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The Julian day is the continuous count of days since the beginning of the Julian period, and is used primarily by
astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either obse ...
s, and in
software Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work. At the lowest programming level, executable code consists o ...
for easily calculating elapsed days between two events (e.g. food production date and sell by date). The Julian period is a
chronological Chronology (from Latin ''chronologia'', from Ancient Greek , ''chrónos'', "time"; and , '' -logia'') 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. ...
interval of 7980 years; year 1 of the Julian Period was . The Julian calendar year is year of the current Julian Period. The next Julian Period begins in the year . Historians used the period to identify Julian calendar years within which an event occurred when no such year was given in the historical record, or when the year given by previous historians was incorrect. The Julian day number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon
Universal Time Universal Time (UT or UT1) is a time standard based on Earth's rotation. While originally it was mean solar time at 0° longitude, precise measurements of the Sun are difficult. Therefore, UT1 is computed from a measure of the Earth's angle with ...
, with Julian day number 0 assigned to the day starting at noon on Monday, January 1, 4713 BC,
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 i ...
(November 24, 4714 BC, in the
proleptic Gregorian calendar The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to the dates preceding its official introduction in 1582. In nations that adopted the Gregorian calendar after its official and first introduction, dates occ ...
), a date at which three multi-year cycles started (which are:
Indiction An indiction ( la, indictio, impost) was a periodic reassessment of taxation in the Roman Empire which took place every fifteen years. In Late Antiquity, this 15-year cycle began to be used to date documents and it continued to be used for this p ...
, Solar, and Lunar cycles) and which preceded any dates in
recorded history Recorded history or written history describes the historical events that have been recorded in a written form or other documented communication which are subsequently evaluated by historians using the historical method. For broader world hi ...
. For example, the Julian day number for the day starting at 12:00 UT (noon) on January 1, 2000, was 2 451 545. The Julian date (JD) of any
instant In physics and the philosophy of science, instant refers to an infinitesimal interval in time, whose passage is instantaneous. In ordinary speech, an instant has been defined as "a point or very short space of time," a notion deriving from its ety ...
is the Julian day number plus the fraction of a day since the preceding noon in Universal Time. Julian dates are expressed as a Julian day number with a decimal fraction added."Resolution B1" 1997. For example, the Julian Date for 00:30:00.0 UT January 1, 2013, is 2 456 293.520 833. This page was loaded at – expressed as a Julian date this is . []


Terminology

The term ''Julian date'' may also refer, outside of astronomy, to the day-of-year number (more properly, the ordinal date) in the
Gregorian calendar The Gregorian calendar is the calendar used in most parts of the world. It was introduced in October 1582 by Pope Gregory XIII as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years diff ...
, especially in computer programming, the military and the food industry,USDA c. 1963. or it may refer to dates in the
Julian calendar The Julian calendar, proposed by Roman consul Julius Caesar in 46 BC, was a reform of the Roman calendar. It took effect on , by edict. It was designed with the aid of Greek mathematicians and astronomers such as Sosigenes of Alexandria. ...
. For example, if a given "Julian date" is "October 5, 1582", this means that date in the Julian calendar (which was October 15, 1582, in the Gregorian calendar—the date it was first established). Without an astronomical or historical context, a "Julian date" given as "36" most likely means the 36th day of a given Gregorian year, namely February 5. Other possible meanings of a "Julian date" of "36" include an astronomical Julian Day Number, or the year AD 36 in the Julian calendar, or a duration of 36 astronomical Julian years). This is why the terms "ordinal date" or "day-of-year" are preferred. In contexts where a "Julian date" means simply an ordinal date, calendars of a Gregorian year with formatting for ordinal dates are often called ''"Julian calendars"'', but this could also mean that the calendars are of years in the Julian calendar system. Historically, Julian dates were recorded relative to
Greenwich Mean Time Greenwich Mean Time (GMT) is the mean solar time at the Royal Observatory in Greenwich, London, counted from midnight. At different times in the past, it has been calculated in different ways, including being calculated from noon; as a cons ...
(GMT) (later, Ephemeris Time), but since 1997 the
International Astronomical Union The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach ...
has recommended that Julian dates be specified in
Terrestrial Time Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth. For example, the Astronomical Almanac uses T ...
. Seidelmann indicates that Julian dates may be used with
International Atomic Time International Atomic Time (abbreviated TAI, from its French name ) is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid. TAI is a weighted average of the time kept by over 450 atomi ...
(TAI),
Terrestrial Time Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth. For example, the Astronomical Almanac uses T ...
(TT),
Barycentric Coordinate Time Barycentric Coordinate Time (TCB, from the French Temps-coordonnée barycentrique) is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits of planets, asteroids, comets, and i ...
(TCB), or
Coordinated Universal Time Coordinated Universal Time or UTC is the primary time standard by which the world regulates clocks and time. It is within about one second of mean solar time (such as UT1) at 0° longitude (at the IERS Reference Meridian as the currently use ...
(UTC) and that the scale should be indicated when the difference is significant. The fraction of the day is found by converting the number of hours, minutes, and seconds after noon into the equivalent decimal fraction. Time intervals calculated from differences of Julian Dates specified in non-uniform time scales, such as UTC, may need to be corrected for changes in time scales (e.g.
leap second A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise observe ...
s).


