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Decimal Time - Decimal Dates
Decimal Dates
Astronomers, geophysicists, computer programmers and others often record dates as a single number, representing a count of days from a specified starting date, or epoch, in order to easily calculate the amount of time between any two dates. Some computer programmers call such a day-count an integer date when it is an integral number of days. The count of days may also include a decimal fraction, which represents the time of the day as the fractional day since midnight. Computer programmers sometimes call a floating-point number of days a serial date.
Here is a table of decimal dates:
| Name | Origin | TS | JD Offset | Comments |
|---|---|---|---|---|
| Julian Date Variants | ||||
| Julian Date | -4712-01-01 | AT | 0.0 | aka Geocentric or Astronomical JD |
| Heliocentric | -4712-01-01 | AT | 0.0 | adjusted to solar position |
| Chronological | -4712-01-01 | LT | −0.5 | |
| Reduced | 1858-11-17 | AT | 2400000.0 | |
| Modified | 1858-11-17 | UT | 2400000.5 | |
| Truncated | 1968-05-24 | UT | 2440000.5 | |
| Dublin | 1900-12-31 | AT | 2415020.0 | |
| INTEGRAL | 2000-01-01 | UT | 2451544.5 | used only for INTEGRAL |
| Other decimal dates | ||||
| Lilian | 1582-10-15 | UT | 2299159.5 | |
| Rata Die | 0001-01-01 | UT | 1721422.5 | |
| ANSI COBOL | 1601-01-01 | UT | 2305812.5 | |
| Excel Serial | 1900-01-01 | LT | 2415018.5 | unreliable before 1900-03-01 |
Years are zero or negative before the beginning of the Common or Christian Era, so -4712 is the same as 4713 BC, and 0000 is 1 BC. All negative years here are in the proleptic Julian calendar, and all other dates are in the Gregorian calendar, which is proleptic before 1582-10-15.
TS stands for "Time Scale". AT is Astronomical Time which is offset 12 hours from UT; UT is Universal Time; TT is Terrestrial Time; LT is local civil time. Some dates shown as AT or UT may actually be given in relation to UTC, GMT, ET, TDT, TT or other time scales.
JD Offset is the number of days to add to the decimal date to convert it to the Julian Date, or to subtract from the Julian Date to convert to the equivalent decimal date. UT is assumed for local time.
Julian Day Number
The Julian Day Number is a whole-number count of days from noon of the first day the year 4713 BC. (-4712-01-01.5 JC) This is the beginning of the Julian Period, which was named by Joseph Scaliger in 1582, being the last date when three chronological cycles began on the same day. It was so-named because it was based on the (proleptic) Julian calendar, and not for Scaliger's father, Julius, as is often claimed. (Coincidently, the Julian calendar was replaced with the Gregorian around the same time.) In 1849, the astronomer John Herschel proposed counting the days in the Julian Period, rather than just years, creating the Julian Day Number. British astronomers then reckoned days as starting at noon in Greenwich, so astronomical Julian Days are still counted beginning at noon Greenwich Mean Time. (Herschel's original proposal actually specified noon at Alexandria, Egypt, as Greenwich was not yet universally accepted.) The Julian Day is sometimes called the Geocentric Julian Day to distinguish it from the Heliocentric Julian Day, and the Astronomical Julian Day to distinguish it from the so-called Chronological Julian Day.
Julian Date
Julian Dates are the Julian Day Number plus the fractional day. They are used mostly by astronomers, and thus could be considered real "stardates". (These should not be confused with ordinal dates, which are sometimes erroneously called "Julian Dates," or with Julian calendar dates.) They are used to calculate the exact time between any two events in history, such as variable star observations. The fractional day for Julian Dates is 0.0 at 12:00 Universal Time and 0.5 at 00:00 UT. Julian Ephemeris Dates (JED) are the same as Julian Dates but always start 0.0 at 12h Terrestrial Time (TT) for recent dates and 12h Ephemeris Time (ET) for older dates. TT is now officially preferred by the IAU for Julian Dates, although UT is still often used.
Reduced Julian Day/Date
The Reduced Julian Day Number is the Julian Day Number with the left-most two digits truncated, thereby being a count of days since 1858-11-17.5. Like the Julian Day, but unlike the more well-known Modified Julian Day, the Reduced Julian Day begins and ends at 12:00 (noon) Universal Time. It can be calculated as RJD = JD - 2400000. (The NASA team responsible for the Microwave Anisotropy Probe has introduced their own version, the MAP Reduced Julian Day, defined as JD - 2450000, to gain more pecision.)
