Julian day

The Julian date - not to be confused with the date in the Julian calendar - is a common in the natural sciences and day count is abbreviated as JD ( engl. Julian Date). It indicates the time in days that ( BC 4713 ) Duration 12:00 clock has passed since January 1, -4712. Date Sunday, March 30, 2014, 10:56:13 UT clock corresponds, for example, the Julian date 2456746.95571.

As consecutive day counting the Julian date free of irregularities such as leap days, months of different lengths, etc., as they occur in most calendars. Therefore, it is mainly used in astronomy to describe time-dependent variables, it is very light time differences can be computed with him.

  • 3.1 Calculation
  • 3.2 Notes
  • 3.3 Examples

History

The Julian date was suggested in 1583 by the French philologist and historian Joseph Justus Scaliger. The name is derived possibly from the Julian calendar then in use. Other sources report that Scaliger had named his system after his father, Julius Caesar Scaliger.

The counting of the days within a period of 7980 years, the so-called Julian period, continuously. The length is calculated as the least common multiple of the Zykellängen the indiction (15 years), the Golden Number (19 years) and the solar cycle (28 years, results from the four-year leap-year cycle, multiplied by the seven days of the week ). The final collapse of the three cycles (ie, the last time that all three cycles at the same time the annual number "1" had ) was in the year 4713 BC

The British astronomer John Herschel suggested before in 1849 in his book Outlines of Astronomy to use the Scaliger'sche scheme for time measurement in astronomy. This eliminated the complications that could occur when using different calendars. He also introduced the fractional share for the time. The day beginning in Europe at midday, so that during the night ( because the astronomers then just watch yes ) no date change occurs.

Astronomical Julian date

Properties

In astronomy, the Julian date is used as a continuous time counting that any time assigns a unique point number, with the number of elapsed days as the integer part and the elapsed fraction of the day in the decimal ( the discrete Julian date of chronology, however, only counts whole days, see below). In international usage, the Julian date is abbreviated as " JD ".

The scientific measurement of time used several different time scales side by side, which are particularly suitable for particular purposes, such as Universal Time "UT ", International Atomic Time " TAI " Terrestrial Dynamic Time " TDT " Barycentric Dynamic Time " TDB " and so on each of these time scales can be introduced a continuous time counting in the form of a julian date, where a " day " usually corresponds to 86.4 thousand seconds of the relevant time scale. Since the individual time scales different from each other, the respective Julian data for one and the same event are different. It must therefore be stated in doubt, on what time scale the Julian date used is counted, for example, " JD (UT1 ) ", " JD ( TDT ) " etc. The International Astronomical Union ( IAU) recommends the use of Terrestrial Dynamic time as the underlying time scale, with a consisting of 86,400 SI seconds a day. The frequently encountered abbreviation " JDE " means a counted after Ephemeris Julian date, but is also used frequently for his successor, " JD ( TDT ) ".

If a Julian date is used, based on a non-uniform time scale (eg, UTC ), then in the calculation of time differences where appropriate, a correction is required ( in the example UTC: account of leap seconds).

The Julian date is a pure continuous day count and has no calendrical structures, such as a division into years, months, etc. It has, despite the similarity in name nothing to do with the Julian calendar. Even the English Julian Date suffers from the same confusion, so instead uses the term Julian Day Number or simply Julian Day, for example, Jean Meeus as an author of relevant works. In the language of the IAU but under Julian Day Number, only the integer portion of the Julian date to understand and the full date to be the Julian date. In German names have as Julian day number or Julian day count also so far not enforced.

Calculation from the calendar date

The astronomical Julian date can be calculated from a given in the Julian or Gregorian calendar date ( the Julian date can not be negative, this calculation is based on the implementation of the Gregorian calendar in 1582, some states set their calendar at other times to ) the following algorithm:

If month > 2 then Y = year, M = month                    otherwise Y = year -1, M = month 12         D = Day         H = Stunde/24 Minute/1440 Sekunde/86400         if TT.MM.YYYY > = 15.10.1582          then Gregorian Calendar: A = Int ( Y/100 ), B = 2 - A Int (A / 4 )                   if TT.MM.YYYY < = 04/10/1582          then Julian calendar: B = 0          otherwise error: The date between 04.10.1582 and 15.10.1582 which does not exist.                   Followed on the 04/10/1582 ( Julian calendar )                   immediately of 15.10.1582 ( Gregorian calendar).          JD = int ( 365.25 * (Y 4716 )) Int ( 30.6001 * (M 1 )) D H B - 1524.5 The variables day, month, year, hour, minute and second contain the components of the date to be processed, the result is returned in JD. The Int function truncates the fractional part of a number.

Calculation in programming languages

Since most programming languages ​​for the internal representation of date and time values ​​using a consecutive numbering from a specific reference point in days or milliseconds, the daily difference can often be determined at a defined time by simple subtraction. It should be noted, however, that the lower limit of the date variable is not exceeded (usually the 1/1/1900 or 1/1/1970 ).

