Relative hour

In old times, the hour was detected by observation of the position of the sun,[12] or when the first three stars appeared in the night sky. During the first six hours of the day, the sun is seen in the eastern sky. At the sixth hour, the sun is always at its zenith in the sky, meaning, it is either directly overhead, or parallel (depending on the hemisphere).[13] Those persons living in the Northern Hemisphere, the sun at noon time will appear overhead slightly towards the south, whereas for those living in the Southern Hemisphere, the sun at noon time will appear overhead slightly towards the north (an exception being in the tropics, the sun can sometimes be directly overhead). From the 6th and a half hour to the 12th hour, the sun inclines towards the west, until it sets. The conclusion of a day at the end of twilight may slightly vary in minutes from place to place, depending on the elevation and the terrain.[14] Typically, nightfall ushers in more quickly in the low-lying valleys, than it does on a high mountaintop.[15]

There are two major opinions how to calculate these times:

• The Magen Avraham (Shulhan Arukh, Orach Chaim 58:1) holds that because one may do "daytime" activities between daybreak and nightfall, one calculates the day from daybreak (מעלות השחר‎) to nightfall, and divides that period into twelve parts. Although this is known as the opinion of the Magen Avraham, he only says it explicitly with regards to the Recital of the Shema because the time for that mitzvah begins at ʿalot hashachar ("break of dawn"). Nevertheless, this is the opinion of Tosafot,[16] the Rashba,[17] the Ritva,[18] the Ra'ah,[19] the Terumat ha-deshen,[20] the Bach,[21] the Eliyah Rabba,[22] and the Pri Chadash[23] regarding all of the times of the day. Usually this time is computed using daybreak as 72 minutes before sunrise - or more accurately using when the sun is 16.1 degrees below the horizon, as it is in Jerusalem at the equinox 72 minutes before sunrise - before sunrise, and nightfall as 72 minutes after sunset. However, the common practice in Jerusalem (following the Tucazinsky luach) is to compute it using 20 degrees (90 minutes at the equinox).
  • Another variation of this opinion[24] is to consider the day as beginning at daybreak (מעלות השחר‎), reckoning the "first hour" of the day with the rise of dawn (Hebrew: עמוד השחר), that is to say, approximately 72 minutes before sunrise,[25] and the end of the day commencing shortly after sunset when the first three medium-size stars have appeared in the night sky.[26] From the moment of sunset when the sun is no longer visible until the appearance of the first three medium-size stars is a unit of time called evening twilight (Hebrew: בין השמשות). In the Talmud, twilight is estimated at being the time that it takes a person to walk three quarters of a biblical mile (i.e. 1,500 cubits, insofar that a biblical mile is equal to 2,000 cubits).[27] According to Maran's Shulhan Arukh, a man traverses a biblical mile in 18 minutes,[28] meaning, one is able to walk three quarters of a mile in 13½ minutes. According to Maimonides, a man walks a biblical mile in 24 minutes, meaning, three quarters of a mile is done in 18 minutes. In Jewish law, the short period of dusk or twilight (from the moment the sun has disappeared over the horizon until the appearance of the first three stars) is a space of time whose designation is doubtful, partly considered day and partly considered night. When the first medium-size star appears in the night sky, it is still considered day; when the second star appears, it is an ambiguous case. When the third star appears, it is the beginning of the first hour of the night. Between the break of dawn and the first three medium-size stars that appear in the night sky there are always 12 hours. This version of this opinion is followed by many Sephardic communities. Nevertheless, Rabbi Yehosef Schwartz,[29] Rabbi Yechiel Michel Tucazinsky,[30] Rabbi Avraham Chaim Naeh,[31] Rabbi Yitzchok Yaakov Weiss,[32] Rabbi Aharon Kotler[33] and many others reject this opinion because it causes "midday" to be at a time when the sun is not at its highest point, and the Talmud[34] says explicitly that the sun is at its highest point at noon (Heb. chatzot). These poskim thus insist that even if one would rule according to the Geonim with regards to the emergence of stars, the time of the day are computed using tzeit kol ha-kokhavim in order to make midday when the sun is at its highest point.
• The Vilna Gaon holds that although "daytime" activities can start as early as daybreak and end as late as nightfall, their proper time lechatchila (ab initio) is from sunrise to sunset, so one calculates the day from sunrise to sunset and divides that period into twelve parts.[35] This is also the opinion of Rav Nisim Gaon,[36] Rav Saadya Gaon,[37] Rav Hai Gaon,[38] Rabbeinu Chananel,[39] Maimonides,[40] Rabbeinu Yonah,[41] and the Levush.[42]

These are the same as unequal hours.

In the Modern Age of astral science and of precise astronomical calculations, it is now possible to determine the length of the ever-changing hour by simple mathematics. To determine the length of each relative hour, one needs but simply know two variables: (a) the precise time of sunrise, and (b) the precise time of sunset. Since according to the first opinion, the day begins approximately 72 minutes before sunrise and ends approximately 72 minutes after sunset (and according to the variant understanding of this opinion, ends approximately 13½ or 18 minutes after sunset), or begins at sunrise and ends at sunrise according to the second opinion, by collecting the total number of minutes in any given day and dividing the total number of minutes by 12, the quotient that one is left with is the number of minutes to each hour. In summer months, when the days are long, the length of each hour during daytime can be quite long depending on one's latitude, whereas the length of each hour during nighttime can be quite short again depending on one's latitude. It should also be noted that according to those opinions that the 72 minutes are computed according to 16.1 degrees, the further one goes from the equator, the longer it will get, such that in northern latitudes it could become 2 hours or longer.