In total the idea is dubious. I had several discussions on this. The calendar was official set by witnesses, and they were mixed up on purpose sometimes, when The day of Atonement fell near Shabbat. The leap year was proclaimed by Synedrion. So, I cannot see, why Jews needed exact calculations of calendar, except practical - when to start harvest, but the Lunar Month is unimportnat for it. The length of the year in Jewsih calendar is not precize at all. The 19-year cycle was [also] discivered by some Meton in Greece. Rambam says he took all calculations from Greeks. Rabbam Gamliel learned Greek wisdom. "Almagest" of Ptolemy also had the Lunar length. Jews thought that the earth was flat (in Babilonian Gemara, at least), while Greeks measured radius. Every single fact from the above can be argued, but together they seem against supernatural Jewish knowledge of calendar.
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The calendar was official set by witnesses, and they were mixed up on purpose sometimes, when The day of Atonement fell near Shabbat. The leap year was proclaimed by Synedrion.
So, I cannot see, why Jews needed exact calculations of calendar, except practical - when to start harvest, but the Lunar Month is unimportnat for it. The length of the year in Jewsih calendar is not precize at all.
The 19-year cycle was [also] discivered by some Meton in Greece.
Rambam says he took all calculations from Greeks. Rabbam Gamliel learned Greek wisdom. "Almagest" of Ptolemy also had the Lunar length. Jews thought that the earth was flat (in Babilonian Gemara, at least), while Greeks measured radius.
Every single fact from the above can be argued, but together they seem against supernatural Jewish knowledge of calendar.