A Very Low Moon

Did you have a very difficult time locating the moon for קידוש לבנה this past מוצאי שבת? It was extremely low and close to the horizon. I was discussing this with Rabbi Dovid Heber and he provided some very interesting findings, after noting that he doesn't recall ever having such difficulty seeing the moon for קידוש לבנה due to altitude.

First, a little background discussion on "moon mechanics" may be necessary to understand what was going on. I find it somewhat surprising but it seems there are many who are not aware that the moon rises in the east and sets in the west just like the sun. However, the precise location and times fluctuate much more erratically than that of the sun. Let's not worry for now about where it is but more about when it is. 

At the beginning of the month, on the מולד, the moon sits between the earth and the sun. Therefore, it follows that the moon should rise and set at the same time as the sun, approximately. However, as the month goes on, the moon rotates around the earth and so its rise and set times will quickly deviate (later) from the sun's. How much should it deviate? That is relatively simple to calculate. While it spends the entire month rising and setting later and later, when we get back to the beginning of the next month, it's right back where it started. This means that the rise/set times have come around full circle - approximately 24 hours. Divide 24 by the average length of a month, approximately 29½ days and that yields...

If you want to avoid the math, skip here: the moon should rise and set close to 49 minutes later every day of the month. The מולד of אלול was on Tuesday afternoon. Four days later, the moon should be setting close to 3½ hours after sunset. That should leave it sufficiently high in the sky after מעריב to be seen by all. However, observe the moonset times here. (This is for Baltimore but the phenomenon is related to the moon's path and is evident no matter what city you look at.) Somehow, it is only advancing around 20 minutes - or even less - every day. Later in the month (starting tomorrow) the times seem to skew the other way such that everything more or less evens out by the time. So, the moon was still setting much closer to sundown than one would expect that many days in to the month and that is why it was so low. 

Unfortunately, my ability to explain this even ends here. I can only illustrate that this was happening but I don't know exactly why. I have not done a full inspection but I assume if this happened once, it probably happens with some degree of frequency. But I haven't inspected moonset times on a greater scale yet to have any idea what that is. I hope this cleared up some things. And if you weren't able to say קדוש לבנה yet, you do have until... uh oh, there is a lunar eclipse coming up next week. See more

Like the Stars of the Heavens

As part of Moshe Rabbeinu's introduction to his review of the last forty years, he makes mention of the fact that (1:10) "HaShem has allowed you to multiply and you are now numerous like the stars in the sky." Rashi is bothered by the obvious exaggeration. B'nei Yisroel were a nation of merely 600,000 men which is infinitesimal compared to the infinite stars. Rashi offers an alternate understanding of the pasuk. However, I believe it is possible that Moshe was indeed comparing B'nei Yisroel to the stars in the sky at that very time.

This understanding is based on a commentary of R' Chayim Kanievsky in Parshas Lech Lecha (Bereishis 15:5). HaShem brings Avraham Avinu outside and tells him to observe the uncountable stars and tells him that his progeny will be likewise uncountable. Rashi there quotes a Midrash that states that HaShem removed Avraham from the atmosphere and placed him above the stars to observe them. R' Chayim questions, why was this necessary? Why was it not sufficient to simply look at the stars from where he was? He answers that we are taught in the adjacent commentary to Rambam's Hilchos Yesodei HaTorah (3:8) that there are a finite number of stars visible from Earth, 1022 to be exact. Beyond the scope of our vision there exists an abundance of stars which are too many to be counted. Avraham had to be removed from Earth in order to appreciate that.

Therefore, when Moshe Rabbeinu spoke to B'nei Yisroel, they were very much comparable to the stars in the sky. In a very short time, B'nei Yisroel had indeed multiplied from a mere 70 to an impressive 600,000. Like the stars that are visible from Earth, they were great in number, yet still countable.

The word "larov" here is assumed to mean "for multitudes" which would imply that the multitudes have already been achieved. This is what is bothering Rashi. While this is, in fact, the meaning of the word in most of its many occurrence in Tanach, it may also be used as a verb, to multiply (as in Bereishis 6:1). Perhaps Moshe was not stating that B'nei Yisroel were multitudes like the stars, but rather, they will multiply like the stars. Just as the visible stars may be a countable finite group, yet "potentially" infinite, B'nei Yisroel were a countable many, with the potential to become infinite. After all, has anyone ever calculated how many total Jews have lived in the history of the world?

