## 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.

### Julian Date

The Julian Period was named by Joseph Scaliger in 1582 because it was based on the (proleptic) Julian calendar, and began on the last year when three chronological cycles began on the same year. In 1849, the astronomer John Herschel proposed counting the number of days from noon of the of the first day January of the first year of the Julian Period, 4713 BCE, for the meridian of Alexandria, which he chose because it was the basis of all of Ptolemy's calculations, which were used by astronomers for hundreds of years.  However, British astronomers based their calculations on what came to be called the Prime Meridian at the Royal Greenwich Observatory in England, and adjusted Julian days accordingly.  They switched from starting astronomical days at Greenwich mean noon to midnight in 1925, but Julian days still start at noon in order to remain consistent with earlier recordings.

Julian Dates are the whole Julian day number plus the fractional day.  (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 decimal fraction for Julian Dates is 0.0 at noon GMT and 0.5 at midnight. To to be precise, modern Julian Dates are usually given according to Coordinated Universal Time (UTC, which is kept within a fraction of a second of GMT by adding leap seconds) or Terrestrial Time (TT, which is not adjusted with leap seconds, and is currently about a half-minute ahead of UTC).

### Modified Julian Date

The Modified Julian Date was adopted in 1957 by the Smithsonian Astrophysical Observatory for tracking artificial satellites with low-precision computers of the time that had difficulty with the full Julian Date.  They are formed by taking the Julian day and truncating the first two digits and moving the start of the day from noon to midnight UT, or by subtracting 2400000.5.  Modified Julian Date 0.0 is 1858 November 17 at 00:00 GMT, which is called the Smithsonian date.

### Truncated Julian Date

The Truncated Julian Day was introduced by NASA 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 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 values up to 65535, which occurs in the year 2147.  There are five-digits recorded for TJDs after 1995.

### Other Julian Dates

Other variations of the Julian Date have been used.
• The Reduced Julian Date truncates the first two digits of the Julian Date, but unlike the Modified Julian Date, it keeps the astronomical day beginning at noon UT.
• The Dublin Julian Date was named for the 1955 meeting of the International Astronomical Union in Dublin, Ireland and counts days from the 1900 epoch, which was 1899 December 31 at noon GMT.
• The Heliocentric Julian Date is the same as the (geocentric) Julian Date, except that it is corrected so that the frame of reference is the sun or, more precisely, the center of gravity of the solar system, and thus may be up to 16 minutes different from the Geocentric Julian Date.
• The Chronological Julian Date was proposed recently by Peter Meyer to be the same as the (astronomical) Julian Date, but instead of beginning the day at noon GMT, it starts at midnight relative to whatever timezone is being referred to.

### 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 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 PC, 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

An ordinal date is defined by ISO 8601 as the year number combined with the ordinal day of the year, i.e. the number of days from the beginning of the current year.  The day of year is often erroneously called the "Julian date". The day of the year is numbered 001-365 (366 in leap years).

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, in Universal Time. Years are in the range 1957-2056.  For example, 99365.99999999 was immediately followed by 00001.00000000, representing the transition from 1999-12-31 to 2000-01-01.

## 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.

### Julian year

Each Julian year is exactly 365.25 days and is prefixed by the letter 'J'.  The standard epoch J2000.0, now used for new star-position catalogues and in solar-system-orbital calculations, corresponds to 2000 January 1.5 TT = Julian Date 2451545.0.  J1900.0 was one Julian century, or 36525 days, earlier, at 1900 January 0.5, i.e. twelve hours before the first day of the Gregorian year 1900.

### Stardates

The stardates in the TV program Star Trek: The Next Generation (TNG) divided the year into 1000 stardates.  It was never stated whether stardate years started with the calendar year. Stardate 41986.0 was set in the year 2364, which would make the epoch 41.986 years earlier, either sometime in the year 2322 or the beginning of 2323.  There was never a detailed standard published for converting dates, so fans have developed various versions.  The game Star Trek Online converts current dates into TNG stardates 400 years in the future using an epoch of May 25, 1922 (2322-400).