## 1.0 Calendars and Dates

DEFINITION: The Julian calendar is the calendar established by Julius Caesar in 46 B.C. (or the year -45, if the convention of a year zero and negative numbers is used). In this calendar, the year is fixed at 365 days except for every 4th year when it has 366 days. Alternatively, the year can be considered to be 365.25 days long but fractions are ignored until they accumulate to make a full day. Dates in the Julian Calendar are called Julian dates and are not to be confused with Julian Day numbers.

DEFINITION: The Gregorian calendar is the reformed Julian calendar with the year fixed at 365 days except for leap years which contain 366 days. Leap years are years that are exactly divisible by 4 except for century years which must also be divisible by 400. This is the calendar in common use today. Dates in the Gregorian calendar are called Gregorian dates.

DEFINITION: The Julian proleptic calendar is a calendar formed by applying the rules of the Julian calendar back in time, even before the Julian calendar was invented.

DEFINITION: The Rata Die number is a date specified as the number of days relative to a base date of December 31 of the year 0. Thus January 1 of the year 1 is Rata Die day 1.

DEFINITION: The Julian Day Number, Julian Day, or JD of a particular instant of time is the number of days and fractions of a day since 12 hours Universal Time (Greenwich mean noon) on January 1 of the year -4712, where the year is given in the Julian proleptic calendar. The idea of using this reference date was originally proposed by Joseph Scalizer in 1582 to count years but it was modified by 19th century astronomers to count days. One could have equivalently defined the reference time to be noon of November 24, -4713 if were understood that Gregorian calendar rules were applied. Julian days are Julian Day Numbers and are not to be confused with Julian dates.

If the JD number is expressed as an integer, it represents the number of whole days since the reference instant to noon of that day. Table 1 gives some examples.

Table 1
Gregorian DateTimeJD number
December 31, 1979noon2444239.0
January 1, 1980start of the day (just after midnight)2444239.5
January 1, 1980noon2444240.0
January 1, 1980no time specified2444240
January 1, 1980midnight commencing January 22444240.5

A Julian date is a date in the Julian calendar. Similarly, a Gregorian date is a date in the Gregorian calendar. Table 2 shows how Julian dates and Gregorian dates relate to the Julian Day Number. The year, month, and day given in the table can represent either a Julian date or a Gregorian Date. If it is considered a Julian date, the Julian Day Number is given in the column with heading "JD for Julian date." If the date is considered a Gregorian date, the Julian Day Number is given in the column with heading "JD for Gregorian date."

Numbers in the "Day" column represent days that begin at midnight. This contrasts with Julian Day Numbers which start at noon and continue up until noon of the following day. Thus a day number such as 24.5 represents noon and has a JD number that ends in zero tenths.

Table 2
YearMonthDayJD for Julian dateJD for Gregorian dateComment
-4713 11 24.0 -38.5 -0.5 middle of JD before Gregorian reference
-4713 11 24.5 -38.0 0.0 Gregorian date of JD reference
-4713 11 25.0 -37.5 0.5 middle of JD reference day (midnight)
-4712 1 1.0 -0.5 37.5 middle of day before JD reference
-4712 1 1.5 0.0 38.0 Julian date of JD reference
-4712 1 2.0 0.5 38.5 middle of JD reference day
0 1 1.0 1721057.5 1721059.5 The first day of 1 B.C.
0 2 29.0 1721116.5 1721118.5 Rata Die = -306
0 3 1.0 1721117.5 1721119.5 Rata Die = -305
0 12 31.0 1721422.5 1721424.5 Rata Die = 0
1 1 1.0 1721423.5 1721425.5 Rata Die = 1
1582 10 4.0 2299159.5 2299149.5 last day before Gregorian reform
1582 10 15.0 2299170.5 2299160.5 first day of Gregorian reform
1840 12 31.0 2393482.5 2393470.5 M programming language reference
1858 11 17.0 2400012.5 2400000.5 Modified Julian Day 0.0
1900 1 1.0 2415032.5 2415020.5
1901 1 1.0 2415398.5 2415385.5 start of the 20th century
1970 1 1.0 2440600.5 2440587.5 Unix reference
1980 1 1.0 2444252.5 2444239.5 PC (DOS) reference

The Julian Day Number is defined relative to the Julian proleptic calendar so that from noon of October 4, 1582, the last day in the Julian Calendar, there are 2299160.0 days to noon of the Julian Day Number reference time. This count is a result of considering dates that have leap years every 4 years. Noon of the day following Thursday, October 4, 1582, (Julian Calendar) is the first day of the Gregorian reform (designated as Friday, October 15, 1582, in the Gregorian calendar) and is JD 2299161.0. Normally from this date, the Gregorian calendar is used and the Gregorian calendar rules for leap year apply. It is, of course, possible to continue the use the Julian Calendar after the Gregorian reform or the Gregorian Calendar before the Gregorian reform. Using the Julian Day Number avoids this possible confusion but the system is not in common, everyday use by the general public.