Moshe Rabbeinu was speaking to B'nei Yisroel as they were on the verge of crossing over into Eretz Yisroel and realizing the ultimate goal of their deliverance from Egypt. This was a reminder of the star-like potential they were promised to realize following this auspicious moment in their history. It is therefore fitting that Moshe followed this statement with a blessing that HaShem will indeed multiply B'nei Yisroel thousand-fold, to develop them from a modestly small nation like the countable, visible stars, to a prolific nation like the infinite stars of the universe.

Eclipses in הלכה and מחשבה

In light of (no pun intended) the upcoming solar eclipse here in the USA, I thought I'd post a piece I wrote about eclipses a couple of years ago.

B’nei Yisrael are traditionally symbolized by the moon. The generations from Avraham are likened to the cycle of the moon. David and Shelomoh were the 14th and 15th generations from Avraham Avinu. It was during their reign that B’nei Yisrael was at its pinnacle. They conquered their enemies, stretched out their borders and built the beis hamikdash. This is just like the moon which is biggest on days 14 and 15. After Shelomoh, national stability began to deteriorate and B’nei Yisrael lost their splendour, just as the moon wanes after the 15th day.

There are many insights to be taken from this symbolism. The gemara (Rosh HaShanah 25a) quotes the pasuk (Tehillim 104:19) “shemesh yada mevo’o,” the sun knows its path. The gemara comments that the sun knows its path but the moon does not. The relative path of the sun as it changes from season to season is quite predictable and easy to figure out. The path of the moon, however, is erratic in nature and seems not to follow a specific pattern. We may understand this as analogous to the way in which the world is run. The nations of the world, traditionally symbolized by the sun, are governed, to a certain degree, by the laws of nature. There is a less focused Divine Providence that guides their everyday events. This is akin to the predictable path of the sun. One need not delve too deeply to realize that B’nei Yisrael are governed in quite a different manner. The great miracles that adorn our history, as well as the day-to-day twists and turns that befall our nation to this day are clear indications that there is nothing haphazard about the course of events that befall us. There are no patterns or laws of nature to rely on, just as the moon follows a seemingly unpredictable path.

The gemara (Sukkah 29a) tells us that when there is an eclipse of the sun, it is a bad sign for the gentiles. When there is an eclipse of the moon, it is a bad omen for B’nei Yisrael because we follow the lunar calendar and they follow the solar calendar. There is an intriguing insight that lies beneath the surface here as well. An eclipse of the moon happens when the moon moves into a position behind the earth such that the light of the sun cannot reach it. One might say that it is “the moon’s fault” that it was eclipsed. This is the way we must view calamities that befall us. We must search within for the causes and realize that it is our own deeds and actions that have brought them about.

An eclipse of the sun happens when the moon moves in front of the earth in such a way that it blocks the sun’s light from reaching certain spots on the earth. Here, too, we see that it is path of the moon that has caused the eclipse. The sun and earth are insignificant players in a solar eclipse. The lesson learned from this gemara is that everything that happens in this world is, in some way, connected to B’nei Yisrael. Despite our relatively insignificant size, like that of the moon to the sun, the world was created for us and continues to be governed according to our actions. This is not something to take advantage of but rather, a great responsibility that we must bear on our shoulders at all times.

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Every month, on the Shabbos before Rosh Chodesh, as part of "Birkas HaChodesh," the time of the molad is announced. This time refers to the birth of the new moon on which Rosh Chodesh is based. Astronomically, this is when the moon passes between the earth and the sun, thereby completing its monthly cycle. Although the time of the molad no longer determines the exact day of Rosh Chodesh since our calendars are set, we use this figure to determine when we may recite kiddush levanah. Based on the gemara (Sanhedrin 41b), we may only recite kiddush levanah when the moon is new, that is, when it is waxing. Knowing the midpoint between the two molados allows us to determine this exact time (Rema OC 426:3). Also, we do not begin to say kiddush levanah until three whole days after the molad, when the moon is big enough to see.

The period of time from molad to molad (synodic period) that we use for these calculations is 29 days, 12 hours, 44 minutes and 3 and a third seconds. However, this is not an exact, constant figure. Rather, it is the average length of a synodic period as indicated by Rambam (Hilchos Kiddush HaChodesh 6:3). The time we use for the molad may differ from the time of the actual molad, lunar conjunction, by a couple of hours one way or the other. In general, we don't really know when it does differ and we just rely on the average synodic period for all halachic calculations. However, nature can sometimes tell us that our calculations are off - with an eclipse.

