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PLEASE DO NOT MAKE ANY HALACHIC DECISIONS BASED ON THIS TEXT WITHOUT CONSULTING A QUALIFIED RAV
The following list of sources is in no way intended to be exhaustive. This is a brief treatment of the profound subject matter.

Introduction
Mathematical definitions for the times of צאת ג' כוכבים and זמן ציצית ותפילין have not been given by the Gemara and early Poskim. Many different minhagim exist. In the tables below, we list some of these minhagim, together with some of the many sources supporting them. Each table concludes with an outline of the ranges for the times returned by the Zmanim server.

It is well known that the length of בין השמשות varies from place to place and from season to season (see Computation by Degrees Explained). To facilitate comparison, we have (where possible) presented the definitions in a common form: in terms of the latest time of occurrence for a particular location.

Explanation
Let's now analyze one definition from the list below:

    In New York and New Jersey, Motzoei Shabbos is never later than 50 minutes past Shkio. (Igros Moshe)

 Although the length of בין השמשות varies throughout the year, the time for מוצאי שבת (in New York and New Jersey) will never exceed 50 minutes past שקיעה. So during the month of June (when בין השמשות is longest), מוצאי שבת will be 50 minutes past שקיעה. However, during the months of March and September (when בין השמשות is shortest), מוצאי שבת will get as early as 40 minutes past שקיעה. That is, the degree of darkness that is present 40 minutes past שקיעה, on a mid-March or late-September day, is equivalent to the degree of darkness that is present 50 minutes past שקיעה, on a mid-June day.

Q: Okay, that's great for New York, but what does that have to do with everywhere else?
A: The time for מוצאי שבת in any other location, can be found by determining the time at which the degree of darkness in the given location matches the degree of darkness that is present 50 minutes past שקיעה on a summer day in New York. For example, let us consider ירושלים. Using standard astronomical calculations, it can be shown that on a summer day, the degree of darkness that is present 43 minutes past שקיעה in ירושלים is equivalent to the degree of darkness that is present 50 minutes past שקיעה in New York. We can therefore conclude that during the summer, מוצאי שבת in ירושלים is approximately 43 minutes past שקיעה. Interestingly enough, that's exactly what emerges according to
ספר בין השמשות (see table below).

Accounting for Elevation
שקיעה-times in ירושלים are delayed several minutes because of the elevation factor. Therefore, when we see the Poskim using שקיעה as a "landmark" for defining צאת הכוכבים in ירושלים, we must bear in mind that the שקיעה-times to which they refer, may be a few minutes later than שקיעה-times at sea level.

To illustrate, according to ר' יחיאל מיכל טוקצינסקי זצ״ל: Three "smaller stars" emerge no later than 40 minutes past Shkio. It is evident from his Luach, that the שקיעה-times to which ר' טוקצינסקי refers, are 2 to 3 minutes later than the times for שקיעה at sea level. As such, an equivalent of the above definition can be stated as follows: Three smaller stars emerge no later than 42/43 minutes past Shkio at sea level.

מוצאי שבת - צאת ג' כוכבים
In ירושלים, the time of ג' כוכבים קטנים is never later than 43* minutes past שקיעה.ספר בין השמשות
מאת ר' יחיאל מיכל
טוקצינסקי זצ״ל
In ירושלים, the time of ג' כוכבים קטנים is never later than 40 minutes past שקיעה.ספר נברשנת
מאת ר' דוד שפיטצער
In "ארץ ישראל וסוריא וארץ שנער", the time of
לילה ודאי לענין מו"ש ויוה"כ is never later than
40 minutes past שקיעה.		כף החיים
In New York and New Jersey, מוצאי שבת is never later than 50 minutes past שקיעה. אגרות משה
In ירושלים: The time for "8.5 Degrees" varies between 36 and 43 minutes past "שקיעה at sea level".
In New York City: It varies between 40 and 51 minutes past שקיעה.		MyZmanim.com
What We Print
8.5 Degrees


סוף זמן הצומות שהן מדרבנן - צאת ג' כוכבים בינונים
In ירושלים, the time of ג' כוכבים בינונים is never later than 31* minutes past שקיעה.ספר בין השמשות
מאת ר' יחיאל מיכל
טוקצינסקי זצ״ל
In ירושלים, the time of ג' כוכבים בינונים is never later than 28 minutes past שקיעה.ספר נברשנת
מאת ר' דוד שפיטצער
סוף ביה"ש לענין מילה is 25 minutes past שקיעהשמירת שבת כהלכתה
בשם ר' שלמה זלמן אויערבך זצ״ל
In New York,
"גמר תעניות דרבנן למי שקשה לפניו להתענות"
is never later than 41 minutes past שקיעה. 		אגרות משה
In ירושלים: The time for "6.45 Degrees" varies between 26 and 31 minutes past
"שקיעה at sea level".
In New York City: It varies between 29 and 37 minutes past שקיעה.

In ירושלים: The time for "7.12 Degrees" varies between 29 and 35 minutes past
"שקיעה at sea level".
In New York City: It varies between 33 and 41 minutes past שקיעה.

 MyZmanim.com
What We Print
6.45° and 7.12°

6.45° - מנהג ארץ ישראל
(כהוראת רא״י זילבר)

7.12° - ר' משה פיינשטיין


זמן ציצית ותפילין
In ירושלים, the time of משיכיר is 60 minutes before הנץ.כף החיים
In ארץ ישראל, the time of
"זמן עטיפת הטלית וזמן הנחת תפילין"
is 60 minutes before הנץ.		ספר ארץ ישראל
מאת ר' יחיאל מיכל
טוקצינסקי זצ״ל
In ירושלים, the time of משיכיר is never later than 52 minutes before הנץ.ספר נברשנת
מאת ר' דוד שפיטצער
In ירושלים, the time of "זמן הנחת טלית ותפילין" is 52 minutes before הנץ. However, לכתחילה one should be מחמיר to wait until 42 minutes before הנץ. ספר בית ברוך
מאת ר' בנימין יהושע זילבר
In ירושלים: The time for "10.2 Degrees" varies between 44 and 52 minutes before הנץ.
In New York City: It varies between 49 and 63 minutes before הנץ.

In ירושלים: The time for "11.5 Degrees" varies between 50 and 60 minutes before הנץ.
In New York City: It varies between 56 and 73 minutes before הנץ. 		MyZmanim.com
What We Print
11.5°, 11° and 10.2°

10.2° - קובץ אוצרות ירושלים 11.0° - הוראת ר' מאיר פוזנא 11.5° - מנהג ארץ ישראל

* 3 minutes have been added to compensate for the fact that the שקיעה times (for ירושלים) printed in ר' טוקצינסקי-'s luach, are 2 to 3 minutes later than the times for "sea level שקיעה". Definitions provided by other Poskim may also be subject to a similar translating.


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