The Julian date (abbreviated JD for English Julian Date in all languages ) is a common day counting in the natural sciences, especially astronomy . It gives the time in days and fractions of a day that has passed since January 1st −4712 ( 4713 BC ), 12:00 UT . For example, Tuesday, August 25, 2020, 12:30:55 UT corresponds to the Julian date 2,459,087.02147. The Julian Day Number (abbreviated JDN for English Julian Day Number ) is the integer part of the Julian date. It numbers the days starting with 0 for January 1st −4712; The day starts at 12 noon UT.
In German, the usage of the language is not uniform: For the JD, besides the frequent "Julian date", there is also, for example, "Julian day number" (which stands for the JDN) or "Julian day value". The JDN is usually only found in phrases like "the Julian day 2,452,276". The German terms used here are taken from a dictionary.
As a continuous day count, the Julian date is free from irregularities such as leap days or months of different lengths, as occur in most calendars . It is therefore very easy to calculate time differences. For areas such as ephemeris calculation, in which a completely uniform time measurement is required, the IAU recommends using terrestrial time (TT) as the basis of the Julian date instead of Universal Time (UT) .
An important variant of the Julian date is the Modified Julian Date (abbreviated MJD in all languages ).
A first step towards today's Julian date was made with the book De emendatione temporum by the French humanist Joseph Scaliger , published in 1583 , which "because of its ... analytical precision had an enormous effect on any chronological or historical work". Scaliger systematically dealt with all important calendar systems of antiquity and the Middle Ages and related them to a reference calendar. To this end he introduced a Julian period lasting 7980 years , which he called “ quia ad annum Iulianum duntaxat accomodata est. ”(German:“ because it is of course adapted to the Julian year. ”). Their length is the smallest common multiple of the period length of three important cycles for the calendar calculation, the 28-year solar cycle , the 19-year lunar circle and the 15-year cycle of indiction . As year 1 of the Julian period he chooses the year 4713 BC. Because in that year all three cycles began a new run at the same time; the year 7980 of the Julian period is thus the year 3267 AD. For each year of the Julian period, the position in one of the three cycles can now be determined by calculating the remainder when dividing by the respective cycle length.
A continuous measure of time, called “ day current of the Julian period ” (German: “current day of the Julian period”), which coincides with today's Julian date except for one detail, was published in 1849 by the British astronomer John Herschel in his book Outlines of Astronomy suggested. Here, like today, a date or point in time is determined by the time that has passed since the epoch January 1st −4712 (4713 BC), 12:00 o'clock and measured in days and fractions of a day. The only difference is that Herschel based his definition not on the mean local time of 12:00 noon in Greenwich, i.e. today's UT, but rather on the basis of 12:00 noon mean local time in Alexandria . As a justification he stated that the Nabonassar era used by Claudius Ptolemy was based on this . Herschel's definition therefore provides values 0.083 larger than the one used today. After the introduction of Greenwich Mean Time, now known as UT, in 1884, the Julian date (JD) was used at the latest in 1893 with this name and the definition still valid today (epoch January 1st −4712, 12:00 UT). The year of the epoch and the "Julian" in the name therefore go back to Scaliger. Starting the day at noon and using fractions of the day has been a common practice in astronomy since ancient times.
Herschel had already spoken out in favor of shifting the astronomical start of the day to midnight, but it was not until the first half of the 20th century that astronomers gradually joined the general agreement and moved “their” start of the day forward by 12 hours. Before January 1, 1925, Greenwich Mean Time, as it was used in astronomy, had its day change at noon; it was only from this date that the day began at midnight. As recently as 1928, the IAU asked to indicate when the day started for all work. "UT" stands for the beginning of the day at midnight; the term “GMT” should no longer be used.
As a result, the noon change of day for the Julian date was increasingly perceived as disturbing, and so the IAU decided in 1973, in order to avoid uncontrolled growth in the form of many different dating systems, to introduce a variant in addition to the JD with the day beginning at midnight in Resolution 4: It proposed the Designation “ Modified Julian Date ” (German: “Modified Julianisches Datum”) (MJD) to be used only for the size defined by JD - 2,400,000.5. This daily count had already been introduced in 1957 by the SAO for its program to observe the first Soviet Sputnik satellites. In the 1990s, however, there were efforts among astronomers to withdraw this recommendation. Out of consideration for neighboring disciplines such as geodesy , geophysics and space travel , in which the MJD was widely used, the recommendation from 1973 was not repealed. Rather, the IAU confirmed the parallel use of JD and MJD in 1997 in Resolution B1 and carried out a “ Julian day number ”(German:“ Julianische Tagesnummer ”) (JDN), which indicates the sunny days (starting at noon) since 4713 BC. Numbered consecutively. For astronomical purposes it recommends the use of the Julian date, while it recommends the Modified Julian date "in those cases where it is convenient to use a day beginning at midnight".
