The original article in Hebrew appeared here

Among religious preachers, especially Orthodox Jewish ones, there are many references to the amusing discussion on the alleged vast knowledge of our holy ancestors about the exact length of the moon cycle, also known as the synodic month, which is the basis for the Jewish calendar as well as several other calendars. You can see an example of this here.

The moon, as we know nowadays, has been drifting away from us since its formation, probably following the collision of some celestial body with Earth. While the Earth’s rotation slows down (causing the day to be longer), the lunar orbit time also becomes gradually longer. During Talmudic times (about two millennia ago) it was roughly 29.530586 days and nowadays it’s approximately 29.530589 days. When looking at different geological eras, we see much bigger differences measured in hours and even days.

But even if we limit ourselves to this tiny era that consists of the last few thousands of years… how could the ancient Babylonians and Greeks reach such seemingly-impossible precision, calculating the lunar cycle?

Let’s start by stating that the precision in question is not that high. When talking in days, the number 29.53059 looks pretty impressive (5 decimal digits!), however, if we translate this to shorter periods of times, we’ll notice it’s not extraordinary. The difference between 29.53058 and 29.53059 days is about one second. Not something which is unthinkable for ancient measuring. The ancient Babylonian calculation reached an accuracy of about 2 seconds per month.

Ancient clocks of those times typically used technological means such as measuring the angle of a shadow (sundial) or using “water clocks”, in which time was measured by the regulated flow of water (or other liquid) into or out of a vessel.

In these eras which we discuss here, a lunar eclipse takes a few hours and a solar eclipse lasts a few minutes. Both occur about twice a year, if we include partial eclipses, and much more rarely if counting only full eclipses.

We’ll spare you the simple explanations (learned in school) for the essence of these eclipses. We’ll only indicate that both types of eclipse occur only when the moon is in a specific lunar phase: A lunar eclipse – only when there is a full moon (middle of the month), and a solar eclipse – exactly during the time of the new moon (beginning/end of month).

All these facts didn’t go unnoticed by ancient astronomers, whose main occupation was watching the sky during ideal ancient darkness. As we already saw, they also had the ability to measure time periods of minutes with an accuracy of seconds, and time periods of days with an accuracy of minutes.

Now, suppose you – the educated reader – are a respectable astronomer in ancient Babylon. You are equipped with all the above simple knowledge, and with state-of-the-art water clocks, courtesy of your patron king. You waited patiently between eclipses and managed a detailed record of events, as precise as those times enable. For the sake of simplicity, let’s assume we’re discussing two lunar eclipses, two years apart, for which you attempted to precisely measure (say, two-minute precision) the moment that is easiest to detect – the initial “bite” of the full moon by the Earth’s shadow.

Your records tell you that since that moment of the previous eclipse, 708 days, 17 hours and approximately 37 minutes have elapsed. You know this, since you measured in minutes the amount of time between sunset and the beginning of the eclipse. As we’re talking about the same season in the year, the sunset is more-or-less at the same minute of the day. If you are an experienced astronomer, you already took into consideration the small differences of the actual sunset (up to 8 minutes in our case).

Now you do some math: If 24 lunar months took exactly 708 days, 17 hours and 37 minutes, what’s the length of a single month? Exact arithmetic is a must for an astronomer who desires job stability: 17 hours and 37 minutes are 0.743 days. Thus we divide 708.734 by 24 and get… 29.53058 days. Should we stick to kosher food from now on?

The secret is of course that precision of seconds per month is more-or-less equivalent to a precision of minutes per year. It’s much easier to associate the latter with ancient measuring. The above simulation is imaginary, but similar to the real methods by which ancient calculations were performed. Perhaps there were more years and less minute precision. Perhaps vice versa. Maybe solar eclipses were used instead, and possibly several rather than just two.

This way or the other, there’s no need for “divine knowledge” and no celestial inspiration is required in order to achieve the results actually reached by the ancient Babylonians and Greek astronomers. All you need is clear sky, free time and old instruments. You also need some common sense, patience, accuracy, and basic knowledge of arithmetic – things that are not necessarily the top priorities of modern day religious preachers.