Julian day
Encyclopedia
Julian day is used in the Julian date (JD) system of time measurement for scientific use by the astronomy community, presenting the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon. Julian date is recommended for astronomical use by the International Astronomical Union
.
The Julian Day Number (JDN) is the Julian day with the fractional part ignored. It is sometimes used in calendrical calculation
, in which case, JDN 0 is used for the date equivalent to Monday January 1, 4713 BC in the Julian calendar
.
The term Julian date is widely used to refer to the dayofyear (ordinal date
) although incorrectly.
, but the International Astronomical Union
now recommends that Julian Dates be specified in Terrestrial Time
, and that when necessary to specify Julian Dates using a different time scale, that the time scale used be indicated when required, such as JD(UT1). The fraction of the day is found by converting the number of hours, minutes, and seconds after noon into the equivalent decimal fraction.
The term Julian date is also used to refer to:
The use of Julian date to refer to the dayofyear (ordinal date) is usually considered to be incorrect although it is widely used that way in the earth sciences, computer programming, military and the food industry.
The Julian date (JD) is the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon, Julian proleptic calendar. In precise work, the timescale, e.g., Terrestrial Time
(TT) or Universal Time
(UT), should be specified.
The Julian day number (JDN) is the integer part of the Julian date (JD). The day commencing at the abovementioned epoch
is JDN 0. Now, at the Julian day number is . Negative values can be used for dates preceding JD 0, though they predate all recorded history
. However, in this case, the JDN is the greatest integer not greater than the Julian date rather than simply the integer part of the JD.
A Julian date of 2454115.05486 means that the date and Universal Time is Sunday January 14, 2007 at 13:18:59.9.
The decimal parts of a Julian date:
0.1 = 2.4 hours or 144 minutes or 8640 seconds
0.01 = 0.24 hours or 14.4 minutes or 864 seconds
0.001 = 0.024 hours or 1.44 minutes or 86.4 seconds
0.0001 = 0.0024 hours or 0.144 minutes or 8.64 seconds
0.00001 = 0.00024 hours or 0.0144 minutes or 0.864 seconds.
Almost 2.5 million Julian days have elapsed since the initial epoch
. JDN 2,400,000 was November 16, 1858. JD 2,500,000.0 will occur on August 31, 2132 at noon UT.
If the Julian date of noon is applied to the entire midnighttomidnight civil day centered on that noon, rounding Julian dates (fractional days) for the twelve hours before noon up while rounding those after noon down, then the remainder upon division by 7 represents the day of the week (see the table below). Now at the nearest noon JDN is yielding a remainder of .
The Julian day number can be considered a very simple calendar
, where its calendar date
is just an integer. This is useful for reference, computations, and conversions. It allows the time between any two dates in history to be computed by simple subtraction
.
The Julian day system was introduced by astronomers to provide a single system of dates that could be used when working with different calendars and to unify different historical chronologies. Julian day and Julian date are not directly related to the Julian calendar
, although it is possible to convert any date from one calendar to the other.
In the table below, Epoch refers to the point in time used to set the origin (usually zero, but Day 1 where explicitly indicated) of the alternative convention being discussed in that row. The date given is a Gregorian calendar
date if it is October 15, 1582 or later, but a Julian calendar
date if it is earlier.
The Heliocentric Julian Day (HJD) is the same as the Julian day, but adjusted to the frame of reference of the Sun
, and thus can differ from the Julian day by as much as 8.3 minutes, that being the time it takes the Sun's light to reach Earth
. As two separate astronomical measurements can exist that were taken when the Earth, astronomical objects, and Sun are in a straight line but the Earth was actually on opposite sides of the Sun for the two measurements, that is at one roughly 500 light seconds nearer to the astronomical than the Sun for the first measure, then 500 light seconds further from the astronomical object than the Sun for the second measure, then the subsequent light time error between two Julian Day measures can amount to nearly as much as 1000 seconds different relative to the same Heliocentric Julian Day interval which can make a significant difference when measuring temporal phenomena for short period astronomical objects over long time intervals. The Julian day is sometimes referred to as the Geocentric Julian Day (GJD) in order to distinguish it from HJD.
in 1583, at the time of the Gregorian calendar
reform, but it is the multiple of three calendar
cycles used with the Julian calendar
:
Its epoch
falls at the last time when all three cycles (if they are continued backward far enough) were in their first year together — Scaliger chose this because it preceded all historical dates.
Although many references say that the Julian in "Julian day" refers to Scaliger's father, Julius Scaliger
, in the introduction to Book V of his Opus de Emendatione Temporum ("Work on the Emendation of Time") he states, "Iulianum vocavimus: quia ad annum Iulianum dumtaxat accomodata est", which translates more or less as "We have called it Julian merely because it is accommodated to the Julian year." This Julian refers to Julius Caesar
, who introduced the Julian calendar in 46 BC.