In addition to the coordinated universal time UTC, scientific time measurement uses several different time scales , each of which is particularly suitable for certain purposes, e.g. B. Universal Time UT1, International Atomic Time TAI, Terrestrial Time TT, Barycentric Dynamic Time TDB etc. On each of these time scales, a continuous time count can be introduced in the form of a Julian date, whereby the epoch is January 1st −4712 , 12:00 on the relevant time scale. The unit is the day with 86,400 seconds on the relevant scale; An exception is where the individual days a UTC leap second will be extended to 86,401 seconds. On the time scales UTC (from 1972), TAI and TT, the second is the SI second . Since the individual time scales differ from one another, the relevant Julian dates for one and the same event are also different. In case of doubt, it must therefore be stated on which time scale the Julian date used is counted, e.g. B. "JD (UT1)", "JD (TT)" etc. The IAU recommends the use of terrestrial time as the underlying time scale. The abbreviation “JDE”, which is often encountered, denotes a Julian date counted after the Ephemeris , but is also often used for its successor “JD (TT)”.
UTC as a scale for the Julian date is problematic because of the leap seconds if an accuracy of 1 s or better is desired. In the SOFA library, which contains software for basic algorithms developed on behalf of and under the control of the IAU, the JD (UTC) in connection with leap seconds is referred to as "quasi-JD". And the developers point out that their treatment of the problem has no official status.
|May 27 −668||01:59 UT||1,477,217.583||Rising of the eclipsed sun in Babylon|
|Jan. 1||00:00 UT||1,721,423,500|
|Sep 14 763||12:00 UT||2,000,000,000|
|Jul.Oct. 4, 1582||24:00 UT||2,299,160,500||same time; s. Adoption of the Gregorian calendar|
|greg.Oct. 15, 1582||00:00 UT|
|Nov 17, 1858||00:00||2,400,000,500||Epoch of the modified Julian date, time scale UT or DD|
|Dec 31, 1899||19:31:28 DD||2,415,020.31352||Standard epoch B1900.0|
|Jan. 1, 2000||12:00:00 TT||2,451,545.00000||Standard epoch J2000.0 (= Jan. 1, 2000, 11: 58: 55.8 UTC)|
|25 Aug 2020||12:30:55 UTC||2,459,087.02147|
The Julian date uses the same time scale as the respective calendar date.
Calculate with the Julian date
Calendar date conversion → JD
The Julian date can be calculated from a Julian or Gregorian calendar date using the following algorithm . The input is expected in the variables
Jahr, which can
Tagalso contain a fraction of a day ( hour / 24 + minute / 1440 + second / 86400); the output is in
wenn Monat > 2 dann Y = Jahr; M = Monat sonst Y = Jahr−1; M = Monat+12 D = Tag // inklusive Tagesbruchteil wenn julianischer Kalender dann B = 0 sonst // gregorianischer Kalender B = 2 − ⌊Y/100⌋ + ⌊Y/400⌋ JD = ⌊365,25(Y+4716)⌋ + ⌊30,6001(M+1)⌋ + D + B − 1524,5
The algorithm correctly handles both Julian and Gregorian calendar dates even if they denote days before the calendar was actually introduced, that is, if the calendar's rules are applied proleptically ; Irregularities in the placement in the early stages of the Julian calendar are not taken into account. For the pre-Christian years, astronomical, not historical, counting is also assumed, i.e. 0 for 1 BC. BC, −1 for 2 BC Chr. Etc.
It must be known in which of the two calendar systems the date is present. The earliest and most frequently used change in dating took place in 1582: October 4th (Julian) was followed by October 15th (Gregorian). However, many countries later switched, and some used the Julian calendar even into the 20th century (see Adoption of the Gregorian calendar ).
The square bracket ⌊ x ⌋ is the lower Gaussian bracket that rounds x down (⌊5,8⌋ = 5; ⌊ − 5,2⌋ = −6). In many programming languages it is called
floor. For calendar dates from March −4716 (March 0 for Gregorian dates), the rounding off can be replaced by cutting off the decimal places, since the arguments of the Gaussian brackets are always nonnegative there.
