Category: Zmanim

FAQ: Chatzos Hayom VS Chatzos Halayla (Solar Noon VS Astronomical Midnight)

The sundial on the Zoharei Chama Synagogue as it appears on a 2014 Israeli stamp.

Question:

Is there a difference in time between the zmanim of chatzos hayom and chatzos halayla (astronomical midnight and astronomical high noon / midday) besides the obvious 12 hour difference?

Answer:

I was recently asked by a developer why the KosherJava zmanim library does not have distinct calculations for chatzos halayla. The answer is that the zmanim API does indeed have the getSolarMidnight() calculation, but for the most part there is no real need for it. The time of chatzos halayla / midnight or chatzos hayom (solar transit / solar noon or midday) stays pretty constant from day to day. In the worst case scenario (on around December 22nd), the length of the solar day would increase by about 30.16 seconds from one day to the next. This does not change by location, but is the same anywhere in the world. This would mean that chatzos halayla could be a maximum of 15.08 seconds different than just using midday + 12 hours. This is something that should not really impact people. In addition, the developer in question does not even show seconds, making this a moot point. In short, chatzos on any given day should be considered accurate enough for both chatzos hayom and chatzos halayla of that day. It should be noted that the Mishnah Berurah quoting a number of achronim and the Shulchan Aruch Harav are of the opinion that chatzos halayla is exactly 12 hours after chatzos hayom. The Mishnah Berurah states in הלכות הנהגת אדם בבקר א׳ ט׳

וזמן חצות הוא תמיד באמצעות הלילה ממש בכל מקום ואפילו בלילות הארוכות או הקצרות והיא י״ב שעות אחר חצי היום …

and the Shulchan Aruch Harav in הלכות השכמת הבוקר א׳ ח׳ states that

וזמן חצות לילה הוא שוה בקיץ ובחורף לעולם י״ב שעות אחר חצי היום שהוא אמצע הלילה ממש …

Chatzos Halayla on the Seder Night

MatzosThe time of year that the zman of chatzos has the greatest impact is during the Pesach seder when people want to finish the afikoman before chatzos. During this time of the year the solar days are shrinking slightly from day to day, resulting in chatzos halayla being slightly earlier than chatzos hayom + 12 hours. The difference in the length of the solar day from solar noon on erev Pesach to solar noon on the first day of Pesach ranges from 11 to 18 seconds depending on the year. On the very late erev Pesach on April 24 that last occurred in 1929 and 1967 and will next occur in 2043 and 2062 there is an 11 second difference. On the extremely early erev Pesach of March 25 that occurred in 1899 and 2013 and will occur next in 2089 (see Rabbi Dovid Heber’s Why is This Pesach the Earliest Since 1899?) there is an 18 second difference. This 5.5 to 9 second difference in the time of chatzos hayom VS chatzos halayla on erev Pesach is something that has almost no real world impact. It is interesting to note that based on the fact that the average Jewish year is slightly longer than the average solar year, the early March 25 erev Pesach will never happen again after 2089.

Equation of Time (EoT)

You may have expected that the longest day of the year – the summer solstice (June 20 or 21 depending on the year) would be the day with the earliest sunrise / netz (or hanetz) and latest sunset / shkiah (and therefore the day with the latest start of Shabbos). However the earliest sunrise actually occurs on or about June 14 (at latitude 40° – it varies slightly based on latitude), a week before the longest day, and the latest sunset occurs on or about June 28, a week after the summer solstice. As mentioned above, the length of the day that we know to be exactly 24 hours on a clock is actually only an average over the year. The length of the day varies slightly from day to day. This length of day range is from a minimum of 23 hours, 59 minutes and 38.64 seconds around September 17 to a maximum of 24 hours and 30.16 seconds around December 22 vs the previous day. This accumulated length of the day difference is known as the equation of time. While the day starts shortening after the solstice, chatzos (and by extension the entire day) is moving slightly forward as the solar day (midday to midday) grows at this time of the year, resulting in the day ending later despite it being shorter.

Note: The rest of the article is somewhat technical and can be skipped if you have no interest in detailed explanations as to why days differ in length.

The cause of the change is due to the following two main factors. The very minor impact of nutations (such as the Chandler wobble), axial precession and other factors are too small to make a practical difference in the EoT calculations.

The tilt of the Earth’s Rotational Axis

The tilt of the Earth’s rotational axis (also known as the axial tilt or the obliquity of the ecliptic) as compared to the plane of its orbit around the sun is one factor that impacts the length of the solar day. To understand this, note that the earth rotates on it’s axis in 23 hours 56 minutes and 4.1 seconds in relation to the stars. This is called a sidereal day. The remaining 3 minutes and 55.9 seconds or about 0.98° of rotation must be made up every earth day. Due to the 23.44° axial tilt, this 3 minutes and 55.9 seconds is only an average.

