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.
Dionysius Exiguus
The epact, since it originally marked the new moon, was zero in all first decennovenal years, making Dionysius the first known medieval Latin writer to use a precursor of the number zero. The Latin word "nulla" meaning "no/none" was used because no Roman numeral for zero existed. To determine the decennovenal year, the Dionysian year plus one was divided by 19. If the result was zero (to be replaced by 19), it was represented by the Latin word "nihil", also meaning "nothing". Both "zeros" continued to be used by (among others) Bede, by whose extension of Dionysius Exiguus’ Easter table to a great Easter cycle all future Julian calendar dates of Easter Sunday were fixed unambiguously at last. However, in medieval Europe one had to wait as late as the second millennium to see the number zero itself come into use, although it had come into being around the year 600 in India.