In his book Outlines of Astronomy, first published in 1849, the astronomer John Herschel
wrote:
Astronomer
s adopted Herschel's Julian Days in the late nineteenth century, but used the meridian of Greenwich instead of Alexandria, after the former was adopted as the Prime Meridian
after the International Meridian Conference
in Washington in 1884. This has now become the standard system of Julian days. Julian days are typically used by astronomers to date astronomical
observations, thus eliminating the complications resulting from using standard calendar
periods like eras, years, or months. They were first introduced into variable star
work by Edward Charles Pickering
, of the Harvard College Observatory
, in 1890.
Julian days begin at noon because when Herschel recommended them, the astronomical day began at noon (it did so until 1925). The astronomical day had begun at noon ever since Ptolemy
chose to begin the days in his astronomical periods 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
s. Nevertheless, he doubledated most nighttime observations with both Egyptian
days beginning at sunrise and Babylonian days beginning at sunset. This would seem to imply that his choice of noon was not, as is sometimes stated, made in order to allow all observations from a given night to be recorded with the same date.
The months (M) January to December are 1 to 12. For the year (Y) astronomical year numbering
is used, thus 1 BC is 0, 2 BC is −1, and 4713 BC is −4712. D is the day of the month. JDN is the Julian Day Number, which pertains to the noon occurring in the corresponding calendar date.
You must compute first:
then compute:
NOTE: When doing the divisions, the fractional parts of the quotients must be dropped. All years in the BC era must be converted to a negative value then incremented toward zero to be passed as an astronomical year, so that 1 BC will be passed as y=0.
s (divisions are real numbers):
So, for example, January 1, 2000 at midday corresponds to JD = 2451545.0
The day of the week
can be determined from the Julian day number by calculating it modulo
7, where 0 means Monday.
The calculations below (which use integer division [div] and modulo [mod] with positive numbers only) are valid for the whole range of dates since −4800. For dates before 1582, the resulting date components are valid only in the Gregorian proleptic calendar. This is based on the Gregorian calendar but extended to cover dates before its introduction, including the preChristian era. For dates in that era (before year AD 1), astronomical year numbering
is used. This includes a year zero, which immediately precedes AD 1. Astronomical year zero is 1 BC in the proleptic Gregorian calendar and, in general, proleptic Gregorian year (n BC) = astronomical year (Y = 1 − n). For astronomical year Y (Y < 1), the proleptic Gregorian year is (1 − Y) BC.
The operations div and mod used here are intended to have the same binary operator priority as the multipication and division, and defined as:
You can also use only integers in most of the formula above, by taking J = floor(JD + 0.5), to compute the three integers (Y, M, D).
The time of the day is then computed from the fractional day T = frac(JD + 0.5). The additive 0.5 constant can also be adjusted to take the local timezone into account, when computing an astronomical Gregorian date localized in another timezone than UTC. To convert the fractional day into actual hours, minutes, seconds, the astronomical Gregorian calendar uses a constant length of 24 hours per day (i.e. 86400 seconds exactly), ignoring leap second
s inserted or deleted at end of some specific days in the UTC Gregorian calendar. If you want to convert it to actual UTC time, you will need to compensate the UTC leap seconds by adding them to J before restarting the computation (however this adjustment requires a lookup table, because leap seconds are not predictable with a simple formula); you'll also need to finally determine which of the two possible UTC date and time is used at times where leap seconds are added (no final compensation will be needed if negative leap seconds are occurring on the rare possible days that could be shorter than 24 hours).
is the term used to describe the manner in which UNIXlike
operating systems internally maintain time. The variable type time t defines UNIX time in terms of seconds elapsed since midnight January 1, 1970 UTC, a point in time referred to as the epoch. Negative time_t values represent dates prior to the epoch. Assuming the variable U has been defined to be of type time_t, the following mathematical progression may be used to break down a UNIX time value to its civil time
equivalent:
where ss are seconds, mm minutes and hh hours. Day, month and year can be calculated as in the section Gregorian calendar from Julian day number, applying calculations to:
and D being:
International Astronomical Union
The International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...
.
The Julian Day Number (JDN) is the Julian day with the fractional part ignored. It is sometimes used in calendrical calculation
Calendrical calculation
A Calendrical calculation is a calculation concerning calendar dates. Calendrical calculations can be considered an area of applied mathematics.Some examples of calendrical calculations:* The number of days between two dates....
, in which case, JDN 0 is used for the date equivalent to Monday January 1, 4713 BC in the Julian calendar
Julian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
.
The term Julian date is widely used to refer to the dayofyear (ordinal date
Ordinal date
An ordinal date is a calendar date typically consisting of a year and a day of year ranging between 1 and 366 , though year may sometimes be omitted...
) although incorrectly.
Julian Date
Historical Julian dates were recorded relative to GMT or Ephemeris TimeEphemeris time
The term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:...
, but the International Astronomical Union
International Astronomical Union
The International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...
now recommends that Julian Dates be specified in Terrestrial Time
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for timemeasurements of astronomical observations made from the surface of the Earth....
