.The Talmud in Pesachim 93b-94a brings the dispute concerning how much time passes from amud hashachar (dawn) until netz hachamah (sunrise). According to Ula it is approximately the amount of time it takes to walk the distance of five mil, and according to Rav Yehudah, four mil. The Rishonim disagree concerning how long it takes to walk the distance of a mil. There are those who say 18 minutes (Rambam in his commentary on Mishnah Berachot 1:1), some who say 22.5 minutes, and others who say 24 minutes (see Shulchan Aruch, Orach Chaim 459:2 and Bei’ur Halachah there). In practice, there are two main opinions: 1) 72 minutes, approximately the amount of time it takes to walk the distance of four mil (where every mil is 18 minutes). 2) Ninety minutes (where every mil is 22.5 minutes), which is what is printed in many calendars. Also see Rav Chaim Benish’s book HaZemanim BaHalachah 21:6-9.
According to the Magen Avraham and Pri Megadim, amud hashachar is the appearance of the first light in the east, and according to Eliyah Rabbah and the Gra it arrives a little later, when the eastern skies are illuminated. The Bei’ur Halachah 58:4 and section 89:1 favors the latter opinion. One should know that both opinions are talking about a very slight light visible in the east, and someone who is in a place that has electric lighting, or one who comes from an illuminated area and has constricted pupils, cannot distinguish between these changes in the east. Similarly, a person who is not accustomed to seeing amud hashachar usually cannot detect the first light in the east, nor even discern when the eastern skies are slightly illuminated.
The approach that maintains that the time from amud hashachar until netz hachamah is 72 minutes is understandable since in Jerusalem in the days of Nisan and Tishrei, the eastern skies are illuminated 72 minutes before netz. At that time, the sun is 16.1 degrees below the horizon. The rest of the year is calculated according to that same position of the sun during the days of Nisan and Tishrei, as I have written above. Still, there are those who maintain that the calculation of 72 minutes is consistent throughout the whole year and their proof is from the Gemara in Pesachim which provides a fixed measure – four mil. However, this opinion is problematic, for the determining factor is when the east becomes illuminated and not how much time has passed. The Bei’ur Halachah 261:2 s.v. “Shehu” writes similar ideas. Therefore, it must be that the time that lapses between amud hashachar and netz hachamah fluctuates according to the seasons of the year. See HaZemanim BaHalachah chapter 17, as well as chapter 16, where he explains the reasons for the differences according to the seasons.
It is worthy of mention that all these calculations pertain to Jerusalem and to all locations along the same parallel line of latitude. The closer a person gets to the north and south poles, the longer the time difference becomes between amud hashachar and netz hachamah. Even in Israel there are distinctions. In Tzfat, which is north of Jerusalem, the time difference is longer than Jerusalem by approximately a minute and a half.
Many calendars calculate amud hashachar as 90 minutes before netz in the days of Nisan and Tishrei, when the sun is 19.75 degrees beneath the horizon. Based on this calculation, in the height of the summer, amud hashachar comes out to be 112 minutes before netz. This is very problematic, because in all these times, there is no visible light in the east. According to the astronomical calculation, before the sun arrives at 18 degrees below the horizon, even people with excellent eyesight cannot notice any light, all the more so when it is 19.75 degrees beneath the horizon. Therefore, in practice it is very difficult to rely on these calendars.
However, the opinion which maintains that four mil is 90 minutes can be explained as referring to the height of summer, since then at approximately 90 minutes before netz, the east is illuminated. It is also possible to say that according to this approach, amud hashachar is the first light in the east, and is seen when the sun is approximately 17.5 degrees below the horizon. In the days of Nisan and Tishrei, it is approximately 78 minutes before netz; in the height of the winter 85 minutes before netz; and in the height of the summer, 96 minutes before netz. Perhaps 90 minutes before netz is the average time at which one can see the first light in the east. (In addition, this opinion may possibly follow the approaches which put netz a few minutes later, since it takes the mountains into consideration, see halachah 6, and then indeed 90 minutes before netz comes out to be the average time throughout the whole year. Even the approach which maintains that a mil is 24 minutes and 4 mil is 96 minutes can be explained as referring to the height of summer.)
Therefore, in summary, the law is established based on the position of the sun. There are two main approaches. The first is when the east is illuminated, when the sun is 16.1 degrees below the horizon, which comes out to be 72 minutes before netz in the days of Nisan and Tishrei. The second is from the first light, when the sun is 17.5 degrees below the horizon, which is 78 minutes before netz in the days of Nisan and Tishrei. I have chosen to write primarily according to the opinion which maintains that amud hashachar is when the eastern skies are illuminated, when the sun is 16.1 degrees below the horizon, because that is the opinion favored by the Bei’ur Halachah, and what is written by the Yechaveh Da’at 2:8, based on the Rambam and Shulchan Aruch. In addition to that, those who follow this opinion regarding the matter of Keriat Shema and the Amidah fulfill their obligation according to all, for by that time the day has certainly begun; however, the time prior to that is controversial. It is possible to accurately calculate these times anywhere with the help of Rav Eitan Tzikuni’s computer program, “Chazon Shamayim.”
.In the halachic writings of the Acharonim, a number of opinions are mentioned regarding designating the time of misheyakir. The Yechaveh Da’at 2:8 writes that it is 66 minutes before netz, and Kaf HaChaim 18:18 writes 60. In Jerusalem they follow 50-55 minutes before netz, and in some places in Bnei Brak, 45 minutes before netz. In practice, many books, such as Tefillah Kehilchatah 3:4 and Ishei Yisrael 18:1, write that it is approximately 50 minutes before netz. However, as we have learned, there are differences between the seasons of the year, and it is difficult to comprehend how these opinions ignore those discrepancies. Perhaps some of the poskim who write different times do not disagree at all, but rather each calculated the time at a different season of the year. See HaZemanim BaHalachah 23:6.
According to different visual observations, some poskim acknowledged the time of misheyakir to be when the sun reaches 12 degrees below the horizon, some say 11 degrees, and others only 10 degrees. In practice, it seems that it should be calculated according to the position of the sun when it reaches 11 degrees below the horizon. This comes out to 48 minutes before netz during Nisan and Tishrei, 52.5 minutes before netz at the height of winter (December 22nd), and 58 minutes before netz at the height of summer (June 22nd). Indeed, most of the year it comes out to around 50 minutes. Nevertheless, it is good to postpone the time of misheyakir another five minutes, although in extenuating circumstances, one may make it five minutes earlier.
I should add that in the past, when there were no clocks and people did not wear watches, these times were surely calculated according to human eyesight, and if the day was cloudy, the time of misheyakir was delayed a bit so as to avoid uncertainty. However, now that there are clocks and watches, Shut Sho’el U’Meishiv, Third Edition, part 2, 162, writes that the times are calculated according to them.