|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{Use mdy dates|date=January 2014}}
| | The name of the writer is Nestor. Some time ago I chose to live in Arizona but I need to move for my family members. Interviewing is what she does in her working day occupation but soon her husband and her will begin their personal business. To play croquet is some thing that I've carried out for years.<br><br>Also visit my web page [http://Cancertreatmentaz.com/user-profile/userid/63389 car warranty] |
| {{redirect|Julian date|dates in the Julian calendar|Julian calendar|day of year|Ordinal date|the comic book character Julian Gregory Day|Calendar Man}}
| |
| {{Distinguish|Julian year}}
| |
| | |
| '''Julian day''' refers to a continuous count of days since the beginning of the Julian Period used primarily by [[Astronomy|astronomers]].
| |
| | |
| The '''Julian Day Number '''('''JDN''') is the integer assigned to a whole solar day in the Julian day count starting from noon [[Greenwich Mean Time]], with Julian day number 0 assigned to the day starting at noon on January 1, [[4713 BC|4713 BC]], [[proleptic Julian calendar]] (November 24, 4714 BC, in the [[proleptic Gregorian calendar]]). For example, the Julian day number for January 1, 2000, was 2,451,545.<ref>McCarthy & Guinot 2013, 91–2</ref>
| |
| | |
| The '''Julian Date''' ('''JD''') of any instant is the Julian day number for the preceding noon plus the fraction of the day since that instant. Julian Dates are expressed as a Julian day number with a decimal fraction added.<ref name="IAU">[http://www.iers.org/nn_10910/IERS/EN/Science/Recommendations/resolutionB1.html Resolution B1 on the use of Julian Dates by The XXIIIrd International Astronomical Union General Assembly]</ref> For example, the Julian Date for 00:30:00.0 [[Universal Time|UT]] January 1, 2013, is 2,456,293.520833.<ref>US Naval Observatory 2005</ref> | |
| | |
| The term ''"Julian date"'' may also refer, outside of astronomy, to the day-of-year number (more properly, the [[ordinal date]]) in the [[Gregorian calendar]], especially in computer programming, the military and the food industry,<ref name="usda">[http://www.dm.usda.gov/procurement/toolkit/docs/calendar.pdf USDA Julian date calendar]</ref>— or it may refer to dates in the [[Julian calendar]]. For example, if a given "Julian date" is "May 12, 1629", this means that date in the [[Julian calendar]] (which is May 22, 1629, in [[Gregorian calendar]]— the date of the [[Treaty of Lübeck]]). Outside of an astronomical or historical context, if a given "Julian date" is "40", this most likely means the fortieth day of a given Gregorian year, namely February 9. But the potential for mistaking a "Julian date" of "40" to mean an astronomical Julian Day Number (or even to mean the year 40 {{scaps|ad}} in the Julian calendar, or even to mean a duration of 40 astronomical [[Julian year (astronomy)|Julian years]]) is justification for preferring the terms "[[ordinal date]]" or "day-of-year" instead. In contexts where a "Julian date" means simply an ordinal date, calendars of a Gregorian year with formatting for ordinal dates are often called ''"Julian calendars"'',<ref name="usda"/> in spite of the potential for misinterpreting this as meaning that the calendars are of years in the [[Julian calendar]] system.
| |
| | |
| The '''Julian Period''' is a [[Chronology|chronological]] interval of 7980 years beginning 4713 BC. It has been used by [[History|historians]] since its introduction in 1583 to convert between different [[calendar]]s. {{currentyear}} is year {{#expr: {{currentyear}} + 4713 }} of the current Julian Period. The next Julian Period begins in the year 3268 AD.
| |
| | |
| == Time scales ==
| |
| 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. Time intervals calculated from differences of Julian Dates specified in non-uniform time scales, such as [[Coordinated Universal Time]] (UTC), may need to be corrected for changes in time scales (e.g. [[leap second]]s).<ref name="IAU" />
| |
| | |
| == Variants ==<!-- This section is linked from [[Epoch (reference date)]] -->
| |
| 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 (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. JD stands for Julian Date. 0h is 00:00 midnight, 12h is 12:00 noon, UT unless specified else wise.