Explanation of the algorithm
- Before the actual invoice, the monthly and annual numbers are renumbered , which counts January and February as the 13th and 14th months of the previous year. A possible leap day is always the last day of the year that has arisen, and it is no longer necessary to differentiate between the date to be treated as to whether it is in the (original) year before or after the leap day.
- In the Julian calendar, March 1st −4712, 12 midnight has JD 30.5 + 29 = 59.5. By March 1, Y , 0 o'clock, another Y +4712 renumbered years with a total of ⌊365.25 (Y + 4712) ⌋ days have passed. In this term, the additional leap day due every four years is automatically taken into account through the fractional part of the factor 365.25. So the YD of March 1, Y , 0 o'clock is 59.5 + ⌊365.25 (Y + 4712) ⌋. So that the argument of the Gaussian brackets ⌊… ⌋ does not become negative for January and February of the (original) year –4712, so that it can also be replaced here by the cutoff function, the base year is brought forward by four years and the 3 · 365 contained therein + 366 = 1461 days subtracted. The YD of March 1, Y , 0 o'clock is 59.5 + (⌊365.25 (Y + 4716) ⌋ - 1461).
- In the Gregorian calendar, a day has a different YD than the day with the same date in the Julian calendar. In the renumbered years Y = 0,…, 99 the difference is B = JD (greg.) - JD (jul.) = B ₀ with initially still unknown B ₀. With the beginning of the new (renumbered) century Y = 100,…, 199, B is reduced by 1, since March 1st July. by the leap day February 29, 100, which is not available in the Gregorian calendar, occurs one day later, i.e. with the JD increased by 1. This is repeated in the following centuries - except when the first year of the century is divisible by 400. So B = B ₀ - ⌊ Y / 100⌋ + ⌊Y / 400⌋. In the renumbered years Y = 1500,…, 1599 the difference is B = −10 (October 5, 1582 jul. = October 15, 1582 greg. ), From which B ₀ = 2 follows. Together we have JD (greg.) = JD (July) + B with B = 2 - ⌊ Y / 100⌋ + ⌊Y / 400⌋.
- The number of days since the beginning of the renumbered year Y on March 1st is made up of two parts, the number of days until the beginning of the month and the number D - 1 of the days since the beginning of the month ( D also with a fraction of the day). The first contribution results from the month lengths for March ( M = 3) to February ( M = 14): 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 31, 28/29. The days in the previous months then add up to 0, 31, 61, 92, 122, 153, 184, 214, 245, 275, 306, 337; the length of February doesn't add. These values result, as can be seen by recalculation, from the expression ⌊30.6 ( M +1) ⌋ - 122. Since the factor 30.6 cannot be exactly represented in binary (for the problem, see properties of floating point arithmetic ), it becomes replaced by the (within certain limits arbitrary) value 30.6001, because otherwise the result for April ( M +1 = 5), for example, could be ⌊152.999.998⌋ - 122 = 30 instead of the correct 31. The number of days since the beginning of the renumbered year Y is thus (⌊30.6001 ( M +1) ⌋ - 122) + ( D - 1).
- In total (with B = 0 for Julian calendar dates) JD = 59.5 + (⌊365.25 (Y + 4716) ⌋ - 1461) + B + (⌊30.6001 (M + 1) ⌋ - 122) + ( D - 1) or rearranged JD = ⌊365.25 (Y + 4716) ⌋ + ⌊30.6001 (M + 1) ⌋ + D + B - 1524.5.
Conversion of JD → calendar date
The Julian or Gregorian calendar date can be calculated from a Julian date using the following algorithm . The input, the Julian date, is
JDexpected in the variable ; the output, the calendar date you are looking for, is in
Jahr, which can
Tagalso contain a fraction of a day ( hour / 24 + minute / 1440 + second / 86400).
