389-85-6. Tabulates length of tropical year from −500 to 2000 at 500 year intervals using a formula by Laskar (1986); agrees closely with values in this section near 2000, departs by 6 seconds in −500.
  17. "Science Bowl Questions, Astronomy, Set 2" (PDF). Science Bowl Practice Questions. Oak Ridge Associated Universities. 2009. Archived from the original (PDF) on March 7, 2010. Retrieved December 9, 2009.
  18. Rowlett, Russ. "Units: A". How Many? A Dictionary of Units of Measurement. University of North Carolina. Retrieved January 9, 2009.
  19. "AGU publications: Grammar and Style Guide". American Geophysical Union. September 1, 2017. Archived from the original on September 18, 2019. Retrieved January 9, 2009.
  20. North American Commission on Stratigraphic Nomenclature (November 2005). "North American Stratigraphic Code". The American Association of Petroleum Geologists Bulletin (Article 13 (c) ed.). 89 (11): 1547–1591. doi:10.1306/07050504129.
  21. Thompson, Ambler; Taylor, Barry N. (2008). "Special Publication 811 – Guide for the Use of the International System of Units (SI)" (PDF). National Institute of Standards and Technology (NIST). para 8.1.
  22. Schadow, Gunther; McDonald, Clement J. "Unified Code for Units of Measure". Archived from the original on May 20, 2008.
  23. http://aurora.regenstrief.org/~ucum/ucum.html#para-31 Archived March 4, 2010, at the Wayback Machine
  24. Holden, Norman E.; Bonardi, Mauro L.; De Bièvre, Paul; Renne, Paul R. & Villa, Igor M. (2011). "IUPAC-IUGS common definition and convention on the use of the year as a derived unit of time (IUPAC Recommendations 2011)" (PDF). Pure and Applied Chemistry. 83 (5): 1159–1162. doi:10.1351/PAC-REC-09-01-22. S2CID 96753161.
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