Interesting Calendrical Facts About the Mabul

We are taught that the Mabul began at midday. (Bereishis 7:13) Rashi cites that the reason for this was to demonstrate that, with Hashem's protection, Noach was able to enter the Teivah in front of all the wicked people of his generation and none of them was able to harm him.

Rav Yehonasan Eibshitz zt"l offers an additional explanation that has to do with the way the calendar works. Rav Eibshitz mentions that the historic date which the dove found dry land in the year after the Mabul was the first of the first month and was a Shabbos. If so, then the year preceding this one, the year when the Mabul began, the first day of the first month was Tuesday. (Clearly Rav Eibshitz is using a regualry styled year in which half the months contain 30 days and the other half have 29. The months alternate with 30 then 29 and so forth throughout the year.) Since the first month was a Tuesday then the subsequent month, the month in which the Mabul started, started on a Thursday. Thus, the 17th of that month, the day which the Mabul started, was Shabbos. Since the Gemara teaches that rain on Friday night is a blessing, the rain, instead, began during the daytime as not to give the wicked people even one iota of blessing. (Taanis 23a) Rav Eibshitz continues that, additionally, the mazal of Shabbos daytime is Saturn which symbolizes mass destruction and that was befitting for the beginning of the Mabul. (See Rashi Berachos 59b and the Ibn Ezra's Reishis Chachma) (Tiferes Yehonasan Bereishis 7:13)

The World's First Boat?

For 100 years Noach toiled and endured much ridicule from his neighbours as he built the ark. Sure enough, Noach had the last laugh when the flood finally came and wiped out everyone else on the planet. Having completely denigrated Noach and ignored his warnings, the people were completely unprepared. However, the ark was nothing more than a large boat. Didn’t anyone have a boat of their own to escape the destruction of the flood?

This fascinating question was asked of me by R’ Sander Goldberg of Baltimore and he followed it up with a fascinating answer from his sefer נחל חיים (Page 30.) There is some discussion regarding the general climate and environmental conditions before the flood and how they were changed forever by the flood. One of the principal catalysts for these theories is the first reference to seasons after the flood (8:22) which seems to imply that there were no seasons beforehand.

מלבי"ם writes that before the flood planet Earth was not on the 23.5 degree tilt on which it finds itself currently. The tilt was as direct consequence of the environmental havoc wreaked by the flood. When the earth is not tilted the climate conditions throughtout the world are at complete equilibrium. That is to say that weather conditions are completely uniform throughout the world and throughout the year. There is simply no reason for conditions to be any different in one place from another. Cloud cover as we know it did not exist either. After all, a partially cloudy sky means that there are clouds over one part of the land and not over the other. Rather, the skies slowly became saturated with moisture uniformly and once every forty years, writes מלבי"ם, the entire earth would be drenched with rain and the process would begin anew. (This explains why the people were not overly taken aback by the flood when it began.) מלבי"ם also attributes the longer lives lived before the flood to the consistency of the climate.

(Now THAT's climate change!)

Another condition that would result from a world climate in equilibrium is uniform atmospheric pressure. Without varying pressure, there can be no wind. Wind is a result of air moving from a high pressure area to a lower pressure area like the air flowing out of a balloon. Before the age of the motor, all large boats relied on wind to move. If there were no wind, there would have been no boats. This explains why Noach’s project appeared so strange and also explains why no one else had any means to survive the flood.

(He goes on to explain that due to this extreme difference in global climate fermentation was something that did not happen before the flood and that explains how Noach could go so terribly wrong afterwards getting drunk - alcohol hadn't existed either.)

Sailing the Friendly Skies

Perhaps it was the fact that this week’s Parsha discusses a boat, but there was some interesting astronomical news this week that got me thinking about a certain passage from the Gemara in Horiyos (10a). There, the Gemara relays a story in which Rabban Gamliel and Rebbi Yehoshua were traveling on a ship. Rebbi Yehoshua had packed extremely durable food, whereas Rabban Gamliel packed meals befitting a standard seafarer. The ship was delayed and Rabban Gamliel’s supply was exhausted. Rabban Gamliel was only able to be sustained due to Rebbi Yehoshua’s careful planning. Rabban Gamliel inquired of Rebbi Yehoshua how he knew the journey would take so long. Rebbi Yehoshua responded:

".[כוכב אחד לשבעים שנה עולה ומתעה את (הספינות) [הספנים] ואמרתי שמא יעלה ויתעה [אותנו"

“There is a star that appears in seventy years and tricks the sailors. I said to myself that perhaps it will rise and trick us.”

