About the Jewish Calendar (Hebrew calendar)

לוּחַ עִבְרִי

Until the year 4119 (ד'קי"ט or 359 AD) there was no actual Jewish Calendar.

How did Jews back then determine the Hebrew date? The end of each month was set on the night the moon disappeared, and the beginning of the month was set when the moon appeared again. The reappearance of the moon is called Molad. When the 30th night of the month came, a tribunal would sit and wait for a witnesses who saw Molad to come and testify before them. If witnesses came and testified that they saw the Molad, a court would sanctify the month and state that today is Rosh Chodesh.

If there were no witnesses, the tribunal would continue the current month, which means adding another day to the current month (up to 30 days), and the beginning of the next month will be on the next day.

Since they did not know in advance when the witnesses would arrive, and even if they arrived towards the end of the day, their testimony would be accepted, the thirtieth day of the previous month was treated as Rosh Chodesh. If the witnesses arrived, it turned out retrospectively that this is indeed Rosh Chodesh and the first (1) of the next month, and if not, then the next day will also be Rosh Chodesh, so in fact Rosh Chodesh was actually two days. This is why even today there are months where Rosh Chodesh is two days.

In addition, Pesach (Passover) should always be in the spring and not in another season. In order to keep that, the Hebrew calendar must also consider the sun year and not just the lunar year. When the tribunal saw that the month of Nissan came too early (according to all kinds of calculations and signs), they would leap the year - that is, determine that the next month would be Adar Bet and not Nissan, and thus the year became a Leap year (Shana MeUberet). This affected the dates of all the Jewish holidays, including Rosh Hashanah. The need for the Leap Year (Shana Meuberet) is because of the difference in length between the sun year (about 365 days and a half), and the lunar year (about 354 days). The difference is over 11 days, so once every few years (two or three years), a month had to be added to close the gap, so Passover could be celebrated in the spring.

Since there was no calendar, they did not know in advance when the holidays would start. As soon as they sanctified (or passed) the month, all Jews in the world had to be notified so they will know when to celebrate the holidays. In those days there was no internet or other electronic media, but there was still a way to immediately announce the sanctification of the month - they would prepare beacons (bonfires) on the mountain tops. Once the month was set, they would light the beacon in Jerusalem (on the Mount of Olives), which they would see from the top of the next mountain (Sartaba) and so on until all over Israel they would see the beacons light up and so they knew that the month was set.

This method worked fine, but there were people who wanted to disrupt the system and light fires even when no witnesses arrived and the month was not set. In those days the tribunal did not have the means to fight them, and they had to stop this method of communication and settle for sending messengers.

The messengers took much longer to pass on the news than the beacons, so where the messengersdid not arrive until the holidays, the Jews did not know when the holiday was set. This is why they decided to celebrate each holiday for two days. Even though we now have a calendar and know the exact date, Jews continue to celebrate doubled-day holidays abroad.

The most difficult holiday to announce in time is Rosh Hashanah. Because it applies to the beginning of the month itself, many times it was two days anyway, as we explained each month. But even when the witnesses arrived on the first day, there was little-to-no time to announce that, because the sending of the message did not surpass the sanctity of the holiday, and messengers could not be sent on holiday nights. That is why even in Eretz Yisrael (except for places close to the court that was at first in Jerusalem, then in Yavne, etc.), they would celebrate Rosh Hashana for two days, and continue to do so even today. Now that the Hebrew calendar exists, the first day of Rosh Hashana is the 30th night of the previous month (Elul) and the second day is for the beginning of the next month (Tishrei).

In the year 4119 (ד'קי"ט or 359 AD), the Jewish court headed by Hillel Hanassi (not to be confused with Hillel Hazaken who lived in the days of the second Temple), but a Presidential Hillel many years before they understood that it was very difficult and sometimes impossible to abide by the procedure of the sanctification this month, so they decided to create a Jewish calendar, and the same Jewish calendar remains to this day.

