Gemara

(Beraisa - R. Yehudah): A person can walk 40 Mil in a day. He walks four Mil from dawn until sunrise, and four from sunset until Tzeis ha'Kochavim.

Shabbos 34b (Beraisa) Question: When is Bein ha'Shemashos?

Answer #1 (R. Yehudah): It is after sundown, as long as Penei Mizrach (the western sky) is reddish. When the horizon darkens, but not the middle of the sky, it is Bein ha'Shemashos. When the middle of the sky is as dark as the horizon, it is night;

Answer #2 (R. Nechemyah): It lasts the amount of time needed to walk (1000 Amos, i.e.) half a Mil after sunset. After this, it is night;

Answer #3 (R. Yosi): It lasts as long as the blink of an eye (a moment). Immediately after it comes, it is night. One cannot know the exact moment.

Question: R. Yehudah said that as long as Penei Mizrach is reddish, it is Bein ha'Shemashos. This implies that once the horizon darkens, it is night;

He says also that when (only) the horizon is dark, it is Bein ha'Shemashos!

Answer #1 (Rabah): Bein ha'Shemashos lasts as long as Penei Mizrach is reddish, and also when only the horizon is dark;

When the middle of the sky is as dark as the horizon, it is night.

Answer #2 (Rav Yosef): As long as Penei Mizrach is reddish, it is still day. When only the horizon is dark, this is Bein ha'Shemashos. When the middle of the sky is as dark as the horizon, it is night.

(Rabah): Bein ha'Shemashos lasts the time to walk three parts (quarters) of a Mil.

(Rav Yosef): It lasts the time to walk two parts (thirds) of a Mil.

35a (Rav Yehudah): Kohanim may immerse during Bein ha'Shemashos of R. Yehudah (and eat Terumah at night, i.e. it is day).

This is according to R. Yosi;

One might have thought that R. Yosi's Shi'ur is during R. Yehudah's, towards the end. Rav Yehudah teaches that this is not so. It begins after R. Yehudah's Shi'ur ends.

(Rav Yehudah): When (it begins to get dark and) one may see (only) one star it is still day. When two stars are visible, it is Bein ha'Shemashos. When three stars are visible, it is night.

Rishonim

Rambam (Hilchos Shabbos 5:4): From Sheki'ah until three medium stars are seen is called Bein ha'Shemashos. It is Safek day, Safek night. In all cases we are stringent about it.

Rosh (Shabbos 2:23): We cannot say that R. Yosi's Bein ha'Shemashos is right after R. Yehudah's Bein ha'Shemashos ends. Why would we need to rule like R. Yehudah, just to obligate waiting another eye's blink?! It cannot be long after it, for Shmuel taught that R. Yosi permits Kohanim to immerse during R. Yehudah's Bein ha'Shemashos. This implies that they may not immerse after it! Rather, the Amora'im were unsure whether it is right after, or long after. Alternatively, they knew the Shi'ur. Shmuel did not teach that R. Yosi permits Tevilah after R. Yehudah's Bein ha'Shemashos, for there is not enough time to immerse afterwards before night. A Tosefta (Zavim 1:1) connotes that the time to immerse is the time to walk 50 Amos (about 25 seconds). Presumably, we try to make the opinions as close as possible (R. Yosi's Shi'ur is right after R. Yehudah's).

Ran (Shabbos 15a DH Amar): R. Tam says that there are two Shki'os. Our Sugya discusses the end of Sheki'ah, when it sets in the Raki'a (firmament), but it is still even with the window (through which it passes). Therefore, the Raki'a is still red opposite where the sun is. Pesachim discusses the beginning of Sheki'ah. There are three quarters of a Mil between the two Shki'os. The Yerushalmi says so.

Beis Yosef (DH u'Mah): Also the Magid Mishneh said so in the name of R. Tam. The Ramban agreed. The Rashba challenged this from the Yerushalmi and left it difficult. It seems that the Rosh was unsure about this, therefore he omitted this, and so did the Tur. However, in Ta'anis (1:12) he brought R. Tam. This shows that he holds like R. Tam. Why did the Tur omit this?

Tosfos (35a DH Trei): Our Gemara connotes that from sunset until Tzeis ha'Kochavim, i.e night, is only three quarters of a Mil. R. Yehudah himself says that from sunset until Tzeis ha'Kochavim is four Mil! R. Tam explains that it is four Mil from the beginning of Sheki'ah, after the sun enters the thickness of the firmament. The Ri asked what the Tana'im argue about. Tzeis ha'Kochavim is night! He answered that R. Yehudah is unsure about all stars visible from Sheki'ah until the top of the sky is dark. Perhaps they are medium.

Poskim

Shulchan Aruch (OC 261:2): The Tosefes (addition to Shabbos) must be sometime between the beginning of Sheki'ah, when the sun goes below the horizon, until Bein ha'Shemashos, which begins three Mil and a quarter later.

