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A year is the orbital period of the Earth moving in its orbit around the Sun. For an observer on the Earth, this corresponds to the period it takes the Sun to complete one course throughout the zodiac along the ecliptic.
Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by changes in weather, the hours of daylight, and consequently vegetation and fertility. In temperate and subpolar regions, generally four seasons are recognized: spring, summer, autumn and winter, astronomically marked by the Sun reaching the points of equinox and solstice, although the climatic seasons lag behind their astronomical markers. In some tropical and subtropical regions it is more common to speak of the rainy (or wet, or monsoon) season versus the dry season.
A calendar year is an approximation of the Earth's orbital period in a given calendar. A calendar year in the Gregorian calendar (as well as in the Julian calendar) has either 365 (common year) or 366 (leap year) days. The average length of the year in the Gregorian (modern) calendar is 365.2425 days (taking account of the century rule for leap years). In an informative annex, the International Standard ISO 80000-3 proposes the symbol a (for Latin annus) to represent a year of either 365 or 366 days. In English the abbreviations y and yr are used.
The word "year" is also used of periods loosely associated but not strictly identical with either the astronomical or the calendar year, such as the seasonal year, the fiscal year or the academic year, etc. By extension, the term year can mean the orbital period of any planet: for example, a "Martian year" or "Venerian year" is the time in which Mars or Venus completes its own orbit. The term is also applied more broadly to any long period or cycle, such as the "Great Year".
- 1 Etymology
- 2 Civil year
- 3 Astronomical years
- 3.1 Julian year
- 3.2 Sidereal, tropical, and anomalistic years
- 3.3 Draconic year
- 3.4 Full moon cycle
- 3.5 Lunar year
- 3.6 Vague year
- 3.7 Heliacal year
- 3.8 Sothic year
- 3.9 Gaussian year
- 3.10 Besselian year
- 3.11 Variation in the length of the year and the day
- 3.12 Summary
- 4 "Greater" astronomical years
- 5 Seasonal year
- 6 Symbol
- 7 See also
- 8 References
- 9 Further reading
- 10 External links
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 (Gothic e is always a long vowel), all from a PIE *yeh₁rom "year, season". Cognates outside of Germanic are Avestan yārǝ "year", Greek ὥρα "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).
Both *yeh₁-ro- and *h₂et-no- are based on verbal roots expressing movement, *h₁ey- and *h₂et- respectively, both meaning "to go" generally (compare Vedic Sanskrit éti "goes", atasi "thou goest, wanderest").
The Greek word for "year", ἔτος, is cognate with Latin vetus "old", from PIE *wetos- "year", also preserved in this meaning in Sanskrit vat-sa- "yearling (calf)" and vat-sa-ras "year".
|This section needs additional citations for verification. (November 2014)|
No astronomical year has an integer number of days or lunar months, so any calendar that follows an astronomical year must have a system of intercalation such as leap years. Financial and scientific calculations often use a 365-day calendar to simplify daily rates.
In Western calendars
In the Julian calendar, the average 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 four years.
The Gregorian calendar attempts to keep the northward equinox on or shortly before March 21, hence it follows the northward equinox year. The mean length of the year is 365.2425 days (as 97 out of 400 years are leap years); this is within one ppm of the current length of the mean tropical year (365.24219 days), and even closer to the current March equinox year of 365.2424 days that it aims to match. It is estimated that, by the year 4000, the northward equinox will fall back by one day in the Gregorian calendar, not because of this difference, but because of the slowing down of the Earth's rotation and the associated lengthening of the day.
The Revised Julian calendar, as used in some Eastern Orthodox Churches, tries to synchronize with the tropical year. The average length of this calendar's year is 365.242222 days (as 218 out of 900 years are leap years). Gregorian and Revised Julian calendars will start to differ in 2800.
A calendar era is used to assign a number to individual years, using a reference point in the past as the beginning of the era. In many countries, the most common era is from the traditional (though now believed incorrect) year of the birth of Jesus. Dates in this era are designated Anno Domini (Latin for "in the year of the Lord"), abbreviated AD, or CE (for "common era"). The year before 1 AD or CE is designated 1 Before Christ (BC) or Before the Common Era (BCE), the year before that 2 BC/BCE, etc. Hence there was no year 0 AD/CE.
When computations involving years are done involving both years AD and years BC, it is common to use Astronomical year numbering, in which 1 BC is designated 0, 2 BC is designated −1, and so on.
Other eras are also used to enumerate the years in different cultural, religious or scientific contexts.
In Persian calendar
The Persian calendar, in use in Afghanistan and Iran, has its year begin on the day of the northward equinox as determined by astronomical computation (for the time zone of Tehran), as opposed to using an algorithmic system of leap years.
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.
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 and USA divide the academic year into three roughly equal-length terms (called "trimesters" or "quarters" in the USA), 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 USA, excluding weekends and breaks, while 190 days for pupils in state schools in the United Kingdom, New Zealand and Canada.
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.
