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Julian 11

Julian day

"Julian " and "JDN" redirect here. For dates in the Julian , see . For the military IT system, see Joint Data Network. For day of , see . For the comic book character Julian Gregory Day, see Calendar Man. Not to be confused with (disambiguation). refers to a continuous count of days since the beginning of the Julian Period used primarily by astronomers. The Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from Greenwich Mean , with Julian day number 0 assigned to the day starting at noon on , 4713 BC proleptic Julian calendar. (November 24, 4714 BC in the proleptic .) The Julian day number for today, 4 February 2013, is unknown operator: u'strong'.. 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. [1][1] The current Julian Date is . The "Julian date" may also refer, outside of , to the day-of-year number (more properly, the ordinal [2][2] date) in the Gregorian calendar, especially in computer programming, the military and the food industry, — — or it may refer to dates in the Julian calendar. For example, if a given "Julian date" is "12 May 1629", this means that date in the Julian calendar (which is 22 May 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 ad in the Julian calendar, or even to mean a of 40 astronomical Julian ) is justification for preferring the terms "ordinal date" or "day-of-year" instead. In contexts where a "Julian date" means simply an ordinal date, of a Gregorian year with formatting for [2][2] ordinal dates are often called "Julian calendars" ,, 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 chronological interval of 7980 years beginning 4713 BC. It has been used by since its introduction in 1583 to convert between different calendars. 2013 is year 6726 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 Time, but the International Astronomical Union now recommends that Julian Dates be specified in , 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 , , and after noon into the equivalent decimal fraction. Time intervals calculated from differences of Julian Dates specified in non-uniform time scales, such as Coordinated (UTC), may need to be corrected for changes in time scales (e.g. leap seconds).[1][1] Julian day 2

Alternatives Because the starting point or reference 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, are given in 24 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 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 , 12h is 12:00 noon, GMT unless specified else wise.

Name Epoch Calculation Currentva lue Notes

Julian Date 12h Jan 1, 4713 unknown operator: u'strong' BC

Reduced JD 12h Nov 16, 1858 JD − 2400000 unknown operator: u'strong'

Modified JD 0h Nov 17, 1858 JD − 2400000.5 unknown operator: u'strong' Introduced by SAO in 1957

Truncated JD 0h May 24, 1968 JD − 2440000.5 unknown operator: u'strong' Introduced by NASA in 1979

Dublin JD 12h Dec 31, 1899 JD − 2415020 unknown operator: u'strong' Introduced by the IAU in 1955

Chronological 0h Jan 1, 4713 BC JD + 0.5 + tz unknown operator: Specific to JD u'strong'(UT)

Lilian date Oct 15, 1582 (1) floor (JD − 2299160.5) unknown operator: u'strong' Count of days of the Gregorian calendar

ANSI Date Jan 1, 1601 (1) floor (JD − 2305812.5) unknown operator: u'strong' Origin of COBOL integer dates

RataD ie Jan1 ,1 ( 1) floor( JD − 1721424.5) unknown operator: u'strong' Count of days of the Common (Gregorian)

UnixT ime 0hJ an1 ,1 970 (JD − 2440587.5) × unknown operator: u'strong' [3] Count of seconds 86400

Mars Sol Date 12h Dec 29, 1873 (JD − 2405522)/1.02749 unknown operator: u'strong' Count of Martian days

• The Modified Julian Date (MJD) was introduced by the Smithsonian Astrophysical Observatory in 1957 to record the of Sputnik via an IBM 704 (36- machine) and using only 18 until August 7, 2576. MJD is the epoch of OpenVMS, using 63-bit date/time postponing the next Y2K campaign to July 31, 31086 [4] 02:48:05.47. MJD is defined relative to midnight, rather than noon. • The Truncated Julian Day (TJD) was introduced by NASA/Goddard in 1979 as part of a parallel grouped binary time code (PB-5) "designed specifically, although not exclusively, for applications." TJD was a 4-digit day count from MJD 44000, 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 45000, 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 [5][6][7] values up to 65535, which will occur in the year 2147. There are five digits recorded after TJD 9999. • 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 and Ernest W. Brown's Tables of the Motion of the (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 1955 meeting in [8] Dublin, Ireland. Julian day 3

• The Chronological Julian Date was recently proposed by Peter Meyer[9][10] and has been used by some students [11] of the calendar and in some scientific software packages. CJD is usually defined relative to local , 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 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 [12] into effect. The original paper defining it makes no mention of the time zone, and no mention of time-of-day. It was named for , 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.

