The Gemara was written more than 1500 years ago, yet it says the exact lunar renewal cycle duration with one milisecond more than Berlin university's measure of 29.530589, which in itself is one milisecond more than NASA's measure of 29.530588 calendar days (old measure, they updated it or are rounding their measure https://eclipse.gsfc.nasa.gov/SEhelp/moonorbit.html )

Video explaining the Gemara passage
https://youtu.be/HvQ25hj0Zzc?t=120

https://www.sefaria.org/Rosh_Hashanah.25a.10?ven=William_Davidson_Edition_-_English&vhe=William_Davidson_Edition_-_Vocalized_Aramaic&lang=en&with=all&lang2=en

>However, Rabban Gamliel said to them: This is the tradition that I received from the house of my father’s father: The monthly cycle of the renewal of the moon takes no less than twenty-nine and a half days, plus two-thirds of an hour, plus seventy-three of the 1,080 subsections of an hour.

29.5 days (meaning calendar days, each 24 hours) and 2 thirds of an hour plus 73 parts of the 1,080 subsections of an hour (in ancient times people divided hours in 1,080 instead of 60 parts, but the days had the same duration) equals 29.5 days and 793 parts of an hour (which is 793/1080 in percentage). This is equal to 29.5 plus 0.03059 calendar days (you need to divide the percentage by 24 hours, the duration of the day).

All in all this means the writers of Gemara, 1500+ years ago, knew the precise length of lunar renewal is 29.530590 days.