In the International System of Quantities
In the International System of Quantities, the year (symbol a) is defined as either 365 days or 366 days.
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" (symbol "a" from the Latin annus) 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.
365.25 days of 86400 seconds = 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 mean solar days (365 d 6 h 9 min 9.76 s) (at the epoch J2000.0 = January 1, 2000, 12:00:00 TT).
Today the tropical year is defined as the period of time for the mean ecliptic longitude of the Sun to increase by 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, 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 (= 365.24219 days of 86400 SI seconds), averaged over equinoxes and solstices, with the northern equinox tropical year (used for the Gregorian calendar) currently being 365.2424 days.
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 3 in 2011), and the aphelion, where the Earth is farthest from the Sun (July 4 in 2011). 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).
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). This period 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 34 seconds) (at the epoch J2000.0).
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.
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 Ancient Egypt, Iran, Armenia and in Mesoamerica among the Aztecs and Maya.
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).
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):
- B = 1900.0 + (Julian dateTT − 2415020.31352) / 365.242198781
Variation in the length of the year and the day
|This section needs additional citations for verification. (October 2012)|
- The positions of the equinox and solstice points with respect to the apsides of Earth's orbit change: the first because of precession, and the apsides 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.
|Type of year||days||hours||minutes||seconds|
|346.62||Draconic, also called eclipse.|
|365||Vague, and a common year in many solar calendars.|
|365.24219||Tropical, also called solar, averaged and then rounded for epoch J2000.0.|
|365.2425||Gregorian, on average.|
|365.25636||Sidereal, for epoch J2000.0.|
|365.259636||Anomalistic, averaged and then rounded for epoch J2011.0.|
|366||Leap in many solar calendars.|
An average Gregorian year is 365.2425 days = 52.1775 weeks = 8765.82 hours = 525949.2 minutes = 31556952 seconds. For this calendar, a common year is 365 days = 8760 hours = 525600 minutes = 31536000 seconds, and a leap year is 366 days = 8784 hours = 527040 minutes = 31622400 seconds. The 400 year cycle of the Gregorian calendar has 146097 days and hence exactly 20871 weeks.
"Greater" astronomical years
The Great Year, or equinoctial cycle, corresponds to a complete revolution of the equinoxes around the ecliptic. Its length is about 25,700 years, and cannot be determined precisely as the precession speed is variable.
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.
 In English, the abbreviations "y" or "yr" are sometimes used, 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.
NIST SP811 and ISO 80000-3:2006 suggest the symbol a (in the International System of Units, although a is also the symbol for the are, the unit of area used to measure land area, but context is usually enough to disambiguate). In English, the abbreviations y and yr are also used.
- ar for are and:
- at = a_t = 365.24219 days for the mean tropical year
- aj = a_j = 365.25 days for the mean Julian year
- ag = a_g = 365.2425 days for the mean Gregorian year
- a = 1 aj (without further qualifier)
A definition jointly adopted by the International Union of Pure and Applied Chemistry and the International Union of Geological Sciences is to use annus, with symbol a, for year, defined as the length of the tropical year in the year 2000:
- a = 365.24219265 days = 31556925.445 seconds
The notation has proved controversial; 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.
SI prefix multipliers
For the following, there are alternative forms which elide the consecutive vowels, such as kilannus, megannus, etc.
- ka (for kiloannus), is a unit of time equal to one thousand (103) years. This is typically used in geology, paleontology, and archaeology for Holocene and Pleistocene periods where a nonradiocarbon dating technique, i. e., ice core dating, dendrochronology, uranium-thorium dating, or varve analysis, is used as the primary dating method for age determination. If age is primarily determined by radiocarbon dating, then the age should be expressed in either radiocarbon or calendar (calibrated) years Before Present.
- Ma (for megaannus), is a unit of time equal to one million (106) years. It 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 (ago may not always be mentioned; if the quantity is specified while not explicitly discussing a duration, one can assume that "ago" is implied; the alternative "mya" unit includes "ago" explicitly). 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 gigaannus), is a unit of time equal to 109 years (one billion on the short scale, one milliard on the long scale). It is commonly used in scientific disciplines such as cosmology and geology to signify extremely long time periods in the past. For example, the formation of the Earth occurred approximately 4.57 Ga (4.57 billion years) ago.
- Ta (for teraannus), is a unit of time equal to 1012 years (one trillion on the short scale, one billion on the long scale). It 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 star.
- Pa (for petaannus), is a unit of time equal to 1015 years (one quadrillion on the short scale, one billiard on the long scale). The half-life of the nuclide cadmium-113 is about 8 Pa. 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 exaannus), is a unit of time equal to 1018 years (one quintillion on the short scale, one trillion on the long scale). The half-life of tungsten-180 is 1.8 Ea.
Symbols y and yr
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". They are not SI units, using y to abbreviate 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). These abbreviations include:
|non-SI abbreviation||SI-prefixed equivalent||order of magnitude|
|kya or tya||"ka ago"|
|bya or gya||"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. This ad hoc distinction between "absolute" time and time intervals is somewhat controversial amongst members of the Geological Society of America.