Variants

Because the starting point or reference epoch is so long ago, numbers in the Julian day can be quite large and cumbersome. A more recent starting point is sometimes used, for instance by dropping the leading digits, in order to fit into limited computer memory with an adequate amount of precision. In the following table, times are given in 24-hour notation. In the table below, ''Epoch'' refers to the point in time used to set the origin (usually zero, but (1) where explicitly indicated) of the alternative convention being discussed in that row. The date given is a Gregorian calendar date unless otherwise specified. JD stands for Julian Date. 0h is 00:00 midnight, 12h is 12:00 noon, UT unless otherwise specified. Current value is as of and may be cached. [] * The Modified Julian Date (MJD) was introduced by the Smithsonian Astrophysical Observatory in 1957 to record the orbit of Sputnik 1, Sputnik via an IBM 704 (36-bit machine) and using only 18 bits until August 7, 2576. MJD is the epoch of VAX/VMS and its successor
OpenVMS OpenVMS, often referred to as just VMS, is a multi-user, multiprocessing and virtual memory-based operating system. It is designed to support time-sharing, batch processing, transaction processing and workstation applications. Customers using Op ...
, using 63-bit date/time, which allows times to be stored up to July 31, 31086, 02:48:05.47. The MJD has a starting point of midnight on November 17, 1858, and is computed by MJD = JD − 2400000.5 * The Truncated Julian Day (TJD) was introduced by NASA/
Goddard Goddard may refer to: People * Goddard (given name) * Goddard (surname) Places in the United States * Goddard, Kansas * Goddard, Kentucky *Goddard, Maryland *Goddard College, a low-residency college with campuses in Vermont and Washington * G ...
in 1979 as part of a parallel grouped binary time code (PB-5) "designed specifically, although not exclusively, for spacecraft applications". TJD was a 4-digit day count from MJD 40000, which was May 24, 1968, represented as a 14-bit binary number. Since this code was limited to four digits, TJD recycled to zero on MJD 50000, or October 10, 1995, "which gives a long ambiguity period of 27.4 years". (NASA codes PB-1–PB-4 used a 3-digit day-of-year count.) Only whole days are represented. Time of day is expressed by a count of seconds of a day, plus optional milliseconds, microseconds and nanoseconds in separate fields. Later PB-5J was introduced which increased the TJD field to 16 bits, allowing values up to 65535, which will occur in the year 2147. There are five digits recorded after TJD 9999. * The Dublin Julian Date (DJD) is the number of days that has elapsed since the epoch of the solar and lunar
ephemerides In astronomy and celestial navigation, an ephemeris (pl. ephemerides; ) is a book with tables that gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position (and possibly ve ...
used from 1900 through 1983,
Newcomb's Tables of the Sun Newcomb's Tables of the Sun (full title ''Tables of the Motion of the Earth on its Axis and Around the Sun'') is a work by the American astronomer and mathematician Simon Newcomb, published in volume VI of the serial publication ''Astronomic ...
and
Ernest W. Brown Ernest William Brown FRS (29 November 1866 – 22 July 1938) was an English mathematician and astronomer, who spent the majority of his career working in the United States and became a naturalised American citizen in 1923. His life's work was ...
's ''Tables of the Motion of the Moon'' (1919). This epoch was noon UT on :January 0, 1900, which is the same as noon UT on December 31, 1899. The DJD was defined by the International Astronomical Union at their meeting in
Dublin Dublin (; , or ) is the capital and largest city of Ireland. On a bay at the mouth of the River Liffey, it is in the province of Leinster, bordered on the south by the Dublin Mountains, a part of the Wicklow Mountains range. At the 2016 cen ...
,
Ireland Ireland ( ; ga, Éire ; Ulster-Scots: ) is an island in the North Atlantic Ocean, in north-western Europe. It is separated from Great Britain to its east by the North Channel, the Irish Sea, and St George's Channel. Ireland is the s ...
, in 1955. * The Lilian day number is a count of days of the Gregorian calendar and not defined relative to the Julian Date. It is an integer applied to a whole day; day 1 was October 15, 1582, which was the day the Gregorian calendar went into effect. The original paper defining it makes no mention of the time zone, and no mention of time-of-day. It was named for
Aloysius Lilius Aloysius Lilius (c. 1510 – 1576), also variously referred to as Luigi Lilio or Luigi Giglio, was an Italian doctor, astronomer, philosopher and chronologist, and also the "primary author" who provided the proposal that (after modifications) b ...
, the principal author of the Gregorian calendar. *
Rata Die Rata Die (R.D.) is a system for assigning numbers to calendar days (optionally with time of day), independent of any calendar, for the purposes of calendrical calculations. It was named (after the Latin ablative feminine singular for "from a fixed ...
is a system used in
Rexx Rexx (Restructured Extended Executor) is a programming language that can be interpreted or compiled. It was developed at IBM by Mike Cowlishaw. It is a structured, high-level programming language designed for ease of learning and reading. ...
, Go and
Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (pr ...
. Some implementations or options use
Universal Time Universal Time (UT or UT1) is a time standard based on Earth's rotation. While originally it was mean solar time at 0° longitude, precise measurements of the Sun are difficult. Therefore, UT1 is computed from a measure of the Earth's angle with ...
, others use local time. Day 1 is January 1, 1, that is, the first day of the Christian or
Common Era Common Era (CE) and Before the Common Era (BCE) are year notations for the Gregorian calendar (and its predecessor, the Julian calendar), the world's most widely used calendar era. Common Era and Before the Common Era are alternatives to the or ...
in the
proleptic Gregorian calendar The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to the dates preceding its official introduction in 1582. In nations that adopted the Gregorian calendar after its official and first introduction, dates occ ...
. In Rexx January 1 is Day 0. The Heliocentric Julian Day (HJD) is the same as the Julian day, but adjusted to the frame of reference of the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
, and thus can differ from the Julian day by as much as 8.3 minutes (498 seconds), that being the time it takes light to reach
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surface ...
from the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
.


