To study the Hebrew lunar calendar and view Gregorian and Julian dates on it, see torahcalendar.com. The beginnings of months are based on careful astronomical calculations of the probable first visibility of the new moon. The beginnings of years are based on the Spring Equinox. A new feature that’s recently been added to TorahCalendar will be very useful. It now shows on what dates lunar eclipses of various types have occurred or will occur.