• Rata Die is a system (or more precisely a family of three systems) used in the book . It uses the local timezone, and day 1 is January 1, 1, that is, the first day of the Christian or in the proleptic Gregorian calendar. The (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 . 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 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 , the Earth is on the opposite side of the Sun from that object. Then, the two measurements would differ by about 1 000 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 Scaliger in 1583, at the time of the Gregorian , as it is the multiple of three calendar cycles used with the Julian calendar: 15 ( cycle) × 19 () × 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. 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 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 , 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 added the counting of days elapsed from the beginning of the Julian Period: 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 Julian day 4

order were first introduced into .[13] We owe its invention or revival to Joseph Scaliger, who is said to have received it from the of . 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 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 refers the commencement of the era of Nabonassar, the basis of all his calculations.[14] Astronomers adopted Herschel's "days of the Julian period" in the late nineteenth , but used the meridian of Greenwich instead of Alexandria, after the former was adopted as the 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 [15] fraction added to calendar dates in his book, Traité de Mécanique Céleste, in 1799. Other astronomers added fractions of the day to the Julian day number to create Julian Dates, which are typically used by astronomers to date astronomical observations, thus eliminating the complications resulting from using standard calendar periods like eras, years, or . They were first introduced into variable work by Edward Charles Pickering, of the [16] Harvard College Observatory, in 1890. Julian days begin at noon because when Herschel recommended them, the 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 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 . 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. When this practice ended in 1925, it was decided to keep Julian days continuous with previous practice.

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 . 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.[17] The meaning of the variables are explained by the Computer Department of the University of Texas at San Antonio. You must compute first:

Then, if starting from a Gregorian calendar date compute: Julian day 5

Otherwise, if starting from a Julian calendar date 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 year 0.

Finding Julian date given Julian day number and time of day

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

So, for example, January 1, 2000 at 12:00:00 corresponds to JD = 2451545.0

Finding day of given Julian day number

The US day of the week W1 can be determined from the Julian Day Number J with the expression: W1 = mod( J + 1, 7) [18]

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 = mod( J , 7)

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

• 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 Julian day 6

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 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 , 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 = dg − c × 36524; • let b = dc div 1461; let db = dc mod 1461; • let a = (db div 365 + 1) × 3 div 4; let da = db − a × 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 Julian day 7

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).

Footnotes

[1] Resolution B1 on the use of Julian Dates by The XXIIIrd International Astronomical Union General Assembly (http:/ / www.iers.org/ nn_10910/ IERS/ EN/ Science/ Recommendations/ resolutionB1.html) [2] USDA Julian date calendar (http:/ / www.dm.usda.gov/ procurement/ toolkit/ docs/ calendar.pdf) [3] Astronomical for the year 2001, 2000, p. K2 [4] Worsham 1988 [5] A Grouped Binary Time Code for Telemetry and Applications (http:/ / ntrs.nasa.gov/ archive/ / casi.ntrs.nasa.gov/ 19800007830_1980007830.pdf) 1979 [6] CCSDS Recommendations for Time Code Formats (http:/ / ntrs.nasa.gov/ archive/ nasa/ casi.ntrs.nasa.gov/ 19890006406_1989006406. pdf) [7] SDP Toolkit Time Notes (http:/ / newsroom.gsfc.nasa.gov/ sdptoolkit/ primer/ time_notes.html#PB5) [8] Ransom c. 1988 [9] Peter Meyer.(2004). Message Concerning Chronological Julian Days/Dates. (http:/ / www.hermetic.ch/ cal_stud/ cjd.htm) author. [10] Peter Meyer. (n.d.). Chronological Julian Date. (http:/ / www.hermetic.ch/ cal_stud/ chron_jdate.htm) author. Retrieved February 8, 2009. [11] Michael L. Hall. (January 20, 2010). The CÆSAR Code Package (http:/ / www.lanl.gov/ Caesar/ Caesar.html) (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][12] Ohms 1986 [13] Ideler, Handbuch, &c. vol. i. p. 77. [14] Herschel (http:/ / books.google.com/ books?id=uj0DAAAAQAAJ) 1858, P. 678 [15] Laplace (http:/ / books.google.com/ books?id=QjEVAAAAQAAJ&pg=PA348) 1799, p.349 [16] Furness (http:/ / books.google.com/ books?id=5jQJAAAAIAAJ&printsec=toc#PPA206,M1) 1988, p. 206. [17] Tøndering, Claus. "Frequently Asked Questions about Calendars" (http: / / www.tondering.dk/ claus/ cal/ julperiod.php#formula). . [18] Urban & Seidelmann 2013, pp. 592, 618.