An eclipse of the moon happens when the moon is in a position behind the earth such that the sun's rays cannot reach it. Clearly, this can only happen at the exact middle of the month, lunar opposition, when the moon is exactly behind the earth with respect to the sun. An eclipse of the sun is when the moon moves directly in front of the sun, obstructing the view of the sun from earth. This will only happen at the exact beginning of the month when the moon is exactly between the earth and the sun, i.e. the molad.

The issue of eclipses is discussed in Beis Yosef and Darchei Moshe OC 426. The consensus there is that if an eclipse of the moon is witnessed, then kiddush levanah may no longer be recited, even if this is before the prescribed time for sof zeman kiddush levanah, the halfway point between molados. [9/26/2015: This halachah was especially significant in this area of the world this month. The official time for sof zeman kiddush levanah was 12:47 am EDT on Thursday night (Friday morning, officially). However, there was a much anticipated full lunar eclipse that night. According to NASA, the time of mid-eclipse, essentially the official middle of the month was 11:40 pm EDT. Therefore, kiddush levanah should have been recited before that time, despite whatever is written in the calendars.]

A solar eclipse, however, is not as simple. Beis Yosef writes that a solar eclipse may not be used to determine the proper time after which one may not say kiddush levanah. However, there does not seem to be any discussion about beginning to say kiddush levanah. If the time of the molad were preceded by a solar eclipse, as the molad of Teves 5761 was by eight hours, would that allow us to recite kiddush levanah earlier? Conversely, if the molad were to precede the eclipse, would that move back the time at which we may recite kiddush levanah? For our upcoming solar eclipse, the peak time is actually around a full half day before the recorded time of the molad.

Perhaps, the reasoning behind Beis Yosef's ruling with regard to sof zeman kiddush levanah would not apply to techilas zeman kiddush levanah. When a lunar eclipse indicates that we may no longer recite kiddush levanah it is because we may not rely on an average when there is a clear indication that the average is incorrect. When it is an average against a clear natural indication, we dispense with the average. However, the calculation for sof zeman kiddush levanah is achieved by adding half of the average synodic period to the previous molad. To allow a solar eclipse to determine sof zeman would be to combine the clear evidence with an average. We must rely on one or the other but we may not combine the two.

To allow the solar eclipse to determine when we may begin to recite kiddush levanah is relying only on the clear evidence of the eclipse and not on any other averages. Therefore, it would seem that we may adjust the time based on a solar eclipse. Furthermore, the apparent source for the custom to wait three days is Talmidei Rabbeinu Yonah (End of Berachos 4.) But the specific wording used is that one should recite kiddush levanah when people derive benefit from the moon's light - after two or three days. In fact, Yad Ramah on Sanhedrin writes that it may be recited after one day. Therefore, to be lenient in this regard when there is sufficient astronomical evidence on our side does not seem so farfetched.

It should be noted that Darchei Moshe adds his own rationale - that a lunar eclipse is more widely viewed whereas a solar eclipse is only visible in a very limited area of the world. With that explanation, we wouldn't use the solar eclipse in any way to modify our average figures.

A Scratch on the Wall

According to the Midrashim quoted by Rashi, Yitzchak was born precisely a year after the angels visited Avraham and Sarah, on the first day of Pesach. (According to the gemara Rosh HaShanah 11a the angels visited on Sukkos.) Rashi (21:2) writes that HaShem gave Avraham a sign. On the day the angels visited, HaShem made an etching in a wall and told Avraham, "When the sun reaches this point again next year, you will have a son." This sign requires some clarification. How exactly did this work?

An object that is standing upright in the path of the sun will form a shadow on the ground. The exact direction of the shadow depends on the position of the sun in the sky. As the sun moves through the eastern sky in the first half of the day, the shadow will be pointing westward and vice versa for the second half of the day. However, the exact direction of the shadow, i.e., its northerly or southerly bearing, will constantly change. As well, the size of the shadow is dependent on the north/south position of the sun as well. These are the principals behind the sundial. All of the factors change throughout the day and the daily patterns change throughout the year as a result of the change in direction of the earth's tilt. However, one thing is certain. At midday, the sun is not in the eastern sky or the western sky. Rather, it is either due north or due south, depending on where you are in the world. What is relevant to us is that since Eretz Yisroel, at approximately 31^o North, is above the Tropic of Cancer (23.5^o North), the sun will always be in the southern sky at midday. The size of the shadow depends on the angle of the sun in the sky which depends directly on the time of year.