| |
| | |
| {| class="wikitable" border="1"
| |
| |-
| |
| ! Name
| |
| ! Epoch
| |
| ! Calculation
| |
| ! Value for {{datetime}}
| |
| ! Notes
| |
| |-
| |
| | Julian Date
| |
| | 12h Jan 1, 4713 BC
| |
| |
| |
| |align='right'| '''{{#expr: {{CURRENTJULIANDAY}} round 5 }}'''
| |
| |
| |
| |-
| |
| | Reduced JD
| |
| | 12h Nov 16, 1858
| |
| | JD − 2400000
| |
| |align='right'| '''{{#expr: {{CURRENTJULIANDAY}} - 2400000 round 5 }}'''
| |
| |
| |
| |-
| |
| | Modified JD
| |
| | 0h Nov 17, 1858
| |
| | JD − 2400000.5
| |
| |align='right'| '''{{#expr: {{CURRENTJULIANDAY}} - 2400000.5 round 5 }}'''
| |
| | Introduced by [[Smithsonian Astrophysical Observatory|SAO]] in 1957
| |
| |-
| |
| | Truncated JD
| |
| | 0h May 24, 1968
| |
| | JD − 2440000.5
| |
| |align='right'| '''{{#expr: floor( {{CURRENTJULIANDAY}} - 2440000.5 ) }}'''
| |
| | Introduced by [[NASA]] in 1979
| |
| |-
| |
| | Dublin JD
| |
| | 12h Dec 31, 1899
| |
| | JD − 2415020
| |
| |align='right'| '''{{#expr: {{CURRENTJULIANDAY}} - 2415020 round 5 }}'''
| |
| | Introduced by the [[IAU]] in 1955
| |
| |-
| |
| | Chronological JD
| |
| | 0h Jan 1, 4713 BC
| |
| | JD + 0.5 + [[Time zone|tz]]
| |
| | align='right'| '''{{#expr: {{CURRENTJULIANDAY}} + 0.5 round 5 }}'''(UT)
| |
| | Specific to time zone
| |
| |-
| |
| | [[Lilian date]]
| |
| | Oct 15, 1582 (1)
| |
| | floor (JD − 2299159.5)
| |
| |align='right'| '''{{#expr: floor( {{CURRENTJULIANDAY}} - 2299159.5 ) }}'''
| |
| | Count of days of the [[Gregorian calendar]]<ref>IBM 2004, [http://publib.boulder.ibm.com/infocenter/comphelp/v7v91/index.jsp?topic=%2Fcom.ibm.aix.cbl.doc%2Frpsrv06.htm "CEEDATE—convert Lilian date to character format"]</ref>
| |
| |-
| |
| | [[American National Standards Institute|ANSI]] Date
| |
| | Jan 1, 1601 (1)
| |
| | floor (JD − 2305812.5)
| |
| |align='right'| '''{{#expr: floor( {{CURRENTJULIANDAY}} - 2305812.5 ) }}'''
| |
| | Origin of [[COBOL]] integer dates
| |
| |-
| |
| | [[Rata Die]]
| |
| | Jan 1, 1 (1)
| |
| | floor (JD − 1721424.5)
| |
| |align='right'| '''{{#expr: floor( {{CURRENTJULIANDAY}} - 1721424.5 ) }}'''
| |
| | Count of days of the [[Common Era]] (Gregorian)
| |
| |-
| |
| | [[Unix Time]]
| |
| | 0h Jan 1, 1970
| |
| | (JD − 2440587.5) × 86400
| |
| |align='right'| '''{{#expr: ( {{CURRENTJULIANDAY}} - 2440587.5 ) * 86400 round 0 }}'''
| |
| | Count of seconds <ref>''Astronomical almanac for the year 2001'', 2000, p. K2</ref>
| |
| |-
| |
| | [[Timekeeping on Mars#Sols|Mars Sol Date]]
| |
| | 12h Dec 29, 1873
| |
| | (JD − 2405522)/1.02749
| |
| |align='right'| '''{{#expr: ( {{CURRENTJULIANDAY}} - 2405522 )/1.02749125 round 5 }}'''
| |
| | Count of Martian days
| |
| |}
| |
| | |
| *The '''Modified Julian Date''' (MJD) was introduced by the Smithsonian Astrophysical Observatory in 1957 to record the orbit of [[Sputnik 1|Sputnik]] via an IBM 704 (36-bit machine) and using only 18 bits until August 7, 2576. MJD is the epoch of [[OpenVMS#Timekeeping|OpenVMS]], using 63-bit date/time, postponing the next [[Year 2000 problem|Y2K campaign]] to July 31, 31086, 02:48:05.47.<ref>Worsham 1988</ref> MJD is defined relative to midnight, rather than noon.