, and that when necessary to specify Julian Dates using a different time scale, that the time scale used be indicated when required, such as JD(UT1). The fraction of the day is found by converting the number of hours, minutes, and seconds after noon into the equivalent decimal fraction.
The term Julian date is also used to refer to:
 Julian calendarJulian calendarThe Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
dates  ordinal dates (dayofyear)
The use of Julian date to refer to the dayofyear (ordinal date) is usually considered to be incorrect although it is widely used that way in the earth sciences, computer programming, military and the food industry.
The Julian date (JD) is the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon, Julian proleptic calendar. In precise work, the timescale, e.g., Terrestrial Time
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for timemeasurements of astronomical observations made from the surface of the Earth....
(TT) or Universal Time
Universal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...
(UT), should be specified.
The Julian day number (JDN) is the integer part of the Julian date (JD). The day commencing at the abovementioned epoch
Epoch (reference date)
In the fields of chronology and periodization, an epoch is an instance in time chosen as the origin of a particular era. The "epoch" then serves as a reference point from which time is measured...
is JDN 0. Now, at the Julian day number is . Negative values can be used for dates preceding JD 0, though they predate all recorded history
Recorded history
Recorded history is the period in history of the world after prehistory. It has been written down using language, or recorded using other means of communication. It starts around the 4th millennium BC, with the invention of writing.Historical accounts:...
. However, in this case, the JDN is the greatest integer not greater than the Julian date rather than simply the integer part of the JD.
A Julian date of 2454115.05486 means that the date and Universal Time is Sunday January 14, 2007 at 13:18:59.9.
The decimal parts of a Julian date:
0.1 = 2.4 hours or 144 minutes or 8640 seconds
0.01 = 0.24 hours or 14.4 minutes or 864 seconds
0.001 = 0.024 hours or 1.44 minutes or 86.4 seconds
0.0001 = 0.0024 hours or 0.144 minutes or 8.64 seconds
0.00001 = 0.00024 hours or 0.0144 minutes or 0.864 seconds.
Almost 2.5 million Julian days have elapsed since the initial epoch
Epoch (reference date)
In the fields of chronology and periodization, an epoch is an instance in time chosen as the origin of a particular era. The "epoch" then serves as a reference point from which time is measured...
. JDN 2,400,000 was November 16, 1858. JD 2,500,000.0 will occur on August 31, 2132 at noon UT.
If the Julian date of noon is applied to the entire midnighttomidnight civil day centered on that noon, rounding Julian dates (fractional days) for the twelve hours before noon up while rounding those after noon down, then the remainder upon division by 7 represents the day of the week (see the table below). Now at the nearest noon JDN is yielding a remainder of .
The Julian day number can be considered a very simple calendar
Calendar
A calendar is a system of organizing days for social, religious, commercial, or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years. The name given to each day is known as a date. Periods in a calendar are usually, though not...
, where its calendar date
Calendar date
A date in a calendar is a reference to a particular day represented within a calendar system. The calendar date allows the specific day to be identified. The number of days between two dates may be calculated. For example, "24 " is ten days after "14 " in the Gregorian calendar. The date of a...
is just an integer. This is useful for reference, computations, and conversions. It allows the time between any two dates in history to be computed by simple subtraction
Subtraction
In arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...
.
The Julian day system was introduced by astronomers to provide a single system of dates that could be used when working with different calendars and to unify different historical chronologies. Julian day and Julian date are not directly related to the Julian calendar
Julian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
, although it is possible to convert any date from one calendar to the other.
Alternatives
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 Day 1 where explicitly indicated) of the alternative convention being discussed in that row. The date given is a Gregorian calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
date if it is October 15, 1582 or later, but a Julian calendar
Julian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
date if it is earlier.
Name  Epoch  Calculation  Current value  Notes 

Julian Date (JD)  12:00 January 1, 4713 BC, Monday  
Julian Day Number (JDN)  12:00 January 1, 4713 BC, Monday  JDN = floor (JD)  The day of the epoch is JDN 0. Changes at noon UT or TT. (JDN 0 = November 24, 4714 BC, Gregorian proleptic.) 

Reduced Julian Date (RJD)  12:00 November 16, 1858, Tuesday  RJD = JD − 2400000  Used by astronomers  
Modified Julian Date (MJD)  00:00 November 17, 1858, Wednesday  MJD = JD − 2400000.5  Introduced by SAO Smithsonian Astrophysical Observatory The Smithsonian Astrophysical Observatory is a research institute of the Smithsonian Institution headquartered in Cambridge, Massachusetts, where it is joined with the Harvard College Observatory to form the HarvardSmithsonian Center for Astrophysics .History:The SAO was founded in 1890 by... in 1957, Note that it starts from midnight rather than noon. 