History


Julian Period

The ''Julian day number'' is based on the ''Julian Period'' proposed by
Joseph Scaliger Joseph Justus Scaliger (; 5 August 1540 – 21 January 1609) was a French Calvinist religious leader and scholar, known for expanding the notion of classical history from Greek and Ancient Roman history to include Persian, Babylonian, Jewish an ...
, a classical scholar, in 1583 (one year after the Gregorian calendar reform) as it is the product of three calendar cycles used with the Julian calendar: Its epoch occurs when all three cycles (if they are continued backward far enough) were in their first year together. Years of the Julian Period are counted from this year, , as , which was chosen to be before any historical record. Scaliger corrected chronology by assigning each year a tricyclic "character", three numbers indicating that year's position in the 28-year solar cycle, the 19-year lunar cycle, and the 15-year indiction cycle. One or more of these numbers often appeared in the historical record alongside other pertinent facts without any mention of the Julian calendar year. The character of every year in the historical record was unique – it could only belong to one year in the 7980-year Julian Period. Scaliger determined that was Julian Period . He knew that had the character 9 of the solar cycle, 1 of the lunar cycle, and 3 of the indiction cycle. By inspecting a 532-year
Paschal cycle The Paschal cycle, in Eastern Orthodox Christianity, is the cycle of the moveable feasts built around Pascha (Easter). The cycle consists of approximately ten weeks before and seven weeks after Pascha. The ten weeks before Pascha are known as ...
with 19 solar cycles (each year numbered 1–28) and 28 lunar cycles (each year numbered 1–19), he determined that the first two numbers, 9 and 1, occurred at its year 457. He then calculated via remainder division that he needed to add eight 532-year Paschal cycles totaling 4256 years before the cycle containing in order for its year 457 to be indiction 3. The sum was thus . A formula for determining the year of the Julian Period given its character involving three four-digit numbers was published by
Jacques de Billy : ''For the English patristic scholar and Benedictine abbot, see Jacques de Billy (abbot) (1535–1581).'' Jacques de Billy (March 18, 1602 – January 14, 1679) was a French Jesuit mathematician. Born in Compiègne, he subsequently entere ...
in 1665 in the ''
Philosophical Transactions of the Royal Society ''Philosophical Transactions of the Royal Society'' is a scientific journal published by the Royal Society. In its earliest days, it was a private venture of the Royal Society's secretary. It was established in 1665, making it the first journa ...
'' (its first year). John F. W. Herschel gave the same formula using slightly different wording in his 1849 ''Outlines of Astronomy''.
Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
introduced the
modulo operation In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is th ...
in 1801, restating de Billy's formula as: where ''a'' is the year of the indiction cycle, ''b'' of the lunar cycle, and ''c'' of the solar cycle. John Collins described the details of how these three numbers were calculated in 1666, using many trials. A summary of Collin's description is in a footnote. Reese, Everett and Craun reduced the dividends in the ''Try'' column from 285, 420, 532 to 5, 2, 7 and changed remainder to modulo, but apparently still required many trials.Reese, Everett and Craun 1981 The specific cycles used by Scaliger to form his tricyclic Julian Period were, first, the indiction cycle with a first year of 313. Then he chose the dominant 19-year Alexandrian lunar cycle with a first year of 285, the
Era of Martyrs The Era of the Martyrs ( la, anno martyrum), also known as the ''Diocletian era'' ( la, anno Diocletiani), is a method of numbering years used by the Church of Alexandria beginning in the 4th century AD/CE and by the Coptic Orthodox Church of ...
and the Diocletian Era epoch, or a first year of 532 according to
Dionysius Exiguus Dionysius Exiguus (Latin for "Dionysius the Humble", Greek: Διονύσιος; – ) was a 6th-century Eastern Roman monk born in Scythia Minor. He was a member of a community of Scythian monks concentrated in Tomis (present day Constanța ...
.Dionysius Exiguus 2003/525 Finally, Scaliger chose the post-Bedan solar cycle with a first year of 776, when its first quadrennium of
concurrent Concurrent means happening at the same time. Concurrency, concurrent, or concurrence may refer to: Law * Concurrence, in jurisprudence, the need to prove both ''actus reus'' and ''mens rea'' * Concurring opinion (also called a "concurrence"), a ...
s, , began in sequence. Although not their intended use, the equations of de Billy or Gauss can be used to determined the first year of any 15-, 19-, and 28-year tricyclic period given any first years of their cycles. For those of the Julian Period, the result is AD3268, because both remainder and modulo usually return the lowest positive result. Thus 7980years must be subtracted from it to yield the first year of the present Julian Period, −4712 or 4713BC, when all three of its sub-cycles are in their first years. Scaliger got the idea of using a tricyclic period from "the Greeks of Constantinople" as Herschel stated in his quotation below in Julian day numbers.Herschel 1849, p. 634 Specifically, the monk and priest Georgios wrote in 638/39 that the Byzantine year 6149 AM (640/41) had indiction 14, lunar cycle 12, and solar cycle 17, which places the first year of the
Byzantine Era The Byzantine calendar, also called the Roman calendar, the Creation Era of Constantinople or the Era of the World ( grc, Ἔτη Γενέσεως Κόσμου κατὰ Ῥωμαίους, also or , abbreviated as ε.Κ.; literal translation of ...
in 5509/08BC, the Byzantine Creation. Dionysius Exiguus called the Byzantine lunar cycle his "lunar cycle" in argumentum 6, in contrast with the Alexandrian lunar cycle which he called his "nineteen-year cycle" in argumentum 5. Although many references say that the ''Julian'' in "Julian Period" refers to Scaliger's father, Julius Scaliger, at the beginning of Book V of his ' ("Work on the Emendation of Time") he states, "", which Reese, Everett and Craun translate as "We have termed it Julian because it fits the Julian year." Thus ''Julian'' refers to the
Julian calendar The Julian calendar, proposed by Roman consul Julius Caesar in 46 BC, was a reform of the Roman calendar. It took effect on , by edict. It was designed with the aid of Greek mathematicians and astronomers such as Sosigenes of Alexandria. ...
.


