The average duration of the lunar (moon-based) month is, according to NASA site, 29.530589 days. Jewish tradition offers two concepts, basic to the Jewish calendar:
Baharad and Ve-Yad.
Both are related to an “attempt” to include the six days of creation (no regular days by any account) in the regular Jewish calendar. This is done by defining an imaginary year that preceded the start of the first lunar renewal in the Jewish calendar (starting, according to Jewish tradition, with the completion of the creation of Adam).
In the article, linked below, I show that these two concepts alone, Baharad and Ve-Yad, are sufficient to obtain a solution to an algebraic equation, which implies that the average duration of the lunar month is 29.530594 days (a deviation of 0.000005 days from the value cited at NASA site).
Same article appears in Hebrew in a separate post.