# Julian day

The Julian day or Julian day number (JDN) is the number of days that have elapsed since 12 noon Greenwich Mean Time (UT or TT) on Monday, January 1, 4713 BC in the proleptic Julian calendar 1. That day is counted as Julian day zero. The Julian day system was intended to provide astronomers with a single system of dates that could be used when working with different calendars and to unify different historical chronologies.

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## Julian Date

The Julian Date (JD) is the Julian day number plus the decimal fraction of the day that has elapsed since noon. 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.

## Alternatives

• 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. The Julian day is sometimes referred to as the Geocentric Julian Day (GJD) in order to distinguish it from HJD.
• Another version of the Julian day, introduced by Peter Meyer, is the chronological Julian Day (CJD), in which the starting point is set at midnight at the beginning of January 1, 4713 BC (proleptic Julian calendar) local time rather than noon UT. Chronographers found the Julian day concept useful, but they didn't like noon as the starting time. So CJD = JD + 0.5 (in the Greenwich time zone, anyway). Note that JD may use Universal Time (UT) or Terrestrial Time (TT), and so it is the same for all time zones and is independent of Summer Time or Daylight-Saving Time (DST). On the other hand, CJD is not, so it changes with different time zones and takes into account the different local DSTs. Users of CJD sometimes refer to the Julian day as astronomical Julian Day (AJD) to distinguish it from CJD.

Because the starting point 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.

• The Modified Julian Day (MJD), introduced by the Smithsonian Astrophysical Observatory in 1957 to record the orbit of Sputnik, is defined in terms of the Julian day as follows:
MJD = JD - 2400000.5
The offset of 0.5 means that MJD started at midnight at the beginning of November 17, 1858, and that every Modified Julian Day begins and ends at midnight UT or TT.
• The Reduced Julian Day (RJD) is also used by astronomers and counts days from the same day as MJD, but from noon UT or TT, and thus is defined as:
RJD = JD - 2400000
• The Truncated Julian Day (TJD) was introduced by NASA for the space program. TJD began at May 24, 1968. Since TJD exceeded four digits on October 10, 1995, some now count TJD from this date in order to maintain a four-digit number. It can be defined as:
TJD = JD - 2440000.5
or
TJD = (JD - 0.5) mod 10000
• The Dublin Julian Day (DJD) is a count of days from midnight at the beginning of January 1, 1900. The source of the name is unknown. It is used in computer programs, such as Lotus 1-2-3 and Microsoft Excel. In these particular programs, this date is counted as day 1, instead of day 0, because the year 1900 was erroneously (http://support.microsoft.com/default.aspx?scid=kb;en-us;214326) treated as a leap year.
• 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.

## 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 were in their first year together — Scaliger chose this because it pre-dated all historical dates.

Note: 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 Tempore (Work on the Emendation of Time) he states: "Iulianum vocauimus: quia ad annum Iulianum dumtaxat accomodata est" which translates more or less as "We call this 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 19th century, but using the meridian of Greenwich instead of Alexandria, after the former was made the Prime Meridian by international conference 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, months, or weeks.

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. Thus the astronomical day did not begin at noon to allow all observations of a single night to be in a single day.

## Calculation

The Julian day number can be calculated using the following formulas:

All divisions (except for JD) are integer divisions, meaning the remainder in the division is discarded. The months January to December are 1 to 12. Astronomical year numbering is used, thus 1 BC is 0, 2 BC is −1, and 4713 BC is −4712.

[itex]\begin{matrix}a & = & {14 - month \over 12} \\ \\y & = & year + 4800 - a \\ \\m & = & month + 12a - 3 \\\end{matrix}[itex]

For a date in the Gregorian calendar (at noon):

[itex]\begin{matrix}JDN & = & day + {153m + 2\over 5} + 365y + {y \over 4} - {y \over 100} + {y \over 400} - 32045\end{matrix}[itex]

For a date in the Julian calendar (at noon):

[itex]\begin{matrix}JDN & = & day + {153m + 2\over 5} + 365y + {y \over 4} - 32083\end{matrix}[itex]

For the full Julian Date (divisions are real numbers):

[itex]\begin{matrix}JD & = & JDN + {hour - 12 \over 24} + {minute \over 1440} + {second \over 86400}\end{matrix}[itex]

The day of the week can be determined from the Julian day number by calculating it modulo 7, where 0 means Monday.

 JD mod 7 0 1 2 3 4 5 6 Day of the week Mon Tue Wed Thu Fri Sat Sun

## References

• Gordon Moyer, "The Origin of the Julian Day System," Sky and Telescope 61 (April 1981) 311-313.
• Explanatory Supplement to the Astronomical Almanac, edited by P. Kenneth Seidelmann. University Science Books, 1992. ISBN 0935702687

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