Could the Hebrew calendar calculations have been know since the time of Moses?

Question

Many years ago, I read (non-Jewish source, without explicit external references) that the calendar calculations have actually been in effect since Moses, but were kept in secret for many centuries. Occasionally, the leap year cycle would be adjusted to resynchronize with the solar year. My notes say that the current leap year cycle dates back to 142 CE, and before that each leap year occurred one year earlier in the cycle.

Are there Jewish sources that confirm (or deny) this?

(I'm particularly interested in the 142 CE postponement, or other specific dates for calendar adjustments.)

The following, from History of the Jews, Volume II, by Heinrich Graetz., provides some support, in particular the aspect of the calculation being kept secret.

Page 433:

This unexpected end of the persecution recalled the fugitives to their native land. The seven disciples of Akiba—the only heirs to the spiritual heritage of former times—who, for the most part, had emigrated to Babylon, now returned. These were Meïr, Judah ben Ilai, José ben Chalafta, Jochanan of Alexandria, Simon ben Jochai, Eleazar ben Jacob (or ben Shamua) and Nehemiah. They repaired directly to the plain of Rimmon, made notable during the Revolution, to consider the introduction of a leap year, the calendar probably having become incorrect. At the first meeting a fierce contest ensued, probably with reference to one of the Halachas of Akiba, but the dispute terminated in a friendly settlement.

Page 443:

The wisdom of the Patriarch Simon II. deftly avoided this breach. Chananya established a sort of Synhedrion in Nahar-Pakod, probably in the neighborhood of Nahardea, of which he was the president, whilst a certain Nechunyan, perhaps the Prince of the Captivity, appears to have supported him. The Babylonian community, until then under the control of Judæa, and now left uncared for through the destruction of all religious institutions in the fatherland, welcomed a Synhedrion in their midst as of joyful import, and gratefully accepted its ordinances and decisions. Chananya immediately introduced a leap year, and the celebration of the festivals as had been customary in Judæa.

Page 572:

The custom had prevailed up till now of keeping secret the computation of the new moon and the leap year, and of making known the times of the festivals to the communities in the neighboring lands by announcing them by messengers.

Answer 1

The mathematical part of the Rabbinic calendar was developed in the period C.E. 700-950. (Sacha Stern, Calendar and Community Oxford University Press 2001.) It was not known to Moses.

Answer 2

This is definitly the case. I recall seeing somehwere (I am sure it was in 'The Pirush' on Rambam in Kidush Hachodesh) saying "obviously all that Hillel knew, Moshe surely knew."

There are some other sources relevant to this.

See Rambam Kidush Hachodesh chap 18. where he enumerated when the Sanhedrin would fall back to using all the calculations (no witness, cloudy etc.)

[These difficulties were avoided due to the following] tradition which existed among our Sages, [having been] transmitted from one to another in a chain extending back to Moses our teacher: When the moon was not sighted at the beginning of the months, month after month, the court establishes [the following sequence], one full month with thirty days, one lacking month with twenty-nine days. In this manner, they would calculate and establish one full month and one lacking month - establishing these months, but not sanctifying them.7 For the sanctification of the months is dependent solely on the sighting [of the moon]. At times they would have a full month follow another full month, or a lacking month follow another lacking month, depending on the results of their calculations."

Furthermore the sages would have to know the calculations to catch false-witnesses claiming to have seen the new moon.

Answer 3

Many years ago, I read (non-Jewish source, without explicit external references) that the calendar calculations have actually been in effect since Moses, but were kept in secret for many centuries. Occasionally, the leap year cycle would be adjusted to resynchronize with the solar year.

It is semi correct and a matter of dispute .The astronomy behind the calendar calculations had to have been known since the time of Moshe but basing the the calendar itself on that knowledge is questionable.

Rabbeinu Bachya (Shemos 12:2) brings from Rabbeinu Chananel that Kidush ha'Chodesh is based on calculations of the Sod ha'Ibur given to Moshe Rabeinu at Har Sinai. It was complelty independent of the testimony of witnesses.The only reason they had witnesses was to disprove the Tzedukim who did not accept their calculations.

The Rambam disagrees because there are explicit Gemoras which indicate they made Rosh Chodesh based on the witnesses testimony.

Others ask that if there really was independent calculation that they used then why is there two days of Rosh HaShana in Eretz Yisroel and for all Yom Tovim in chutz la'aretz. Why didn't they know when Yom Tov was based on the independent calculation?

When in comes to leap years, the Gemara Sanhedrin 11B discusses how they decided whether to make a leap year or not.The decision(not) to make a leap year was not only dependant on resynchronizing with the solar year. There were other factors involved as well. The Gemara goes on at length to discuss how it was determined. Being that some of what the Gemara mentions had been written in the Tosefta the manner of determining leap years does not seem to have ever been a secret.