Lunar Observations in Rosh Hashanah

The Daf Yomi cycle just finished studying Masechet Rosh Hashanah. Mazal tov to all those who have completed this study!

In Masechet Rosh Hashanah observations of the Moon play a very significant role. A major topic of study in this tractate is how the ancient Jewish “calendar” worked. In fact, it was not really a “calendar” in the modern way we think of them at all…

Rosh(ei) Chodesh(im) – the “New Month(s)” – were declared based on two witnesses coming to testify that they saw the first visible sliver of the new moon and testifying before the Sanhedrin – the “Supreme Court” – in Jerusalem (or later in Yavneh, Usha, or wherever the court was sitting.)
The molad – “new moon” (upper left) over modern day Jerusalem

The Court then cross-examined the witnesses and, if valid, declared (“sanctified”) the new month. The Talmud describes the questions that the sages of the court asked the witnesses:

ראש השנה דף כג,ב

 משנה  כיצד בודקין את העדים זוג שבא ראשון בודקין אותו ראשון ומכניסין את הגדול שבהן ואומרין לו אמור כיצד ראית את הלבנה לפני החמה או לאחר החמה לצפונה או לדרומה כמה היה גבוה ולאין היה נוטה וכמה היה רחב אם אמר לפני החמה לא אמר כלום ואח”כ היו מכניסין את השני ובודקין אותו אם נמצאו דבריהם מכוונים עדותן קיימת ושאר כל הזוגות שואלין אותן ראשי דברים לא שהיו צריכים להם אלא כדי שלא יצאו בפחי נפש בשביל שיהו רגילים לבוא:

דף כג,ב גמרא  היינו לפני החמה היינו לצפונה היינו לאחר החמה היינו לדרומה אמר אביי פגימתה לפני החמה או לאחר החמה אם אמר לפני החמה לא אמר כלום דא”ר יוחנן מאי דכתיב (איוב כה) המשל ופחד עמו עושה שלום במרומיו מעולם לא ראתה חמה פגימתה של לבנה ולא פגימתה של קשת פגימתה של לבנה דחלשה דעתה פגימתה של קשת דלא לימרו עובדי החמה (דף כד,א)  גירי קא משדייא:  כמה היה גבוה ולאין היה נוטה כו’:  תנא חדא לצפונה דבריו קיימין לדרומה לא אמר כלום והתניא איפכא לדרומה דבריו קיימין לצפונה לא אמר כלום לא קשיא כאן בימות החמה כאן בימות הגשמים

MISHNAH. How do they test the witnesses? The pair who arrive first are tested first. The senior of them is brought in and they say to him, tell us how you saw the moon — in front of the sun or behind the sun? To the north of it or the south? How big was it, and in which direction was it inclined? How broad was it? If he says [he saw it] in front of the sun, his evidence is rejected. After that they would bring in the second and test him. If their accounts tallied, their evidence was accepted, and the other pairs were only questioned briefly, not because they were required at all, but so that they should not be disappointed, [and] so that they should not be dissuaded from coming.

GEMARA. ‘In front of the sun’ is surely the same as ‘To the north of it’, and ‘Behind the sun’ is surely the same as To the south of it’? — Abaye said: [It means], whether the concavity of the moon is in front of the sun or behind the sun. If he says, in front of the sun, his evidence is rejected, since R. Johanan has said: What is meant by the verse, Dominion and fear are with him, He maketh peace in his high places? Never did the sun behold the concavity of the new moon nor the concavity of the rainbow. It never sees the concavity of the moon, so that she should not feel humiliated. It never sees the concavity of the rainbow so that the worshippers of the sun should not say, (24a ) he is shooting arrows [at those who do not worship him]. “How high was it and in which direction was it inclined.” One Tanna taught: [If he says], To the north, his evidence is accepted; [if he says], To the south, his evidence is rejected. But it has been taught to the opposite effect: ‘[If he says], To the south, his evidence is accepted; [if he says], To the north, his evidence is rejected’? — There is no contradiction; one statement speaks of the dry season, the other of the rainy season.

The rabbis clearly have a very good understanding of observations of the Moon and what is physically possible and what is not.

A list of the phases of the Moon

We can understand and explain many of these statements with our knowledge of astronomy.

How to understand the Gemara’s questions that equate “Before the sun” and “North of it” and vice versa are initially not so obvious. However, Abaye answers and clarifies that they are not equivalent; that “in front of the sun” vs. “behind the sun” refers to whether the curve of the Moon’s crescent is facing towards the sun or away from it. This makes it clear why if the witness says “before the sun” (i.e. interior of the curve towards the sun) their testimony is not accepted.

The diagram of the cycle of the Moon’s orbit around the Earth (counterclockwise in the diagram), shown below, makes it clear that (interior of) the Moon’s curve always faces away from the Sun. The inner circle in the diagram shows the position of the Moon around the Earth (not to scale) and that one side of it is illuminated by the Sun, and the viewing angle from the Earth determines which portion of it is visible from Earth. If one adds an imaginary plane perpendicular to the dashed Earth-Moon line that “cuts” the Moon in half (i.e. along the circle of the Moon’s orbit), the half of the Moon facing Earth in each phase shows what is visible from Earth. That view is depicted in the outer circle, each picture of the Moon’s phases corresponding to the position in the inner circle.

The “molad” new moon that the witnesses testified about seeing, if their testimony was accurate, was always between the phases labeled “new moon” and “waxing crescent” on the diagram. (The term “new moon” in modern astronomy parlance refers to the phase when none of the Moon is visible, slightly different from the talmudic usage.) Thus it is clear that the curve must always face away from the Sun, because only a crescent of the illuminated side is visible from Earth and the curved edge of the Moon that is visible is always closer to the direction of Sun (viewed from Earth).

