Rata Die
Encyclopedia
Rata Die is a system for assigning numbers to calendar days (optionally with time of day), independent of any calendar, for the purposes of calendrical calculation
s.
It was named (after the Latin
for "fixed date") by Edward Reingold
and Nachum Dershowitz for their book Calendrical Calculations.
However, essentially the same system (including the same epoch) was used previously by the REXX
programming language and by others.
Rata Die is somewhat similar to Julian Dates (JD), in that the values are plain real number
s that increase by 1 each day.
The systems differ principally in that JD takes on a particular value at a particular absolute time, and is the same in all contexts, whereas RD values are relative to timezone. This makes RD more suitable for work on calendar dates, whereas JD is more suitable for work on time per se. The systems also differ trivially by having different epochs: RD is 1 at midnight (00:00) local time on January 1, AD 1 in the proleptic Gregorian calendar
, JD is 0 at noon (12:00) Universal Time
on January 1, 4713 BC in the proleptic Julian calendar
, and the REXX count of days begins with 0 at midnight (00:00) local time on January 1, AD 1 in the proleptic Gregorian calendar.
, 5 hours behind UT
, Zoff = -5/24.)
The first form of RD is a continuously-increasing fractional number, taking integer values at midnight local time. It may be defined in terms of the Julian Date as
In the second form, RD is an integer that labels an entire day, from midnight to midnight local time. This is the result of rounding the first form of RD downwards (towards negative infinity). It is the same as the relation between Julian Date and Julian Day Number (JDN). Thus:
In the third form, the RD is an integer labelling noon local time, and incapable of labelling any other time of day. This is defined as
where the RD value must be an integer, thus constraining the choice of JD. (The fractional part of the JD must have a particular value which depends on Zoff.) This form of RD is used in the book for conversion of calendar dates between calendars that separate days on different boundaries.
The book does not explicitly distinguish between these three forms, using the abbreviation "RD" for all of them.
The Lilian Day Number
(LDN) is an integer labelling a whole day (like the second form of RD). LDN is 1 on October 15, 1582, which is the first day of the Gregorian calendar. It is named after Aloysius Lilius
, the inventor of the Gregorian calendar
. It can be defined mathematically as:
See the "Julian Date" article for systems that are independent of timezone.
Calendrical calculation
A Calendrical calculation is a calculation concerning calendar dates. Calendrical calculations can be considered an area of applied mathematics.Some examples of calendrical calculations:* The number of days between two dates....
s.
It was named (after the Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
for "fixed date") by Edward Reingold
Edward Reingold
Edward M. Reingold is a computer scientist active in the fields of algorithms, data structures, graph drawing, and calendrical calculations.He has co-authored the standard text on calendrical calculations, Calendrical Calculations, with Nachum Dershowitz...
and Nachum Dershowitz for their book Calendrical Calculations.
However, essentially the same system (including the same epoch) was used previously by the REXX
REXX
REXX is an interpreted programming language that was developed at IBM. It is a structured high-level programming language that was designed to be both easy to learn and easy to read...
programming language and by others.
Rata Die is somewhat similar to Julian Dates (JD), in that the values are plain real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
s that increase by 1 each day.
The systems differ principally in that JD takes on a particular value at a particular absolute time, and is the same in all contexts, whereas RD values are relative to timezone. This makes RD more suitable for work on calendar dates, whereas JD is more suitable for work on time per se. The systems also differ trivially by having different epochs: RD is 1 at midnight (00:00) local time on January 1, AD 1 in the proleptic Gregorian calendar
Proleptic Gregorian calendar
The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to dates preceding its official introduction in 1582.-Usage:...
, JD is 0 at noon (12:00) Universal Time
Universal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...
on January 1, 4713 BC in the proleptic Julian calendar
Proleptic Julian calendar
The proleptic Julian calendar is produced by extending the Julian calendar to dates preceding AD 4 when its quadrennial leap year stabilized. The leap years actually observed between its official implementation in 45 BC and AD 4 were erratic, see the Julian calendar article for details.A calendar...
, and the REXX count of days begins with 0 at midnight (00:00) local time on January 1, AD 1 in the proleptic Gregorian calendar.
Forms
There are three distinct forms of RD. In this section they will each be defined in terms of Julian Dates. "Zoff" is the offset of the timezone being used, in fractional days. (For example, in Eastern Standard TimeEastern Standard Time
Eastern Standard Time may refer to:*North American Eastern Time Zone, UTC-5*Australian Eastern Standard Time, UTC+10*An album by Hip Hop group Kooley High...
, 5 hours behind UT
Universal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...
, Zoff = -5/24.)
The first form of RD is a continuously-increasing fractional number, taking integer values at midnight local time. It may be defined in terms of the Julian Date as
- RD = JD - 1721424.5 + Zoff
In the second form, RD is an integer that labels an entire day, from midnight to midnight local time. This is the result of rounding the first form of RD downwards (towards negative infinity). It is the same as the relation between Julian Date and Julian Day Number (JDN). Thus:
- RD = floor(JD - 1721424.5 + Zoff)
In the third form, the RD is an integer labelling noon local time, and incapable of labelling any other time of day. This is defined as
- RD = JD - 1721425 + Zoff
where the RD value must be an integer, thus constraining the choice of JD. (The fractional part of the JD must have a particular value which depends on Zoff.) This form of RD is used in the book for conversion of calendar dates between calendars that separate days on different boundaries.
The book does not explicitly distinguish between these three forms, using the abbreviation "RD" for all of them.
Similar system
There is another day count system that is based on local time.The Lilian Day Number
Lilian date
A Lilian date is the number of days since the beginning of the Gregorian Calendar on October 15, 1582, regarded as Lilian date 1. It is named for Aloysius Lilius who devised the Gregorian Calendar. It was invented by Bruce G. Ohms of IBM in 1986....
(LDN) is an integer labelling a whole day (like the second form of RD). LDN is 1 on October 15, 1582, which is the first day of the Gregorian calendar. It is named after Aloysius Lilius
Aloysius Lilius
Aloysius Lilius , also variously referred to as Luigi Lilio, Luigi Giglio, or Aluise Baldassar Lilio, was an Italian doctor, astronomer, philosopher and chronologist, and also the "primary author" who provided the proposal that became the basis of the Gregorian Calendar reform of 1582.The crater...
, the inventor of the Gregorian calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
. It can be defined mathematically as:
- LDN = floor(JD - 2299159.5 + Zoff)
See the "Julian Date" article for systems that are independent of timezone.