Principles for calculating the Hebrew calendar:

1. The years are divided into cycles of 19 years each. In each such cycle, there are 7 leap years (years 3, 6, 8, 11, 14, 17, and 19). Therefore, every 19 years, the Hebrew and Gregorian calendars meet again. Although there may be day-to-day differences between them (for various reasons we will see later), usually after 19 or 38 years, the Hebrew and Gregorian birthday dates fall on the same day.
2. An 'Average Molad' (Molad Emtza'i) is set every 29 days, 12 hours, and 793/1080 of one hour. After 12 such Molads have passed, from one Rosh Hashanah Molad, the next Rosh Hashanah is set.
3. There are occasions in which the Rosh Hashanah is postponed:
   1. Rosh Hashanah will not apply on a Sunday, Wednesday or Friday.
   2. If Molad is first seen after 12 noon, ie after 18 hours from the night before.
   3. If in a year that is not leaped, and the Molad is on a Tuesday after nine hours and 204 parts. In this case, Rosh Hashanah is postponed for two days and will only be Thursday, because the next day is Wednesday where Rosh Hashanah is forbidden to apply.
   4. If after a Leap Year (Shana Meuberet), the Molad is on a Monday, after 15 hours and 689 parts.
   The first postponement (לא אד'ו ראש), is to prevent Yom Kippur starting close to Saturday, or from Hoshana to start close to Saturday. The second postponement (מולד זקן) is not entirely clear, it may be because the birth of the moon was so late anyway they would not have seen it and do not declare the birth of the month and the new year. The other two postponements are to prevent the year from being longer than 355 days or less than 353 days in a regular year, or more than 385 days or less than 383 days in Leap Year (Shana Meuberet).
4. All months have a fixed length except for Cheshvan and Kislev. A 30-day month is called a full month, and a 29-day month is called a missing month. These are the fixed lengths of the months:
   • Tishrei - 30 days
   • Cheshvan - 29 or 30 days
   • Kislev - 29 or 30 days
   • Tevet - 29 days
   • Shevat - 30 days
   • Adar - 29 days
   • Adar I (in a leap year) - 30 days
   • Adar II (in a leap year) - 29 days
   • Nissan - 30 days
   • Iyar - 29 days
   • Sivan - 30 days
   • Tammuz - 29 days
   • Av - 30 days
   • Elul - 29 days
5. If the months of Cheshvan and Kislev are both missing, then the year is called a deficient year. If both are full, this year is called a complete year. If the month of Cheshvan is missing and Kislev is full (but never the other way around), this year is called a regular year. The reason for the differences in the lengths of Cheshvan and Kislev is due to the New Year postponements mentioned in section 2.
6. A simple year is 354 ± 1 days and a leap year is 384 ± 1 days.
7. The year can be described using a 'three-letter' sign.
   This sign indicates on which days of the week key events of the year will occur and determines the weekly 'Parasha' readings.
   This means that two years with the same sign will have the same schedule for these events and Torah readings.
   The sign consists of three letters:
   • The first letter indicates on which day of the week 'Rosh Hashanah' falls.
   • The second letter indicates whether the year is regular (כ), complete (ש), or deficient (ח).
   • The third letter indicates on which day of the week Passover falls.
   The standard (non-leap) year signs are: בח'ג, בש'ה, גכ'ה, הכ'ז, הש'א, זח'א, זש'ג.
   The signs for leap years are: בח'ה, בש'ז, גכ'ז, הח'א, הש'ג, זח'ג, זש'ה."

Rules for Postponements and Advancements of Holidays and Festivals:

1. Holidays written in the Torah: Yom Kippur, Sukkot, Shemini Atzeret (a.k.a Simchat Torah), Passover and Shavuot are never postponed or advanced. Rosh Hashana has some occasions in which the New Year is postponed.
2. Hanukkah is never advanced or postponed.
3. When Purim falls on a Friday, in places surrounded by a wall since the days of Yehoshua ben Nun (e.g., Jerusalem), a 'Purim Meshulash' (Three-Day Purim) is celebrated.
   • Friday (14 of Adar): Read the Megillah.
   • Saturday (Shabbat 15 of Adar): Include the 'Al Hanisim' prayer.
   • Sunday (16 of Adar, Purim Meshulash): Make a feast and rejoice, send food portions to friends (Mishloach Manot).
4. If Purim falls on a Sunday, the Fast of Esther (Taanit Esther) is observed on the preceding Thursday to avoid fasting on Shabbat or Purim itself.
5. The following fast days are postponed to Sunday if they fall on Shabbat (Saturday): Tisha B'Av, Tzom Shiva Asar B'Tammuz, and Tzom Gedaliah.
6. On holidays established by the state law of Israel, it is stipulated that they will be advanced or postponed to prevent desecration of the Sabbath or other Jewish holidays.

Now we will explain the different methods for calculating the times and their significance.

