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.]

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

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.

The Two Luminaries

Pasuk 16 refers to the sun and the moon as "shnei hame'oros hagedolim", the two large luminaries but concludes by referring to the sun as the "maor hagadol" and the moon as the "maor hakaton". On this pasuk there is the well-known Rashi, quoting the Midrash, that the moon and the sun were created equal but the moon complained that "two kings cannot share one crown". Therefore, it was reduced to a smaller luminary. However, this is certainly an allegorical understanding of the pasuk. What, then, is the simple understanding?

In In the Beginning: Biblical Creation and Science, a fascinating book reconciling the Biblical account of creation with modern science, Professor Nathan Aviezer offers an eye-opening interpretation. An astronomical body is measured both by its true size and by its apparent size or angular diameter. The apparent size specifies how large it appears to an observer on Earth. This figure is the ratio of the true size of the object to its distance from the Earth. This figure is expressed as the angle that the object subtends from the position of an observer on Earth. That means, if you were pointing to the bottom of the object, the apparent size is the number of degrees you must rotate your arm to be pointing at the top of the object. The sun is 400 times bigger than the moon. It is also exactly 400 times further away from Earth. As a result, the apparent size for the sun and moon are identical at 0.53 degrees! Now we can understand the pasuk as follows: The first part of the pasuk is referring to the point of view of an Earth observer. From our point of view, the sun and moon are the biggest heavenly bodies and in fact, appear identical in size. The second part of the pasuk refers to the true size of the sun and moon.

Please see Pi's comment below with some nice alternative understandings of this פסוק.

Let's Face It

If your average gentile passed by a group of Jews saying קדוש לבנה they would probably be quite confused - not because a group of individuals appear to be blessing the moon but because they see ten Jews facing eleven directions. Many people seem to face all sorts of different directions in order not to face the moon. While this seems like a perfectly innocent practice, there are some serious issues involved.

The reason why people do this is so as to not appear to be gazing at the moon (either so as not appear to be praying to or worshiping the moon or simply to avoid the prohibition to gaze at the moon.) This is certainly a concern that is brought up in halachah. Mishnah Berurah (426:13-14) quotes from poskim that one should not gaze at the moon, even during the berachah. Rather, one should give a quick glance beforehand. He also states that we dance by standing on our toes because the bending of our knees might appear as bowing. However, nowhere, does it mention that one should turn away from the moon. I do not know of any other sources who do suggest to turn away but what I do know is this: It is nothing short of blasphemy to direct the following words at HaShem:

ברוך יוצרך, ברוך עושך, ברוך קונך, ברוך בוראך

These words must be directed at the moon. I would think that the same would hold true for כשם שאני רוקד כנגדך ... which again is certainly talking about the moon. I am not sure if people just don't know what they're saying or just aren't thinking but I myself have seen people face away from the moon towards the shul from the beginning of קדוש לבנה until the end. I think this an unfortunate example of over-zealousness gone awry. I might even go as far as to put this in the same league as people turning their backs on ברכת כהנים - a practice which is fortunately diminishing but is still found here and there. I feel rabbanim should bring this to their congregants' attention.

UPDATE: A reader has brought to my attention two sources which actually do discuss this practice.

:לבושי מרדכי

:יסוד ושורש העבודה

I nevertheless still maintain that the source for this is obscure, at best. And certainly of note is the point made by יסוד ושורש העבודה to which I was מכוין, regarding those two phrases. If there is a concern related to gazing at the moon, I still do not feel that is reason to turn away. But at the very least, if that is to be the practice, everyone ought to get together and decide to face the same direction. In או"ח צ"ד, it is made very clear how careful one must be with the direction they face for שמונה עשרה, so as not to make the ציבור appear disjointed. While this is outside of the בית הכנסת, I think the same care should be taken. (Especially now considering the יסוד ושורש העבודה suggesting that one needs to stand in the same manner as in שמונה עשרה.)

Ominous Eclipse Predictability

For those in the Western United States, you will be able to see a full lunar eclipse just before dawn this Shabbos!

Chazal tell us in Sukkah (quoted by Rashi in Bereishis) that eclipses are ominous signs. I have often been asked whether this is true with regard to contemporary times because we know how to predict eclipses. My answer has always been, "Yes." Even amongst the other ancient civilizations we find the ability to predict eclipses. The ability to predict eclipses was known as far back as the time of the Chaldeans. Even the Babylonians and Greeks were also very familiar with the necessary calculations.