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.
- International Astronomical Union "SI units" accessed February 18, 2010. (See Table 5 and section 5.15.) Reprinted from George A. Wilkins & IAU Commission 5, "The IAU Style Manual (1989)" (PDF file) in IAU Transactions Vol. XXB
- 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)."
- International Earth Rotation and Reference System Service. (2010).IERS EOP PC Useful constants.
- 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.
- Astronomical Almanac for the Year 2011. Washington and Taunton: U.S. Government Printing Office and the U.K. Hydrographic Office. 2009. p. M18 (Glossary).
- Astronomical Almanac for the Year 2011. Washington and Taunton: U.S. Government Printing Office and the U.K. Hydrographic Office. 2009. pp. A1, C2.
- Calendar Description and Coordination Maya World Studies Center
- Astronomical Almanac for the Year 2010. Washington and Taunton: U.S. Government Printing Office and the U.K. Hydrographic Office. 2008. p. B3.
- The Astronomical Almanac Online
- 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.
- 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.
- Taff, Lawrence G. (1985). Celestial Mechanics: A Computational Guide for the Practitioner. New York: John Wiley & Sons. p. 103. ISBN 0-471-89316-1. 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.
- Seidelmann, P. Kenneth (2013). Explanatory Supplement to the Astronomical Almanac. Sean E. Urban (ed.) (3 ed.). Univ Science Books. p. 587. ISBN 1-891389-85-8. 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.
- "Science Bowl Questions, Astronomy, Set 2" (PDF). Science Bowl Practice Questions. Oak Ridge Associated Universities. 2009. Retrieved December 9, 2009.
- Russ Rowlett. "Units: A". How Many? A Dictionary of Units of Measurement. University of North Carolina. Retrieved January 9, 2009.
- "AGU Editorial Style Guide for Authors". American Geophysical Union. September 21, 2007. Archived from the original on 2008-07-14. Retrieved 2009-01-09.
- 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.
- Ambler Thompson, Barry N. Taylor (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.
- "ISO 80000-3:2006, Quantities and units". Geneva: International Organization for Standardization. 2006. Part 3: Space and time.
- Gunther Schadow, Clement J. McDonald. "Unified Code for Units of Measure".
- Norman E. Holden, Mauro L. Bonardi, Paul De Bièvre, Paul R. Renne, and Igor M. Villa (2011). "IUPAC-IUGS common definition and convention on the use of the year as a derived unit of time (IUPAC Recommendations 2011)". Pure and Applied Chemistry 83 (5): 1159–1162. doi:10.1351/PAC-REC-09-01-22.
- Celeste Biever (April 27, 2011). "Push to define year sparks time war". New Scientist. Retrieved April 28, 2011.
- P. Belli et al. (2007). "Investigation of β decay of 113Cd". Phys. Rev. C 76 (6): 064603. Bibcode:2007PhRvC..76f4603B. doi:10.1103/PhysRevC.76.064603.
- F. A. Danevich et al. (2003). "α activity of natural tungsten isotopes". Phys. Rev. C 67: 014310. arXiv:nucl-ex/0211013. Bibcode:2003PhRvC..67a4310D. doi:10.1103/PhysRevC.67.014310.
- North American Commission on Stratigraphic Nomenclature. "North American Stratigraphic Code".
(c) Convention and abbreviations. – The age of a stratigraphic unit or the time of a geologic event, as commonly determined by numerical dating or by reference to a calibrated time-scale, may be expressed in years before the present. The unit of time is the modern year as presently recognized worldwide. Recommended (but not mandatory) abbreviations for such ages are SI (International System of Units) multipliers coupled with "a" for annus: ka, Ma, and Ga for kilo-annus (103 years), Mega-annus (106 years), and Giga-annus (109 years), respectively. Use of these terms after the age value follows the convention established in the field of C-14 dating. The "present" refers to 1950 AD, and such qualifiers as "ago" or "before the present" are omitted after the value because measurement of the duration from the present to the past is implicit in the designation. In contrast, the duration of a remote interval of geologic time, as a number of years, should not be expressed by the same symbols. Abbreviations for numbers of years, without reference to the present, are informal (e.g., y or yr for years; my, m.y., or m.yr. for millions of years; and so forth, as preference dictates). For example, boundaries of the Late Cretaceous Epoch currently are calibrated at 63 Ma and 96 Ma, but the interval of time represented by this epoch is 33 m.y.
- Bradford M. Clement (April 8, 2004). "Dependence of the duration of geomagnetic polarity reversals on site latitude". Nature 428 (6983): 637–40. Bibcode:2004Natur.428..637C. doi:10.1038/nature02459. PMID 15071591.
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- Whitrow, Gerald James (2003). What is Time?. Oxford: Oxford University Press. ISBN 0-19-860781-4. OCLC 265440481.
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