The sun’s path through the sky during the March equinox. The equatorial grid is blue, the ecliptic grid is orange and the ecliptic (the sun’s apparent path) is yellow.
During the equinoxes the earth’s 23.44° tilt results in the sun having to travel a drop farther (1.09° for every 1° of eastward travel) to cover a line of longitude, since its path is angled and traveling a drop northwards or southwards on its path west. This results in the day being slightly shorter, since the sun only travels about 0.9° along the equator as opposed to the average of 0.98° per day.
The sun’s path through the sky during the December winter solstice. The equatorial grid is blue, the ecliptic grid is orange and the ecliptic (the sun’s apparent path) is yellow.
In the winter and summer the sun’s path is parallel to the equator and has a direct east/west path. In addition, since the longitude lines are closer together at 23.44° degrees from the equator the sun travels further moving 1.09° parallel to the equator for every 1° of eastward travel. This results in a slightly longer day. A technical and detailed explanation can be found in Mike G’s explanation of the subject at the astronomy section of StackExchange (where the above Stellarium generated images are from) and in Art Carlson’s equation of time explanation.

The elliptical orbit of the earth

The elliptical orbit of the earth (or the eccentricity of the Earth’s orbit) is the second factor that impacts the length of the day. The earth’s orbit around the sun is an ellipse and not a perfect circle. Following Kepler’s second law, the earth moves slightly faster in orbit when it is closer to the sun, and slower when it is farther away. During the perihelion (it ranges between January 2 and 6 depending on the year) when the earth is closest to the sun at 91,402,500 mi / 147,098,070 km distance, it travels at 30.287 km/s, while at the aphelion (between July 3 and 7) when it is 94,509,100 mi / 152,097,700 km away, it travels at 29.291 km/s. In addition, the angular velocity of the sun is faster (in relation to the stars) when it is closer to earth. Despite it being somewhat counter-intuitive, the sun is closer to earth in middle of the northern hemisphere’s winter than during the summer. This non-uniform orbital speed impacts the length of the solar day.

The Accumulated Difference

This difference between our standard clock time and the time that would be based on the exact position of the sun in the sky accumulates and is referred to as the equation of time (EoT). Equation in this case refers to equality and not a mathematical equation (though the calculations certainly involve mathematical equations), and adding or subtracting this time allows us to sync solar time and clock time (mean solar time / universal time).
Please see the references section below for links that cover the topic in detail.

Note: This article is explained using a heliocentric based model. I would appreciate if my readers who follow the geocentric model would be able to post a detailed explanation of this article based on that view.

Thank you.

References

I would like to thank my son Shai for the detailed work on the technical part of this article.

Halachic Dateline and the Incheon Airport (near Seoul, South Korea)

Chazon Ish Dateline Map
Chazon Ish Line on the Dateline Map

A primer on the Halachic Dateline

A primer for this halachic dateline post if you are not familiar with the subject, is the earlier Halachic Date Line Map post about the Jewish קו התאריך date-line. Based on the opinion of the בעל המאור Ba’al Hamaor, the חזון איש Chazon Ish ruled that the dateline is 90° east of Yerushalayim, and it can’t split a landmass. The concept of גרירה / graira is used to drag the land past the dateline to the water’s edge. This concept of graira is based on the יסוד עולם Yesod Olam, a תלמיד/disciple of the רא״ש Rosh. For this reason, according to the Chazon Ish, Korea and Australia follow the local date and not the previous date.

Islands Connected to Mainland by a Bridge

A question touched on in the previous article that was mostly theoretical, was about an island connected by a bridge to the mainland. Would the concept of graira apply to the island? The kollel members in Melbourne and others do not visit Phillip Island on Sundays for this reason, but Chabad chassidim who do not follow the Chazon Ish’s opinion, do visit Phillip Island on Sundays.

