The Precise Length of the Lunar Month in the Talmud and Modern Science

As is well known, at the beginning of every month the moon appears as a thin crescent, and it gradually grows until it becomes full in the middle of the month. From that point the moon begins to diminish until it disappears and is “born” again. The day of the lunar renewal is the day of Rosh Chodesh, the beginning of the Hebrew month.

The time that passes from one lunar renewal to the next is called the length of the lunar cycle.

It is important to note that the dates of the festivals in the Torah are determined according to the day of the month, exactly as they are stated in the Torah. For example, Passover is on the fifteenth of Nisan, Sukkot is on the fifteenth of Tishrei, Yom Kippur is on the tenth of Tishrei, and so on.

For this reason, great halachic importance is attached to determining the day of Rosh Chodesh, which depends on the precise timing of the lunar renewal.

The Talmudic Tradition of Rabban Gamliel

In the Talmud (Rosh Hashanah 25a) the following account is recorded: “Once the sky was covered with clouds, and a form resembling the moon was seen on the twenty ninth day of the month. The people thought that it must be the new moon and therefore that the next day should be declared Rosh Chodesh.

Rabban Gamliel said to them: This is the tradition that I received from the house of my grandfather. The renewal of the moon cannot occur in less than twenty nine days and a half, plus two thirds of an hour and seventy three parts.”

Rabban Gamliel thus testifies that he received through the Oral Torah, passed down through generations of the leaders of Israel, a precise tradition about the length of the lunar cycle. According to this tradition, the renewal of the moon occurs exactly every twenty nine and a half days, plus two thirds of an hour and seventy three parts.

Calculating the Length of the Lunar Cycle

Let us examine the calculation according to the Torah tradition.

First, twenty nine and a half days.

Next, two thirds of an hour. In the ancient system used by the Sages, each hour is divided into 1080 parts. These are not minutes but a finer unit of division that allows precise fractions such as halves, quarters, eighths, thirds, sixths, ninths, fifths, and tenths.

Two thirds of an hour therefore equals 720 parts.

Adding the additional seventy three parts results in a total of 793 parts.

In hours, this equals 793 divided by 1080, which is 0.734259 hours.

In days, this equals 0.03059 days, since a full day contains 24 hours.

Adding this to the remaining 29.5 days produces a total of 29.53059 days.

Modern Scientific Measurement

Now consider the conclusion of modern scientific research.

The following statement appears in the work of Carl Sagan, the chief scientist associated with NASA, the United States space agency. According to his findings, the length of the lunar cycle from one renewal to the next is:

29.530588 days, which in practical terms is 29.53059 days. The difference is only a tiny fraction of a second.

This measurement was obtained through sophisticated technology. American astronauts placed a glass prism on the surface of the moon. A laser beam is sent from Earth to this prism and reflected back. Using powerful telescopes and atomic clocks, scientists can measure the exact distance and motion of the moon with extraordinary precision.

It should be emphasized that without such instruments, which were developed only in recent decades, modern science would have had no way to reach such a precise result.

More recent research conducted in Berlin, Germany, has further narrowed the difference of those tiny fractions of a second between the Torah tradition and modern scientific measurements.

According to that study, the lunar cycle from one renewal to the next is 29.530589 days.

The Spiritual Lesson

For those who know with certainty that the Torah was given to the Jewish people by the Creator of the universe, it is clear that many details of the commandments contain profound insights into the natural world. The Giver of the Torah revealed these facts because they are necessary for the correct observance of the mitzvot.

The example above, which is needed for determining the dates of the Torah’s festivals, is only one of many. Yet even this single example is sufficient for an open minded observer, free from preconceived assumptions, to recognize that it is impossible for the Torah of Israel to have been written by a human author.

Why Rabban Gamliel Rejected the People’s Observation

This also explains how Rabban Gamliel was not deterred from ruling against the opinion of the people who believed they had seen the moon. He relied on the tradition he had received from his ancestors, according to which it was impossible for the moon to appear at that time.

Today, in light of modern scientific findings, it is clear that the form seen on the twenty ninth day was not the moon at all but merely some reflection within the clouds. Rabban Gamliel already knew this then, because he understood that the source of his knowledge was the Torah of the Creator, and the Creator of the world does not make mistakes.

Wisdom Recognized by the Nations

All that remains for us is to wait patiently for science to take another step in its pursuit of the Torah’s wisdom, until it can measure even another tiny fraction of a second and reach the absolute truth about the length of the lunar cycle.

“For this is your wisdom and your understanding in the eyes of the nations, who will hear all these statutes and say: Surely this great nation is a wise and understanding people.” (Devarim 4:6)

What kind of wisdom and understanding is visible to the nations? The Sages explain that it refers to the calculation of the seasons and the constellations.