The calculation required is knowledge of the Saros Cycle. The Saros Cycle is a duration of 18 years, 11 days and 8 hours. In each cycle, one will have eclipses at the same intervals as the one that preceded it. Every three cycles will have an eclipse at the same approximate location relative to Earth.

In fact, in the early 1900's an ancient Greek shipwreck was discovered. One of the items found was something that became known as the Antikythera Device (named for the location of the wreck). Its gearwork was so intricate that scientists were astounded. Something like this should not have been able to have been made in the time period this ship went down (approximately 100 years prior to the Churban Bayis Sheini). Not only was it clear that it had been made, it was clear that many prototypes had had to have been made prior to it, because this one was perfected. After much analysis, it became clear that the device was an ancient "calculator". It would display the movement of the Sun, Moon, stars and planets. It also would show when the next eclipse would happen.

This is more proof that they were able to calculate eclipses. They had even put the calculations into machines to do the dirty work for them. When Chazal made their statement, eclipses were already predictable events. If so, how could an eclipse be an ominous sign?

It seems that the answer is that when Hashem created the world He placed in it times that are naturally times of judgment (similar to Rosh Hashana). It was through His mercy that He shows us (and we can even predict) when these times will be, so the affected parties can repent.

THE BOOK (BEING PUBLISHED BY ISRAEL BOOK SHOP), THE SECRETS OF THE STARS, WILL BE IN STORES NEXT WEEK!!! KEEP YOUR EYES OPEN!

Yam Suf 7 or 8 Days from the Exodus?

Most people assume that Krias Yam Suf and its ensuing song happened on the seventh day of Pesach. However, Rashi at the end of this week's Parsha clearly states that it happened on the eighth day of Pesach. Rashi states that the eight strings of Tzitzis are symbolic of the eight days of travel from when we left Egypt until the sea split and we sang our Shira. (Rashi Bamidbar 15:41)

One of the issues that has been addressed regarding this Rashi is that it seems contradictory to another Rashi. When commenting on the events of Krias Yam Suf, Rashi mentions that it happened on the seventh day of the Exodus. Rashi even states that this is the basis for the custom to read the Torah portion of Krias Yam Suf on the seventh day of Pesach. (Rashi Shemos 14:5)

I would like to offer two suggestions that our founded on how to calculate when one's day begins. The first answer is suggested by Rabbeinu Bachye. He maintains that even though Jewish law usually recognizes night as preceding day, when it comes to sacrificial offerings the day comes first (regarding sacrifices, the portion placed on the Mizbeach is able to be burnt the night following the day in which the blood was sprinkled).

Our Exodus began on the 14 of Nisan when the Korbon Pesach, a sacrificial offering, was brought in the early afternoon. Thus, the morning of what we would refer to as the seventh day of Pesach is actually the eighth day from the Exodus if one is utilizing the sacrificial offering system. In this regard both the Rashi that maintained that it was day seven and the one that states that it was day eight are correct, they are just describing the event based on separate systems. (Rabbeinu Bachye Bamidbar 15:41)

Seeming to support this assumption is the fact that the Rashi that maintained that it was day eight focused on the time when Klal Yisrael sang and not when the Egyptians perished in the sea. They perished just before morning, (Shemos 14:27) but we did not sing until after daybreak. (Rashi Shemos 14:5) Unfortunately, Rabbeinu Bachye leaves hidden the reason why Tzitzis reflect the sacrificial offering system and the Torah portion read on Pesach reflects the regular system.

Before presenting another approach I would like to say, as an aside, that it is pretty fascinating that the evening during which the sea split had a very rare occurrence happen in the sky. That night the moon partially blocked Mars making it appear as if the two were touching (I know that I posted a similar thing with Saturn regarding the first Tisha B'Av earlier this week, but these events truly are rare which makes it even more fantastic that they seem to happen on these monumental dates in Jewish history). Astrologically, this event portends malevolent tidings. (Ibn Ezra Reishis Chachma 7) Interestingly, it occurred in the constellation Aquarius which is considered the be the mazal of Klal Yisrael. (Ibn Ezra Shemos 31:18) Aquarius, depicted as a man pouring a bucket of water, would have been seen as being afflicted by this sign. It seems interesting that Hashem bestowed His mercy that evening and saved this young nation. Just as he split the water of the Yam Suf, he "split open" the evil tidings found in the constellation of water that symbolized this nation and protected them miraculously. In fact, quite unbelievably, Rabbeinu Bachye mentions that the Jewish nation should have perished at the Yam Suf because the Egyptians had tapped into the inlfuence of Mars which is associated with death. It was only because of God's tremendous mercy that he saved us. (Rabbeinu Bachye Shemos 14:25)

