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 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 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 June summer solstice. 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 March equinox. 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.

Baal Hatanya’s Zmanim Added to KosherJava Zmanim Library

Baal Hatanya Zmanim (Photo With Hourglass)
While most calendars list the Gra and 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 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 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.

I expect a future post on the subject at some point in the future.

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);
omplexZmanimCalendar 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.

KosherJava Zmanim API Powering Many Mobile Apps

Mobile apps using Kosher Java Zmanim APIIn the past I posted about Android Zmanim, Jay Gindin’s open source Android zmanim project that uses the KosherJava Zmanim API. The fact that Android development uses Java natively means that it is very simple for Android developers to include zmanim in their apps. Since that time there have been a number of other applications (including iPhone apps) using the code. Moshe’s KosherCocoa Obj-C port of the KosherJava Zmanim API will probably result in additional iPhone apps that use the API. Yitzchok’s older Zmanim .NET port of the KosherJava Zmanim API also opened the door for Windows Phone zmanim applications as well (Ari Polski’s Zmaim app already uses it, and there are others in the works). I may post additional details about some of them in the future, including an updated post about Jay’s latest Android Zmanim release. I am aware of the following mobile applications that use the KosherJava Zmanim API.

There are also a few secular apps that are non-zmanim specific that use the API for sunrise and sunset calculations. One that I know of is Jeffrey Blattman’s Dawn to Dusk Widget, and I know that there are some photography apps that use it for sunrise/set calculations as well. There are likely more that I have missed, and a few that are in active development but unreleased. If you are aware of any missed apps, please let me know.