Islands in Bays

There are differing opinions whether an island in a bay would also be included in graira. Rabbi Yitzchok Meir Goldstein in his השבת בכל מושבותיכם (pages 85-88) brings the following opinions. Rabbi Shlomo Zalman Auerbach in הליכות שלמה (Moadim, vol. 2, page 70) is of the opinion that an island in a bay would be considered part of the land that partially surrounds it. In the same vein, (but not specifically in reference to a bay), Rabbi Moishe Sternbuch in מועדים וזמנים vol 7, ch. 236 mentions something similar (that the easternmost border of Australia would be a vertical line from north to south at the longitude of Brisbane, the eastern-most point of Australia). What is not clear is how large a bay can be. Rabbi Goldstein mentions that drawing a line from Siberia to Malaysia (thus creating a “bay”), would put Japan on the same side of the dateline as the Asian mainland. The Chazon Ish clearly stated that Japan was past the dateline. Presumably, Rabbi Shlomo Zalman Auerbach and Rabbi Moshe Sternbuch would agree that such a large area would not be included in graira. Given the lack of detail about the size of bays, it is possible that these poskim would only include very small bays (within the techum perhaps). It should be noted that Japan is only in the “bay” if you use a rhumb-line. Drawing a great circle line would result in Japan being out of the “bay”. Rabbi Dov Landau in the פשר חזון, and Rabbi Moshe Heinemann do not include bays as part of the graira zone. Rabbi Sternbuch was asked about bays by Rabbi Goldstein, and he agreed that according to the Chazon Ish, bays would not be included in graira, so Rabbi Sternbuch either reversed his earlier opinion, or he disagrees with the Chazon Ish’s opinion.
There are related opinions that bays themselves do not drag islands within them into graira unless land to their east is part of graira. See Rabbi Leib Blum’s קו התאריך בכדור הארץ for details. For example the Sea of Okhotsk is to the west of the Kamchatka Peninsula. This means that they are of the opinion that you can’t have land to the east that is part of graira such as the Kamchatka Peninsula, and have Sea of Okhotsk and Sakhalin Island to the west of it that is considered past the line, (and back again to Siberia that is part of graira). The same would be the case in the portion of the Yellow Sea to the west of the Korean Peninsula and east of the Chazon Ish line, as well as the above mentioned Phillip Island and French island that are in the Western Port Bay near Melbourne. Bays such as Moreton Bay that includes Bribie and other islands near Brisbane, as well as Ulleungdo Island in the Sea of Japan would not be included in graira, since there is no graira land to the east of it.

Incheon International Airport and the Halachic Dateline


In January 2019, the Star-K held a Kashrus training seminar in Shanghai for mashgichim who live or work in Asia. Among the sessions, was a shiur about the halachic dateline by Rabbi Dovid Heber who shared the URL to my halachic dateline map with the participants. One of the mashgichim, Rabbi Yosef Wexler, who travels from Eretz Yisrael to Asia regularly, noticed a potential issue related to the Incheon airport, the main airport in South Korea (near Seoul). The airport is located on Yeongjong Island, that is connected to mainland South Korea by two long bridges. The island is within a Bay (formerly Chemulpo Bay), that is itself within the Yellow Sea that is itself a vary large bay. If graira would not apply here (bridges and bays would not be considered a connection) and you followed the opinion of the Chazon Ish, the airport would observe Shabbos on local Sunday (the same issue faced in Japan). This impacts mashgichim who bypass Japan on Sundays, and regularly fly to Korea on flight KE958 on Motza’ei Shabbos from Israel on their way to China etc. The flight lands at about 3pm Sunday local time, when the airport may be observing Shabbos. It would also impact anyone else who plans on flying in or out of the airport between Motza’ei Shabbos and Sunday night.

Psak Halacha

Please consult a posek before relying on this for halacha lema’aseh. There are a number of opinions, and I will touch on a few of them.

As per Rabbi Heber, Rabbi Yonasan Weiner (a posek in Ohr Sameach) asked R’ Chaim Kanievsky about Phillip Island (that as mentioned above, has a bridge and is in a bay), and he answered that “it is צריך עיון“. Based on this, Rabbi Moshe Heinemann ruled that if someone is in the Incheon airport from shkiah on Friday (local day) until it gets dark on Saturday, one should keep regular Shabbos. From when it gets dark on Saturday night until it gets dark on local Sunday deoraisas should be avoided, but derabanans are permissible. This would permit most activities. The following quote in Rabbi Yitzchok Meir Goldstein’s השבת בכל מושבותיכם should be noted:

שמעתי מדודי הגאון רבי משה היינעמאנן שליט״א שאולי גבול היבשה הוא כשיעור תחום שבת מסוף היבשה

Yeongjong Island is at its closest 1,950 meters from mainland South Korea (from the eastern tip of the island to Wolmido, a former island that is now connected to land), and thus beyond tchum Shabbos. It is therefore not within the extended maritime graira zone. This applies to Incheon, but not the Yellow Sea. Rabbi Heber in his note to the Star-K mashgichim stated that melachos deoraisa should not be done within 35 minutes of landing since that is the earliest time the KAL958 flight passes the Chazon Ish line over the Yellow Sea. At this point according to the Chazon Ish it would be Shabbos. This was also mentioned by Rabbi Goldstein as a possible deoraisa. See below for more details.

Permissible Activities on Incheon Island on Sundays

There are many variables and variations in various melachos, so please consult a posek before relying on this for halacha lema’aseh.

Note: This list is only meant for Incheon airport on Sundays (from Motza’ei Shabbos until it turns dark on Sunday night) and other areas where a majority of opinions hold it is a weekday, but an accepted minority hold it is Shabbos. This list should not be used in any other locations or on a day that is accepted as Shabbos.