| |
| | |
| *The '''Truncated Julian Day''' (TJD) was introduced by [[NASA]]/[[Goddard Space Flight Center|Goddard]] in 1979 as part of a parallel grouped binary time code (PB-5) "designed specifically, although not exclusively, for spacecraft applications." TJD was a 4-digit day count from MJD 40000, which was May 24, 1968, represented as a 14-bit binary number. Since this code was limited to four digits, TJD recycled to zero on MJD 50000, or October 10, 1995, "which gives a long ambiguity period of 27.4 years". (NASA codes PB-1—PB-4 used a 3-digit day-of-year count.) Only whole days are represented. Time of day is expressed by a count of seconds of a day, plus optional milliseconds, microseconds and nanoseconds in separate fields. Later PB-5J was introduced which increased the TJD field to 16 bits, allowing values up to 65535, which will occur in the year 2147. There are five digits recorded after TJD 9999.<ref>[http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19800007830_1980007830.pdf A Grouped Binary Time Code for Telemetry and Space Applications] 1979</ref><ref>[http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890006406_1989006406.pdf CCSDS Recommendations for Time Code Formats]</ref><ref>[http://newsroom.gsfc.nasa.gov/sdptoolkit/primer/time_notes.html#PB5 SDP Toolkit Time Notes]</ref>
| |
| | |
| *The '''Dublin Julian Date''' (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 Sun]] 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 Union]] at their meeting in [[Dublin]], [[Republic of Ireland|Ireland]], in 1955.<ref>Ransom c. 1988</ref>
| |
| | |
| *The '''Chronological Julian Date''' was recently proposed by Peter Meyer<ref>Peter Meyer.(2004). [http://www.hermetic.ch/cal_stud/cjd.htm ''Message Concerning Chronological Julian Days/Dates''.] author.</ref><ref>Peter Meyer. (n.d.). [http://www.hermetic.ch/cal_stud/chron_jdate.htm ''Chronological Julian Date.''] author. Retrieved February 8, 2009.</ref> and has been used by some students of the calendar and in some scientific software packages.<ref>Michael L. Hall. (January 20, 2010). [http://www.lanl.gov/Caesar/Caesar.html ''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.</ref> CJD is usually defined relative to local civil time, rather than UT, requiring a time zone (tz) offset to convert from JD. In addition, days start at midnight rather than noon. Users of CJD sometimes refer to Julian Date as '''Astronomical Julian Date''' to distinguish it.
| |
| | |
| <!-- THE REST OF THESE ARE NOT RELATED TO JD -->
| |
| * 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.<ref>Ohms 1986</ref> It was named for [[Aloysius Lilius]], the principal author of the Gregorian calendar.
| |
| | |
| * The '''[[American National Standards Institute|ANSI]] Date''' defines January 1, 1601, as day 1, and is used as the origin of [[COBOL]] integer dates. This [[epoch (reference date)|epoch]] is the beginning of the previous 400-year cycle of leap years in the Gregorian calendar, which ended with the year 2000.
| |
| | |
| * '''[[Rata Die]]''' 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 Era|Christian]] or [[Common Era]] in the proleptic Gregorian calendar.
| |
| | |
| 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 (498 seconds), that being the time it takes the Sun's light to reach [[Earth]].
