Astronomical year numbering
Cassini gave the following reasons for using a year 0:
Fred Espanak of NASA lists 50 phases of the moon within year 0, showing that it is a full year, not an instant in time. Jean Meeus gives the following explanation:
Although he used the usual French terms "avant J.-C." (before Jesus Christ) and "après J.-C." (after Jesus Christ) to label years elsewhere in his book, the Byzantine historian Venance Grumel used negative years (identified by a minus sign, −) to label BC years and unsigned positive years to label AD years in a table. He did so possibly to save space and put no year 0 between them.
Anno Domini
For computational reasons, astronomical year numbering and the ISO 8601 standard designate years so that AD 1 = year 1, 1 BC = year 0, 2 BC = year −1, etc. In common usage, ancient dates are expressed in the Julian calendar, but ISO 8601 uses the Gregorian calendar and astronomers may use a variety of time scales depending on the application. Thus dates using the year 0 or negative years may require further investigation before being converted to BC or AD.