Rata Die

There are three distinct forms of R.D., heretofore defined using Julian Dates.

Dershowitz and Reingold do not explicitly distinguish between these three forms, using the abbreviation "R.D." for all of them.^[1]

Dershowitz and Reingold do not say that the RD is based on Greenwich time, but page 10 state that an R.D. with a decimal fraction is called a moment, with the function moment-from-jd taking the floating point R.D. as an argument and returns the argument −1721424.5. Consequently, there is no requirement or opportunity to supply a time zone offset.

The first form of R.D. is a continuously-increasing fractional number, taking integer values at midnight local time. It is defined as:

RD = JD − 1,721,424.5

Midnight local time on Sunday December 31, year 0 (1 BC) in the proleptic Gregorian calendar corresponds to Julian Date 1,721,424.5 and hence RD 0.

In the second form, R.D. is an integer that labels an entire day, from midnight to midnight local time. This is the result of rounding the first form of R.D. downwards (towards negative infinity). It is the same as the relation between Julian Date and Julian Day Number (JDN). Thus:

RD = floor( JD − 1,721,424.5 )

In the third form, the R.D. is an integer labeling noon time, and incapable of labeling any other time of day. This is defined as

RD = JD − 1,721,425

where the R.D. value must be an integer, thus constraining the choice of JD. This form of R.D. is used by Dershowitz and Reingold for conversion of calendar dates between calendars that separate days on different boundaries.

• Decimal time#Fractional days
• Julian date
• Lilian date