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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 day-of-year (ordinal date) although incorrectly.

## Julian Date

Historical Julian dates were recorded relative to GMT or Ephemeris Time, 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 day-of-year (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.[1]

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.[2] In precise work, the timescale, e.g., Terrestrial Time (TT) or Universal Time (UT), should be specified.[3]

The Julian day number (JDN)[4] is the integer part of the Julian date (JD).[3] The day commencing at the above-mentioned epoch is JDN 0. Now, at 06:49, Tuesday August 3, 2021 (UTC) the Julian day number is 2459429. 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 midnight-to-midnight civil day centered on that noon,[5] 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 06:49, Tuesday August 3, 2021 (UTC) the nearest noon JDN is 2459430 yielding a remainder of 1.

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.

## 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 date if it is October 15, 1582 or later, but a Julian calendar date if it is earlier.

Name Epoch Calculation Current value Notes
Julian Date (JD) 12:00 January 1, 4713 BC, Monday 2459429.78458
Julian Day Number (JDN) 12:00 January 1, 4713 BC, Monday JDN = floor (JD) 2459429 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 59429.78458 Used by astronomers
Modified Julian Date (MJD) 00:00 November 17, 1858, Wednesday MJD = JD − 2400000.5 59429.28458 Introduced by SAO 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
19429.28458
9429.28458
- Definition as introduced by NASA[6]
- NIST definition
Dublin Julian Date (DJD) 12:00 December 31, 1899, Sunday DJD = JD − 2415020 44409.78458 Introduced by the IAU in 1955
Chronological Julian Date (CJD) 00:00 January 1, 4713 BC, Monday CJD = JD + 0.5 + time zone adjustment 2459430.2845833 (UT) Specific to time zone; Changes at midnight zone time; UT CJD given
Lilian Day Number October 15, 1582, Friday (as Day 1) floor (JD − 2299160.5) 160269 The count of days of the Gregorian calendar for Lilian date reckoned in Universal time.
ANSI Date January 1, 1601, Monday (as Day 1) floor (JD − 2305812.5) 153617 The origin of COBOL integer dates
Rata Die January 1, 1, Monday (as Day 1) floor (JD − 1721424.5) 738005 The count of days of the Common Era (Gregorian)
Unix Time January 1, 1970, Thursday (JD − 2440587.5) × 86400 1627973388 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 Sputnik via an IBM 704 (36-bit machine) and using only 18 bits until August 7, 2576. MJD is the epoch of OpenVMS, using 63-bit date/time postponing the next Y2K campaign to July 31, 31086 02:48:05.47.[7]
• The Chronological Julian Day was recently proposed by Peter Meyer[9][10] and has been used by some students of the calendar and in some scientific software packages.[11]
• 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.[12] It was named for Aloysius Lilius, the principal author of the Gregorian calendar.
• The ANSI Date defines January 1, 1601 as day 1, and is used as the origin of COBOL integer dates. This epoch is the beginning of the previous 400-year cycle of leap years in the Gregorian calendar, which ended with the year 2000.

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.

## History

The Julian day number is based on the Julian Period proposed by Joseph Scaliger in 1583, at the time of the Gregorian calendar reform, but it is the multiple of three calendar cycles used with the Julian calendar:

15 (indiction cycle) × 19 (Metonic cycle) × 28 (Solar cycle) = 7980 years

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:

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.

Astronomers 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.[13]

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 clocks. Nevertheless, he double-dated 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.

## 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 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.[14]

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 seconds (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.

 JDN mod 7 Day of the week 0 1 2 3 4 5 6 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 5-month cycle; however, these 5-month 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 pre-Christian 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.

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 = dgc × 36524;
• let b = dc div 1461; let db = dc mod 1461;
• let a = (db div 365 + 1) × 3 div 4; let da = dba × 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 seconds 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 time is the term used to describe the manner in which UNIX-like 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:

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

## Footnotes

1. Cracking the date code on egg cartons
2. This equals November 24, 4714 BC in the proleptic Gregorian calendar.
3. The Astronomical Almanac Online 2008, Glossary s. v. Julian date
4. Information Bulletin No. 81. (January 1998), p. 23.
5. Nachum Dershowitz and Edward M. Reingold 2008. See its applet Calendrica.
6. Noerdlinger, 1995.
7. Worsham 1988
8. Ransom c. 1988
9. Peter Meyer.(2004). Message Concerning Chronological Julian Days/Dates. author.
10. Peter Meyer. (n.d.). Chronological Julian Date. author. Retrieved February 8, 2009.
11. Michael L. Hall. (January 20, 2010). The CÆSAR Code Package (LA-UR-00-5568, LA-CC-06-027). Los Alamos National Laboratory. In this software the definition has been changed from a real number to an integer.
12. Ohms 1986
13. Furness 1988, p. 206.

## References

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