Is there lunar drift in the fixed Hebrew calendar?

Question

It is known that there is a slight discrepancy in the average length of a year according to the Hebrew calendar and the average length of an astronomical solar year which causes a seasonal drift in the Hebrew calendar of about 6.5 minutes per year. My question is, does the fixed calendar slightly drift from the astronomical lunar month or is the average length of a fixed Hebrew-calendar month exactly the same as the average length of an astronomical lunar month? Assuming there is some amount of drift, how much is there?

From my amateur perspective, it seems that if there is a lunar drift, it is much smaller than the solar drift as Rosh Hodesh continues to correspond with the new moon and if there was a significant lunar drift, the new month would begin to occur farther away from the new moon. I understand that the molad often does not fall exactly on the day before Rosh Hodesh, but I don't have much in-depth knowledge of how the molad works and how it relates to Rosh Hodesh.

Answer 1

Wikipedia says:

This [the molad] value is as close to the correct value of 29.530589 days as it is possible for a value to come that is rounded off to whole parts (1/18 minute). The discrepancy makes the molad interval about 0.6 seconds too long. Put another way, if the molad is taken as the time of mean conjunction at some reference meridian, then this reference meridian is drifting slowly eastward. If this drift of the reference meridian is traced back to the mid-4th century, the traditional date of the introduction of the fixed calendar, then it is found to correspond to a longitude midway between the Nile and the end of the Euphrates. The modern molad moments match the mean solar times of the lunar conjunction moments near the meridian of Kandahar, Afghanistan, more than 30° east of Jerusalem.

Furthermore, the discrepancy between the molad interval and the mean synodic month is accumulating at an accelerating rate, since the mean synodic month is progressively shortening due to gravitational tidal effects. Measured on a strictly uniform time scale, such as that provided by an atomic clock, the mean synodic month is becoming gradually longer, but since the tides slow Earth's rotation rate even more, the mean synodic month is becoming gradually shorter in terms of mean solar time.

Answer 2

As discussed by the Shvili D'Rakia (sections ד and ז), each synodic period (the time between two consecutive moladim) is 29 days, 12 hours, and 793 chalakim. However, we can't split a single day between two months. Therefore, generally speaking, months alternate between 29 and 30 days, with a loss of 793 chalakim.

Now, as discussed further by the Tiferes Yisrael (sections יא and יב), this didn't always happen as planned. (In fact, the Tur notes that the months only alternate about 29.5% of the time.)

Thus, over the 247-year cycle, the calendar runs short by 905 chalakim. In order for the calendar to repeat itself exactly, it will take 609,872 years.