  • Traveling as a passenger to and from Incheon airport by plane or car. You do not have to worry about the 12 mil tchum Shabbos.
  • Carrying your belongings more than 4 amos outside the airport, or carrying them into the airport – there is no reshus harabim deoraisa on the island
  • Deplaning with your muktzeh luggage.
  • Walking in the airport including the use of escalators and moving sidewalks.
  • Triggering automatic sensor doors, sensors in bathrooms etc. (there no need to wait for someone else to activate it).
  • Scanning boarding or other passes (including to open electronic gates).
  • Going through security, taking muktzeh out of pockets, and passing through metal detectors.
  • Electronically signing into a lounge.
  • If a paper signature or writing is required, try to avoid it. If there is no other option, use your alternate hand (left for a righty, right for a lefty). An ambidextrous person can’t do shinuy by changing hands, and can’t sign or write.
  • Typing on a computer and typing or calling with cellphones is permissible, but the screen saver or the automated powering down of the monitor has to activate by itself to “erase” your writing. For power saving and security reasons, almost all computers will end up having a screensaver or a monitor power down and clear the screen. If this is not in place, and your “writing” will remain on the screen, it is more of a maaseh ksiva. Saving the document to your hard drive is permissible.

Problematic Activities During This Time

  • Opening a taxi door that causes the dome light to turn on (ask the driver to open your door, or have him open his door first, thus turning on the dome light)
  • Writing (with paper and pen).
  • Showers in the lounge should be avoided since there can be deoriasas involved.
  • Making coffee should be done the same way you would do it on Shabbos. Instant is fine, brewing fresh in a machine should not be done.

Rabbi Shlomo Miller in his approbation to the above mentioned Hashabbos Bechol Moshvosaichem, mentions that:

… והביא שטה אחת דכדי שיראה הוי בכלל אסטרליא וכן הי׳ דעתי נוטה [כמובן א״א להביא ראיות ברורות בזה] אולם יש להוסיף דלפי הגמ׳ בכורות נ״ד: עד ט״ז מיל הוי שעור כדי שיראה ויש אחרונים שהביאו מזה לגבי היקף מחיצות בשבת במחיצות הנעשות מאליהן דצריך שיהא העומד בתוכו רואה את המחיצות ע״כ עד ט״ז מיל יש מקום להסתפק אפשר שנגרר אחר אסטרליא.

This intuition (that he is unsure of) would potentially remove the questionable status of Incheon airport.

Rabbi Shmuel Meir Katz, a posek in Lakewood, discussed the Incheon airport question (focused on the fact that it is on a man-made portion of the island) in his Time Zone Shailos speech at the The Association of Kashrus Organizations’s 2018 Vaadim conference (24:50 into the recording). He said that a chaburah in Lakewood, NJ brought down a תוספתא נגעים פ״ו ה״ג that “בית שבים אין מטמאין בנגעים“. The גר״א has a girsa “בית שבים מטמאין בנגעים“. The ר״ש in נגעים פ׳ י״ב מ״א explains that

בית שבים: מדקתני בית שבים ובית שבספינה משמע דתרי מילי נינהו דשבים אפילו בנוי על גבי קרקע הים שהביאו אבנים וטיט ושפכו בים עד שנעשה כמין תל ובנו עליו בית אין מטמא בנגעים משום דכתיב ״ארץ״ ולא ים

This implies that the only questionable status is for נגעים, but otherwise, man-made land would have the status of natural land. Rabbi Katz holds that the bridge itself would connect the island and give it the same halacha as the mainland. It should be noted that Rabbi Katz also discussed the issue of The Sea of Okhotsk. His opinion is that the line follows the contour of the land, and the Sea of Okhotsk and Sakhalin Island would not be included in graira, but mentioned that Rabbi Leib Blum felt that it should be included due to it being to the west of land that has graira.

Rabbi Mordechai Kuber in his upcoming book, Crossing the Dateline (published a year after this was posted) strongly feels that there is no problem in Incheon airport on Sundays due to it being in a bay (that is in itself a safek). The question of the bridges, its proximity to land, and the many sandbars between it and the land make it at most a sfaik sfaika, which most poskim should agree is not an issue even according to the Chazon Ish. This sfaik sfeka is in addition to the other opinions who do not agree with the Chazon Ish, and are of the opinion that Incheon is not east of the halachic dateline, and therefore Saturday is Shabbos in Incheon, and not Sunday.

