Did a Jewish rabbi precisely calculate the duration of the full moon cycle 1800 years ago?

Question

Attempting to prove to me that Judaism is the only true religion, a friend of mine read to me from a book titled, The Coming Revolution, that the Zohar (a 2nd/3rd century CE commentary on the Torah allegedly written by Rabbi Simeon bar Yochai) uses a highly accurate value for the duration of the full moon cycle (29.530588853), centuries before this calculation could be made by modern calculators. How true is this claim?

My Google "skills" were unable to find who was the first person in history to come up with the calculation (NASA?). The only thing I could find, more or less related is this page using Gematria to calculate the moon cycle. But honestly, I'm not too sure what to make of it.

Note: Some people think the Zohar was written by Moses de León in the 13th century which, if true, would still be ages before NASA.

Answer 1

Maimonidies (12th Century) puts it at 29.530594. His source is the Talmud (Bavli RH 25a) (~7th century quoting a rabbi from the 2nd century).

(For the curious the precise number given is 29 days, 12 hours, and 793/1080 of an hour.)

However, lunar cycles can be calculated pretty accurately even in ancient times by counting between total solar eclipses. Consider (from here) the two solar eclipses from Portugal on July 19, 418 and December 23, 447. As long as someone remembered that there were 364 lunar months between them, they could easily calculate a lunar month length of 29.53021 (accurate to 3 decimal places). With a longer gap between eclipses and more accuracy of when during the day it occurred, even more places can be calculated. This is certainly something the Greeks were capable of doing.

(FWIW Maimonidies himself states that he got all his numbers from the Greeks (see Laws of New Moons 17:24 and Guide to the Perplexed 3:14)).

Answer 2

The measurement of the mean lunar month as 29 days, 12 hours, and 793/1080 of an hour is (in this notation) first found in Treatise on the Computation of the Chronology of the Jews and their Festivals by the Muslim astronomer al-Khwarizmi in the 9th century, then by the Muslim al-Biruni in the 10th/11th century, then by the Jewish scholar Bar Hiyya in the 11th century, and by Maimonides in the 12th century.

The equivalent value in base-sixty notation is given already by Ptolemy (2nd century AD), quoting Hipparchus (2nd century BC), who had it from the ancient Babylonians, so it goes back a long way. The passage in the Talmud (B. RH 25a) quoting Gamaliel as putting the measurement of the month at 29 days, and half a day, and two thirds of an hour, and 73 parts is now generally considered to be an interpolation. See Sacha Stern, Calendar and community. A history of the Jewish calendar second century BCE – tenth century CE, Oxford, 2001, p. 201.

Answer 3

It is written in the Talmud (Rosh Hashanah p.25), which is dated 200-500 CE, and attributed of Gamlial (a Jewish leader early in the first century CE), who claimed to have learnt it from his grandparents.

Here is an English Translation of the passage:

Our Rabbis taught: Once the heavens were covered with clouds and the likeness of the moon was seen on the twenty-ninth of the month. The public were minded to declare New Moon, and the Beth din wanted to sanctify it, but Rabban Gamaliel said to them: I have it on the authority of the house of my father's father that the renewal of the moon takes place after not less than twenty-nine days and a half and two-thirds of an hour and seventy-three halakin.

The footnotes explain that a halakin is 1/1080th of an hour.

Note that the quote provides a minimum time, not an exact time.

Assuming 24 hours a day, 60 minutes per hour, then 29 days + 0.5 day + 2/3 hour + 73/1080 hour = 29.530594136 days.

For comparison, a Synodic Month is actually 29.530588853 days - i.e. slightly less than the minimum time provided.