Part of the problem (with regard to the period of the New Moon) is that everyone thinks you need to have super-advanced clocks to measure that sort of thing and that, without it, there’s no way to accurately measure from one New Moon to the next.
The truth, however, is that it’s not all that hard at all. All you have to do is know how to count and do some long division.
Ancient astronomers used to keep careful track of days and astronomical events. They used to count days, months and years. They also used to track astronomical events, such as eclipses.
A solar eclipse can only happen when the sun and moon are in conjunction (i.e. at the time of the Molad). Therefore, if you know that X number of solar eclipses occured over a period of Y lunar months encompassing Z days, all you have to do is divide Z by Y and presto… you have the length of time from one molad to the next. The more data points (X) you have, the more accurate your measurement becomes.
So, you don’t really need super-advanced clocks to determine this value. All you need is a count of days and months and eclipses. Both Chazal and the ancient Babylonian astronomers are capable of computing this value.
The Wolf