I am certainly not qualified to argue with Rabbeinu Bachye, but I would like to suggest an alternate way one could have read Rashi based on the Meiri. The Meiri states that their are four accepted ways that civilizations have decided to begin their days. One is the Jewish way and that is the start from evening. A second way is to start from daybreak. Another is to start at midnight (like is the practice here in the U.S.) and the last way is to start from midday when the sun is at its peak. This last way, says the Meiri, is based on deep astrological meaning and this is how the ancient Egyptians began their day. (Meiri Pesachim 5a)

Rashi mentions that Paroh sent a messenger with us when we left Egypt to make sure that we would return after three days. When we did not, Paroh came out with his armies and advanced towards our camp on days five and six. The night of the seventh day of our Exodus his battalions were drowned in the sea. (Rashi Shemos 14:5) In fact, this is the same Rashi that mentions the reason for reading this portion on the seventh of Pesach.

The Sifri mentions that we left Egypt at midday. (Sifri Devarim 337) Rashi quotes from this Sifri elsewhere implying that he is of the same opinion. (See Rashi Bereishis 7:13) If Rashi agreed with the Meiri then Paroh sent his messenger with us right at the "beginning" of the first day which coincides with 15 Nisan in the Jewish calendar at midday (this is the day after the Korbon Pesach and the first day of our holiday of Pesach). That means that seven Egyptian days after would have the Egyptian destruction occurring on the night of the eighth day of the Jewish count. Since we do not follow the Egyptian calendar we commemorate this event with the seventh day based on our count and we read the Torah portion of this event on the seventh of Pesach. The Rashi at the end of our Parsha, though, would also be accurate. The Egyptians perished on what we would call the eighth day, but the seventh Egyptian day from our Exodus.

Goodnight Moon

The climactic moment of the Ten Plagues was the final one, the killing of the firstborns at midnight. Last year I posted about the star Sirius' connection to this event. This year I would like to add one more point to that post.

An entire lunar cycle (from our perspective) takes approximately 29 days, 12 hours, 44 minutes and 3 1/3 seconds. Since this tenth plague occurred on the 15th of the lunar month, that means that the moon was full.

Many notice that the moon is sometimes visible in the daytime and at other times at night. The basic overview of its rise and set times is that in the beginning of the lunar month it is visible in the afternoon and sets just after sunset. Every subsequent day it appears a little later in the day and sets a little later in the evening. In the middle of the month it rises at sunset and sets at sunrise and it then begins to rise after sunset and set in the morning until the cycle begins again.

When putting all this together, one can see that at midnight,the moment of the plague, the moon was full and at its peak. The sun, on the other, has its peak at midday and is at its lowest at midnight. The other nations of the world are compared to the sun (see Maharsha Yoma 20) and Klal Yisrael to the moon (see Midrash Tehillim 22). This was finally the moment when Klal Yisrael was shining and at its peak and their oppressors were at their lowest.

Superhuman Sight

Throughout the discussions found in the Gemara (Rosh Hashana 20a-25a), Rashi continuously states that the New Moon is visible after six hours from the lunar conjunction (molad) and that it was visible six hours prior to the molad. The purpose of the Beis Din knowing this fact is to reject any witnesses that testify about the sighting of a New Moon within this time period. Beis Din will not declare that day to be the first of the month and will automatically assume the witnesses were mistaken or lying.

The Rambam and Baal HaMaor clearly state that the Moon disappears for a couple days because it takes approximately twenty-four hours for the Moon to separate from the Sun to reach a distance that we can see.

