Gemara

Question: Does the 50th year count as part of this Yovel, or as part of the next?

Answer (Beraisa): "You will sanctify the 50th year" - it is counted like the 50th year, but not also like the first year of the coming Shemitah cycle;

R. Yehudah says, it also counts like the first year of the coming Shemitah.

Avodah Zarah 9b (Rav Huna brei d'Rav Yehoshua): If you do not know the year of the Shemitah cycle, add one year, calculate the centuries according to Yovelos, and the remaining years according to Shemitos;

Count each century like two years (it contains 14 full Shemitah cycles and two extra years). Add this to the remaining years, and take the remainder after dividing by seven (for these are full cycles). A Siman (way to remember this) is "Zeh Shenasayim ha'Ra'av b'Kerev ha'Aretz."

Erchin12a (Beraisa #1 - R. Yosi): The first Churban was in Motza'ei Shemitah.

Question: "B'Esrim v'Chamesh Shanah l'Galuseinu b'Rosh Hashanah be'Asor la'Chodesh b'Arba Esreh Shanah Achar Asher Huksah ha'Ir" refers to Yovel, when the 10th (Yom Kipur) is like Rosh Hashanah. This 25th year from Galuseinu (when Yechezkel was exiled with 1000 Chachamim, 11 years before the Churban) was 14 years after the Churban.

(Yovel is always Motza'ei Shemitah.) If the Churban was in Motza'ei Shemitah, also the eighth and 15th years from the Churban were Motza'ei Shemitah. We proved from the verse that the 14th year was Yovel!

Answer (Ravina): It was the 14th year after (excluding the year of) the Churban.

(Beraisa #2): The same applies to the second Churban.

Question: The second Churban was not in Motza'ei Shemitah!

Bayis Sheni stood 420 years. Eight Yovel cycles span 400 years (each is 50 years), leaving 20 years, i.e. two complete Shemitah cycles and six years!

Answer #1: Beraisa #2 is R. Yehudah, who says that year 50 (Yovel) also counts as the first year of the next Yovel (each cycle is 49 years). Therefore, we must add eight years to the above calculation (each Yovel cycle has one year less). Bayis Sheni stood 28 years (four complete Shemitos) into the ninth Yovel. The Churban was the next year, i.e. Motza'ei Shemitah.

Question: Beraisa #2 cannot be R. Yehudah. According to him, the first Churban was not in Motza'ei Shemitah!

(Beraisa): Yisrael counted 17 Yovelos from entering Eretz Yisrael until the Churban. (Bayis Rishon was built 440 years after entering, and it stood 410 years).

We cannot say that they began counting Yovel immediately upon entering, for then the Churban would have been in the first year of Yovel (850 years are 17 full cycles). Rather, they began counting after seven years of conquest and seven of division. Therefore, Yovel was 14 years after the Churban.

According to R. Yehudah, 49 years comprise Yovel. There are seventeen extra years, so Yovel would have been three years before the Churban!

Answer: We did not count Yovel from Galus of the 10 tribes until Yirmeyahu returned them. (A new cycle began then, 36 years before the Churban.)

Answer #2 (to Question (9)): Really, the Beraisa is Chachamim. "The same applies to the second Churban" refers to other matters. (It was on Tish'ah b'Av and on Motza'ei Shabbos, but it was not in Motza'ei Shemitah.)

Answer #3 (Rav Ashi): We did not start to count the Yovel cycle until Ezra came from Bavel in the sixth year of Bayis Sheni:

Rishonim

Rambam (Hilchos Shemitah 10:6): The Ge'onim and people of Eretz Yisrael count Shemitos every seven years. This year, 1107 years after the Churban, is Motza'ei Shemitah.

Rosh (Avodah Zarah 1:7): Rav Huna brei d'Rav Yehoshua is Basra. Since he rules like R. Yehudah, this shows that the Halachah follows him, even though elsewhere we expound unlike R. Yehudah. Rashi (9b DH Natfi) says that the Churban was in Motza'ei Shemitah. One who counts from the Churban does not include the year of the Churban. He includes it with the years that the Mikdash stood, for most of the year passed before the Churban (on Tish'ah b'Av). Therefore, one must add a year to get the current year of Shemitah. According to this, the year 5073 was Shemitah.

Rosh and Tosfos (Avodah Zarah 9b DH Hai): Erchin 12b implies that the Churban was in year 421! According to Chachamim we needed to say that they started counting after Ezra came, but not according to R. Yehudah (he holds that the Churban was in year 29)! Rashi himself retracted in Erchin. We must add a year because the Tana counts year 421 with the years that the Mikdash stood.

Question (Rosh and Tosfos): R. Chanina said that Moshi'ach will come 400 years after the Churban. A Beraisa said that he will come in the year 4231. The Gemara said that these are three years apart. If the Churban was in year 421 (3829) they would be only two years apart! Throughout Shas, including the calculation of Shemitah nowadays, we say that Bayis Sheni stood only 420 years! Also, if so the year 4000 was 172 years after the Churban, not 171!

Pilpulei Charifta (40): Rashi said that Seder Olam says that it was 172 years later. (Tosfos says that 'everyone says so.')

Answer #1 (Rosh): Really, the Churban was in year 420. We answered for R. Yehudah that the Churban was in year 421 only before Rav Ashi said that they began to count when Ezra came. According to R. Yehudah, the Churban was in year 22. The Halachah follows R. Yehudah and Rav Ashi.

Answer #2 (Drishah CM 67:9): The Ri can say that Bayis Sheni stood 420 full years. We count 172 years from the Churban until 4000 because part of a year (from Tish'ah b'Av until the end of Elul) is like a full year.

Question (Tosfos): According to Rashi, the Siman teaches only that we follow R. Yehudah. It should teach how many years to add or subtract!

Answer (R. Tam): The Siman teaches to deduct two years or add five, like the Seifa "v'Od Chamesh Shanim..." We count from when Yavan began to rule the world, in year 41 of Bayis Sheni. Their third year was (year 43, i.e.) Shemitah according to R. Yehudah, therefore we must deduct two. The year 5011 or 5012 was Shemitah, depending on whether the Churban was in year 420 or 421.

Poskim

Shulchan Aruch (YD 331:19): The true Shemitah year was 5313.

Beis Yosef (CM 67 DH uv'Cheshbon): According to the Ri and Rambam, 5313 was Shemitah. This is the practice in Mitzrayim and Eretz Yisrael.

Tur: According to the Ri, Shemitah was the year 5088. According to Rashi, it was 5089. Rashi's opinion is primary.

Beis Yosef (DH u'Shemitah): This is a mistake. The correct version is like the Tur in Choshen Mishpat (67), that according to Rashi it was 5087, like the Rosh said in Avodah Zarah (that 5073 was Shemitah). Alternatively, there the Tur counts from Adam ha'Rishon's first year, and here he counts from the previous year (Tohu), and the opinions of the Ri and Rashi became switched.

Note: Even though the Shulchan Aruch says that 5313 (i.e. and hence also 5089) was Shemitah (also Tosfos says that Shemitah was 5088 or 5099), he prefers to say that the Tur counts like the Rosh and says 5087 or 5088.

Rema (CM 67:1): There is an argument about the Shemitah year. The primary opinion says that 5327 (i.e. and hence also 5089) was Shemitah