Julian day numbers

Julian days were first used by Ludwig Ideler for the first days of the Nabonassar and Christian eras in his 1825 ''Handbuch der mathematischen und technischen Chronologie''. John F. W. Herschel then developed them for astronomical use in his 1849 ''Outlines of Astronomy'', after acknowledging that Ideler was his guide. At least one mathematical
astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either obse ...
adopted Herschel's "days of the Julian period" immediately.
Benjamin Peirce Benjamin Peirce (; April 4, 1809 – October 6, 1880) was an American mathematician who taught at Harvard University for approximately 50 years. He made contributions to celestial mechanics, statistics, number theory, algebra, and the philos ...
of
Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
used over 2,800 Julian days in his ''Tables of the Moon'', begun in 1849 but not published until 1853, to calculate the lunar
ephemerides In astronomy and celestial navigation, an ephemeris (pl. ephemerides; ) is a book with tables that gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position (and possibly ve ...
in the new ''American Ephemeris and Nautical Almanac'' from 1855 to 1888. The days are specified for "Washington mean noon", with Greenwich defined as west of Washington (282°57′W, or Washington 77°3′W of Greenwich). A table with 197 Julian days ("Date in Mean Solar Days", one per century mostly) was included for the years –4713 to 2000 with no year 0, thus "–" means BC, including decimal fractions for hours, minutes and seconds. The same table appears in ''Tables of Mercury'' by Joseph Winlock, without any other Julian days. The national ephemerides started to include a multi-year table of Julian days, under various names, for either every year or every leap year beginning with the French ''Connaissance des Temps'' in 1870 for 2,620 years, increasing in 1899 to 3,000 years. The British ''Nautical Almanac'' began in 1879 with 2,000 years. The ''Berliner Astronomisches Jahrbuch'' began in 1899 with 2,000 years. The ''American Ephemeris'' was the last to add a multi-year table, in 1925 with 2,000 years. However, it was the first to include any mention of Julian days with one for the year of issue beginning in 1855, as well as later scattered sections with many days in the year of issue. It was also the first to use the name "Julian day number" in 1918. The ''Nautical Almanac'' began in 1866 to include a Julian day for every day in the year of issue. The ''Connaissance des Temps'' began in 1871 to include a Julian day for every day in the year of issue. The French mathematician and astronomer
Pierre-Simon Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...
first expressed the time of day as a decimal fraction added to calendar dates in his book, , in 1823. Other astronomers added fractions of the day to the Julian day number to create Julian Dates, which are typically used by astronomers to date
astronomical Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galax ...
observations, thus eliminating the complications resulting from using standard calendar periods like eras, years, or months. They were first introduced into
variable star A variable star is a star whose brightness as seen from Earth (its apparent magnitude) changes with time. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as e ...
work in 1860 by the English astronomer Norman Pogson, which he stated was at the suggestion of John Herschel. They were popularized for variable stars by
Edward Charles Pickering Edward Charles Pickering (July 19, 1846 – February 3, 1919) was an American astronomer and physicist and the older brother of William Henry Pickering. Along with Carl Vogel, Pickering discovered the first spectroscopic binary stars. He wrote '' ...
, of the
Harvard College Observatory The Harvard College Observatory (HCO) is an institution managing a complex of buildings and multiple instruments used for astronomical research by the Harvard University Department of Astronomy. It is located in Cambridge, Massachusetts, United St ...
