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Calling all science and math-oriented Judaism.SE-ers!
According to the website MyZmanim.com, today's Halachic times where I work are as follows (only a handful of times are shown because the question would be tedious to edit otherwise):

Dawn עלות השחר
90 minutes as degrees, bef. sunrise 5:34:28 90 דקות במעלות, קודם הנץ

Fixed 72 minutes before sunrise 6:07:32 72 דקות שוות קודם הנץ

72 minutes as 16.1 degrees 5:53:58 72 דקות לפי 16.1 מעלות

Earliest Talis & Tefillin זמן ציצית ותפילין
Sun is 11.5 degrees below horizon 6:18:58 11.5 מעלות תחת האופק

Sun is 11 degrees below horizon 6:21:43 11 מעלות תחת האופק

Sun is 10.2 degrees below horizon 6:26:08 10.2 מעלות תחת האופק

Sunrise הנץ החמה
In a level region 7:19:32 במישור

Latest Shema Magen Avraham סוף זמן קריאת שמע מגן אברהם
Using "90 minutes..." as dawn and nightfall 8:48:59 לפי 90 דקות במעלות
Using "Fixed 72 minutes..." 9:05:31 לפי 72 דקות שוות
Using "72 minutes as 16.1 degrees" 8:58:44 לפי 72 דקות במעלות

Midday & Midnight 12:03:30 חצות

Earliest Mincha מנחה גדולה

30 fixed minutes after midday 12:33:30 30 דקות שוות אחר חצות
Gra & Baal Tanya 12:27:10 גר"א ובעל התניא
LeChumra 12:33:30 לחומרא
Magen Avraham
Using "Fixed 72 minutes..." 12:33:10 מגן אברהם לפי 72 דקות שוות

Mincha Ketana מנחה קטנה
Gra & Baal Tanya 2:49:09 גר"א ובעל התניא
Magen Avraham מגן אברהם
Using "Fixed 72 minutes..." 3:31:09 לפי 72 דקות שוות

Plag HaMincha פלג המנחה
Gra & Baal Tanya 3:48:19 גר"א ובעל התניא
Magen Avraham מגן אברהם
Using "Fixed 72 minutes..." 4:45:19 לפי 72 דקות שוות

Sunset שקיעת החמה
In a level region 4:47:29 במישור

Does this mean that the Magen Avraham holds of only a very minuscule Plag HaMinḥah? Or is there something going on mathematically that just makes it nearly impossible to have a Plag in the winter? Is there something in this Shittah that could explain why many synagogues Daven Minḥah on Friday evenings in the summer well after Plag HaMinḥah as usually published in most calendars? Is M"A's Shittah just that much later?

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Where do you work? First of all, I want to compare the times with other sites in order to be sure that MyZmanim is at least correct. – jutky Dec 15 '11 at 22:30
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A nitpick: P'lag is a time of the day, not a span of time. Everyone holds of a minuscule p'lag: it's an instant. – msh210♦ Dec 15 '11 at 22:31
If you look here you will find a "halachic time app" which tells you how many minutes are in a halachic hour on the day you view the app. During this time of the year, you will notice that a halachic hour is short (only 50 minutes) During the summer, the halachic hour tends to be longer (close to 70 minutes) This would make different key times during the day closer or further apart from eachother. Also during the winter, "Sunset" takes much quicker (sometimes only 10 minutes) while in the summer it can take much longer (close to 20 minutes). – avi Dec 15 '11 at 22:39
@msh210, thank you. I am referring to the span of time between Plag and Sheki'ah. – Seth J Dec 15 '11 at 23:02

2 Answers

up vote 5 down vote accepted

The MA holds that we split up the 12 hours of a day from Alot HaShachar (the beginning of day) to Tzeit HaKochavim (the end of the day). The Gra holds that the 12 hours are split from sunrise to sunset independent of what is considered day or night.

All agree that noon must be when the sun is highest in the sky. (This can be proven from the gemara that says they waited for mincha until 6.5 hours because they wanted to make sure by seeing the shadows grow.)

All agree also that Alot HaShachar is at observed dawn (when you can see light in the eastern sky) which is usually 60-90 minutes before sunrise (at normal latitudes).

(Note: from here on I will be using minutes based on Israel's latitude on an equinox. For other locations everything scales accordingly. Additionally, I assume the length of a 'mil' to be 18 minutes (the most conventional opinion). For other opinions just scale accordingly.)

There are two opinions regarding when sunset and tzeit is. To (greatly) summarize, Rabbeinu Tam holds that day ends 58.5 min after sunset, followed by 13.5 minutes of doubt, and then nightfall 72 minutes after sunset. The Gra holds that sunset is the beginning of the doubt period and nightfall is 13.5 minutes later.

So, for the Magen Avraham, to ensure that noon stays in the middle of the day, he must hold of RT's version of nightfall (and that Alot is by definition the equivalent amount of time before sunrise). As such, his plag, which is 90 minutes (1.25 of his 'hours') before nightfall, ends up about 18 minutes before the Gra's sunset. But since he is holding of RT, day for him ends 76.5 minutes later! (By the solstices, MA plag can be between approx 6-30 minutes before Gra's sunset for Jerusalem latitude.)

Since the majority of the world follows Gra times (lechumra and lekula) the website likely didn't even bother to give you the end of RT's day. But it exists!

This explains your issue with the times.

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Good answer. More precise than mine :) – jutky Dec 15 '11 at 23:04
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Can you provide sources, please? – Seth J Dec 15 '11 at 23:06
Per this answer, am I correct in assuming that the aforementioned synagogues are (hopefully) relying on M"A's time for Plag while still relying on the Ḥumrah of the generally accepted time for Sheki'ah in the summertime (candle-lighting still follows the early sunset time but they Daven "early" late, per M"A, in order to give more people a chance to be there)? – Seth J Dec 15 '11 at 23:10
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For anyone else following it's Igrot Moshe OC 4:62 – Double AA♦ Dec 16 '11 at 0:46
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Double AA - Good answer. BTW, where do you get that the time between Alos and sunrise is "by definition" equivalent to the time between sunset and tzais? – Dave Dec 16 '11 at 3:40
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According to MA day lasts from Dawn till Tzeis Hakochavim of R.Tam. It looks like Sunset on MyZmanim is calculated by other shita than R.Tam (maybe GR"A). That's why it looks like Plag Haminha of MA is 2 minutes before sunset.

Here is a source that also states this. In paragraph: השעות הזמניות ודיניהן.

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According to MA, can you daven Mincha any time before Tzeit, as long as you daven Ma'ariv after Tzeit (the way we generally treat sundown)? – Isaac Moses Dec 15 '11 at 22:44
Tzeis and sundown is not the same, and we so not threat sundown as tzeis. I'm not sure I understood you. – jutky Dec 15 '11 at 22:48
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I'm getting at how far he goes with Tzeit being the end of the day. If he would allow Mincha until Tzeit, then the period that matters following Plag would not end up being miniscule. – Isaac Moses Dec 15 '11 at 22:50
I do not know much about the point you mention. It just happened to me to code a site that calculates halahic times for some cities by their geographical position, so I know what formulas to use for calculations of MA times :) . Not more than that. – jutky Dec 15 '11 at 22:56
@IsaacMoses see my answer for more details. I'll just add for you that even though I said for RT that day ends 58.5 min after sunset, he might agree that mincha ends at sunset because it's based on the timing of the korban tamid. – Double AA♦ Dec 15 '11 at 22:57

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