Rabbi Yitzchok Meir Goldstein in a letter to me mentioned that there is a possibility of a deoraisa in flying on a flight that is completely or partially on Shabbos

… this is comparable to one who boards a plane which takes off before Shabbos and lands after Shabbos, which, as the Shailos U’Teshuvos Minchas Yitzchok 2:106, the Shailos U’Teshuvos Tzitz Eliezer 1:21 and the Shailos U’Teshuvos Shraga HaMeir 7:27 write, involves an issur d’oraysa transgressing the chiyuv of “shabosson” which is not fulfilled while on an airplane ride. (However, it could be that there is a sevara to say that there is a difference in the d’oraysa of “shabosson” between flying on an airplane for the whole Shabbos and flying over the Yellow Sea for a short time …). If, indeed, this involves an issur d’oraysa, this creates a problem not only for people who follow the opinion of the Chazon Ish with regard to the dateline, but even for people who refrain from issurim d’oraysa on the Shabbos of the Chazon Ish. If so, regardless of whether or not the sevara of graira applies to Incheon Airport, I would think that people should still not be flying to that airport on Sunday. Second of all, even if I am mistaken in the above comparison and there is no issur d’oraysa to fly over the Yellow Sea while it is Shabbos in the Yellow Sea, it would be worthwhile for you to mention in your article that at least while the airplane is flying over the Yellow Sea one should certainly be careful not to perform any melacha d’oraysa such as writing. I am not trying to offer a psak about these points, but I think there is reason to consult with a poseik whether these issues need to be mentioned in your article.

It should also be noted that on page 83 of השבת בכל מושבותיכם, Rabbi Chaim Kanievsky is quoted with a different psak than the one quoted above by Rabbi Yonasan Weiner. Rabbi Goldstein sent the following question to Rabbi Chaim Kanievsky

שמעתי שבחוף הים של אוסטרליה יש גשרים ובנינים שנבנו בידי אדם שיוצאים מן היבשה לתוך קצה הים, האם גם בנינים אלו וגשרים אלו המחוברים ליבשה נגררים אחר שאר ארץ אוסטרליה או רק הארץ שנעשה שם בידי שמים ולא מה שניתוסף בידי אדם בתוך הים?

Rabbi Kanievsky replied with his typical brevity

נגררים

I would like to thank Rabbi Dovid Heber, Rabbi Shmuel Meir Katz, Rabbi Yitzchok Meir Goldstein, Rabbi Mordechai Kuber, My father-in-law R’ Feivel Muller and my wife for reviewing this article.
This article is published in memory of my mother-in-law Mrs. Helen Muller חיה בת ר׳ יצחק הכהן ע״ה.

Baal Hatanya’s Zmanim Added to KosherJava Zmanim Library

Baal Hatanya Zmanim (Photo With Hourglass)
While most calendars list the גר״א Gra and בעל התניא Baal Hatanya zmanim as identical, things are not that simple. Both are based on a day being from sunrise to sunset, but recently some Chabad calendars started using slightly different calculations for the Baal Hatanya’s zmanim. It should be noted that these zmanim are not universally accepted in Chabad (see the Opposing View section below). According to the Baal Hatanya in the סדר הכנסת שבת Seder Hachnasas Shabbos,

Seder Hachnasas Shabbos -Shkiah Amitis

מאד מאד צריך ליזהר בהדלקת נרות להדליק קודם שקיעת החמה, שקיעה הניראית, דהיינו בעוד השמש זורח בראשי האילנות בשדה בארץ המישור שאין שום הר במערב, או בראשי גגים הגבוהים בעיר, ולא לעשות אחר כך שום מלאכה כלל, כדי להוסיף מחול על הקודש מעט. כי אחר סילוק וביאת האור מראשי האילנות וגגים הגבוהים בכמו ד׳ חלקי ששיים משעה (שקורין מינוטין) אזי היא שקיעה האמיתית, שהוא סילוק וביאת האור מראשי ההרים הגבוהים שבארץ ישראל.

zmanim are calculated based on a 4 minute delay in shkiah. These 4 minutes are calculated as the sun’s position in degrees before sunrise and after sunset. While Chabad considers netz (also known as hanetz) as standard sunrise and shkiah as standard sunset, this is lechumra, and other zmanim are based on a slightly earlier sunrise and a slightly later sunset.

About 3 1/2 years ago, I posted information on calculating the Baal Hatanya’s Shkiah. That article was focused on a software developer’s perspective and explained how to use the existing API to calculate a fixed clock 4 minute zman that was not natively supported by the KosherJava zmanim library. Recently Yechiel Paricher contributed code to the KosherJava zmanim API/Library that added native support for various Baal Hatanya zmanim. This will enable users of the Zmanim library to easily include Baal Hatanya zmanim in their software.

According to the Baal Hatanya, shkiah amitis (true halachic sunset) is defined as:

כי אחר סילוק וביאת האור מראשי האילנות וגגים הגבוהים בכמו ד׳ חלקי ששיים משעה (שקורין מינוטין) אזי היא שקיעה האמיתית, שהוא סילוק וביאת האור מראשי ההרים הגבוהים שבארץ ישראל.