Gra (DH she'Hu): The Shulchan Aruch is like Tosfos. This is wrong. If so, we would need to say that from dawn to sunrise equals from sunset to Tzeis ha'Kochavim. Anyone can easily see for himself that from dawn to sunrise is much longer than from sunset to Tzeis ha'Kochavim. In northern countries, in summer dawn begins at midnight. If so, there is no Tzeis ha'Kochavim!

Note: Indeed, above the arctic circle, there are days when the sun does not set at all! Even when it sets for a few minutes, surely there is no Tzeis ha'Kochavim! Where the sun sets for two or three hours, dawn can begin at midnight (the midpoint between sunset and sunrise). If from dawn to sunrise equals from sunset to Tzeis ha'Kochavim, also Tzeis ha'Kochavim is at midnight, i.e. dawn. It is even more absurd where dawn is before midnight, for then Tzeis ha'Kochavim is after midnight, i.e. after dawn.

Gra: Rather, Bein ha'Shemashos begins immediately at Sheki'ah, until the bottom horizon darkens, which is three quarters of a Mil in Bavel in Nisan or Tishrei. Whenever the Gemara discusses Sheki'ah, it is the beginning of Sheki'ah, e.g. 'a fast that did not last until Sheki'ah...' Shabbos 35b says that Tzeis ha'Kochavim is when three medium-size stars can be seen. In Pesachim, the Gemara discusses 'Tzeis ha'Kochavim', i.e. when it is totally dark and even the weakest stars can be seen. This is four Mil after sundown. We find that blood is disqualified at Sheki'ah (for after this it is Safek night). They cursed people who pray with (i.e. when are seen) the last rays of the sun (lest they miss praying during the day). According to Tosfos, this is long before night! Beis Hillel permit several Melachos 'with the sun' (just before it sets).

Gra: Sefer Yere'im (61) says that three medium stars appear five Mil after Sheki'ah, like R. Tam. This is wrong. If so, it is long after when the top of the sky is dark. The Gemara says that R. Yosi's Bein ha'Shemashos is right after R. Yehudah's. There is not even time to immerse in between! R. Yosi says that after one star it is still day, and after three it is night. The Mordechai (Berachos 78) brings that Rav Hai Gaon permits praying Ma'ariv (right) after Sheki'ah. Tosfos asked that the stringency of waiting for R. Yosi's Bein ha'Shemashos after R. Yehudah's is insignificant. He and the Rosh did not give a proper answer. I think that there is a printing mistake. It should say 'Kohanim may eat Terumah immediately after R. Yehudah's Bein ha'Shemashos', for it says "u'Va ha'Shemesh v'Taher."

Damesek Eliezer: I.e. they may eat Bein ha'Shemashos. R. Yehudah permits them during his Bein ha'Shemashos, and R. Yosi permits them only after R. Yehudah's Bein ha'Shemashos.

Gra: There are three Shki'os. The beginning of Sheki'ah begins R. Yehudah's Bein ha'Shemashos. The second is the end of the sun's redness. Then, the Nitzutzei (sparks) set. This is R. Yosi's Bein ha'Shemashos, immediately after R. Yehudah's. Tzeis ha'Kochavim comes immediately. R. Yosi taught the laws of one, two and three stars. They come in rapid succession, therefore it says 'like an eye's wink.' In Berachos we say that Kohanim eat at Tzeis ha'Kochavim. This is like R. Yosi. The Gemara asked whether they eat after Bi'as Shimsho or Bi'as Oro. The latter is the third Sheki'ah, which Pesachim discusses, which is four Mil after Sheki'ah, when all stars are visible.

Mishnah Berurah (20): R. Tam holds that the first Sheki'ah (its beginning) is when the sun cannot be seen. The next three and a quarter Mil it is still day. Then begins the second (end of) Sheki'ah. Then, the light totally sets. It last three quarters of a Mil. This is Bein ha'Shemashos. Then three medium stars come out, which show that it is night. Many disagree and say that once the sun cannot be seen, it is Bein ha'Shemashos, which is Safek night.

Bi'ur Halachah (DH mi'Tchilas): We find the Gra's opinion already in Maharam Alshakar (96), Rav Shrirah Gaon, Rav Hai Gaon, R. Nisim Ga'on, and the Rambam's son says that the Rif, Rambam and Rashi hold like this. The Shach (YD 261:11) brought this. The Mordechai any many others rules like this. We must be stringent like this for all Torah laws.

Kaf ha'Chayim (1): Ginas Veradim says that in all places people follow the Ge'onim. The Birkei Yosef says that even if you will say that it is an even argument, we follow the custom. One who wants to be stringent like R. Tam (on Motza'ei Shabbos) will be blessed, but we do not protest against one who is lenient.