Computation by Degrees Explained
The Gemara in Psachim (.צד) states that the time span between Alos HaShachar (Dawn) and Hanetz HaChama (Sunrise) is as long as the amount of time it takes an average person to walk a distance of 4 "milin" (plural of "mil"). According to most Poskim, it takes 18 minutes for an average person to walk a distance of one mil, and therefore 72 minutes to walk 4 milin. As a result, they hold that Alos Hashachar occurs 72 minutes before sunrise. Others say it takes 22.5 minutes to walk a mil, and therefore 90 minutes to walk 4 milin. Accordingly, Alos HaShachar occurs 90 minutes before sunrise. Either way, Alos HaShachar refers to a specific point in the gradual transition from night to day. Likewise, Tzes HaKochavim (nightfall) refers to a point in the transition between day and night. These transitions occur at a rate, which varies from place to place and season to season.
- Place to Place: In locations close to the equator, the process of nightfall occurs faster than it does in locations further away from the equator. To illustrate: For any given date, it will be darker a half hour after sunset in Miami, than it will be a half hour after sunset in Montreal. That is, the same "half hour after sunset" corresponds to visually different stages of nightfall, in different locations.
- Season to Season: The process of nightfall occurs slowest in the summer, and fastest in March and September. As such, for any given location, it will be darker a half hour after sunset on a September day, than it will be a half hour after sunset on a summer day. That is, the same "half hour after sunset" corresponds to visually different stages of nightfall, during different seasons.
Taking these facts into account, the Gra and others ruled, that Alos HaShachar cannot be defined in terms of a fixed amount of time before sunrise, and Tzes HaKochavim cannot be defined in terms of a fixed amount of time after sunset. All figures of the Gemara involving a fixed time span were stated specifically in reference to the equinox days (the days of Nissan and Tishrei, in which day and night are equally long). Furthermore, the figures stated by the Gemara were stated only with regard to Bavel and Eretz Yisroel. For other places and other dates, different but corresponding figures apply.
Alos HaShachar: - The Gemara, as we said above, states that Alos HaShachar occurs 4 milin (72 minutes) before sunrise. The figure of 72 minutes applies only, to the equinox days in Bavel and Eretz Yisroel. Actual times of Alos HaShachar in other settings may be more or less than 72 minutes before sunrise. The figure of 72 minutes was given as a means of identifying a specific point in the process of dawn, which defines Alos HaShachar. This point can be identified astronomically according to the position of the sun. Where is the sun 72 minutes before sunrise, on an equinox day, in Yerushalayim? The answer is, 16.1 degrees below the horizon. As such, Alos can be defined for all settings, as the time when the sun reaches 16.1 degrees below the horizon. According to this interpretation, Alos HaShachar has the same appearance during all seasons of the year, anywhere in the world. This example involves Alos HaShachar, but the same method can be applied to calculate Tzes HaKochavim and Misheyakir by interpreting the figures of the Gemara and Poskim in this way.
- Tzes HaKochavim: Some Poskim say that "emergence of 3 smaller stars" occurs 36 minutes (2 milin) after sunset. The figure of 36 minutes applies only, to the equinox days in Bavel and Eretz Yisroel. Times in other settings may vary. Since the angle of the sun - 36 minutes after sunset, on the equinox days in Yerushalayim - is 8.5 degrees below the horizon, the time for "Emergence of 3 smaller stars" can be identified in all settings, as the moment when the sun has descended 8.5 degrees below the horizon.
Note that computation by degrees has ramifications, not only with regard to Alos and Tzes, but also with regard to those zmanim times which are based on Alos and Tzes, such as Sof Zman Krias Shema according to the Magen Avrohom.
ע' באור הגר"א או"ח ס' רס"א וס' תנ"ט.
באור הלכה סימן רס"א ד"ה שהוא
וכן הוא גם דעת הגר"א בבאורו דכל שעורי הגמרא בין דד' מילין שהוא עד צאת כל הכוכבים לשיטתו ובין דג' רבעי מיל שהוא זמן בין השמשות הכל הוא בזמן ניסן ותשרי מה שאין כן בזמן אחר משתנה לפי הזמן ובימי הקיץ הבין השמשות מאריך הרבה יותר. וכן כתב הגר"א עוד דשעורי הגמרא לא נאמר רק באפק בבל.
By Dovid Eisikowitz