Any sign involving a shadow would surely have been simplest to arrange at midday. It is therefore most noteworthy that the gemara (.ברכות כ"ז) infers from the words (18:2) "kechom hayom," in the heat of the day, that the angels visited in the sixth hour. After the food was prepared and served and the angels conversed with Avraham, it seems altogether plausible that it was exactly midday. It seems that the sign that was given was that at that moment, the southern wall (or other standing object) was casting a shadow on the northern wall. The scratch that was made on the wall indicated the end of the shadow. When the shadow reached the exact same point at midday sometime in the next year, it would indicate that a complete year had passed.

With all this considered the Midrash is quite troubling. All these details are specific to the solar year. However, Yitzchak was born precisely one year later by the lunar calendar, not the solar calendar. What significance could any sun-related sign have to the passing of a lunar year?

I particularly enjoyed the answer that Pi offered in the comments:

On pasuk 18:10, Seforno says: שוב אשוב אליך - למועד המילה כפעם בפעם.‏ This suggests that the time the angels would return a (solar) year later was not the exact day of Yitzchak's birth, but rather some time later. The book קונטרס די שמיא by Alexander Shutz on pages 18-19 claims that the ריב"א asks your question, and that ר' צבי יודא פריידמאן suggests the following answer: The angel Rephael would come back three days after Yitzchak's bris mila to heal him, which would be (about) 11 days after his birth, so that could have been the occasion when the sun reached the line that was marked on the wall.

Witnesses to Sedom's Destruction

Rashi on 19:24 notes that the destruction of Sedom happened at day break, when the sun and moon were in the sky at the same time. This was because they used to worship the sun and moon. HaShem therefore brought the destruction when both were out as a proof to all the sun and moon worshipers that the sun and moon are powerless. Had the destruction taken place when they were not in the sky, one could have argued that they were not "there" to save them. This is a rather simple statement by Rashi but the astronomical basis for it is quite interesting.

 

It is not always that the sun and moon are out together at day break. It is also not always that it is the only time that they are out together. The moon rises and sets approximately 49 minutes later each day. This is a result of the moon orbiting the earth. Just as the moon's position is reset at the end of every month, so are its rising and setting times. (The math is as follows: Every full moon cycle (month), moonrise and moonset make a full circle of 24 hours such that the times are as they were precisely one month previous. The figure of 49 minutes is achieved by dividing 24 hours by the duration of the lunar cycle, 29.5 days, 44 minutes, 3 and a third seconds. More precisely, the figure is 48 minutes, 45.5 seconds.)

At the beginning of the month, the moon follows a very similar schedule to the sun. The moon rises at the beginning of the day and sets at sundown. As the month progresses, the moon rises and sets later and later. At the middle of the month, the moon has virtually the opposite schedule to the sun. It rises when the sun sets and sets when the sun rises. As we enter the second half of the month, the moon begins to rise later in the night and thus, becomes visible at the beginning of the day.

The Midrash (Bereishis Rabba 50) teaches that Sedom was destroyed on the 16th of Nissan. As explained above, at that time of the month, the moon would have risen shortly after sunset and set very shortly after sunrise. Therefore, the only time in the entire day that both the sun and moon were out at the same time was very early in the morning and that is why the destruction took place specifically at the very beginning of the day. [Nevertheless, it is puzzling that Rashi uses the term "Alos HaShachar" which refers to a time before sunrise.]

The Mysterious Midrash

The parsha begins with Avraham Avinu sitting at the doorway of his tent awaiting the opportunity to invite guests in for a meal and, perhaps, teach them of Hashem's ways. The Torah tells us that Avraham was sitting there in the heat of the day. (Bereishis 18:1) Rashi cites from a Midrash that Hashem took the sun out of its shield in order for its rays to be more powerful. Thus, the day was unnaturally hot. Since the pasuk says that it was in the heat of the day, it must mean that it was an unnatural heat. What exactly could this Midrash be referring to when it mentions that the sun was taken out of its shield? Also, why are we to assume that the wording of, "in the heat of the day," means an unnatural heat, maybe it just means during the hottest part of the day?

By analyzing a perplexing passage from Rabbeinu Bacheye's commentary to this portion one can, perhaps, gain better insight. Rabbeinu Bacheye cites a Midrash that Avraham was sitting at the doorway at the fourth hour of the day. This is the a time when, historically, people would be hungry and looking for a meal. Therefore, Avraham wished to capitalize on this opportunity to find a wayfarer in need of a meal and invite him in. It is unclear what Midrash Rabbeinu Bacheye is citing from because we do not seem to have anything that expresses this point. Additionally, this Midrash appears to be in conflict with the Gemara in Berachos (27a) that seems to state that Avraham was sitting there at midday. Why would Rabbeinu Bacheye choose to convey the message of an obscure Midrash as opposed to the Gemara's interpretation?