| |
| | |
| To illustrate the ambiguity that could arise, consider the two separate astronomical measurements of an astronomic object from the earth: Assume that three objects — the Earth, the Sun, and the astronomical object targeted, that is whose distance is to be measured — happen to be in a straight line for both measure. However, for the first measurement, the Earth is between the Sun and the targeted object, and for the second, the Earth is on the opposite side of the Sun from that object. Then, the two measurements would differ by about 1000 light-seconds: For the first measurement, the Earth is roughly 500 light seconds closer to the target than the Sun, and roughly 500 light seconds further from the target astronomical object than the Sun for the second measure. | |
| | |
| An error of about 1000 light-seconds is over 1% of a light-day, which can be a significant error when measuring temporal phenomena for short period astronomical objects over long time intervals. To clarify this issue, the ordinary 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 Justus Scaliger|Joseph Scaliger]] in 1583, at the time of the [[Gregorian calendar]] reform, as it is the multiple of three [[calendar]] cycles used with the [[Julian calendar]]:
| |
| | |
| : 15 ([[indiction|indiction cycle]]) × 19 ([[Metonic cycle]]) × 28 ([[Solar cycle (calendar)|Solar cycle]]) = 7980 years
| |
| | |
| Its [[Epoch (reference date)|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. Years of the Julian Period are counted from this year, 4713 BC.
| |
| | |
| Although many references say that the ''Julian'' in "Julian Period" refers to Scaliger's father, [[Julius Caesar Scaliger|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." Thus ''Julian'' refers to [[Julius Caesar]], who introduced the Julian calendar in 46 BC.
| |
| | |
| Originally the Julian Period was used only to count years, and the Julian calendar was used to express historical dates within years. In his book ''Outlines of Astronomy'', first published in 1849, the astronomer [[John Herschel]] added the counting of days elapsed from the beginning of the Julian Period:
| |
| | |
| <blockquote>The period thus arising of 7980 Julian years, is called the Julian period, and it has been found so useful, that the most competent authorities have not hesitated to declare that, through its employment, light and order were first introduced into chronology.<ref>Ideler, Handbuch, &c. vol. i. p. 77.</ref> We owe its invention or revival to Joseph Scaliger, who is said to have received it from the Greeks of Constantinople. 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 BC, 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.<ref>[http://books.google.com/books?id=uj0DAAAAQAAJ Herschel] 1858, P. 678</ref></blockquote>
| |
| | |
| [[Astronomer]]s adopted Herschel's "days of the Julian period" 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 numbers.
| |
| | |
| The French mathematician and astronomer [[Pierre-Simon Laplace]] first expressed the time of day as a decimal fraction added to calendar dates in his book, ''Traité de Mécanique Céleste'', in 1799.<ref>[http://books.google.com/books?id=QjEVAAAAQAAJ&pg=PA348 Laplace] 1799, p.349</ref> Other astronomers added fractions of the day to the Julian day number to create Julian Dates, which are typically used by astronomers to date [[astronomy|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.<ref>[http://books.google.com/books?id=5jQJAAAAIAAJ&printsec=toc#PPA206,M1 Furness] 1988, p. 206.</ref>
| |
| | |
| Julian days begin at noon because when Herschel recommended them, the [[astronomical day]] began at noon. 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 double-dated most nighttime observations with both [[Ancient Egypt|Egyptian]] days beginning at sunrise and [[Babylonia]]n 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. When this practice ended in 1925, it was decided to keep Julian days continuous with previous practice.
| |
| | |
| == Calculation ==<!-- This section is linked from [[Gregorian calendar]] -->
| |
| 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 Julian or Gregorian calendar date to Julian Day Number===
| |
| The algorithm is valid at least for all positive Julian Day Numbers.<ref>{{cite web |last=Tøndering |first=Claus |title=Frequently Asked Questions about Calendars |url=http://www.tondering.dk/claus/cal/julperiod.php#formula}}</ref> The meaning of the variables are explained by the [[#CS1063|Computer Science Department of the University of Texas at San Antonio]].
| |
| | |
| It is worth noting that this algorithm does not follow the NASA<ref>''HORIZONS System'' 2013''</ref> or the US Naval Observatory<ref>''Julian Date Converter'' 2013</ref> - the convention in these systems being that the Gregorian Calendar did not exist before the date October 15, 1582 (Gregorian). This algorithm effectively back-dates the Gregorian calendar onto the Julian calendar for dates before the introduction of the Gregorian calendar. Thus any calculations made with this formula before October 15, 1582, will not agree with these previous ephemerides.