Let's start with Halachic Times concepts:

1. Hour: The term 'hour' does not refer to the standard 60-minute hour used in today's clocks. Instead, it refers to 'Shaah Zmanit' (a proportional hour), which is calculated by dividing the time between sunrise to sunset into 12 equal parts, and the time from sunset to sunrise into 12 equal parts.
2. Chatzot Hayom (Midday): Chatzot Hayom is the midpoint between sunrise and sunset; this point is after 6 proportional hours (Shaah Zmanit), because, as we explained, the day is divisible by 12, so half a day is 6. Equally, a quarter of the day is after 3 hours, and a third today is after 4 hours, etc.
3. Walking time: According to Chazal, a "mediocre man goes on ten horseshoes” a day, which is forty miles, and every mil is two thousand "ama." (We will not elaborate on that, but one "ama” ranges from 48 to 60 cm, also depending on the method you are measuring by.) If we can define what a day is, we will also know how to measure times using this method. For example, half a day is five horseshoe walking hours. One Shaah Zmanit is three miles and a third of a mile. It turns out the walking time of a mile is 18 minutes (Zmaniot!).
4. Degrees- When referring to specific times, the timing is typically accurate when day and night are equal (e.g., on March 21 and September 23). But what happens at other times of the year? In some cases, times are calculated using fixed minutes, while in others, temporary minutes (of Shaah Zmanit) are used. However, the most precise method is to calculate using degrees. For example, if Alot HaShachar (Dawn) occurs 72 minutes before sunrise on a day when day and night are equal, we can calculate the sun's angle below the horizon at that moment. On any other day, when the sun reaches the same angle below the horizon, we know that dawn has occurred, signaling the beginning of the day. The reasoning behind this method is that the same amount of light is present when the sun is at the same angle, regardless of the time of year.

From the times we calculated earlier, for example, the latest time to recite Krias Shema is up to a quarter of the day, which is three proportional hours (Shaot Zmaniot) from the beginning of the day. Similarly, a third of the day is four proportional hours from the start of the day, and so on.

To calculate both the temporal hour and walking time, we need to determine when the day begins and ends.

There are two main opinions on how to calculate this:

1. Dawn to stars: According to one opinion, the day begins at dawn (Alot HaShachar) and ends when the stars are visible (Tzeit HaKochavim).
2. Sunrise to sunset: The second opinion is that the day begins at sunrise (Netz HaChama) and ends at sunset (Shkiah).

Sunrise (Netz HaChama): Sunrise is defined as the moment when at least part of the sun’s body is visible above the horizon (not just the sunlight). In locations without mountains, this time can be calculated mathematically as the point when the sun is 0.8 degrees below the horizon.

Although it appears that the sun is already above the horizon, this is due to the refraction of light in the Earth’s atmosphere, which bends the rays of sunlight. As a result, we perceive the sun as being above the horizon even when it is still slightly below it.

This sunrise is referred to in our calendar as 'Plain Sunrise' (Mishorit), because it is accurate for locations on flat terrain near sea level, such as the middle of the ocean. But what happens when there are mountains in your area?

In such cases, two factors must be considered:

1. Elevation: The higher your location, the earlier you will see the sunrise (and the later the sunset).
2. Obstructions: If there are mountains to the east that block the sun, you will see the sunrise later.

The first factor, elevation, can be calculated mathematically with relative ease. In our calendar, this is referred to as 'Astronomical Sunrise.' The second factor, however, is much more complex. When accounting for mountains that block the view of the sun, the resulting sunrise is called 'Visible Sunrise' or 'Visible Netz.'

A Further Question: If someone is, for example, in a deep valley surrounded by high mountains, where the sun only becomes visible at a much later hour, should this later time be considered their 'Netz'? Or do we instead consider the Netz to be the time they would have seen the sunrise had they climbed above the valley to a point unobstructed by the mountains? In other words, to what extent do we factor in the surrounding topography when determining the Netz?

The custom regarding this subject is generally to consider distant mountains. For example, in Jerusalem, we take into account the Moav Mountains, which are located in present-day Jordan. However, when it comes to nearby mountains, there is disagreement, and the matter remains unresolved.

It is customary to use a Netz (sunrise) visible to "Vatikin", who begin their morning prayers (Shacharit) precisely at the moment of the Netz. To do so, they must recite Krias Shema a few minutes beforehand.

Sunlight as the Ultimate Indicator: Regardless of what is written in the calendar, any situation where the sun is visibly in the sky is considered daytime. This principle gives rise to the phrase 'clear as the sun.'

Sunset Calculation: The calculation of sunset is similar to that of sunrise. Sunset occurs when the sun is 0.8 degrees below the horizon, but this time on the western side. As with sunrise, there are three types of sunset:

• Plain Sunset: Calculated for flat, sea-level terrain.
• Astronomical Sunset: Adjusted for elevation.
• Visible Sunset: Takes into account obstructions like mountains.