It is common knowledge that ancient sailors were extremely dependent on astronomical knowledge in order to navigate. Without modern equipment such as GPS devices, the most accurate method of determining one’s position is based on the stellar positions. The stars move through the sky in very specific patterns. Some are always in the north and others in the south. With this knowledge, sailors can navigate the seas. Additionally, apparent celestial position changes based on latitude, so one can determine his latitude with extreme precision based on how high specific stars are from the horizon. Thus, if a “tricky” star were to “appear” it could be disastrous to the sailors because it could send them way off course.

Rashi explains that the celestial object mentioned refers to a star that rises once every seventy years. This star sometimes appears in the north and sometimes in the south. If the sailor, unaware of this star’s nature, were to see it in the north at the beginning of the journey and later, unbeknownst to him, it would change position then he would think he was traveling in one direction but would actually be going in the opposite direction. Rebbi Yehoshua was nervous that this would occur to them while they were on their journey so he packed extra durable food.

While much has been written throughout the ages expressing the symbolic meaning behind this passage, it is very unclear as to the identity of this “star” in the plain meaning of the text. “Regular” stars have set positions in the sky and cannot change from north to south, so it seems unlikely that it could be a regular star. The planets’ orbits do not have them rising once every seventy years and switching from north to south during that time so they are also not viable options.

At first glance one may think that this star is a comet. Comets move across the sky and could theoretically be good candidates for what is being discussed. There is only one comet that has a short orbital period that is easily seen by the naked eye and interestingly it happens to appear once every 75-76 years, Comet Halley (Halley’s Comet). This comet has been recorded by ancient astronomers at least as far back as 240 BCE, so it had been sighted prior to the time of Rebbi Yehoshua. If Rebbi Yehoshua was rounding the 75-76 years and referencing it as 70, then perhaps he was discussing this comet. This would be exceptionally fantastic because history gives credit to Edmund Halley as figuring out that the various comets recorded throughout history at 75-76 year intervals were all the same object and that this is that comet’s periodicity was 75-76 years. This “discovery” would not occur until over 1,500 years after Rebbi Yehoshua in the year 1705 CE!!!

There is one major problem with this assertion, though. The only arrival of Comet Halley during Rebbi Yehoshua’s lifetime would have been in 66 CE. Rabban Gamliel would have been an extremely young child at this time and in the ensuing parts of the story he is displayed as being older. (See Rashash, Pesachim 74a) Additionally, it would seem that he already achieved the title Rabban meaning that he was the Nasi and that did not happen until after the destruction of the second Beis Hamikdash which occurred in 70 CE. (See Gittin 56b; also see Seder Hadoros’ biographical synopsis of Rebbi Zeira for a discussion of the usage of titles in the Gemara indicating that the individual had already achieved that status at the time being referenced by the Gemara.) Thus, this story had to have happened well after Comet Halley’s appearance in 66 CE. To assert that Rebbi Yehoshua did not remember that the last appearance was in 66 CE and, therefore, was nervous that it would appear during the journey; or that he thought it would come sooner than 75 years this particular instance is unlikely. Rebbi Yehoshua mentions the 70 year interval in his statement; thereby displaying that he was aware of the orbital period. If he was aware of this fact, then it is unreasonable that he would not have remembered the last magnificent appearance of this comet which would have happened in his own lifetime and that he felt its periodicity was not subject to change.

