When is צאת הכוכבים?

Yesterday's and today's daf (Shabbos 34-35) discuss this issue. Most of what I write here is based on R' Willig's piece in his sefer on berachos עם מרדכי.

There is a famous machlokes R' Tam and the Geonim. In Shabbos (34) R' Yehuda says that from suntil until צאת הכוכבים is 3/4 of a mil (we will define how long a mil is later). The gemara in Pesachim (94) states that according to R' Yehuda there are 4 mil from sunset until צאת הכוכבים. R' Tam (and many Rishonim such as the Ramban, Rashba and the Shulchan Aruch and the Rama) explain as follows. There are 2 shkia's, from sunset until 3.25 mil after sunset it is day then there is 3/4 of a mil bein hashmoshos (safek day safek night) and then night. The Geonim hold that bein hashmoshos starts right away after sunset and night is 3/4 of a mil later. The Gra popularized this shita and explained that the Gemara in pesachim is talking about when all the stars come out. The Gra's main proof against R' Tam is החוש מכחיש, R' Tam is against reality. well before 4 mil after sunset it is pitch black outside and you can see hundreds of stars.

There are 2 other related disputes.

1. How do we count the hours of the day? The halacha always divides the day into 12 equal hours, do we count from sunrise until sunset or from alos hashachar until צאת הכוכבים?
It would seem that is dependent on the machlokes R' Tam and the Geonim. According to the Geonim it makes no sense to count from alos until צאת הכוכבים the day wouldn't be balanced, and since the day ends at sunset it makes sense to count until sunset. According to R' Tam it makes little sense to count only until sunset, it is still day for another hour. In addition the Rishonim say explicitly that Plag Hamincha (10.75) is an 1.25 hours before צאת הכוכבים

2. How long is a mil? The gemara in Pesachim says that a person walks 40 mil in a day. If you divide 720 by 40 you get 18. Others hold that it is 22.5.
R' Willig brings a very strong proof that R' Tam holds 22.5 based on the fact that the Rishonim (Ramban, Rashba and others) state that Plag Hamincha is 1/6 of a mil before sunset. If you do the math the only it works out is if a mil is 22.5 minutes.

R' Moshe claims that even according to R' Tam after 50 minutes it is definately night in NY because it is pitch black. However, this is very difficult. This was exactly the Gra's question on R' Tam, that it is against reality. The fact is that R' Tam says 4 mil which is at least 72 minutes, according to R' Moshe there is no such case.

The simple understanding is that the times given are for Israel at the equinox, during the year and in other places the times will change. We see this from the fact that the gemara also gave astronomical signs, these clearly change from place to place and season to season. Therefore in any place further from the equator then Israel bein hashmeshos will be longer.

R' Willig concludes that holding 72 minutes is NY is meaningless for the following reasons:
1. R' Tam would seem to hold that a mil is 22.5 minutes (4 mil = 90 minutes)
2. Whatever the shiur of a mil is, NY is further from the equator then Israel and therefore bein hashmeshos will be longer so even if a mil is 18 minutes that is only in israel at the equinox in NY it is longer.

R' Tam's shita has always really bothered me. The Gra's question of החוש מכחיש is so powerful and obvious I don't understand how the Rishonim could have said what they said. Did they never go outside an hour after sunset and see that it was pitch black and you could see hundreds of stars?

In any case we see a very important point from this Gra, החוש מכחיש (reality contradicts) is a good question. Torah has to correspond to reality, if it doesn't we are misunderstanding the Torah.