[D66] Astronomical Year Numbering

[R.O.]

  4. Astronomical Year Numbering

Astronomers designate years prior to 1 A.D. by means of zero and 
negative numbers, according to the sequence of numbers ..., -2, -1, 0, 
1, 2, .... Between the year 1 and the year -1 there occurs the year 0. 
Thus astronomers adopt the following convention:

1 A.D. = 1 C.E. =  year 1
1 B.C. = 1 B.C.E. = year 0
2 B.C. = 2 B.C.E. = year -1 and so on

More generally, a year popularly designated /n/ B.C. or /n/ B.C.E. is 
designated by astronomers as the year /-(n-1)/.

The rules for leap years work for years prior to 1 C.E. only if those 
years are expressed according to the astronomical system, not if 
expressed as years B.C.E.  4 C.E. is a leap year in both calendars, 
1 B.C.E. = astronomical year 0, 5 B.C.E. = year -4, 9 B.C.E. = year -8, 
and so on, are all leap years. 101 B.C.E. = year -100 is a leap year in 
the (proleptic 
<https://www.hermetic.ch/cal_stud/cal_art.html#Proleptic>) Julian 
Calendar but not in the (proleptic) Gregorian Calendar. These 
statements, however, are only theoretically true, because (as noted 
above) prior to 4 C.E. the leap years were not observed correctly by the 
Roman calendrical authorities.

The choice of which system of numbering years to use is relevant to the 
question: When Does the New Millennium Begin? 
<https://www.hermetic.ch/cal_stud/newmill.htm> as can be seen from the 
following:

Gregorian   Religiously   Common Era
Calendar     Neutral       Calendar
3 BC         3 BCE          -2 CE
2 BC         2 BCE          -1 CE
                       CE millennium begins 0-01-01 CE
1 BC         1 BCE           0 CE
Gregorian millennium usually taken to begin 1-1-1 AD
1 AD         1 CE            1 CE
2 AD         2 CE            2 CE
...          ...            ...
1998 AD      1998 CE        1998 CE
1999 AD      1999 CE        1999 CE
                       CE millennium ends   1999-12-31 CE
                       CE millennium begins 2000-01-01 CE
2000 AD      2000 CE        2000 CE
Gregorian millennium usually taken to end   2000-12-31 AD
Gregorian millennium usually taken to begin 2001-1-1 AD
2001 AD      2001 CE        2001 CE

January 1st, 1 AD is usually taken to be the start of the first 
Christian millennium, but a case could be made for January 1st, 1 BC 
(see the comment above concerning the Incarnation 
<https://www.hermetic.ch/cal_stud/cal_art.html#Dionysius>), which would 
imply that the third Christian millennium began on January 1st, 2000 AD.

https://www.hermetic.ch/cal_stud/cal_art.html

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