Truncated Julian Date (TJD)  00:00 May 24, 1968, Friday 00:00 November 10, 1995, Tuesday 
TJD = JD − 2440000.5 TJD = (JD − 0.5) mod 10000 

 Definition as introduced by NASA  NIST definition 
Dublin Julian Date (DJD)  12:00 December 31, 1899, Sunday  DJD = JD − 2415020  Introduced by the IAU IAU IAU may refer to:*International Astronomical Union*International American University*International American University College of Medicine*International Association of Universities*International Association of Ultrarunners... in 1955 

Chronological Julian Date (CJD)  00:00 January 1, 4713 BC, Monday  CJD = JD + 0.5 + time zone adjustment  (UT)  Specific to time zone; Changes at midnight zone time; UT CJD given 
Lilian Day Number Lilian date A Lilian date is the number of days since the beginning of the Gregorian Calendar on October 15, 1582, regarded as Lilian date 1. It is named for Aloysius Lilius who devised the Gregorian Calendar. It was invented by Bruce G. Ohms of IBM in 1986.... 
October 15, 1582, Friday (as Day 1)  floor (JD − 2299160.5)  The count of days of the Gregorian calendar Gregorian calendar The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter... for Lilian date reckoned in Universal time. 

ANSI American National Standards Institute The American National Standards Institute is a private nonprofit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organization also coordinates U.S. standards with international... Date 
January 1, 1601, Monday (as Day 1)  floor (JD − 2305812.5)  The origin of COBOL COBOL COBOL is one of the oldest programming languages. Its name is an acronym for COmmon BusinessOriented Language, defining its primary domain in business, finance, and administrative systems for companies and governments.... integer dates 

Rata Die Rata Die Rata Die is a system for assigning numbers to calendar days , independent of any calendar, for the purposes of calendrical calculations.... 
January 1, 1, Monday (as Day 1)  floor (JD − 1721424.5)  The count of days of the Common Era Common Era Common Era ,abbreviated as CE, is an alternative designation for the calendar era originally introduced by Dionysius Exiguus in the 6th century, traditionally identified with Anno Domini .Dates before the year 1 CE are indicated by the usage of BCE, short for Before the Common Era Common Era... (Gregorian) 

Unix Time Unix time Unix time, or POSIX time, is a system for describing instants in time, defined as the number of seconds elapsed since midnight Coordinated Universal Time of Thursday, January 1, 1970 , not counting leap seconds, which are declared by the International Earth Rotation and Reference Systems Service... 
January 1, 1970, Thursday  (JD − 2440587.5) × 86400  Counts by the second, not the day 
 The Modified Julian Day is found by rounding downward. The MJD was introduced by the Smithsonian Astrophysical Observatory in 1957 to record the orbit of SputnikSputnik 1Sputnik 1 ) was the first artificial satellite to be put into Earth's orbit. It was launched into an elliptical low Earth orbit by the Soviet Union on 4 October 1957. The unanticipated announcement of Sputnik 1s success precipitated the Sputnik crisis in the United States and ignited the Space...
via an IBM 704 (36bit machine) and using only 18 bits until August 7, 2576. MJD is the epoch of OpenVMS, using 63bit date/time postponing the next Y2K campaignYear 2000 problemThe Year 2000 problem was a problem for both digital and nondigital documentation and data storage situations which resulted from the practice of abbreviating a fourdigit year to two digits.In computer programs, the practice of representing the year with two...
to July 31, 31086 02:48:05.47.
 The Dublin Julian Day (DJD) is the number of days that has elapsed since the epoch of the solar and lunar ephemerides used from 1900 through 1983, Newcomb's Tables of the SunNewcomb's Tables of the SunNewcomb's Tables of the Sun is the short title and running head of a work by the American astronomer and mathematician Simon Newcomb entitled "Tables of the Motion of the Earth on its Axis and Around the Sun" on pages 1–169 of "Tables of the Four Inner Planets" , volume VI of the serial publication...
and Ernest W. Brown'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 UnionInternational Astronomical UnionThe International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...
at their 1955 meeting in Dublin, IrelandRepublic of IrelandIreland , described as the Republic of Ireland , is a sovereign state in Europe occupying approximately fivesixths of the island of the same name. Its capital is Dublin. Ireland, which had a population of 4.58 million in 2011, is a constitutional republic governed as a parliamentary democracy,...
.
 The Chronological Julian Day was recently proposed by Peter Meyer and has been used by some students of the calendar and in some scientific software packages.
 The Lilian day number is a count of days of the Gregorian calendarGregorian calendarThe Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
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 timeofday. It was named for Aloysius LiliusAloysius LiliusAloysius Lilius , also variously referred to as Luigi Lilio, Luigi Giglio, or Aluise Baldassar Lilio, was an Italian doctor, astronomer, philosopher and chronologist, and also the "primary author" who provided the proposal that became the basis of the Gregorian Calendar reform of 1582.The crater...
, the principal author of the Gregorian calendar.
 The ANSIAmerican National Standards InstituteThe American National Standards Institute is a private nonprofit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organization also coordinates U.S. standards with international...