The time is calculated as the point at which the center of the sun’s disk is 1.583° below the horizon. Chabad applies the same degree based offset to netz amiti (true halachic sunrise). This degree based calculation can be found in Rabbi Shalom DovBer Levine’s commentary on The Baal Hatanya’s Seder Hachnasas Shabbos. From an elevation of 546 meters at the top of Har Hacarmel (based on the Gemara Shabbos 35a), the sun disappears at sunset when it is 1.583° (1° 35′) below the sea level horizon. There are other opinions that are not included in the code (but can easily be calculated using the API). One such example is a very similar (degree-wise) netz amiti from Rabbi Yosef Yitzchok Feigelstock. Rabbi Feigelstock calculates shkiah amitis as the degrees below the horizon 4 minutes after sunset in Yerushalaym (on the equinox). That degree based zman is listed in his letter to Rabbi Levine published in the back of the Seder Hachnasas Shabbos as 1.583°. The 1.583° is a typo (confirmed by Rabbi Feigelstock since it is identical to the 1° 35′ zman) and should be 1.683°. The calculations added to the KosherJava Zmanim library are used by most Chabad calendars that follow the Baal Hatanya’s Zmanim. See About Our Zmanim Calculations @ Chabad.org.

Zmanim based on shaos zmaniyos are based on a day between netz amiti and shkiah amitis calculated as 1.583° below the horizon. The various Baal Hatanya zmanim now part of the zmanim library include:

  • Alos 16.9° – based on the sun’s position below the horizon 72 minutes before netz amiti in Yerushayim around the equinox.
  • Sunrise or netz amiti – calculated as 1.583° below the horizon. This method is private and is only used as a base for other calculations.
  • Sof Zman Shma – calculated as 3 shaos zmaniyos (or a 1/4 of the day) after netz amiti.
  • Sof Zman Tfila – calculated as 4 shaos zmaniyos (or a 1/3 of the day) after netz amiti.
  • Sof Zman Achilas Chametz – calculated as 4 shaos zmaniyos (or a 1/3 of the day) after netz amiti.
  • Sof Zman Biur Chametz – calculated as 5 shaos zmaniyos after netz amiti.
  • Mincha Gedola – calculated as 6.5 shaos zmaniyos after netz amiti.
  • Mincha Gedola – Greater Than 30 – As above, but with a minimum 30 clock minutes after chatzos.
  • Mincha Ketana – calculated as 9.5 shaos zmaniyos after netz amiti.
  • Plag Hamincha – calculated as 10.75 shaos zmaniyos after netz amiti.
  • Sunset or shkiah amitis – calculated as 1.583° below the horizon. This method is private and is only used as a base for other calculations.
  • Tzais – calculated as the time when the sun is 6° below the western horizon. Note that as per Rabbi Yosef Yitzchok Feigelstock, for Motzai Shabbos, Motzai Yom Kippur and Motzai Yom Tov, the 8.5° time should be used. The time between 6° and 8.5° is part of tosfos Shabbos and tosfos Yom Kippur. Other zmanim such as zman krias shema can use the 6° zman. The 8.5° zman has always been part of the API, and sample code for calculating tzais 8.5° can be seen below.

These zmanim (not my implementation) that Chabad.org spent 2 years researching, have a haskama (endorsement) from Chabad Dayanim. Chabad.org zmanim do not provide seconds (appropriate due to expected refraction variances), but with the rounding rules provided by Rabbi Mordechai Sandhaus, the lead developer at Chabad.org, I was able to confirm that the Baal Hatanya zmanim generated by the KosherJava zmanim library match the Chabad.org times.

Please note that there are various Chabad shittos for netz, shkiah and tzais zmanim. The above are the commonly used ones. Other opinions on Baal Hatanya based zmanim that are less commonly used are not included in the API, but given the flexibility of the KosherJava Zmanim API they can easily be calculated.These include:

  • Netz Amiti 1.683° as calculated by Rabbi Feigelstock and mentioned above (only used for calculating other zmanim).
  • Shkiah Amitis 1.683° as calculated by Rabbi Feigelstock and mentioned above (only used for calculating other zmanim).
  • Tzais 5.833° as calculated by Rabbi Shalom DovBer Levine lekula for derabanans.
  • Tzais 6.3° as calculated by Rabbi Avrohom Altein, Chabad of Winnipeg, Manitoba, Canada.
  • Tzais 6.833° as calculated by Rabbi Shalom DovBer Levine lechumra for deoraysas.
  • Tzais 8.5° as commonly used by Chabad lechumra and mentioned above.

Code samples for these zmanim can be seen below.

Opposing Views

The relatively new calculations of zmanim based on netz amiti and shkiah amitis are not universally accepted in Chabad. Rabbi Avrohom Altein, the Rov of Chabad of Winnipeg, Manitoba, mentioned in a correspondence, that it is difficult to accept these new zmanim calculations as is.