Sunlight as an Indicator at Sunset: As with sunrise, as long as the sun is visible, it is still daytime, and the current date remains unchanged. After the sun has set, doubts begin, as explained earlier. In this article, we will later see that the term 'sunset' may also refer to another time.

According to Halakhah, the visible sunset determines whether it is day or night: if the sun is visible, it is still day; if the sun is no longer visible, it is considered night.

Dawn – As mentioned, dawn is the time when the morning begins to lighten. It’s not yet bright enough for the sun’s light to be seen directly, but you can already see a faint glow breaking from beneath the horizon. From that moment onward, the night has ended, and if you perform the Mitzvot of the day, you have fulfilled your obligations—at least in retrospect.

Chazal said that dawn occurs when the sun is still four mil (a Talmudic unit of distance) away from sunrise. To understand this measure, you need to define when the day begins and ends. If the day begins at sunrise and ends at sunset, then on the equinox, dawn occurs 72 minutes before sunrise (according to most ruling Rabbis).

On other days, it can be calculated by the sun’s position—specifically, when it is 16.1 degrees below the horizon. According to the opinion of the Spanish Rabbis (Rishonim), dawn consistently occurs 72 minutes before sunrise throughout the year, regardless of the season.

On the other hand, if it is said that the day begins at dawn and ends when the stars appear (this is the opinion of the late Rabbi Yechiel Michel Tukachinsky), then it turns out that the "ten mil" walking time—forty mil in total—includes the time from dawn to sunrise, and likewise the time from sunset to the appearance of the stars.

In this calculation, we must assume these two periods (from dawn to sunrise and from sunset to nightfall) are equal. Therefore, for now, we will set aside the varying opinions on when the stars appear (tzeit hakochavim) and suppose that the time between sunset and nightfall is the same as the time between dawn and sunrise.

According to this view, there is one mil (which equals four mil before sunrise) and another mil after sunset. This leaves eight mil (32 mil) for the period between sunrise and sunset. The conclusion is that a person walks two and two-thirds mil per hour. That means it takes approximately 22.5 minutes to walk one mil.

To summarize the opinions regarding dawn (Alot HaShachar): There is one opinion that places it at 72 minutes before sunrise, and another opinion that holds it is 90 minutes before sunrise. Following that, there is a dispute regarding days that are not the equinox—whether the calculation should be based on degrees (the sun’s position below the horizon) or on proportional (seasonal) hours.

Appearance of the Stars: This is the time when night begins without any doubt. However, the exact moment is subject to uncertainty. On the one hand, there is a physical definition: night begins when you can see three medium-sized stars. For calculating the end of Shabbat, the strictest halachic authorities (Chumra) rule that these stars must be small, and that you need to see at least three of them at the same time, in a single glance. Large stars (such as the planet Venus) can be seen even during the day and therefore are not considered a reliable sign for the beginning of the night.

According to the Talmud (Gemara), the time between sunset and the appearance of the stars is equivalent to walking three-quarters of a mil. As we have seen in the calculation for dawn, there is an opinion that walking a mil takes 18 minutes. If so, three-quarters of a mil would be 13.5 minutes. On the days of the equinox, when the sun is 4.9 degrees below the horizon, the problem is that stars still do not appear at this time. Therefore, we rely on this time only according to the strictest halachic authorities (Chumra). For them, it is no longer permitted to pray Mincha or perform other mitzvot that are obligatory during the day alone. However, we do not rely on this time according to the lenient opinions—that is, we do not yet perform mitzvot that must be done specifically at night or on the following day.

According to the ruling of the Chatam Sofer, the appearance of the stars (Tzeit HaKochavim) occurs when the sun is 8.5 degrees below the horizon.

All of the above follows the method of the Geonim, whose definition of sunset has already been explained.

However, according to Rabbeinu Tam and many other *Rishonim*, as well as the ruling of the *Shulchan Aruch*, the concept of sunset is divided into two distinct times: The first is the visible sunset—when we see the sun disappear below the horizon (as explained earlier). The second is a later time, corresponding to the walking distance of three and a quarter *mil*, after which the appearance of the stars (*Tzeit HaKochavim*) occurs.

According to Rabbeinu Tam, there is an astronomical reasoning for this: the time between the first sunset and the appearance of the stars is equal to the time between dawn (*Alot HaShachar*) and sunrise. As explained earlier, when following the view that the day begins at dawn and ends with the appearance of the stars, this balance is necessary; otherwise, midday (*Chatzot*) would occur much earlier than the actual moment when the sun is at its highest point in the sky.