Var J2000 = new Date (); / / Reference point is the 1.1.2000 00:00 UT ( JD 2451544.5 corresponds )      j2000.setUTCFullYear ( 2000,0,1 );      j2000.setUTCHours ( 0,0,0,0 );           var date = new Date ();      datum.setUTCFullYear ( year, month -1, day ); / / Months must be passed in the value range 0 .. 11      datum.setUTCHours ( hour, minute, second, msec );           var jd = 2451544.5 ( date - J2000 ) / 86400000; / / Count in milliseconds, 1 day = 86,400,000 ms It is important to be passed as UTC value, otherwise the subtraction into account any time zone differences (summer / winter time).

Example, in Microsoft Excel

= 2451544.5 A1 - DATE (2000, 1, 1) A1 contains a date or a combined date and time value. Attention: as in Microsoft Excel 1900 as a leap year, valid values ​​are supplied only from the 03/01/1900. From this value, the leap year rule, however, properly implemented.

Conversion of a date in the Julian format into a readable date format in Microsoft Excel

= A1 DATE (2000, 1, 1) -2,451,544.5 explanation

  • For the period before the introduction of the Gregorian calendar here the use of the proleptic, not the historic Julian calendar is assumed. That is, the calendar data are given as if the Julian calendar had always existed and always would have been completely regularly. In particular, occurred in the early years of the historic Julian calendar irregularity of the circuit is ignored.
  • For the pre-Christian years also the astronomical, not historical counting is required. The year ahead to the year 1 AD is therefore counted as year 0 ( astronomical), not as year 1 BC ( historically ), the year ahead will be this year as -1 and not as year 2 v. counted AD, etc. the year 4713 BC in historical census example, corresponds to the year -4712 astronomical counting.
  • Before the actual invoice a renumbering of the monthly and annual figures will be carried out which are January and February counts as the 13th and 14th month of the previous year. A possible leap is thus always the last day of the resulting year, and it must be no longer distinguished for the date to be treated, whether it is in the ( original ) years before or after the leap day. In addition, as of the irregular episode 31 28 31 30 31 30 31 31 30 31 30 31 of the month lengths arises the regular beginning with the March episode 31 30 31 30 31 31 30 31 30 31 31 28 Note that the lying before the 28 part of the sequence can be regarded as section of the periodic sequence ... 30 31 31 30 31 30 31 31 30 31 30 31 31 30 ...
  • First, assume the Julian calendar was used throughout January 1, -4712 to the present day. The number of days since the beginning of the ( re-numbered ) year -4712 completely past years, Int ( 365.25 × ( Y ( -4712 ))) or Int ( 365.25 × (Y 4712 ) ). In this formula, the leap day every four years, in addition due is automatically taken into account by the fractional factor of 365.25. So you created for Y = -4712, -4711, -4710, -4709, -4708, ... the correct number sequence 0, 365, 730, 1095, 1461, ... Given the above- made ​​renumbering of the years the argument of the Int function for January and February of the ( original ) -4712 year is however negative. Since the Int functions of different programming languages ​​on negative arguments react differently, the formula is reformulated in order to avoid negative arguments: int ( 365.25 * ( Y 4716 ) ) - 1461.
  • For this purpose, the number of days is added into the since ( as renumbered ) beginning completely past few months. For M = 3, 4, 5, ... so is the series of numbers 0, 31, 61, ... to produce; it corresponds to the cumulative sums of the second above-mentioned result of the length of the month. The 28 in that sequence is never needed because during the last month of the year renumbered the last month is never completely gone and in the following month, the daily sum to be calculated here again starting with 0 ( while Y was increased by 1). It is therefore sufficient that also mentioned above strictly to generate periodic sequence and to select a suitable section of it. This is done by the formula Int ( 30.6001 * (M 1)) -122, which provides for M = 3 .. 14 the desired number sequence. The factor of 30.6001 is a for later reduction to integers useful approximation to the average, uninfluenced leap year month length of the months from March to January dar. Instead of the factor 30.6001 could be used 30.6 in mathematical terms, the numerical value. Rounding errors in the numerical calculation with a limited number of places, however, would in some cases result in connection with the Int function to erroneous results. This is prevented by the slight modification of the numerical value ( other possibilities would be 30.61, 30.601, etc.). The subtracted value 122 represents the likewise unaffected by leap years the number of days in the months March to June, to be deducted because of the choice of the expression ( M 1) as a monthly factor. Otherwise a more complicated determination of the monthly factors would be required.
  • If D is the date of the day, so is the number of already fully last days in that month D-1. For this purpose, the time from the already calculated last fraction H of the day to be treated must be added. However, a half-day of which must be subtracted, as the initial time of the Julian day count is not as in today's calendar is on midnight, but only at 12 noon clock: D - 1 H - 0.5 = D H - 1.5.
  • If the date is to be treated according to the ( varying regional ) introduction of the Gregorian calendar, so the result so far is to correct the number B of days to distinguish themselves Julian and Gregorian calendar on that date. The difference began on October 15, 1582 with B = -10 days and grows in all not divisible by 400 hundred years by -1 day is a total given by B = -10 -A Int (A / 4 ) 12 or = B 2 - A int ( A / 4 ), where A = INT ( Y/100 ). The change from the Julian to the Gregorian calendar occurred in many countries in 1582: On the 4th of October ( Julian ) was followed by October 15 (Gregorian ). Some countries, however, later presented to, in some cases until the 20th century.
  • Calculated from the beginning of the original, not renumbered year are January and February -4712 additional 31 29 = to count 60 days. The February -4712 was a leap month.
  • Overall, as the number of days that have passed Int ( 365.25 × (Y 4716 ) ) - 1461 Int ( 30.6001 * (M 1)) - 122 D H - 1,5 B 60 = Int ( 365.25 × (Y 4716 )) Int ( 30.6001 * (M 1 )) D H B - 1524.5.