| |
| | |
| You must compute first the number of years (''y'') and months (''m'') since March 1 −4800 (March 1, 4801 BC):
| |
| | |
| <math>\begin{align}
| |
| a & = \left\lfloor\frac{14 - \text{month}}{12}\right\rfloor && \mbox{(1 for January and February, 0 for other months)}\\
| |
| y & = \text{year} + 4800 - a \\
| |
| m & = \text{month} + 12a - 3 && \mbox{(0 for March, 11 for February)}
| |
| \end{align}</math>
| |
| | |
| All years in the BC era must be converted to astronomical years, so that 1 BC is year 0, 2 BC is year −1, etc. Convert to a negative number, then increment toward zero.
| |
| | |
| Then, if starting from a Gregorian calendar date compute:
| |
| | |
| <math>
| |
| J\!D\!N =
| |
| \text{day} +
| |
| \left\lfloor\frac{153m+2}{5}\right\rfloor +
| |
| 365y+
| |
| \left\lfloor\frac{y}{4}\right\rfloor -
| |
| \left\lfloor\frac{y}{100}\right\rfloor +
| |
| \left\lfloor\frac{y}{400}\right\rfloor -
| |
| 32045
| |
| </math>
| |
| | |
| Otherwise, if starting from a Julian calendar date compute:
| |
| | |
| <math>
| |
| J\!D\!N =
| |
| \text{day} +
| |
| \left\lfloor\frac{153m+2}{5}\right\rfloor +
| |
| 365y+
| |
| \left\lfloor\frac{y}{4}\right\rfloor -
| |
| 32083
| |
| </math>
| |
| | |
| Note: (153''m''+2)/5 gives the number of days since March 1 and comes from the repetition of days in the month from March in groups of five:
| |
| {|
| |
| | Mar–Jul: || 31 30 31 30 31
| |
| |-
| |
| | Aug–Dec: || 31 30 31 30 31
| |
| |-
| |
| | Jan–Feb: || 31 28
| |
| |}
| |
| | |
| ===Finding Julian date given Julian day number and time of day===
| |
| For the full Julian Date (divisions are real numbers):
| |
| | |
| <math>\begin{matrix}J\!D & = & J\!D\!N + \frac{\text{hour} - 12}{24} + \frac{\text{minute}}{1440} + \frac{\text{second}}{86400}\end{matrix}</math>
| |
| | |
| So, for example, January 1, 2000, at 12:00:00 corresponds to ''JD'' = 2451545.0
| |
| | |
| ===Finding day of week given Julian day number===
| |
| The US day of the [[week]] '''W1''' can be determined from the Julian Day Number '''J''' with the expression:
| |
| : '''W1''' = [[Modular arithmetic|mod]](''J'' + 1, 7) <ref>Richards 2013, pp. 592, 618.</ref>
| |
| | |
| {|border="1" class="wikitable"
| |
| |-style="text-align:center;"
| |
| !'''W1'''
| |
| | 0 || 1 || 2 || 3 || 4 || 5 || 6
| |
| |-
| |
| !'''Day of the week'''
| |
| |Sun||Mon||Tue||Wed||Thu||Fri||Sat
| |
| |}
| |
| | |
| The ISO day of the [[week]] '''W0''' can be determined from the Julian Day Number '''J''' with the expression:
| |
| : '''W0''' = [[Modular arithmetic|mod]](''J'', 7)
| |
| | |
| {|border="1" class="wikitable"
| |
| |- style="text-align:center;"
| |
| !'''W0'''
| |
| | 0 || 1 || 2 || 3 || 4 || 5 || 6
| |
| |-
| |
| !'''Day of the week'''
| |
| |Mon||Tue||Wed||Thu||Fri||Sat||Sun
| |
| |}
| |
| | |
| === Gregorian calendar from Julian day number ===
| |
| This is an algorithm by Richards to convert a Julian Day Number, '''J''', to a date in the Gregorian calendar (proleptic, when applicable). Richards does not state which dates the algorithm is valid for.<ref>Richards 2013, 617–9</ref> Reminder: all variables are integers, and the solidus (/) indicates [[integer division]]. The symbol * indicates multiplication and mod(A,B) denotes the [[Modular arithmetic|modulus operator]].