The Gemara cited above is trying to determine how much of the day can be considered morning. At one point it cites a verse that states that when the sun is hot it will melt the manna and this is applied to the beginning of the fourth hour. The Gemara challenges this by asking that perhaps it means until midday since the sun continues to heat up until that point. To this the Gemara cites the pasuk from our parsha and says that since our pasuk is referring to midday, the pasuk referring to the sun's heat must mean until the fourth hour. Rashi explains that the pasuk from our parsha mentions that the day is hot as opposed to the other pasuk which mentions that the sun is hot. The implications of our pasuk are that it is not just the areas in direct sunlight that are hot, but even areas that are normally shady are hot since the pasuk says, "the heat of the day," and not, "the heat of the sun." Once we find that the Torah uses two forms of expression when referring to the heating of the sun and day, the Gemara concludes that the two must be referring to different times of the day. The one mentioning when the sun is hot is not as hot as the one that mentions that the day is hot.

Perhaps, the above understanding can help answer all the above questions. The normal implications of the wording of our pasuk indicate a time when even shady areas are hot and this is midday because the sun is high in the sky and the actual shadows are relatively small. This leaves a significant area that is normally covered in shade to be exposed to the heat of the sun. This time is called in the "heat of the day." Since this language is conveying this message, the other pasuk cited in Berachos refers to the fourth hour which is when the sunny areas begin to feel hot, thus it is called, "the sun's heat." It is important to note that it is irrelevant to the Gemara whether or not the time period discussed in the pasuk in our parsha was actually midday. The Gemara is just proving that it is referring to a time when both sunny and shady areas are hot. This would normally occur at midday and that means that the other pasuk must refer to the fourth hour. However, since Hashem took the sun out of its shield it is possible that the phenomenon of shady areas being hot actually happened earlier and it just felt like midday. The Torah is just letting us know where the sun was positioned and not how many hours of the day had passed.

Rabbainu Bacheye's Midrash provides the logic upon which it is based. Avraham would sit in the doorway at the most opportune time. Since people are hungry at the fourth hour, it stands to reason that this event happened at that time. If so, how could it be that the pasuk uses language to tell us that the heat was equal to that of midday, the pasuk should have stated that the sun was hot since this is less extreme? This would seem to be where the Midrash that Rashi cites starts from. It must be that Hashem took the sun out of its shield, meaning that he raised it higher in the sky so that the rays were more direct and there were fewer shadows. The heat was comparable to midday, but the actual time was only the fourth hour. Thus, Rabbeinu Bacheye, the Midrash cited by Rashi, and the Gemara all complement each other as opposed to contradict one another. I apologize if this was confusing, this is not normally the style in which these posts are written. I just found it pretty amazing that the elusive identity of the Midrash of Rabbeinu Bacheye might actually be a Midrash that was in plain sight!!!

Lot's Twilight Escape

There is a dispute in the Gemara as to the length of halachic twilight in the morning hours. One opinion mentions that this is a 4 mil time interval and the other states 5. As a proof to the opinion of 5 the Gemara cites from this week's parsha when Lot was escorted out of Sedom in the early hours of the morning. The Gemara maintains that he traversed a 5 mil distance in the exact amount of time between dawn and sunrise. (See Pesachim 93b)

Although this proof is ultimately rejected because it seems that Lot was rushing and the Gemara is referring to people traveling at an average pace, it seems that barring this point that the Gemara would have been content with this proof. The question one may ask is that twilight periods vary based on latitude and also based on the time of the year. How did the Gemara know that the case of Lot was a good proof, perhaps, it happened in a location other than the one the Gemara was discussing, or at a time of year different from the one in the Gemara?

The Gemara's discussion was regarding Korbon Pesach, so we can deduce that the location of its discussion is in Eretz Yisrael. We can also deduce that the time of year it was discussing was at the beginning of spring since that is when Pesach falls. How did the Gemara know that Lot's escape was at this time and location?

Regarding the location, the Gemara easily knew that Lot's escape was in Eretz Yisrael because it happened in Sedom. The Gemara also seems to be of the opinion of the Bereishis Rabbah regarding the time of Lot's escape. Bereishis Rabbah maintains that it happened on the second day of Pesach. (Bereishis Rabbah 48:12) In fact, Rashi also mentions the fact that it was on Pesach. (Rashi Bereishis 19:3) So, with these facts being presented one can clearly see that had it not been for the fact that Lot was running for his life, the Gemara would have had an adequate proof.