Currently, astronomers use a tool called the Danjon Limit. This limit is defined as the distance, in degrees, that the Moon needs to travel from the Sun in order for us to be able to see it. If the Moon is too close to the Sun, the sunlight will outshine the Moon. The Danjon Limit is set at approximately 7 degrees; however, practically most people (under most conditions) need more like 10.5 degrees of separation. The average should come to approximately twenty-four hours from the lunar conjunction which is consistent with the Rambam and Baal HaMaor's opinion. The record (without optical aid) is set at about 15 hours and with optical aid (telescope), the record is close to 12 hours. This is still a far cry from Rashi's six hours. This is something that is easily seen; Rashi was able to witness this phenomenon every month, why would he state such a hard to understand opinion?

(There is a sefer that is cited in the back of the Gemara that mentions that Kepler and Reinhold witnessed a New Moon in Seville on March 13, 1553 and that that sighting proved Rashi's opinion. There seems to be a typo, because the conjunction would have been on March 14, but I believe the reputable author of this sefer was misled by misinformation. Reinhold died in February of 1553 and Kepler was not born until 1571; also, the Moon was far below the Danjon Limit and, if this were true, we would have records still available to us from Kepler's writings verifying this sighting.)

Perhaps, the answer is that Rashi agrees that they could not have seen the Moon. Rashi cites that in many of these cases, the ramifications are only according to the opinion that, when necessary, we trick witnesses into thinking they saw a New Moon even if they did not. This, and other nuances found in Rashi, seem to show that Rashi's overall opinion (even when discussing the opinion that we do not trick witnesses in this fashion) is that we want our calendar to be consistent with the lunar cycles (while making some necessary exceptions when we will have holidays falling on days we do not want) and as long as someone testifies about an event that will keep this consistency, we will admit it into the court. This is even if we know that the witnesses did not really see that which they claim to have seen. This opinion is very similar to that of Rabbeinu Chananel and Rav Saadiah Gaon who maintain that the main focus is the lunar calculations, and the witnesses just verify the sighting for us to be able to apply our calculations.

There are two reasons why the Moon is invisible to us when it is too close to the Sun. One is that the surface of the Moon has mountains and bumps, and therefore, until the Sun can shine above these bumps the sunlight is not reflected to Earth. The second reason is that the human eye cannot detect the faint light reflected from the Moon until there is sufficient darkness around the surrounding area. When the Sun is too close it is still daytime and we cannot see the Moon. In other words, one is a factor because of the Moon's inability to reflect the light; the other is the inability of the human to see the reflection. If we only focus on the constraint caused by the Moon, we can lessen the Danjon Limit to somewhere close to 2 degrees. This is much more consistent with Rashi's opinion. If witnesses would testify that they saw the Moon, we would know that they did not, but we would still accept the testimony because the Moon is at a point where it is new and it is clear from Rashi that the main focus of the process is that the Moon and calendar be in sync and not that we care whether the witnesses actually saw the Moon. This would be another example of us not being so careful with testimony of the Moon which is a concept that even the Rambam records.

I would also suggest one more point. It is clear from Rav Saadiah Gaon and Rabbeinu Chananel (and I would suggest, Rashi) that the commandment upon Beis Din to regulate a calendar is to do so via calculation and not eyewitness accounts. Therefore, the machlokes in R"H 24b - 25a between Rabban Gamliel and other Tanaim as to whether to trust certain suspect witnesses is clearly rooted in a machlokes of whether or not to follow calculation or witnesses. It is interesting to see that Rabban Gamliel invokes a tradition from his family to support his claim. A few lines later Rebbi seems to be expressing a similar claim. Rebbi was a descendant of Rabban Gamliel. It would seem that the household of the Nasi (Rabban Gamliel's family) was in charge with regulating the calendar.

Now, when looking at the famous Mishna later when witnesses came late in the day on Rosh Hashana and the Levi'im sang a weekday shir instead of a yom tov shir, we can see something fantastic! One could have asked why they were bothering with witnesses and not using calculations (according to Rav Saadiah Gaon, Rabbeinu Chananel and Rashi). The answer may be that the Nasi at the time (and posek for these matters, as mentioned in the Mishna) was Rabban Yochanan ben Zakai. He was a temporary Nasi. Rabban Shimon ben Gamliel I was horrifically murdered and his son Rabban Gamliel II was in hiding. The position of Nasi was therefore given to Rabban Yochanan ben Zakai until it could go back to Rabban Gamliel II. Clearly, Rabban Yochanan ben Zakai, not being from the family of the Nasi, did not have their tradition. He was of the opinion of those that argued with Rabban Gamliel (II) on 24b - 25a.