Diagram of the Sun-Moon-Earth positions throughout a lunar cycle (month) (Not to scale!)

The Gemara’s next discussion focuses on an apparent contradiction between two Tannaitic statements; one taught that if a witness says, To the north, his evidence is accepted; and if he says to the south, his evidence is rejected. But another tannaitic statement says the exact opposite! The Talmud explains that one is talking about during the summer months and the other about the winter months. Rashi and other commentaries give a complicated explanation of this, regarding the Moon’s location near the western horizon at sunset in relation to the Sun’s position at sunset, which seems like an unsatisfying explanation.

However a simpler explanation would be that just like the Sun, the Moon follows a more northern arc across the sky in the summer than in the winter. (See the diagram below.) Therefore, the Gemara’s answer would easily make (more) sense if the Moon’s north and south position was understood to be not in relation to the Sun’s position, but simply reflect the seasonal change that both exhibit. Although Abaye has already explained the Gemara’s initial question as “before/after” equating to “north/south” this could also resolve that question: the north and south refer to north/south location (seasonal) independent of the Sun, not north/south on a given day relative to the Sun, whereas “before/after” refer to position on their celestial paths relative to the Sun on a given day (in addition to, and related to, Abaye’s explanation.) The new Moon of Rosh Chodesh should never appear before – i.e. more west – than the Sun.

To better picture this, look at the position marked “B” in the lunar orbit and phases diagram. That is where a person on Earth is located at (their local) sunset. Viewing from that point, the Sun will have set before the Moon (which would be near to a waxing crescent phase, and still above their horizon) hence the Sun is always “before” – i.e. more to the west than – the Moon on their path across the sky at that time of the month. (The opposite would be true at the end of the month.)

Showing the seasonal changes of the daily paths of the Sun across the sky (in the Northern Hemisphere)

However, there is another explanation possible as well. The Moon’s orbit is tilted by about 5 degrees from the plane of the ecliptic (the plane of the Earth’s orbit around the Sun; see the diagram below). This is why we do not see a solar or lunar eclipse every month, because only at the points where the Moon crosses the ecliptic plane is it possible for the Sun, Moon and Earth to line up exactly to create an eclipse condition.

Therefore, sometimes the Moon’s path across the sky on a given day may appear as much as 5 degrees north or south of the Sun’s path on the same day! This is not a simple cycle, but there were ancient astronomers who could calculate / predict eclipses, so it stands to reason that the ancient rabbis could have similarly known when the Moon would be north or south of the Sun’s path in the sky, and used that knowledge to examine the witnesses.

Diagram showing different possible orientations of the tilt of the Moon’s orbit around Earth relative to the Earth’s orbital plane around the Sun (= the ecliptic) (Not to scale!)

Lastly, another detail from lunar observations that the Mishna includes in the interrogation questions is how wide or broad the Moon was.

One simple understanding of this is that they were asking about how “developed” the crescent was when the witnesses saw it. However, since the testimony of the witnesses was always about the first visible sliver of the Moon each cycle (always on that one day when it was possible to see that sliver), there would hardly have been much noticeable variation of width based on the lunar phases changing.

There is another way to understand this. We may naively think that the Moon’s size does not change much, but that is not correct. Since the Moon’s orbit is an ellipse, there are times when the Moon is closer to and farther from the Earth. When the Moon is closest, its angular size (i.e. apparent size from Earth) is larger by about 14-5 degrees than when it is farthest from Earth in its orbit. This is most noticeable when the Moon is full (e.g. when there is a “supermoon”) but it would be proportionately bigger also for a “new” moon. This gave the rabbis another data point on which to interrogate the witnesses.

All of these demonstrate that the ancient rabbis had an excellent knowledge of ancient astronomy! In fact, a subsequent Mishnah also shows that to be true:

דף כד,א משנה

דמות צורות לבנה היו לו לרבן גמליאל בטבלא ובכותל בעלייתו שבהן מראה את ההדיוטות ואומר הכזה ראית או כזה

דף כד,א גמרא ומי שרי והכתיב (שמות כ) לא תעשון אתי לא תעשון כדמות שמשיי אמר אביי לא אסרה תורה אלא שמשין שאפשר לעשות כמותן

איבעית אימא דפרקים הוה ואיבעית אימא להתלמד עבד וכתיב (דברים יח) לא תלמד לעשות אבל אתה למד להבין ולהורות

MISHNAH. R. Gamaliel used to have a diagram of phases of the moon on a tablet [hung] on the wall of his upper chamber, and he used to show them to the unlearned and say, did it look like this or this?

GEMARA. Is this allowed, seeing that it is written, Ye shall not make with me, which we interpret, ‘Ye shall not make the likeness of my attendants’? — Abaye replied: The Torah forbade only those attendants of which it is possible to make copies  …

… If you like I can say that it was [drawn] in sections, or if you like I can say that he did it for purposes of study, and it is written, Thou shalt not learn to do, which implies that you may learn to understand and to teach.

Here we see that Rabban Gamliel was so familiar with ancient astronomy that he had his own diagrams – similar to the ones above, no doubt! – for showing and instructing those who were in need of more astronomy knowledge to express their own lunar observations. The gemara then questions the halachic legality of this practice, but ultimately declares that it is allowed for the purposes of teaching and understanding, as is our purpose here! We are in good company in our astronomy study with Rabban Gamliel!

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