| |
| | |
| {| class="wikitable"
| |
| |+Algorithm parameters for Gregorian calendar
| |
| |-
| |
| ! variable
| |
| ! value
| |
| ! variable
| |
| ! value
| |
| |-
| |
| | ''y'' || 4716 || ''v'' || 3
| |
| |-
| |
| | ''j'' || 1401 || ''u'' || 5
| |
| |-
| |
| | ''m'' || 2 || ''s'' || 153
| |
| |-
| |
| | ''n'' || 12 || ''w'' || 2
| |
| |-
| |
| | ''r'' || 4 || ''B'' || 274277
| |
| |-
| |
| | ''p'' || 1461 || ''C'' || −38
| |
| |}
| |
| | |
| :1. ''f'' = '''J''' + ''j'' + (((4 * '''J''' + ''B'')/146097) * 3)/4 + ''C''
| |
| :2. ''e'' = ''r'' * ''f'' + ''v''
| |
| :3. ''g'' = mod(''e'', ''p'')/''r''
| |
| :4. ''h'' = ''u'' * ''g'' + ''w''
| |
| :5. '''D''' = (mod(''h, s''))/''u'' + 1
| |
| :6. '''M''' = mod(''h''/''s'' + ''m, n'') + 1
| |
| :7. '''Y''' = ''e''/''p'' - ''y'' + (''n'' + ''m'' - '''M''')/n
| |
| | |
| '''D''', '''M''', and '''Y''' are the numbers of the day, month, and year respectively.
| |
| | |
| == See also ==
| |
| * [[Julian year (astronomy)]]
| |
| * [[Julian year (calendar)]]
| |
| * [[Decimal time]]
| |
| * [[Epoch (reference date)]]
| |
| * [[Epoch (astronomy)]]
| |
| * [[Era]]
| |
| * [[Time]]
| |
| * [[Time standard]]s
| |
| * [[Ordinal date]]
| |
| * [[Dual dating]]
| |
| * [[5th millennium BC]]
| |
| * [[Lunation Number]] (similar concept)
| |
| * [[Zeller's congruence]]
| |
| | |
| == Footnotes ==
| |
| <references />
| |
| | |
| == References ==
| |
| * ''Astronomical almanac for the year 2001''. (2000). U.S. Nautical Almanac Office and [[HM Nautical Almanac Office|Her Majesty's Nautical Almanac Office]].
| |
| * [http://asa.usno.navy.mil/ ''Astronomical Almanac Online'']. (2008). U.S. Nautical Almanac Office and [[HM Nautical Almanac Office|Her Majesty's Nautical Almanac Office]].
| |
| * {{Anchor|CS1063}}[http://www.cs.utsa.edu/~cs1063/projects/Spring2011/Project1/jdn-explanation.html "CS 1063 Introduction to Programming: Explanation of Julian Day Number Calculation."] (2011). Computer Science Department, University of Texas at San Antonio.
| |
| * Digital Equipment Corporation. [http://www.slac.stanford.edu/~rkj/crazytime.txt Why is Wednesday, November 17, 1858, the base time for VAX/VMS?] Modified Julian Day explanation
| |
| * Furness, C. E. (1915). [http://books.google.com/books?id=5jQJAAAAIAAJ&printsec=toc#PPA206,M1 ''An introduction to the study of variable stars.''] Boston: Houghton-Mifflin. Vassar Semi-Centennial Series.
| |
| *[http://ssd.jpl.nasa.gov/?horizons ''HORIZONS System'']. (April 4, 2013). NASA.
| |
| *[http://www.iau.org/static/publications/IB81.pdf ''Information Bulletin No. 81'']. (January 1998). [[International Astronomical Union]].
| |
| * [http://aa.usno.navy.mil/data/docs/JulianDate.php ''Julian Date Converter''] (March 20, 2013). US Naval Observatory. Retrieved September 16, 2013.
| |
| * Kempler, Steve. (2011). [http://disc.gsfc.nasa.gov/julian_calendar.shtml Day of Year Calendar]. Goddard Earth Sciences Data and Information Services Center.
| |
| * [[Dennis McCarthy (scientist)|McCarthy, D.]] & Guinot, B. (2013). Time. In S. E. Urban & P. K. Seidelmann, eds. ''Explanatory Supplement to the Astronomical Almanac'', 3rd ed. (pp. 76–104). Mill Valley, Calif.: University Science Books. ISBN 978-1-89138-985-6
| |
| * Richards, E. G. (2013). Calendars. In S. E. Urban & P. K. Seidelmann, eds. ''Explanatory Supplement to the Astronomical Almanac'', 3rd ed. (pp. 585–624). Mill Valley, Calif.: University Science Books. ISBN 978-1-89138-985-6
| |
| * Moyer, Gordon. (April 1981). "The Origin of the Julian Day System," ''Sky and Telescope'' '''61''' 311−313.