Date defines January 1, 1601 as day 1, and is used as the origin of COBOLCOBOLCOBOL is one of the oldest programming languages. Its name is an acronym for COmmon BusinessOriented Language, defining its primary domain in business, finance, and administrative systems for companies and governments....
integer dates. This epochEpoch (reference date)In the fields of chronology and periodization, an epoch is an instance in time chosen as the origin of a particular era. The "epoch" then serves as a reference point from which time is measured...
is the beginning of the previous 400year cycle of leap years in the Gregorian calendar, which ended with the year 2000.
 Rata DieRata DieRata Die is a system for assigning numbers to calendar days , independent of any calendar, for the purposes of calendrical calculations....
is a system (or more precisely a family of three systems) used in the book Calendrical Calculations. It uses the local timezone, and day 1 is January 1, 1, that is, the first day of the Christian or Common EraCommon EraCommon Era ,abbreviated as CE, is an alternative designation for the calendar era originally introduced by Dionysius Exiguus in the 6th century, traditionally identified with Anno Domini .Dates before the year 1 CE are indicated by the usage of BCE, short for Before the Common Era Common Era...
in the proleptic Gregorian calendarProleptic Gregorian calendarThe proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to dates preceding its official introduction in 1582.Usage:...
.
The Heliocentric Julian Day (HJD) is the same as the Julian day, but adjusted to the frame of reference of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
, and thus can differ from the Julian day by as much as 8.3 minutes, that being the time it takes the Sun's light to reach Earth
Earth
Earth is the third planet from the Sun, and the densest and fifthlargest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
. As two separate astronomical measurements can exist that were taken when the Earth, astronomical objects, and Sun are in a straight line but the Earth was actually on opposite sides of the Sun for the two measurements, that is at one roughly 500 light seconds nearer to the astronomical than the Sun for the first measure, then 500 light seconds further from the astronomical object than the Sun for the second measure, then the subsequent light time error between two Julian Day measures can amount to nearly as much as 1000 seconds different relative to the same Heliocentric Julian Day interval which can make a significant difference when measuring temporal phenomena for short period astronomical objects over long time intervals. The Julian day is sometimes referred to as the Geocentric Julian Day (GJD) in order to distinguish it from HJD.
History
The Julian day number is based on the Julian Period proposed by Joseph ScaligerJoseph Justus Scaliger
Joseph Justus Scaliger was a French religious leader and scholar, known for expanding the notion of classical history from Greek and Ancient Roman history to include Persian, Babylonian, Jewish and Ancient Egyptian history.Early life:He was born at Agen, the tenth child and third son of Italian...
in 1583, at the time of the Gregorian calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
reform, but it is the multiple of three calendar
Calendar
A calendar is a system of organizing days for social, religious, commercial, or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years. The name given to each day is known as a date. Periods in a calendar are usually, though not...
cycles used with the Julian calendar
Julian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
:
 15 (indiction cycleIndictionAn indiction is any of the years in a 15year cycle used to date medieval documents throughout Europe, both East and West. Each year of a cycle was numbered: first indiction, second indiction, etc...
) × 19 (Metonic cycleMetonic cycleIn astronomy and calendar studies, the Metonic cycle or Enneadecaeteris is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the solar year and the synodic month...
) × 28 (Solar cycleSolar cycle (calendar)The solar cycle is a 28year cycle of the Julian calendar with respect to the week. It occurs because leap years occur every 4 years and there are 7 possible days to start a leap year, making a 28 year sequence....
) = 7980 years
Its epoch
Epoch (reference date)
In the fields of chronology and periodization, an epoch is an instance in time chosen as the origin of a particular era. The "epoch" then serves as a reference point from which time is measured...
falls at the last time when all three cycles (if they are continued backward far enough) were in their first year together — Scaliger chose this because it preceded all historical dates.
Although many references say that the Julian in "Julian day" refers to Scaliger's father, Julius Scaliger
Julius Caesar Scaliger
Julius Caesar Scaliger was an Italian scholar and physician who spent a major part of his career in France. He employed the techniques and discoveries of Renaissance humanism to defend Aristotelianism against the new learning...
, in the introduction to Book V of his Opus de Emendatione Temporum ("Work on the Emendation of Time") he states, "Iulianum vocavimus: quia ad annum Iulianum dumtaxat accomodata est", which translates more or less as "We have called it Julian merely because it is accommodated to the Julian year." This Julian refers to Julius Caesar
Julius Caesar
Gaius Julius Caesar was a Roman general and statesman and a distinguished writer of Latin prose. He played a critical role in the gradual transformation of the Roman Republic into the Roman Empire....
, who introduced the Julian calendar in 46 BC.
In his book Outlines of Astronomy, first published in 1849, the astronomer John Herschel
John Herschel
Sir John Frederick William Herschel, 1st Baronet KH, FRS ,was an English mathematician, astronomer, chemist, and experimental photographer/inventor, who in some years also did valuable botanical work...
wrote:
The first year of the current Julian period, or that of which the number in each of the three subordinate cycles is 1, was the year 4713 B.C., and the noon of the 1st of January of that year, for the meridian of Alexandria, is the chronological epoch, to which all historical eras are most readily and intelligibly referred, by computing the number of integer days intervening between that epoch and the noon (for Alexandria) of the day, which is reckoned to be the first of the particular era in question. The meridian of Alexandria is chosen as that to which Ptolemy refers the commencement of the era of Nabonassar, the basis of all his calculations.
Astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
s adopted Herschel's Julian Days in the late nineteenth century, but used the meridian of Greenwich instead of Alexandria, after the former was adopted as the Prime Meridian
Prime Meridian
The Prime Meridian is the meridian at which the longitude is defined to be 0°.The Prime Meridian and its opposite the 180th meridian , which the International Date Line generally follows, form a great circle that divides the Earth into the Eastern and Western Hemispheres.An international...
after the International Meridian Conference
International Meridian Conference
The International Meridian Conference was a conference held in October 1884 in Washington, D.C., in the United States to determine the Prime Meridian of the world. The conference was held at the request of U.S. President Chester A...
in Washington in 1884. This has now become the standard system of Julian days. Julian days are typically used by astronomers to date astronomical
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
observations, thus eliminating the complications resulting from using standard calendar
Calendar
A calendar is a system of organizing days for social, religious, commercial, or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years. The name given to each day is known as a date. Periods in a calendar are usually, though not...
periods like eras, years, or months. They were first introduced into variable star
Variable star
A star is classified as variable if its apparent magnitude as seen from Earth changes over time, whether the changes are due to variations in the star's actual luminosity, or to variations in the amount of the star's light that is blocked from reaching Earth...
work by Edward Charles Pickering
Edward Charles Pickering
Edward Charles Pickering was an American astronomer and physicist, brother of William Henry Pickering.Along with Carl Vogel, Pickering discovered the first spectroscopic binary stars. He wrote Elements of Physical Manipulations .Pickering attended Boston Latin School, and received his B.S. from...
, of the Harvard College Observatory
Harvard College Observatory
The Harvard College Observatory 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, USA, and was founded in 1839...
, in 1890.
Julian days begin at noon because when Herschel recommended them, the astronomical day began at noon (it did so until 1925). The astronomical day had begun at noon ever since Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
chose to begin the days in his astronomical periods 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
Water clock
A water clock or clepsydra is any timepiece in which time is measured by the regulated flow of liquid into or out from a vessel where the amount is then measured.Water clocks, along with sundials, are likely to be the oldest timemeasuring instruments, with the only exceptions...
s. Nevertheless, he doubledated most nighttime observations with both Egyptian
Ancient Egypt
Ancient Egypt was an ancient civilization of Northeastern Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh...
days beginning at sunrise and Babylonian days beginning at sunset. This would seem to imply that his choice of noon was not, as is sometimes stated, made in order to allow all observations from a given night to be recorded with the same date.
Calculation
The Julian day number can be calculated using the following formulas (integer division is used exclusively, that is, the remainder of all divisions are dropped):The months (M) January to December are 1 to 12. For the year (Y) astronomical year numbering
Astronomical year numbering
Astronomical year numbering is based on AD/CE year numbering, but follows normal decimal integer numbering more strictly. Thus, it has a year 0, the years before that are designated with negative numbers and the years after that are designated with positive numbers...
is used, thus 1 BC is 0, 2 BC is −1, and 4713 BC is −4712. D is the day of the month. JDN is the Julian Day Number, which pertains to the noon occurring in the corresponding calendar date.
Converting Gregorian calendar date to Julian Day Number
The algorithm is valid for all Gregorian calendar dates starting on March 1, 4801 BC (astronomical year 4800) at noon UT.You must compute first:
then compute:
NOTE: When doing the divisions, the fractional parts of the quotients must be dropped. All years in the BC era must be converted to a negative value then incremented toward zero to be passed as an astronomical year, so that 1 BC will be passed as y=0.
Finding Julian date given Julian Day Number and time of day
For the full Julian date, not counting leap secondLeap second
A leap second is a positive or negative onesecond adjustment to the Coordinated Universal Time time scale that keeps it close to mean solar time. UTC, which is used as the basis for official timeofday radio broadcasts for civil time, is maintained using extremely precise atomic clocks...
s (divisions are real numbers):
So, for example, January 1, 2000 at midday corresponds to JD = 2451545.0
The day of the week
Week
A week is a time unit equal to seven days.The English word week continues an Old English wice, ultimately from a Common Germanic , from a root "turn, move, change"...
can be determined from the Julian day number by calculating it modulo
Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....
7, where 0 means Monday.
JDN mod 7  0  1  2  3  4  5  6 

Day of the week  Mon  Tue  Wed  Thu  Fri  Sat  Sun 
Gregorian calendar from Julian day number
 Let J be the Julian day number from which we want to compute the date components.
 From J, compute a relative Julian day number j from a Gregorian epoch starting on March 1, −4800 (i.e. March 1, 4801 BC in the proleptic Gregorian Calendar), the beginning of the Gregorian quadricentennial 32,044 days before the epoch of the Julian Period.