, in 1890. Julian days begin at noon because when Herschel recommended them, the
astronomical day An astronomical day refers to a length of day of exactly or nearly 24 hours beginning at noon instead of at midnight. The exact length has been variously defined as either that of a solar day or of a sidereal day. Astronomical days were historical ...
began at noon. The astronomical day had begun at noon ever since
Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
chose to begin the days for his astronomical observations at noon. He chose noon because the transit of the Sun across the observer's meridian occurs at the same apparent time every day of the year, unlike sunrise or sunset, which vary by several hours. Midnight was not even considered because it could not be accurately determined using
water clock A water clock or clepsydra (; ; ) is a timepiece by which time is measured by the regulated flow of liquid into (inflow type) or out from (outflow type) a vessel, and where the amount is then measured. Water clocks are one of the oldest time-m ...
s. Nevertheless, he double-dated most nighttime observations with both Egyptian days beginning at sunrise and Babylonian days beginning at sunset. Medieval Muslim astronomers used days beginning at sunset, so astronomical days beginning at noon did produce a single date for an entire night. Later medieval European astronomers used Roman days beginning at midnight so astronomical days beginning at noon also allow observations during an entire night to use a single date. When all astronomers decided to start their astronomical days at midnight to conform to the beginning of the civil day, on , it was decided to keep Julian days continuous with previous practice, beginning at noon. During this period, usage of Julian day numbers as a neutral intermediary when converting a date in one calendar into a date in another calendar also occurred. An isolated use was by Ebenezer Burgess in his 1860 translation of the ''
Surya Siddhanta The ''Surya Siddhanta'' (; ) is a Sanskrit treatise in Indian astronomy dated to 505 CE,Menso Folkerts, Craig G. Fraser, Jeremy John Gray, John L. Berggren, Wilbur R. Knorr (2017)Mathematics Encyclopaedia Britannica, Quote: "(...) its Hindu inven ...
'' wherein he stated that the beginning of the
Kali Yuga ''Kali Yuga'', in Hinduism, is the fourth and worst of the four ''yugas'' (world ages) in a ''Yuga Cycle'', preceded by ''Dvapara Yuga'' and followed by the next cycle's '' Krita (Satya) Yuga''. It is believed to be the present age, which is ...
era occurred at midnight at the meridian of
Ujjain Ujjain (, Hindustani pronunciation: �d͡ːʒɛːn is a city in Ujjain district of the Indian state of Madhya Pradesh. It is the fifth-largest city in Madhya Pradesh by population and is the administrative centre of Ujjain district and Ujjai ...
at the end of the 588,465th day and the beginning of the 588,466th day (civil reckoning) of the Julian Period, or between or . Robert Schram was notable beginning with his 1882 ''Hilfstafeln für Chronologie''. Here he used about 5,370 "days of the Julian Period". He greatly expanded his usage of Julian days in his 1908 ''Kalendariographische und Chronologische Tafeln'' containing over 530,000 Julian days, one for the zeroth day of every month over thousands of years in many calendars. He included over 25,000 negative Julian days, given in a positive form by adding 10,000,000 to each. He called them "day of the Julian Period", "Julian day", or simply "day" in his discussion, but no name was used in the tables. Continuing this tradition, in his book "Mapping Time: The Calendar and Its History" British physics educator and programmer Edward Graham Richards uses Julian day numbers to convert dates from one calendar into another using algorithms rather than tables.


