Netz hachamah is the time when the sun rises, and even though this definition is presumably clear and simple, in actuality, it is rather complex.
First, the duration of the sun’s ascent, which begins from the second we can see the first edge of the sun until it can be seen entirely, lasts approximately two and a half minutes. The poskim disagree regarding the exact time of netz hachamah. According to most halachic authorities, the time of netz is precisely when the first part of the sun is visible, and at that moment it is necessary to begin the Amidah of vatikin. Yet, there are those who say that netz is at the conclusion of the sun’s ascent. Additionally, there are those who say that netz lasts the whole two and a half minutes that the sun is rising. Moreover, there are those who say it lasts a few more minutes, the entire time that the rays of the sun are still red. In practice, those who pray vatikin make an effort to begin the Amidah at the time the sun begins to rise, but are not overly strict about this because the other opinions are also taken into consideration.
Another uncertainty arises. Are the mountains in the east that block the sunrise taken into consideration, or do we follow the astronomical sunrise (on a straight horizon)? It is clear that one who is under a cliff, or behind a tall building which blocks the east from his view, cannot claim that the sunrise begins when he himself sees the sun, because, if that was the case, then the sunrise, as far as he is concerned, would likely be towards the afternoon. The question is: what is the law, for example, in Jerusalem’s Old City, where the Mount of Olives blocks the eastern horizon and consequently the sun becomes visible only a few minutes later? Even for those who stand on the Mount of Olives, the mountains of Moav rising over the Jordan Valley block the beginning of the sunrise. Some say that the time of netz hachamah is only when one can actually see the sun, meaning after it is visible above the Mount of Olives. Others say that we should not take into account a nearby mountain, like the example of the Mount of Olives, since it is possible to walk to it by foot, but rather that it is necessary to include the distant mountains of Moav. The difference between the two opinions amounts to a few minutes.
There are those who say that we should not consider the mountains in the east at all; rather we calculate the sunrise according to a straight horizon, based on the time that it would be possible to see the sunrise were there no mountains. Nowadays, there are computer programs that allow us to calculate the precise astronomical sunrise in each and every location while disregarding the mountains in the east. Many are accustomed to establishing the time of sunrise according to this calculation.
. According to the majority of poskim, netz is the beginning of the sun’s ascent, as writes the Bei’ur Halachah, 58:1, s.v. “Kemo,” and Halachah Berurah (Yosef) 58:7. Ish Matzliach writes that it is the end of the sun’s ascent (see Yalkut Yosef 89:3). According to the Razah, it is the whole duration of the sun’s ascent. Others say that even slightly after that, as long as the sun is close to the earth and the rays of the sun are still red, it is still considered “Yera’ucha im shamesh” (“Let them fear You from when the sun [shines]”), as can be inferred from the Rambam, responsa 255. (See HaZemanim BaHalachah 24:3-4).
.Divrei Yosef writes that the law depends on actually seeing the sun, and therefore it is necessary to take into consideration the places that the Mount of Olives conceals. However, according to the Maharil Diskin, (brought in Sefer Nivreshet), what is concealed by the Mount of Olives does not enter into the equation since it is closer than the walking distance of one day, but we do take into consideration the parts concealed by the Mountains of Moav (although he does not resolve the matter of Shabbat with regard to sunset). Further, there is uncertainty about a city that is built on mountains: does each neighborhood follow according to its own height or does the whole city practice according to the highest neighborhood in the city, where the sun is visible first? The minhag is to go by the highest neighborhood. An additional doubt is raised – if a skyscraper was built in a city, on the top of which the first rays of the sun shine a minute before the sunrise can be seen on the ground, what is the ruling? Similarly, if the city is very large, do we still go by the highest point in the city, or, due to the city’s size is each area defined by itself? See HaZemanim BaHalachah chapter 7, which mentions these doubts and cites the different opinions.
Even according to the opinion that sunrise and sunset are calculated along a straight horizon, there is doubt as to which height we use to make the calculations, since the higher the place, the earlier the sun is visible when it rises, and the later the sun is seen when it sets. For example, at a height of 800 meters (2624.67 feet) above sea level, the sun is still visible at sunset approximately 4.6 minutes later than on sea level, and at sunrise approximately 4.6 minutes earlier. Indeed, this opinion is divided into three approaches. Some say that we go according to the sunrise on a straight horizon based on the height of the place, while there is still uncertainty with regard to the law of a city in which there are mountains and valleys, i.e., whether we go by each area in the city for itself or the highest point in the city. It is the opinion of the Shulchan Aruch HaRav that in all places we go according to the sunrise at a height of 800 meters above sea level, the altitude of Jerusalem. So it is written in Igrot Moshe Orach Chaim 1:97. (This means that even when the people praying are at sea level, the time of netz will be 4.6 minutes before they can actually see the sun.) Others say that we go by the astronomical sunrise without taking the mountains into account at all; instead we calculate how it would look at sea level (which covers most of the earth’s surface) without mountains, as Rabbi Isser Zalman Meltzer writes. See HaZemanim BaHalachah chapter 7, where all this is discussed.
In the computer program “Chazon Shamayim,” it is possible to determine the precise astronomical time of sunrise in any place, on any day, based on the lines of latitude and longitude and the height of the location. Since the result obtained from a program such as this one is more accurate than all the calculations done by visual observations, many have been accustomed to calculate the time of sunrise with this program. In practice, all the communities living in Gav Hahar (settlements in the heart of the Shomron) do not need to take into account the mountains and valleys to the east of them, for if they were to take them into consideration, they would need to calculate a different time for every house, each according to its height, and according to the mountains that block them from the east, in every season based on the place of the sun’s ascent. Therefore, we follow the astronomical horizon, according to the highest point in that location. In the past, when people lived in open areas, the sunrise was perceptible, and this ruling was mainly based on the visibility of the sun. However, today, when most people live among many buildings, and do not see sunrise, and our methods of calculation have become easier, the sunrise is calculated according to the astronomical horizon. At that time, the rays of the sun are also visible in the highest places in the area. However, when to the east, there is a range of distant mountains that evenly cover the horizon, like, for instance, in the coastal plains of Israel, and they delay the visibility of the sun from that whole area by a few minutes, it seems, that it is necessary to take them into consideration and postpone the time of netz. (The time of misheyakir is dependent upon light, based on the explanation in note 2, when the sun is eleven degrees below the astronomical horizon, and there is no connection to the visible sunrise).