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I have been investigating the various shitoth regarding sheqiah ("sunset") and sseth ha-kokhavim ("tzeit ha-kokhavim" or, when three stars are visible) and cannot find certain info regarding the shitah of the Gr"a (and the Geonim) regarding the time it takes to walk 3/4 mil (i.e. how long it takes after Sheqi`ath HaHamah to become laylah/ sseth ha-kokhavim).

What I have found is that according to the Gr"a - assuming an 18 minute mil - 13.5 minutes after sunset is definite night. Others use the same shitah of calculation, but have a different definition for halikhath mil ("[the time it takes to] walk a talmudic mile"), ranging from 16 minutes to 24 minutes after sunset. However, unless it is just less possible due to street lights, etc. I have a hard time believing that 14 minutes after sunset in Wisconsin would truly be night with three stars visible. I have also heard that this amount of time was only a reality in Bavel and Eress Yisrael.

So, my question is: What would the shitah of the Gra/the Geonim be in various places in the world? What would the calculation be? When would sseth ha-kokhavim be - according to the Gr"a - in Wisconsin for instance?

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It's hard to envisage, but without streetlights it doesn't take long at all for only three stars to be visible. Here are some images of what various major cities would look like later in the evening, were there no light pollution: thechive.com/2013/08/08/… – Shimon bM Oct 22 '13 at 3:56
Hilkhoth Terumoth 7:2 is relevant as well, I think. And he gives a pretty imprecise figure it seems. – Maimonist Oct 22 '13 at 4:47
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When the sun sets, the light decreases in accordance with the sun moving lower and lower than the horizon (of course not the sun is moving but rather the earth is moving). The decreasing of the light is what gradually enables us to see more and more stars, until we reach complete darkness (no light from the sun) and we can see all the visible stars. Therefore, when we want to calculate tzet hakochavim, we are really calculating a certain level of darkness, which is measured today in the degrees the sun is below the horizon. This tells us the level of darkness and how many stars we can see. However, the time it takes to reach that level of darkness flactuates based on two major factors: 1. Your location 2. The time of year Generally speaking, the closer you are to the equator, the shorter the time will be, while the farther you are from the equator, the longer the time will be. Secondly, around the equinox (when the days and nights are equal) in the spring and autumm the time is shorter, while both in the winter and in the summer the time becomes longer (in the summer even more than the winter). For an in depth explanation of why this is so I recommend reading the book Zemanim Bahalacha of Rav Chaim Banish. For a short explanation please see the following teshuva of Eretz Hemdah: http://www.hebrewbooks.org/pdfpager.aspx?req=43791&st=&pgnum=6&hilite= In light of this, how could Chazal have given a time in minutes at all, if this time fluctuates from place to place and from season to season? The Gra answers that the times Chazal gave apply to Eretz Yisrael and Bavel (which approximately are the same distance from the equator) and for the equinox days ("yemei nissan vetishrei") when the days and nights are equal. These times become longer even in Eretz Yisrael and Bavel during the summer and winter (and not shorter in the winter as some mistakenly have stated, for although the days become shorter, the time until tzet hakochavim becomes longer - see in the above sources for the reason why). And they also become longer in countries which are northern to Eretz Yisrael and Bavel. The way to calculate this properly is to check the degrees the sun is below the horizon in Eretz Yisrael 3/4 of a mil after sunset on the equinox, and to use that to calculate tzet hakochavim for any place in the world. For example, if one follows mil being 24 minutes and thus tzet hakochavim 18 minutes, that comes out to approximately 4.9 degrees below the horizon, and this can be calculated (using astronomical calculations) for any place in the world for any date. By zman Motzaei Shabbat in Israel the custom is to be more stringent and to wait until 8.5 degrees, and so on. I hope this explanation was clear and I'll be happy to answer any further questions.

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