Julian day number calculation

The Julian day number can be calculated using the following formulas (
integer division Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication. At an elementary level the division of two natural numbers ...
rounding towards zero is used exclusively, that is, positive values are rounded down and negative values are rounded up): The months January to December are numbered 1 to 12. For the year,
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 w ...
is used, thus 1 BC is 0, 2 BC is −1, and 4713 BC is −4712. ''JDN'' is the Julian Day Number. Use the previous day of the month if trying to find the JDN of an instant before midday UT.


Converting Gregorian calendar date to Julian Day Number

The algorithm is valid for all (possibly
proleptic Proleptic may refer to: * Prolepsis, several meanings related to foreshadowing * Proleptic calendar, a calendar that is applied to dates before its introduction * Proleptic syllogism, a class of syllogism in logic {{disambiguation ...
) Gregorian calendar dates after November 23, −4713. Divisions are integer divisions towards zero; fractional parts are ignored.


Converting Julian calendar date to Julian Day Number

The algorithm is valid for all (possibly
proleptic Proleptic may refer to: * Prolepsis, several meanings related to foreshadowing * Proleptic calendar, a calendar that is applied to dates before its introduction * Proleptic syllogism, a class of syllogism in logic {{disambiguation ...
) Julian calendar years ≥ −4712, that is, for all JDN ≥ 0. Divisions are integer divisions, fractional parts are ignored.


Finding Julian date given Julian day number and time of day

For the full Julian Date of a moment after 12:00 UT one can use the following. Divisions are
real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every r ...
s. So, for example, January 1, 2000, at 18:00:00 UT corresponds to ''JD'' = 2451545.25 For a point in time in a given Julian day after midnight UT and before 12:00 UT, add 1 or use the JDN of the next afternoon.


