Accuracy of the Hebrew calendar

The present Hebrew (Jewish) calendar was put into effect by Hillel II in the year 358 C.E. [1]. Prior to that time, various sages imparted fundamental astronomical data with regard to the lengths of the lunation (synodic lunar month). The elders of the ruling judicial system established the calculations upon which (with corroborations by witnesses) declarations of the new moon were based. The destruction wrought by the Romans and dispersion of the people produced the need for a permanent calendar whose basis could be taught to skilled laymen. It still is complex, since the calendar months are lunar and yet, for example, Passover must occur in the Spring, a solar event. Thus, the Hebrew calendar must be in harmony with both the lunar and solar cycles. The fact that 19 mean solar years contain almost precisely 235 lunar months (the Metonic cycle) makes such a lunar/solar calendar possible. The accuracy of this calendar is examined. It is shown that despite the approximations necessary to provide a fixed calendar, the Hebrew calendarʹs mean lunar month duration discrepancy from current astronomical values (a small positive number) amounts to only one day in 14,000 years. More remarkable yet is that this error was less in the past, since there has been a decrease (very small) in the orbital period of the moon. Several research issues are formulated.