 From j, compute the number g of Gregorian quadricentennial cycles elapsed (there are exactly 146,097 days per cycle) since the epoch; subtract the days for this number of cycles, it leaves dg days since the beginning of the current cycle.
 From dg, compute the number c (from 0 to 4) of Gregorian centennial cycles (there are exactly 36,524 days per Gregorian centennial cycle) elapsed since the beginning of the current Gregorian quadricentennial cycle, number reduced to a maximum of 3 (this reduction occurs for the last day of a leap centennial year where c would be 4 if it were not reduced); subtract the number of days for this number of Gregorian centennial cycles, it leaves dc days since the beginning of a Gregorian century.
 From dc, compute the number b (from 0 to 24) of Julian quadrennial cycles (there are exactly 1,461 days in 4 years, except for the last cycle which may be incomplete by 1 day) since the beginning of the Gregorian century; subtract the number of days for this number of Julian cycles, it leaves db days in the Gregorian century.
 From db, compute the number a (from 0 to 4) of Roman annual cycles (there are exactly 365 days per Roman annual cycle) since the beginning of the Julian quadrennial cycle, number reduced to a maximum of 3 (this reduction occurs for the leap day, if any, where a would be 4 if it were not reduced); subtract the number of days for this number of annual cycles, it leaves da days in the Julian year (that begins on March 1).
 Convert the four components g, c, b, a into the number y of years since the epoch, by summing their values weighted by the number of years that each component represents (respectively 400 years, 100 years, 4 years, and 1 year).
 With da, compute the number m (from 0 to 11) of months since March (there are exactly 153 days per 5month cycle; however, these 5month cycles are offset by 2 months within the year, i.e. the cycles start in May, and so the year starts with an initial fixed number of days on March 1, the month can be computed from this cycle by a Euclidian division by 5); subtract the number of days for this number of months (using the formula above), it leaves d days past since the beginning of the month.
 The Gregorian date (Y, M, D) can then be deduced by simple shifts from (y, m, d).
The calculations below (which use integer division [div] and modulo [mod] with positive numbers only) are valid for the whole range of dates since −4800. For dates before 1582, the resulting date components are valid only in the Gregorian proleptic calendar. This is based on the Gregorian calendar but extended to cover dates before its introduction, including the preChristian era. For dates in that era (before year AD 1), astronomical year numbering
Astronomical year numbering
Astronomical year numbering is based on AD/CE year numbering, but follows normal decimal integer numbering more strictly. Thus, it has a year 0, the years before that are designated with negative numbers and the years after that are designated with positive numbers...
is used. This includes a year zero, which immediately precedes AD 1. Astronomical year zero is 1 BC in the proleptic Gregorian calendar and, in general, proleptic Gregorian year (n BC) = astronomical year (Y = 1 − n). For astronomical year Y (Y < 1), the proleptic Gregorian year is (1 − Y) BC.
 Let J = JD + 0.5: (note: this shifts the epoch back by one half day, to start it at 00:00UTC, instead of 12:00 UTC);
 let j = J + 32044; (note: this shifts the epoch back to astronomical year 4800 instead of the start of the Christian era in year AD 1 of the proleptic Gregorian calendar).
 let g = j div 146097; let dg = j mod 146097;
 let c = (dg div 36524 + 1) × 3 div 4; let dc = dg − c × 36524;
 let b = dc div 1461; let db = dc mod 1461;
 let a = (db div 365 + 1) × 3 div 4; let da = db − a × 365;
 let y = g × 400 + c × 100 + b × 4 + a; (note: this is the integer number of full years elapsed since March 1, 4801 BC at 00:00 UTC);
 let m = (da × 5 + 308) div 153 − 2; (note: this is the integer number of full months elapsed since the last March 1 at 00:00 UTC);
 let d = da − (m + 4) × 153 div 5 + 122; (note: this is the number of days elapsed since day 1 of the month at 00:00 UTC, including fractions of one day);
 let Y = y − 4800 + (m + 2) div 12; let M = (m + 2) mod 12 + 1; let D = d + 1;
 return astronomical Gregorian date (Y, M, D).
The operations div and mod used here are intended to have the same binary operator priority as the multipication and division, and defined as:
You can also use only integers in most of the formula above, by taking J = floor(JD + 0.5), to compute the three integers (Y, M, D).
The time of the day is then computed from the fractional day T = frac(JD + 0.5). The additive 0.5 constant can also be adjusted to take the local timezone into account, when computing an astronomical Gregorian date localized in another timezone than UTC. To convert the fractional day into actual hours, minutes, seconds, the astronomical Gregorian calendar uses a constant length of 24 hours per day (i.e. 86400 seconds exactly), ignoring leap second
Leap second
A leap second is a positive or negative onesecond adjustment to the Coordinated Universal Time time scale that keeps it close to mean solar time. UTC, which is used as the basis for official timeofday radio broadcasts for civil time, is maintained using extremely precise atomic clocks...
s inserted or deleted at end of some specific days in the UTC Gregorian calendar. If you want to convert it to actual UTC time, you will need to compensate the UTC leap seconds by adding them to J before restarting the computation (however this adjustment requires a lookup table, because leap seconds are not predictable with a simple formula); you'll also need to finally determine which of the two possible UTC date and time is used at times where leap seconds are added (no final compensation will be needed if negative leap seconds are occurring on the rare possible days that could be shorter than 24 hours).
