The discussion and sources enumerated below is in no way intended to be exhaustive. This is a brief treatment of the profound subject matter.
Sources for 3 Stars and Earliest Talis Times
Mathematical definitions for the times of צאת ג' כוכבים and זמן ציצית ותפילין are not given by the Gemara
and early Poskim
Many different minhagim
In the tables below, we will list some of these minhagim
together with supporting sources.
Each table concludes with a range during which the times occur.
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
Let's now analyze one definition from the list below:
York and New Jersey, Motzoei Shabbos is never later than 50 minutes
past Shekiah. (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.
Okay, that's great for New York, but what does that have to do with everywhere else
The time for מוצאי שבת in any location, can be found by determining when the degree of darkness in the given location matches the degree of darkness 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 present 43 minutes
past שקיעה in ירושלים
is equivalent to the degree of darkness 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 in a level region
To illustrate, according to ר' יחיאל מיכל טוקצינסקי זצ״ל:
Three כוכבים קטנים emerge no later than 40 minutes past שקיעה.
It is evident from his לוח, that the שקיעה-times to which ר' טוקצינסקי refers, are approximately 3 minutes later than the times
for שקיעה in a level region. As such, the above definition can be restated as: Three כוכבים קטנים emerge no later than 43 minutes past שקיעה in a level region
* 3 minutes were added to compensate for the fact that the
שקיעה times (for ירושלים) printed in ר' טוקצינסקי-'s luach, are approximately 3 minutes later than the times for "level-region שקיעה".
Definitions provided by other Poskim may also be subject to a similar translating.