Gemara

(Ula): It is 15 Mil (a Mil is 2000 Amos, about a kilometer) from Modi'im to Yerushalayim. One cannot walk this distance in half a day;

(Rabah bar bar Chanah): An average person can walk 40 Mil in a day. He walks five Mil from dawn until sunrise, and five from sunset until Tzeis ha'Kochavim. He walks 30 Mil from sunrise to sunset, 15 in the morning and 15 in the afternoon.

94a (Rava): The world (the sun's trajectory during the day) is 6000 Parsah. The thickness of the Raki'a (a thick dome; through which the sun passes between dawn until sunrise, and between sunset and Tzeis ha'Kochavim) is 1000 Parsah.

He holds like Rabah bar bar Chanah. From dawn until sunrise is one sixth of the length of a day.

Question (Beraisa - R. Yehudah): The thickness of the Raki'a is a tenth of the day (from dawn until Tzeis):

A person walks 40 Mil in a day, and he walks four Mil from dawn until sunrise, and four from sunset until Tzeis.

Rava is refuted. (The Beraisa holds that the Raki'a is an eighth of the day from sunrise until sunset, in which time a person walks 32 Mil);

Ula is refuted. (He holds that one walks five Mil from dawn until sunrise.)

R. Yochanan is not refuted. He said only that a person walks 40 Mil in a day. Ula and Rava said that five Mil are from dawn to sunrise

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.

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

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.

(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: Rava saw Abaye looking east.

Rava: 'Penei Mizrach Ma'adimin' means the direction whose rays redden the east, i.e. the west.

(R. Yochanan): The Halachah follows R. Yehudah regarding Shabbos, and R. Yosi regarding Terumah.

Rishonim

Rambam (Hilchos Shabbos 5:4): From Sheki'ah until three medium stars are seen is called Bein ha'Shemashos. These are not big stars seen during the day, or small stars seen only at night. Rather, they are medium stars.

Rosh (Shabbos 2:23): If an individual accepted to fast, Bein ha'Shemashos is permitted. We do not permit until it darkens below, i.e. Bein ha'Shemashos of Rav Yosef.

Gra (OC 261 DH she'Hu): The Rosh is difficult. We must follow R. Yosi regarding fasts, since the Halachah was fixed like him to be stringent!

Tosfos (35a DH Trei): Why can't we simply measure how long it takes an average person to walk four Mil? We are unsure who is called average.

Poskim

Shulchan Aruch (OC 261:2): The beginning of Sheki'ah is when the sun goes below the horizon, until Bein ha'Shemashos, which begins three Mil and a quarter later. The Shi'ur of Bein ha'Shemashos is three quarters of a Mil, i.e. the time for a person to walk 1500 Amos, before night.

Gra: Bein ha'Shemashos starts immediately after sundown. After three quarters of a Mil it is night (in Bavel in Nisan or Tishrei). 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. This is the same time between dawn and sunrise, for it is the thickness of the Raki'a. Whenever the Gemara mentions Tzeis ha'Kochavim, it is when three medium stars are visible. This needs great proficiency (to know that they are medium stars), therefore they gave a Siman 'when it gets dark...' The Shi'ur of four Mil is not the same in all times and places. It is only three quarters of a Mil from Sheki'ah until night, i.e. in a flat place in Bavel and Eretz Yisrael in Nisan or Tishrei. It is more in our lands.

Gra: One may eat (after a fast) immediately after Sheki'ah, for we are lenient about the Safek. The custom is to wait until Tzeis ha'Kochavim, for it is a Safek whether the Halachah follows R. Yehudah or R. Yosi. R. Yosi's Bein ha'Shemashos is after the horizon darkens, i.e. after R. Yehudah's Bein ha'Shemashos finished. Even though we are lenient about the Safek for fasts, the Halachah follows R. Yosi regarding Terumah. We do not adopt two leniencies, i.e. to permit Bein ha'Shemashos and to adopt R. Yehudah's Bein ha'Shemashos.

Mishnah Berurah (23): One may not end Shabbos until three medium stars are visible. Three quarters of a Mil after sundown suffice for the latitude of Bavel in Nisan or Tishrei. In northern lands one must wait much longer.

Kaf ha'Chayim (1): Ginas Veradim says that in all places people follow the Ge'onim. On Motza'ei Shabbos they wait the time to walk two or three Mil, and then light. Our custom is that for matters that require night, e.g. Motza'ei Shabbos or eating Matzah on Pesach, we wait until three medium stars are seen. This is different in different places. In Eretz Yisrael, Surya and Bavel, it is about 40 minutes after sunset.

Bi'ur Halachah (DH she'Hu): The Pri Megadim says that the four Mil are fixed (do not depend on the length of the day). Minchas Kohen says that even according to R. Tam, they are relative, and they are longer in summer. The Gemara discussed only Nisan or Tishrei, when the days and nights are equal. (He concludes to be stringent based on this, but not to be lenient.) The Magen Avraham connotes like him. The Gra holds like him, and says that it depends also on the place. Even according to the Ge'onim, one may not do Melachah on Motza'ei Shabbos until three medium stars are seen. We require small stars, for we are unsure what is called medium. L'Chatchilah one should fulfill R. Tam's opinion for Melachah on Motza'ei Shabbos. If the top of the sky is as dark as the horizon, i.e. there is no redness in the west, and there are three stars, even R. Tam does not require relative hours on long days. Abaye looked to see if it darkened. It seems that he relied on this alone. We are not as expert as they were, but together with three stars, we need not be more stringent. Four Mil is merely one Siman. We are not sure how it varies with the season and place, so we do not use it to say that we erred about the other two Simanim.

Bi'ur Halachah (DH v'Shi'ur): For something for which we are lenient Bein ha'Shemashos and assume that it is night, e.g. an individual's fast, the Rosh and Rashba citing R. Yonah connote that we are lenient even during R. Yehudah's Bein ha'Shemashos. If so, for Sefiras ha'Omer, according to those who are lenient Bein ha'Shemashos (489:2,3), one may count even in R. Yehudah's Bein ha'Shemashos. The same applies to Shevus for the sake of a Mitzvah, which we permit (342:1). According to the Acharonim who permit even on Motza'ei Shabbos, it is permitted even in R. Yehudah's Bein ha'Shemashos, even though R. Yosi holds that it is Vadai day. However, the Gra and Korban Nesan'el challenged the Rosh, who is lenient about fasts, because we hold like R. Yosi to be stringent! He holds that it is not even Safek night before his Bein ha'Shemashos. We do not give two leniencies, i.e. to permit Bein ha'Shemashos and to rule like R. Yehudah, for also this (whom the Halachah follows) is a Safek. If so, perhaps we are stringent about Shevus on Motza'ei Shabbos or Sefiras ha'Omer, since according to R. Yosi it is not a Safek.