The Alter Rebbe only speaks explicitly of shkiya amitis in regards to the beginning of Shabbos. We can draw comparisons to other areas of halacha but those comparisons needs to be carefully evaluated.
I believe that the Alter Rebbe does not calculate shaos zmaniyos based on netz & shkiya amitis, but rather on the standard netz & shkiya. There are several strong proofs to this. In earlier years, all of Chabad calculated shaos zmaniyos for laws of chometz, reading Shema etc., on the basis of standard sunrise and sunset and I believe that’s how the older Colel Chabad Luchos did the calculation. In recent years, this has changed in the Colel Chabad Luchos and chabad.org based on the opinion of Rabbi SDB Levin and Rabbi Feigeslstock — but there are Chabad rabbis that do not agree with their interpretation.

Code Samples

For developers, here is sample code that calculates the new zmanim. This should allow many zmanim apps to add Baal Hatanya zmanim with very little effort.

String locationName = "770 Eastern Parkway";
double latitude = 40.669;
double longitude = -73.943;
double elevation = 30;
TimeZone timeZone = TimeZone.getTimeZone("America/New_York");
GeoLocation location = new GeoLocation(locationName, latitude, longitude, elevation, timeZone);
ComplexZmanimCalendar czc = new ComplexZmanimCalendar(location);
czc.getCalendar().set(1994, Calendar.JUNE, 12);
System.out.println("Alos: " + czc.getAlosBaalHatanya()); //16.9 degrees
System.out.println("Sunrise: " + czc.getSunrise()); //standard sunrise
System.out.println("Sof Zman Shma: " + czc.getSofZmanShmaBaalHatanya());
System.out.println("Sof Zman Tfila: " + czc.getSofZmanTfilaBaalHatanya());
System.out.println("Sof Zman Achilas Chametz: " + czc.getSofZmanAchilasChametzBaalHatanya()); //only use on Erev Pesach
System.out.println("Sof Zman Biur Chametz: " + czc.getSofZmanBiurChametzBaalHatanya()); //only use on Erev Pesach
System.out.println("Mincha Gedola: " + czc.getMinchaGedolaBaalHatanya());
System.out.println("Mincha Gedola Min 30: " + czc.getMinchaGedolaBaalHatanyaGreaterThan30());
System.out.println("Mincha Ketana: " + czc.getMinchaKetanaBaalHatanya());
System.out.println("Plag Hamincha: " + czc.getPlagHaminchaBaalHatanya());
System.out.println("Sunset: " + czc.getSunset()); //standard sunset
System.out.println("Tzais Baal Hatanya: " + czc.getTzaisBaalHatanya()); //6° degrees
System.out.println("Tzais 8.5°: " + czc.getTzaisGeonim8Point5Degrees()); //8.5° degrees lechumra commonly used by Chabad
System.out.println("Shaah Zmanis Baal Hatanya: " + czc.getShaahZmanisBaalHatanya());

Calculating other Baal Hatanya based zmanim not included in the library are very simple. Here are a few examples

System.out.println("Netz Amiti 1.683°: " + czc.getSunriseOffsetByDegrees(90 + 1.683)); //Rabbi Feigelstock netz amiti (only used for calculating other zmanim)
System.out.println("Shkiah Amitis 1.683°: " + czc.getSunsetOffsetByDegrees(90 + 1.683)); //Rabbi Feigelstock shkiah amitis (only used for calculating other zmanim)
System.out.println("Tzais 5.833°: " + czc.getSunsetOffsetByDegrees(90 + 5.833)); //Rabbi Levine lekula for derabanans
System.out.println("Tzais 6.3°: " + czc.getSunsetOffsetByDegrees(90 + 6.3)); //Rabbi Avrohom Altein
System.out.println("Tzais 6.833°: " + czc.getSunsetOffsetByDegrees(90 + 6.833)); //Rabbi Levine lechumra for deoraysas

I would like to thank Rabbi Yosef Yitzchok Feigelstock, the Rov of Chabad in Buenos Aires, Rabbi Avrohom Altein, the Rov of Chabad in Winnipeg and Rabbi Mordechai Sandhaus, the lead developer at Chabad.org for reviewing this post.