References

• Astronomical almanac for the year 2001. (2000). U.S. Nautical Almanac Office and Her Majesty's Nautical Almanac Office. • Astronomical Almanac Online (http:/ / asa.usno.navy.mil/ ). (2008). U.S. Nautical Almanac Office and Her Majesty's Nautical Almanac Office. • "CS 1063 Introduction to Programming: Explanation of Julian Day Number Calculation." (http:/ / www.cs.utsa. edu/ ~cs1063/ projects/ Spring2011/ Project1/ jdn-explanation.html) (2011). Computer Science Department, University of Texas at San Antonio. • Digital Equipment Corporation. Why is Wednesday, November 17, 1858 the base time for VAX/VMS? (http:/ / www.slac.stanford.edu/ ~rkj/ crazytime.txt) Modified Julian Day explanation • Furness, C. E. (1915). An introduction to the study of variable . (http:/ / books.google.com/ books?id=5jQJAAAAIAAJ&printsec=toc#PPA206,M1) Boston: Houghton-Mifflin. Vassar Semi-Centennial Series. • Information Bulletin No. 81 (http:/ / www.iau.org/ static/ publications/ IB81.pdf). (January 1998). International Astronomical Union. • Kempler, Steve. (2011). Day of Year Calendar (http:/ / disc.gsfc.nasa.gov/ julian_calendar.shtml). Goddard Earth Data and Information Services Center. • Moyer, Gordon. (April 1981). "The Origin of the Julian Day System," and Telescope 61 311−313. • Noerdlinger, P. (April 1995 revised May 1996). Metadata Issues in the EOSDIS Science Data Processing Tools for Time Transformations and Geolocation (http:/ / observer.gsfc.nasa.gov/ sec2/ papers/ noerdlinger2.html). NASA Goddard Space Flight Center. Julian day 8

• Ohms, B. G. (1986). Computer processing of dates outside the twentieth century (http:/ / ieeexplore.ieee.org/ xpl/ freeabs_all. jsp?arnumber=5387720). IBM Systems Journal 25, 244 –251. • Ransom, D. H. Jr. (c. 1988) ASTROCLK Astronomical and Celestial Tracking Program pages 69 –143 (http:/ / textfiles.meulie.net/ computers/ DOCUMENTATION/ astroclk.dc2), "Dates and the Gregorian calendar" pages 106 –111. Retrieved September 10, 2009. • Reingold, E. M. & Dershowitz, N. (2008). Calendrical Calculations (http:/ / emr.cs.iit.edu/ home/ reingold/ calendar-book/ third-edition/ ) 3rd ed. Cambridge University Press. • Seidelmann, P. Kenneth (ed.) (1992). Explanatory Supplement to the Astronomical Almanac (http:/ / books. google.com/ books?id=uJ4JhGJANb4C&pg=PA55) pages 55 & 603 –606. University Science Books, ISBN 0-935702-68-7. • Strous, L. (2007) Astronomy Answers: Julian Day Number. (http:/ / aa.quae.nl/ en/ reken/ juliaansedag.html) Astronomical Institute / Utrecht University. • Urban, S. E. & Seidelmann, P. K. (2013), eds. Explanatory Supplement to the Astronomical Almanac, 3rd ed. Mill Valley, Calif.: University Science Books. ISBN 9781891389856

External links • Julian day calculation by IMCCE at (http:/ / www.imcce.fr/ en/ grandpublic/ temps/ jour_julien.php) ± Julian days with 16 significant digits (integer plus fraction) • U.S. Naval Observatory Julian Date Converter (http:/ / www.usno.navy.mil/ USNO/ astronomical-applications/ data-services/ cal-to-jd-conv) no negative Julian days, max year 9999 • Julian Day and Civil Date calculator (http:/ / www.nr.com/ julian.html) • U.S. Naval Observatory Time Service article on Modified Julian Date (http:/ / tycho.usno.navy.mil/ mjd.html) • U.S. Naval Observatory current MJD service (http:/ / tycho.usno.navy.mil/ cgi-bin/ daterdnm.sh) • Outlines of Astronomy by John Herschel, 1849 (http:/ / books.google.com/ books?id=TD0CAAAAYAAJ& pg=PA595) Table of Julian days for remarkable eras • International Astronomical Union Resolution 1B: On the Use of Julian Dates (http:/ / www.iers.org/ nn_10910/ IERS/ EN/ Science/ Recommendations/ resolutionB1.html?__nnn=true) • Calendrica (http:/ / emr.cs.iit.edu/ home/ reingold/ calendar-book/ Calendrica.html) • BASIC Programs from Sky & Telescope (http:/ / www.skyandtelescope.com/ resources/ software/ 3304911. html) with CALJD.BAS (http:/ / media.skyandtelescope.com/ binary/ caljd.bas) and JDCAL.BAS (http:/ / media.skyandtelescope.com/ binary/ jdcal.bas), very small BASIC programs to convert Julian Day numbers. published in the May 1984 issue. Article Sources and Contributors 9

Article Sources and Contributors

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