Z = ⌊JD + 0,5⌋ F = JD + 0,5 − Z wenn julianischer Kalender dann A = Z sonst // gregorianischer Kalender α = ⌊(Z − 1.867.216,25)/36.524,25⌋ A = Z + 1 + α − ⌊α/4⌋ B = A + 1524 C = ⌊(B − 122,1)/365,25⌋ D = ⌊365,25 C⌋ E = ⌊(B − D)/30,6001⌋ Tag = B − D − ⌊30,6001 E⌋ + F // inklusive Tagesbruchteil wenn E ≤ 13 dann Monat = E − 1; Jahr = C − 4716 sonst Monat = E − 13; Jahr = C − 4715
If it is not clear from the outset which of the two possible calendar dates it should be, it must be known which Z belongs to the first day in the Gregorian calendar. At the change in October 1582 this is Z = 2.299.161. The square bracket ⌊ x ⌋ is again the lower Gaussian bracket, which rounds x down (⌊5,8⌋ = 5; ⌊ − 5,2⌋ = −6). It can be replaced by truncating the decimal places if, in the Julian calendar, JD ≥ −0.5 (i.e. for times after January 1st −4712 July ); for the Gregorian calendar, JD must be ≥ 1,867,216.5 (from March 1st 400 greg. ).
Calculation of the day of the week
The regular sequence of the days of the week was not affected by the introduction of the Gregorian calendar: On Thursday, October 4th, 1582 jul. followed Friday October 15th greg. . The day of the week can, therefore, by calculating the remainder of the division of the commercially rounded Julian Date (= ⌊ JD + 0,5⌋) are determined by the 7th Remainder 0 corresponds to Monday, 1 Tuesday, 2 Wednesday, 3 Thursday, 4 Friday, 5 Saturday and 6 Sunday.
Example: JD = 2,459,087.02147 (= August 25, 2020, 12:30:55 UT) results in 2,459,087 by rounding. The remainder of dividing by 7 is 1, which is Tuesday.
Modified Julian date
The Modified Julian Date (abbreviated MJD in all languages) is defined by
Its epoch (zero point) is thus on November 17, 1858 at 00:00 UT. The MJD of times between 1859 and 2131 is two (or more) decimal places less than the JD, and the day starts at midnight. It is mainly used in geodesy , geophysics and space travel , and more rarely in astronomy. The International Service for Earth Rotation and Reference Systems uses it in its Bulletins A and B. For the use of Terrestrial Time TT, what was said above for the Julian date applies.
In addition, an "MJD2000" is occasionally used, which indicates January 1, 2000, 00:00 (JD 2,451,544.5, MJD 51,544.0) or the standard epoch J2000.0 (January 1, 2000, 12: 00 o'clock TT; JD 2,451,545.0, MJD 51,544.5).
Time measures in software
In operating systems , programming languages or application programs , times are often determined by the time that has elapsed since a fixed zero point and is measured in days, seconds, milliseconds or nanoseconds. Or at least there is the possibility to query this time. Often, the starting point is January 1, 1970, 12 midnight UTC, on which Unix time is based. For the starting points listed in the following table, the time is always 0 o'clock, whereby no distinction is made here as to whether UTC or local time is; the Julian dates entered are for UTC.
|Zero point||JD (UTC)||software|
|greg.Jan. 1, 1||1,721,424.5||python|
|Dec. 31, 1600||2,305,812.5||COBOL|
|Jan. 1, 1601||2,305,813.5||Microsoft Windows|
|Dec 30, 1899||2,415,018.5||
|Jan. 1, 1970||2,440,587.5||
With this time measure, the Julian date can be calculated very easily for a calendar date. All that remains is to know the time unit.
In LibreOffice Calc, the time unit is the day. If cell A1 contains a date or a combined date and time value on a timescale such as UTC, you can toggle between displaying this time and displaying it as a decimal number (the time that has elapsed since zero point) by changing the cell formatting. The JD of A1 is then obtained by adding A1 to the Julian date of the zero point:
Alternatively, the difference to any other date with a known YD, e.g. B. the zero point of Microsoft Windows, can be used:
var jd = 2440587.5 + Date.UTC(jahr, monat-1, tag, stunde, minute, sekunde)/86400000; // Date.UTC() liefert die Zeit in ms seit 1. Januar 1970, 00:00 UTC (= JD 2440587,5). // Monate müssen im Wertebereich 0 .. 11 übergeben werden.
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So in C ++ (
std::floor), Java (
java.lang.Math.floor) and Python (
- For Y = –4712, –4711, –4710, –4709, –4708,… the term generates the correct number sequence 0, 365, 730, 1095, 146 1 ,… (the day before March 1st was −4708 a Leap day).
- 30.6 is the average length of 5 consecutive months (excluding February).
- It is Z = ⌊ JD (October 15, 1582 greg. , 0 o'clock) + 0.5⌋ = ⌊2.299.160.5 + 0.5⌋ = 2.299.161.
- If the JD is negative , the commercial rounding can produce an incorrect value: The rounding of JD = −2.5 must result in −2 and not −3.
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