Heliocentric Julian Day/Date
The Heliocentric Julian Date is the same as the Julian Date (also called the Geocentric Julian Date) except that the exact fractional day is corrected so that the frame of reference is positioned at the sun (actually the solar system's barycenter, or center of mass, which is just outside the sun's radius in the direction of Jupiter), which creates a difference of at most about 16 minutes (0.01 d), that being the time it takes for light to cross the earth's orbit.
Modified Julian Day/Date
According to Dennis D. McCarthy of the US Naval Observatory, Modified Julian Dates were created by the General Assembly of the International Astronomical Union in 1955 and subsequently adopted in 1957 by the Smithsonian Astrophysical Observatory for satellite tracking as a variation of Julian Dates, with the first two digits truncated, and beginning at midnight Universal Time (GMT) instead of noon. The Modified Julian Day Number is a count of the whole number of days since 1858 November 17.0 (known as the "Smithsonian Date"). The Modified Julian Date is the Modified Julian Day Number plus the fractional day. The shorter length makes it easier to use than Julian Dates, especially with low-precision computers and calculators. It can be calculated as: MJD = JD - 2400000.5.
Truncated Julian Day/Date
Truncated Julian Dates were created by NASA for use in its space program, and are a count of the number of days since midnight UT, May 24, 1968, which may be found from the formula TJD = JD - 2440000.5.
Some define TJD as a truncation of Modified Julian Dates by one more digit, using the formula TJD = (JD - 0.5) modulo 10000, which originally yielded the same number as NASA. Since NASA's TJD became five digits in 1995, these two formulas now give two different numbers, differing by 10,000. By the alternate formula, TJD is currently the number of days since midnight, October 10, 1995. January 1, 2001, was TJD 1910 by this definition, but TJD 11910 according to NASA. When using the alternate definition, care must be made to specify the epoch (1968-05-24.0 or 1995-10-10.0) or the Julian myriad (the digits truncated from the Julian Day Number, i.e. 244 or 245).
Chronlogical Julian Day/Date
Peter Meyer has proposed Chronological Julian Days, which start at the following midnight for GMT, or for the time zone of the location being referred to. This is in keeping with the original purpose of the Julian Period, to aid chronologists in dating events absolutely that were recorded in different calendar systems. Thus, if a calendar system begins the day at apparent midnight local time, then this is when the corresponding CJD begins; if it begins at sunset, then the relative CJD begins at sunset. Users of CJD refer to the Julian Day as the Astronomical Julian Day.
Dublin Julian Day/Date
According to the ASTROCLK documentation:
[T]he International Astronomical Union (IAU) at their Dublin meeting in 1955 adopted a special Dublin Julian Date (DJD) starting at noon on January 0, 1900 or 1900 January 0.5 and which may be defined as DJD=JD-2415020. The date can be confusing, however, since there obviously is no 0th of January; the selected date is a matter of astronomical convenience and actually is the same as 1899 December 31.5. The resulting number has only five digits to the left of the decimal point (3 February 1988 = 32175.5).In astronomical usage, day 0 of any month is the same as the last day of the previous month. Note that 1900 January 0.5 is also the J1900.0 epoch date.
INTEGRAL Julian Day/Date
As explained on the INTEGRAL web site, "The European astronomical satellite, INTEGRAL, (INTErnational Gamma-Ray Astrophysics Laboratory) is an astronomical satellite for observing the gamma-ray sky...The INTEGRAL Julian Date (IJD) starts on January 1st, 2000, but expressed in Terrestrial Time (TT) and not in UTC. Since TT differs from UTC by 32.183 sec + 32 leap seconds at the start of year 2000, the UTC origin of the IJD is actually 1999-12-31 T23:58:55.817."
Lilian Date
The Lilian Date was named for Aloysius Lilius, co-inventor of the Gregorian Calendar. Day 1 is the first day of the Gregorian Calendar, 1582-10-15. The first use of Lilian Dates has been credited to IBM.
Rata Die
Rata Die, from the Latin "day of calculation," is counted from the first day of the Common or Christian Era (0001-01-01) in the proleptic Gregorian calendar. It was proposed by Edward M. Reingold and Nachum Dershowitz from the University of Illinois in Urbana in their book, Calendrical Calculations.
ANSI Date
ANSI dates are counted from 1601-01-01 and were adopted by the American National Standards Institute for use with COBOL and other computer languages. This epoch is the beginning of the last 400-year cycle by which leap-years are calculated in the Gregorian calendar. The last year of this cycle is the only one divisible by 100 that is a leap-year, which was the year 2000, and which was followed by a new 400-year cycle beginning with 2001. 32-bit versions of the Microsoft Windows operating system count units of one hundred nanoseconds from this epoch.