Gregorian calendar from Unix time
UNIX timeUnix time
Unix time, or POSIX time, is a system for describing instants in time, defined as the number of seconds elapsed since midnight Coordinated Universal Time of Thursday, January 1, 1970 , not counting leap seconds, which are declared by the International Earth Rotation and Reference Systems Service...
is the term used to describe the manner in which UNIXlike
Unixlike
A Unixlike operating system is one that behaves in a manner similar to a Unix system, while not necessarily conforming to or being certified to any version of the Single UNIX Specification....
operating systems internally maintain time. The variable type time t defines UNIX time in terms of seconds elapsed since midnight January 1, 1970 UTC, a point in time referred to as the epoch. Negative time_t values represent dates prior to the epoch. Assuming the variable U has been defined to be of type time_t, the following mathematical progression may be used to break down a UNIX time value to its civil time
Civil time
In modern usage, civil time refers to statutory time scales designated by civilian authorities, or to local time indicated by clocks. Modern civil time is generally standard time in a time zone at a fixed offset from Coordinated Universal Time or from Greenwich Mean Time , possibly adjusted by...
equivalent:
 ss = U mod 60
 a = (U − ss) div 60
 mm = a mod 60
 b = (a − mm) div 60
 hh = b mod 24
 u = U − ss − mm * 60 − hh * 3600
where ss are seconds, mm minutes and hh hours. Day, month and year can be calculated as in the section Gregorian calendar from Julian day number, applying calculations to:
 J = u div 86400 + 2440588
and D being:
 D = d + 1
See also
 Julian year (astronomy)Julian year (astronomy)In astronomy, a Julian year is a unit of measurement of time defined as exactly 365.25 days of 86 400 SI seconds each, totaling 31 557 600 seconds. The Julian year is the average length of the year in the Julian calendar used in Western societies in previous centuries, and for which the unit is...
 Julian year (calendar)
 Decimal timeDecimal timeDecimal time is the representation of the time of day using units which are decimally related. This term is often used to refer specifically to French Revolutionary Time, which divides the day into 10 decimal hours, each decimal hour into 100 decimal minutes and each decimal minute into 100 decimal...
 Epoch (reference date)Epoch (reference date)In the fields of chronology and periodization, an epoch is an instance in time chosen as the origin of a particular era. The "epoch" then serves as a reference point from which time is measured...
 Epoch (astronomy)Epoch (astronomy)In astronomy, an epoch is a moment in time used as a reference point for some timevarying astronomical quantity, such as celestial coordinates, or elliptical orbital elements of a celestial body, where these are subject to perturbations and vary with time...
 EraEraAn era is a commonly used word for long period of time. When used in science, for example geology, eras denote clearly defined periods of time of arbitrary but well defined length, such as for example the Mesozoic era from 252 Ma–66 Ma, delimited by a start event and an end event. When used in...
 TimeTimeTime is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
 Time scales
 Ordinal dateOrdinal dateAn ordinal date is a calendar date typically consisting of a year and a day of year ranging between 1 and 366 , though year may sometimes be omitted...
 Dual datingDual datingIn historical materials, dates will often be indicated with what appears to be duplicate, or excessive digits, sometimes separated by a hyphen or a slash. This is often referred to as double dating. The need for double dating arose from the transition from an older calendar to a newer one...
 5th millennium BC5th millennium BCThe 5th millennium BC saw the spread of agriculture from the Near East throughout southern and central Europe.Urban cultures in Mesopotamia and Anatolia flourished, developing the wheel. Copper ornaments became more common, marking the Chalcolithic. Animal husbandry spread throughout Eurasia,...
 Lunation NumberLunation NumberLunation Number is a number given to each lunation beginning from a certain one in history. There are several series of lunation numbers in use....
(similar concept)
External links
 Julian day calculation by IMCCE at Paris Observatory ± Julian days with 16 significant digits (integer plus fraction)
 U.S. Naval Observatory Julian Date Converter no negative Julian days, max year 9999
 Julian Day and Civil Date calculator
 U.S. Naval Observatory Time Service article on Modified Julian Date
 U.S. Naval Observatory current MJD service
 Outlines of Astronomy by John Herschel, 1849 Table of Julian days for remarkable eras
 International Astronomical Union Resolution 1B: On the Use of Julian Dates
 Calendrica
 BASIC Programs from Sky & Telescope with CALJD.BAS and JDCAL.BAS, very small BASICBASICBASIC is a family of generalpurpose, highlevel programming languages whose design philosophy emphasizes ease of use  the name is an acronym from Beginner's Allpurpose Symbolic Instruction Code....
programs to convert Julian Day numbers. published in the May 1984 issue.