| |
| * IBM. (2004). [http://publib.boulder.ibm.com/infocenter/comphelp/v7v91/index.jsp?topic=/com.ibm.aix.cbl.doc/rpsrv06.htm ''COBOL for AIX Programming Guide''] (1st ed. ver. 2.0).
| |
| * Noerdlinger, P. (April 1995 revised May 1996). [http://observer.gsfc.nasa.gov/sec2/papers/noerdlinger2.html ''Metadata Issues in the EOSDIS Science Data Processing Tools for Time Transformations and Geolocation'']. [[NASA]] [[Goddard Space Flight Center]].
| |
| *Ohms, B. G. (1986). [http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5387720 Computer processing of dates outside the twentieth century]. ''IBM Systems Journal'' 25, 244–251.
| |
| * Ransom, D. H. Jr. (c. 1988) [http://textfiles.meulie.net/computers/DOCUMENTATION/astroclk.dc2 ''ASTROCLK Astronomical Clock and Celestial Tracking Program'' pages 69–143], "Dates and the Gregorian calendar" pages 106–111. Retrieved September 10, 2009.
| |
| * Reingold, E. M. & Dershowitz, N. (2008). ''[http://emr.cs.iit.edu/home/reingold/calendar-book/third-edition/ Calendrical Calculations]'' 3rd ed. Cambridge University Press.
| |
| * Seidelmann, P. Kenneth (ed.) (1992). ''[http://books.google.com/books?id=uJ4JhGJANb4C&pg=PA55 Explanatory Supplement to the Astronomical Almanac]'' pages 55 & 603–606. University Science Books, ISBN 0-935702-68-7.
| |
| * Strous, L. (2007) [http://aa.quae.nl/en/reken/juliaansedag.html ''Astronomy Answers: Julian Day Number.] Astronomical Institute / Utrecht University.
| |
| * US Naval Observatory. (2005, last updated July 2, 2011). ''Multiyear Interactive Computer Almanac 1800–2050'' (ver. 2.2.2). Richmond VA: Willmann-Bell, ISBN 0-943396-84-0.
| |
| | |
| == External links ==
| |
| * [http://www.imcce.fr/en/grandpublic/temps/jour_julien.php Julian day calculation by IMCCE at Paris Observatory] ± Julian days with 16 significant digits (integer plus fraction)
| |
| * [http://www.nr.com/julian.html Julian Day and Civil Date calculator]
| |
| * [http://tycho.usno.navy.mil/mjd.html U.S. Naval Observatory Time Service article on Modified Julian Date]
| |
| * [http://tycho.usno.navy.mil/cgi-bin/daterdnm.sh U.S. Naval Observatory current MJD service]
| |
| * [http://books.google.com/books?id=TD0CAAAAYAAJ&pg=PA595 Outlines of Astronomy by John Herschel, 1849] Table of Julian days for remarkable eras
| |
| * [http://www.iers.org/nn_10910/IERS/EN/Science/Recommendations/resolutionB1.html?__nnn=true International Astronomical Union Resolution 1B: On the Use of Julian Dates]
| |
| * [http://emr.cs.iit.edu/home/reingold/calendar-book/Calendrica.html Calendrica]
| |
| * [http://www.skyandtelescope.com/resources/software/3304911.html BASIC Programs from Sky & Telescope] with [http://media.skyandtelescope.com/binary/caljd.bas CALJD.BAS] and [http://media.skyandtelescope.com/binary/jdcal.bas JDCAL.BAS], very small [[BASIC]] programs to convert Julian Day numbers. published in the May 1984 issue.
| |
| | |
| {{Time measurement and standards}}
| |
| | |
| {{DEFAULTSORT:Julian Day}}
| |
| [[Category:Calendaring standards]]
| |
| [[Category:Celestial mechanics]]
| |
| [[Category:Chronology]]
| |
| [[Category:Time in astronomy]]
| |