Examples

  • Since the times of October 4, 1582 24:00 clock and 00:00 clock October 15, 1582 in those countries fell together that followed the reform of the calendar right away, they did so the same Julian date. Note: This is only a modern convention. At the time of the day, as the 16th century ended usual, always at dusk local time and certainly not at midnight, neither UT nor in local time. Thus, for example, in Rome on 4 October at 21:00 UT (which it did not yet exist), actually already written October 15.

Calculation of the calendar date from the Julian date

The Julian or Gregorian calendar date can be calculated according to the following algorithm from a given Julian date ( the Julian date can not be negative ). It is believed that until October 4, 1582 Julian calendar and from 15 October 1582 Gregorian calendar is to be used.

Z = Int (JD 0.5 )     F = Frac (JD 0.5 )     if Z < 2299161 then A = Z / / results julian                      otherwise g = Int ( (Z - 1867216.25 ) / 36524.25 ) / / result Gregorian                             A = Z 1 g - Int (g / 4)     B = A 1524     C = Int ( (B -122, 1) / 365.25 )     D = Int ( 365.25 * C)     E = Int ( (B- D) / 30.6001 )     Day = B - D - Int ( 30.6001 * E ) F / / day, including fraction of the day     if E < 14 then month = E - 1 / / month               else month = E - 13     if month > 2 then year = C - 4716 / / Year                  else year = C - 4715 The variable contains the JD Julian date to be processed, the variables day, month, year, the components of the resulting calendar date ( also the day the fraction of the day ). The Int function truncates the fractional part of a number. The Frac function returns the fractional part of a number.

Rounding up the Julian date to an integer and determines the modulo 7, so the remainder of a division by 7, we get the week day ( Monday = 0 to Sunday = 6).

Chronological Julian date

The chronological Julian date is also counted from January 1, -4712, but only in integer steps days. It corresponds to the astronomical Julian date for 12h at noon.

Calculation

The following pseudo code calculated from a date in the Gregorian calendar, the chronological Julian date:

Y = year ( month - 2.85) / 12     A = Int ( 367 * y) - 1.75 * Int (y ) day     B = INT ( A) - 0.75 * int ( y / 100)     JD = Int (B) 1721117 The variables day, month, and year components of the date to be processed, the variables y, A and B are auxiliary variables of the calculation and the result is returned in JD. Int stands for the truncation of decimal places.

Comments

  • The calculation is stable when you enter, for example, the nonexistent February 29, 1999, the same Julian date is calculated as for the 1 March 1999. Through back-calculation can be as dates, check their authenticity.
  • Any date with a " zeroth " day of the month ( 0 M. YYYY ) returns the Julian date of the last day of the previous month.
  • About the rest of the division by 7, the integer of the Julian date 0.5 one can determine the day of the week. Remainder is 0 Monday, residue 1 is Tuesday, etc.; therefore was October 4, 1582, a Thursday, and 15 October 1582 Friday ( the first day of validity of the Gregorian calendar ).

Examples

More Julian dates

  • The International Geophysical Year (1957 /58) was introduced by the Smithsonian Institution, a Modified Julian Date ( MJD ), with zero point at the November 17, 1858 0:00 clock UT: MJD = JD (UT ) - 2400000.5. This makes it significantly less than the decimal the Julian date. The MJD is mainly used less frequently in geodesy, geophysics, metrology and space, even in astronomy.
  • Dublin Julian date ( DJD ): Another version of a Julian date starts counting the days to the beginning of 1900 (for example, in Microsoft Excel, Lotus 123, Embarcadero Delphi) or that of the year 1904 ( Microsoft Excel for Mac OS). Since the counting does not begin on January 1, with the zero, but with the value " 1" is the correct zero point of the count December 31, 1899 0:00 clock. For additional confusion ensures that some programs incorrectly view the year 1900 as a leap year and therefore for days before March 1, 1900 provide inconsistent data (zero point is then December 30, 1899 0:00 clock ).
  • The ANSI Date defines the January 1, 1601 as day " 1". It serves as the origin of the date count in the COBOL programming language.
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