I concede that I do not know what the identity of the object that Rashi is describing, however, I would like to suggest another approach to this passage. As I will explain, it would appear that Rashi had a variant text of this passage and I would like to offer a suggestion based on the text present in the standard editions of Gemara that we currently have. Perhaps, Rebbi Yehoshua was not stating that there is a star that appears every seventy years, rather, he was stating that there will be a star to appear in seventy years. He was not discussing a recurring event; he was mentioning that there was going to be a one time event that would happen in seventy years from the time being discussed in the Gemara. If this is, in fact, the case then one may ask why was Rebbi Yehoshua concerned that this star would appear prior to its seventy year date of arrival? The answer is that although based on Rebbi Yehoshua’s calculations the star would be coming in seventy years, nevertheless he may have realized that there was a margin of error in his calculations that would allow for this star to appear prior to that time. Therefore, he stated that there is a star destined to appear in seventy years, but because it was possible that it would appear sooner, he brought along extra provisions. The reason why this suggestion seems more likely based on the text in our Gemara is because the language used is:

"כוכב אחד לשבעים שנה."

and not:

"כוכב אחת לשבעים שנה."

The difference is that the text we have has the word “אחד” “one” in the masculine form and not “אחת” in the feminine. While this may seem like a minor variance, in truth it makes a world of a difference. If in the feminine it would indicate that the “one” is referring to the implicit, “פעם” “occurrence” and it is as if it says, “פעם אחת” “one occurrence.” Note that Rashi has this word in the feminine in his commentary to this passage. This reading of the text would be stating that the star appears once every seventy years and is a recurring event. Since in our text “one” is in the masculine form, it is clearly referring to the star and not referring to the periodicity of the star being seventy years. Thus, the translation of the entire sentence becomes, “One star will appear in seventy years, etc.” and is no longer, “A star appears once every seventy, etc.”

If this is the case, what then could this “star” be? We have ruled out regular stars, planets, and comets already, so what is left to be considered? Perhaps, Rebbi Yehoshua was referring to a new star appearing out of nowhere. Although uncommon, this has happened in extremely rare instances. When this has occurred it has not been that a brand new star was formed, rather, there was a star that was too faint to be seen by the naked eye which then brightened and became visible. At the end of large stars’ lives they experience an event called a supernova. Supernovae are essentially massive explosions during which time tremendous energy and radiance is emitted from dying stars. Supernovae that have become visible to the naked eye have occurred only a handful of times through recorded history.Over several months, these new stars then faded away and disappeared, only to be seen via telescope. Interestingly, the very first known one recorded in history happened in 185 CE. This is now referred to as SN 185 and made the news this week as observations by NASA’s Spitzer and WISE telescopes uncovered many more of the dynamics of how this supernova unfolded. Although Rebbi Yehoshua did not live until 185 CE, he would certainly have been alive and well 70 years prior to this and could easily have been aboard a ship with Rabban Gamliel in 115 CE. Keep in mind that the Gemara does not state that the actual reason for the delay of journey was because the star actually appeared, just that that was the reason Rebbi Yehoshua was prepared for such a delay. Supernovae are very unpredictable, perhaps leaving Rebbi Yehoshua doubting his accuracy and leaving a margin of error. In fact, if Rebbi Yehoshua was able to predict this one, his seventy year margin of error is far more accurate than even today’s predictions for supernovae!!! If this is the case, it is also astounding because even the ability to predict or understand supernovae is not considered to be known by man until the twentieth century and as previously mentioned, the accuracy with which Rebbi Yehoshua predicted this one is still not attainable by contemporary scientists!!!

The question then arises, why could such a star cause such confusion as to mislead a sailor. The rest of the sky would still have the same appearance and the sailor would just see an extra star, but would not head in the wrong direction. Upon further review, however, one can see that SN 185 may have actually been a little more confusing than just appearing as an additional star. The North Star and nearby Big Dipper are integral to celestial navigation as they are always positioned in the north. SN 185 occurred in the ancient constellation of Centaurus. In ancient times most people were not as familiar with those southern constellations since they can only be seen from more southerly parts of Earth. The area of Centaurus where SN 185 appeared would normally not be able to be confused with the Big Dipper and North Star, however, because they appear to have different configurations. The difference in configuration seems so apparent, but in fact is only so striking because this region of Centaurus is missing one bright star that appears in the Big Dipper. SN 185 flared up and appeared in that region so it is possible that a sailor would have glanced to the south quickly and mistaken this constellation for the Big Dipper!


The Big Dipper and North Star in the north:



Centaurus (prior to SN 185's appearance and post its disappearance) in the south:




Centaurus as it would appear with SN 185 in the year 185CE:

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.