Finding day of week given Julian day number

The US day of the
week A week is a unit of time equal to seven days. It is the standard time period used for short cycles of days in most parts of the world. The days are often used to indicate common work days and rest days, as well as days of worship. Weeks are ofte ...
W1 (for an afternoon or evening UT) can be determined from the Julian Day Number J with the expression: If the moment in time is after midnight UT (and before 12:00 UT), then one is already in the next day of the week. The ISO day of the week W0 can be determined from the Julian Day Number J with the expression:


Julian or Gregorian calendar from Julian day number

This is an algorithm by Edward Graham Richards to convert a Julian Day Number, J, to a date in the Gregorian calendar (proleptic, when applicable). Richards states the algorithm is valid for Julian day numbers greater than or equal to 0. All variables are integer values, and the notation "''a'' div ''b''" indicates
integer division Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication. At an elementary level the division of two natural numbers ...
, and "mod(''a'',''b'')" denotes the
modulus operator In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is ...
. For Julian calendar: # ''f'' = J + ''j'' For Gregorian calendar: # ''f'' = J + ''j'' + (((4 × J + ''B'') div 146097) × 3) div 4 + ''C'' For Julian or Gregorian, continue: D, M, and Y are the numbers of the day, month, and year respectively for the afternoon at the beginning of the given Julian day.


Julian Period from indiction, Metonic and solar cycles

Let Y be the year BC or AD and i, m and s respectively its positions in the indiction, Metonic and solar cycles. Divide 6916i + 4200m + 4845s by 7980 and call the remainder r. Example i = 8, m = 2, s = 8. What is the year?


Julian date calculation

As stated above, the Julian date (JD) of any instant is the Julian day number for the preceding noon in Universal Time plus the fraction of the day since that instant. Ordinarily calculating the fractional portion of the JD is straightforward; the number of seconds that have elapsed in the day divided by the number of seconds in a day, 86,400. But if the UTC timescale is being used, a day containing a positive
leap second A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise observe ...
contains 86,401 seconds (or in the unlikely event of a negative leap second, 86,399 seconds). One authoritative source, the Standards of Fundamental Astronomy (SOFA), deals with this issue by treating days containing a leap second as having a different length (86,401 or 86,399 seconds, as required). SOFA refers to the result of such a calculation as "quasi-JD"."SOFA Time Scale and Calendar Tools" 2016, p. 20


See also

*
Julian year (calendar) The Julian calendar, proposed by Roman consul Julius Caesar in 46 BC, was a reform of the Roman calendar. It took effect on , by edict. It was designed with the aid of Greek mathematicians and astronomers such as Sosigenes of Alexandria. ...
*
5th millennium BC The 5th millennium BC spanned the years 5000 BC to 4001 BC (c. 7 ka to c. 6 ka). It is impossible to precisely date events that happened around the time of this millennium and all dates mentioned here are estimates mostly based on geological an ...
* Barycentric Julian Date *
Dual dating Dual dating is the practice, in historical materials, to indicate some dates with what appears to be duplicate, or excessive digits, sometimes separated by a hyphen, a slash or are placed one above the other. The need for dual dating arose from t ...
*
Decimal time Decimal time is the representation of the time of day using units which are decimally related. This term is often used specifically to refer to the time system used in France for a few years beginning in 1792 during the French Revolution, whi ...
*
Epoch (astronomy) 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 per ...
*
Epoch (reference date) In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided by ...
*
Era An era is a span of time defined for the purposes of chronology or historiography, as in the regnal eras in the history of a given monarchy, a calendar era used for a given calendar, or the geological eras defined for the history of Earth. Compa ...
*
J2000 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 per ...
– the epoch that starts on JD 2451545.0 (TT), the standard epoch used in astronomy since 1984 * Lunation Number (similar concept) *
Ordinal date An ordinal date is a calendar date typically consisting of a ''year'' and a day of the year or ordinal day number (or simply ordinal day or day number), an ordinal number ranging between 1 and 366 (starting on January 1), though year may sometime ...
*
Time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, t ...
*
Time standard A time standard is a specification for measuring time: either the rate at which time passes or points in time or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters o ...
s *
Zeller's congruence Zeller's congruence is an algorithm devised by Christian Zeller in the 19th century to calculate the day of the week for any Julian or Gregorian calendar date. It can be considered to be based on the conversion between Julian day and the calendar ...


Notes


References


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