For observant Jews, besides knowing what day it is, the next step is knowing when the day is even before sunrise–the “rise of day”/Alot ha Shachar [“a-'loat ha-sha-'xar,” or in everyday Ashkanazi speech"''oh-lus"].*
A normal was established by the earliest commentators [Gemara] around which interpretation was assayed about this pre-sunrise period: take “a perfect day in Jerusalem,” defined as one where daylight is exactly equal to darkness, and subtract 72 minutes (that figure having to do with walking pace [it’s complicated :)]. So, an equinox. Can someone step me through what I know are elementary steps to arrive at the following?
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.
Now, you can knock yourself out, as over millennia Jews have done, and come up with differing opinions even given modern-day empirical definitions (i.e., so now (heh) what?)–explore that page at leisure.
*Here’s a typical (modern) question, with examples, for a strictly observant Jew: When I wake up before Alot Hshachar and won’t go back to sleep, what can/can’t I do?
I.e., one needs to know the latitude of Jerusalem (and spherical trigonometry). Also, Leo Bloom’s link fails to mention, but I am guessing, that the 16.1-degree figure is for the geometric center of the sun. Note that the center of the sun is 50 minutes below the horizon at the moment of sunrise due to refraction and the radius of the sun’s disc.
I must add, “daylight is exactly equal to darkness” in Jerusalem around March 16 or 17 or so; either way the declination of the sun will not be exactly zero.
The figure 16.1 still seems to me artificially precise; atmospheric refraction will easily vary a tenth of a degree from day to day. I wonder who originally came up with that value, and whether he explains whence the values used in his calculations.
Furthermore, the 72 minutes are explained as about the length of time it takes an average person to walk a certain distance, again not quite a well-defined interval.
It all seems about right, though.
BTW, at what times is a Jew supposed to pray in Polar regions? A Muslim? Is the sun’s altitude still considered relevant?
You want scientific definitions, or definition any person, Jew or otherwise, at any place on earth can use and be correct?
Sunset
When the back edge of the sun dips below the horizon, from where you are standing.
That is sunset for you.
Sunrise is the opposite, the moment the front edge of the sun breaks the horizon.
Night begins when the 1st three stars become visible to you, before that it is Twilight.
So how ever it appears to your eyes where you are is correct.
In polar regions, a jew would simply go by the suns lowest point in the sky and do his best, since the sun will not set. (Or in the other half of the year, refuses to rise)
Most modern people have clocks of some sort, but if a guy was devoid of any tools but his eyeballs God isn’t going to split hairs with him over a sun that is either remaining in view or isn’t coming into view, just do the best you can.
A classic SDGQ move! And I’m the one who usually chimes in alerting OP to that fact.