Considering that the Julian calendar was 10 days off when the Gregorian calendar was adopted in 1582, it can seem amazing how accurate the ancient Hebrews were with their calendar:

“The calculation of the calendar was transmitted to the sages in an unbroken chain going back to Moses… According to the ancient calculations, the exact time between one new moon and the next is 29 days, 12 hours, and 793 chalekim ‘parts of an hour’ (the hour is divided into 1080 parts). In other words, one lunar month has 29.53059 days. It is interesting to note that according to NASA (National Aeronautics and Space Administration), the time between one new moon and the next is 29.530588 days. Of course, NASA has at its disposal the most advanced and sophisticated telescopes and computers. Nevertheless, the difference between NASA’s figures and that used by Hillel II, which originated more than 3000 years ago, is .000002 or two millionths of a day, calculated for the period one month” (The Essence of the Holy Days—Insight from the Jewish Sages by Avraham Yaakov Finkel, 1993, p. 141).