FAQ: Zmanim and Leap Seconds

Leap Second

Questions:

Answers:

  • Yes
  • Yes, but infinitesimally

Before delving into the answer, I would like to note that zmanim accuracy / precision down to the second that are supported by the API are really nonsense, because variations in refraction make this accuracy pointless. The second (or millisecond) zmanim accuracy / precision subject will hopefully have its own article in the future.
Since 1972, 27 leap seconds have been added to UTC time VS International Atomic Time (TAI). This is in addition to the initial 10 seconds added in 1972 to reflect pre-1972 corrections. The reason for adding leap seconds is to correct our clocks for incorrect original estimates of the speed of earth’s rotation. Assuming that you keep your clock time correct (and add the leap seconds), no change in any zmanim calculations by either the KosherJava zmanim library, or any other zmanim programs or APIs are needed. However, if you have a very accurate clock, and did not change it since 1972, your zmanim calculations will be off by 37 seconds. This is not something any zmanim APIs, apps or programs should have to deal with. Had we added any corrections for leap seconds, your zmanim calculations would be inaccurate.
As far as the Tōhoku earthquake in Japan, this is really the same question as the first question. Yes, that earthquake slowed down earth’s rotation by 1.8 microseconds or 1.8 millionth of a second (meaningless for zmanim). This as well as the impact of other earthquakes that impact earth’s rotation are factored into the leap second calculations that “correct” the time of our clocks and ensure that your zmanim are correct.

Technical Details

The leap second corrections address incorrect clock time that result from a slower earth rotation than expected. To get a drop more technical (thank you Pinny Markowitz), when the rate or the angle of rotation changes (due to earthquakes or other natural or man-made changes such as building of the Three Gorges Dam), the changes are minuscule. These small changes as well as the original incorrect calculation of the length of the day add up over time. On occasion (about every 2 years) the accumulated difference is significant enough to warrant introducing (or theoretically removing, something that has yet to happen) a leap second to reconcile our clocks with the natural one. On any given day, UTC time always considers 86,400 (60 * 60 * 24) seconds as a day. On the day with a leap second, UTC time still considers the day as having only 86,400 seconds, but a second is added to account for each of the seconds over a year or more being a drop too short. There are various ways of making system clocks conform with the UTC standard, but the net effect is always the same, an extra second is added. UTC doesn’t view a second the same way that the atomic clocks (International Atomic Time) do. UTC views a second as 1/86,400 of a relative day (that is actually 86,400.002 seconds long on average), while, atomic clocks count a day as 86,400 fixed length seconds. Fortunately, the approach of adding leap seconds is exactly what we need when calculating zmanim. By ignoring leap second events in zmanim code, and instead focusing on the measurements of a relative day, we can yield calculations that will be correct in the context of a relative day (assuming that you properly adjust your clock).

ZIP Codes and Zmanim – Use With Care

99557 ZIP code area (the largest in the USA)
99557 ZIP code area (the largest in the USA)
There are many zmanim services and apps that use ZIP codes as a location finder for calculating zmanim. While very convenient, there is a potential pitfall in using ZIP codes for geolocation. In general, ZIP code geolocation services will provide the center of the ZIP code and zmanim apps calculate zmanim for that location. The issue arises with large ZIP code areas mostly found in rural areas. Take the following two extreme cases that have very large ZIP code areas. ZIP code 89049 for rural Tonopah, NV, is 195 km (121 mi) from east to west. The eastern boundary of this non-contiguous ZIP code has a longitude of -115.417°, while the western boundary is -117.625°. This means that there are 2.2° of longitude between the eastern and western borders of this ZIP code. The earth rotates 1 degree every 4 minutes, so zmanim at the eastern and western edges of this ZIP code are approximately 8.8 minutes apart. Using the typical center of the ZIP based calculations would mean that zmanim would be about 4.4 minutes different at the edges compared to the center. Moving to something a bit more extreme, is the case of ZIP code 99557 of Aniak, Alaska and its surrounding area. This ZIP code is 415 km (258 mi) from east to west. The longitude of the eastern edge of the ZIP code is -153.032°, and the western edge is -160.783°. Being farther north and therefore having shorter distances between degrees of longitude, this ZIP code stretches across 7.7° of longitude. The zmanim difference from the center to the edges of this ZIP code is 15 and a half minutes (31 minutes across the ZIP). While it is indeed rare to have such large distances, there are 193 US ZIP codes that are over 1° of longitude wide, meaning that the zmanim difference for these ZIP codes are at a minimum 4 minutes apart, or 2 minutes off from the center. There are 1,463 or 4.4% of all ZIP codes with 0.5° or greater distance between east and west (a minimum of a 2 minute zmanim difference between the east and west zide of the ZIP code). zmanim software developers should be aware of this, and take care to alert users of possible inaccuracies when using large ZIP code areas, or require addresses or more specific location information for large zip codes.
Let’s contrast the above with Lakewood, NJ. With 0.107° of longitude from east to west, zmanim are 24 seconds later on the west side (the intersection of New Central Ave & N Hope Chapel Rd) than the east side (Shinn Cranes, 1600 Ocean Ave). New York City is larger, and from the western edge of Staten Island to the edge of Glen Oaks, the eastern edge of Queens there is a 2 minute and 11 second difference in zmanim.
See the Calculation of Zmanim VS Other Sites post for additional related material.
I thank Avraham David Gelbfish for generating the ZIP code longitude range for all 33,093 ZIP codes from the US Census Bureau ZIP code shape files.