Excel Serial Day/Date
Microsoft Excel is a spreadsheet program which uses a "serial value" count of days to store both dates and time of day. Excel supports two different epochs. The standard epoch, inherited from Lotus 1-2-3 and used by default in Excel for Windows, uses January 1, 1900, as Day 1. Excel for Macintosh uses the epoch of the Apple Macintosh's clock, January 1, 1904, as Day 0. Either epoch may be selected in the program options. Days always start at midnight, local civil time, including when Daylight Saving Time is in effect.
(By error Lotus calculated 1900 as a leap year, even though in the Gregorian calendar it is not. Due to this, day 60 converts to February 29, 1900, which did not exist. Some software converts day 1 to December 31, 1899, instead.)
Functions within the program convert time/date strings to serial values. DATEVALUE() takes any date or date/time string and returns the serial day integer, and TIMEVALUE() takes a time or date/time string and returns the fractional day. Functions YEAR(), MONTH(), DAY(), WEEKDAY(), HOUR(), MINUTE() and SECOND() take a serial value as an argument and return the specified date/time element. NOW() returns the current serial date, including both the integral and fractional parts, while TODAY() returns only the serial day integer. Cells containing serial dates may be viewed as either a serial number, such as 38251.924194, or as a standard date/time string by changing the cell format.
Ordinal Date
The ordinal date is the year number combined with the ordinal day of the year, i.e. the number of days from the beginning of the current year. This is often called the "Julian date," especially in the military, although it is based upon the Gregorian, not the Julian, calendar. The day of the year is numbered 001-365 (366 in leap years). (By definition, ordinal numbers start with 1, while cardinal numbers start with 0; sometimes day 0, or January 0, of a particular year is referred to, which is the same as December 31 of the previous year.)
According to ISO 8601:2004, the year must be written in full, i.e. YYYYDDD or YYYY-DDD, although previous editions of ISO 8601 permitted a truncated format with just the last two digits, i.e. YYDDD or YY-DDD, or no year, i.e. -DDD. As examples of the current standard, December 31, 1999, may be represented as 1999365 or 1999-365, and January 1, 2000, as 2000-001 or 2000001. The ISO standard permits only standard time representation, prefixed by the letter T, such as 2000-001T12:00:00.
Ordinal dates are sometimes combined with the fractional day to represent the time of the day. NASA/NORAD's Two-Line Elements for the tracking of orbital satellites include an "epoch date" which includes a two-digit epoch year and the ordinal day of year, including the fractional day with eight decimal places of precision. Examples would be 99365.99999999 and 00001.00000000.
Decimal Years
There are different types of years, with slightly different lenths, so it is important to specify which is being referred to. The siderial year is the time it takes the earth to revolve once around the sun, relative to other stars, or 365.256366 days. The anomalistic year is the time it takes the earth to make two successsive passages through the perihelion, or 365.259636 days. The tropical year is the average time between the beginning of the same seasons in successive years, about 365.2421988 days. The vernal equinox year is the time between vernal equinoxes in successive years, or 365.242374 days. The Julian year is the average length of a year in the Julian calendar, i.e. four years divided by four or 365.25 days. The Gregorian year is the average length of a year in the Gregorian calendar, i.e. 400 years divided by 400, or 365.2425 days. (It is worth noting that the Gregorian calendar is based upon the vernal equinox year, not the tropical year, as is often claimed, and thus will not be off by as much as one day from when it was created until the tenth millenium!) The Islamic lunar calendar year is on average 354.432 days long!
Astronomers sometimes use dates comprising of the year and the decimal fraction of the year. Two slightly different standards
have been used, differing by about one half-day:
Besselian year
A quantity introduced by F. W. Bessel in the nineteenth century that has been used into the twentieth century. Bessel introduced a system whereby it would be convenient to identify any instant of time by giving the year and the decimal fraction of the year to a few places, but the starting time of the year was not convenient for dynamical studies that utilize Julian dates (see definition for Julian date), differing by 0.5 day, and the Besselian year varies slowly. Besselian years are prefixed by 'B' to distinguish them from Julian years, which replaced them for standard epochs in 1984. The length of the Besselian year at the 1900.0 epoch was 365.2421988 days, but has varied with the length of the tropical year.
Exactly 365.25 days, in which a century (100 years) is exactly 36525 days and in which 1900.0 corresponds exactly to 1900 January 0.5 (from the Julian-date system, which is half a day different from civil time or UT). The standard epoch J2000.0, now used for new star-position catalogues and in solar-system-orbital calculations, means 2000 Jan. 1.5 Barycentric Dynamical Time (TDB) = Julian Date 2451545.0 TDB. When this dynamical, artificial "Julian year" is employed, a letter "J" prefixes the year.