According to Rabbeinu Tam, the appearance of the stars occurs four *mil* (a walking time of 72 minutes or 90 minutes) after sunset. In terms of degrees, this corresponds to approximately 16 degrees or 19.75 degrees below the horizon, as we explained in the discussion regarding dawn. Here too, there is a debate whether to calculate the time based on degrees (astronomical position), fixed minutes, or proportional (*sha'ot zemaniyot*) hours.

Let us summarize the methods for calculating the appearance of the stars (*Tzeit HaKochavim*):

• According to the method of the Geonim: from as early as 13.5 minutes (or 4.9 degrees below the horizon), to the stricter opinions of up to 36 minutes (or 8.5 degrees), with various intermediate views among different *poskim*.
• According to the method of Rabbeinu Tam: 72 minutes (16 degrees) or 90 minutes (19.75 degrees), with differences of opinion whether to calculate by fixed minutes, proportional hours, or degrees.

Tallit and Tefillin Time: This is the time when there is enough light for a person to recognize his friend from a distance of slightly more than four *amot*. The exact time is subject to debate. The main methods for calculating it are:

• When the sun is 11.5 degrees below the horizon
• 45 minutes before sunrise
• 6 minutes after dawn (*Alot HaShachar*)

End of Time for Kriat Shema (Morning Shema): This is one-quarter of the day, equivalent to three proportional (*sha'ot zemaniyot*) hours. There are two primary methods for calculating this time:

• The method of the Magen Avraham, which defines the day as beginning at dawn (*Alot HaShachar*) and ending at the appearance of the stars (*Tzeit HaKochavim*).
• The method of the Gra (the Vilna Gaon) and the Baal HaTanya, which defines the day as beginning at sunrise and ending at sunset.

Naturally, the calculation according to the Magen Avraham depends on the various opinions regarding dawn and the appearance of the stars, as explained earlier.

End of Morning Prayer Time (Shacharit): This is one-third of the day, equivalent to four proportional (*sha'ot zemaniyot*) hours. Like the time for Kriat Shema, this time depends on the same two approaches mentioned above (Magen Avraham vs. Gra and Baal HaTanya).

Mincha Gedolah (Earliest Time for Mincha): This is half an hour after midday (*Chatzot*). This half-hour can be calculated either in fixed minutes (30 minutes) or proportional minutes (half of a proportional hour). Some stricter opinions follow the longer calculation:

• In the winter, when proportional hours are shorter than fixed hours, they use the fixed time.
• In the summer, when proportional hours are longer, they use proportional time.

Mincha Ketana (Preferred Time for Mincha): This occurs nine and a half proportional hours after the beginning of the day. It corresponds to the time when the *Korban Tamid* (daily offering) was brought in the Temple on weekdays. As before, the calculation of this time depends on the different opinions regarding the length of the day. In most modern calendars, Mincha Ketana is calculated according to the method that defines the day as beginning at sunrise and ending at sunset.

Plag HaMincha: From this time onward, it is permitted to pray the *Arvit* (evening prayer). According to one opinion, it is no longer permitted to pray *Mincha* after this time. It is also permissible to accept Shabbat from this time onward, and in cases of need (*sha'at hadchak*), Hanukkah candles may also be lit from this time. As with the other times, calculating Plag HaMincha depends on the various opinions mentioned earlier. In most calendars, this time is presented according to the opinion that defines the day as from sunrise to sunset.

Summary of the Methods Presented in the JCal Calendar

Chazon Shamayim – This method is compatible with the default settings of the Chazon Shamayim software (Ashkenazi calendar).

Rabbi Eitan Tzikuni - Based on this article by Rabbi Eitan Tzikoni Shlita” (Rabbi Tzikoni is also author of Hazon Shamayim Software featured on Daat website).

Rabbi Zalman Melamed

Or HaChaim – Based on the calendar published by Yeshivat Or HaChaim, edited by Rabbi Shlomo Benizri, Shlit"a. This calendar follows the rulings of the late Rabbi Ovadia Yosef, zt"l, and is commonly practiced in Sephardi communities in Israel.

Summary of Times by Method:

Wherever degrees are mentioned, it refers to the position of the sun that many degrees below the horizon.

Wherever sunrise or sunset is mentioned, it refers to sunrise and sunset as calculated at sea level (on flat plains), unless otherwise specified.