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There are a few halachot from Rambam Hilchot Shmitah v'Yovel chapter 10 that are relevant to the chronology.
(Translation and division of halachot is according to this page)
2. We see from this that in the year 2503 from the Rosh Hashanah after the birth of Adam HaRishon, which is the 2nd year of creation, they began to count. And they did the year 2510 from creation, which is the 21st year from the time they entered Eretz Yisrael, Shmitah. And they counted 7 Shmitah years and sanctified the 50th year, which was the 64th year from the time they entered Eretz Yisrael.
3. Am Yisrael counted 17 Yovels, from the time they entered Eretz Yisrael to the time they left, and the year they left, in which the 1st Beit HaMikdash was destroyed, was the year after Shmitah, and year 36 of the Yovel, for the 1st Beit HaMikdash stood 410 years.
4. And due to the destruction of the Beit HaMikdash, this count ceased, for the land was nullified. And the land remained destroyed, 70 years; and the 2nd Beit HaMikdash was built, and stood 420 years. And in the 7th year from its construction, Ezra came up to Eretz Yisrael, and that is the Bi'ah Shniyah, and from this year a new count began. And they made the 13th year of the 2nd Beit HaMikdash Shmitah, and they counted 7 Shmitah years and sanctified the 50th year, even though there was no Yovel during the time of the 2nd Beit HaMikdash, they would count it in order to sanctify the Shmitah years.
5. We see from this that the year that the 2nd Beit HaMikdash was destroyed, whose start is from Tishrei after the destruction by 2 months, for it is from Tishrei that we count Shmitah and Yovel, that year was the year after Shmitah, and year 15 of the 9th Yovel.
6. And according to this calculation, this year, which is 1107 of the Destruction, which is 1487 to the count of Shtarot, which is 4936 to Creation, is a Shmitah year, and it is year 21 from the Yovel.
7. However, all of the Geonim said that it is a tradition in their hands, from one generation to the next, that they only counted Shmitah during the 70 years between the Destruction of the 1st Beit HaMikdash and the Building of the 2nd Beit HaMikdash, without Yovel, and thus it is since it was destroyed this last time, we don't count the 50th year, but rather just every 7 years alone, from the the beginning of the year of the Destruction. And thus is the conclusion from the Talmud Avodah Zarah, according to this calculation, which is a tradition.
8. And the year of Shmitah is well known by the Geonim and the people of Eretz Yisrael, and all of them counted only from the years of the Destruction, and removing the remainders of 7. And according to this calculation, this year which is 1107 to the Destruction, is the year after Shmitah. And this is what we rely on, and according to this calculation we teach for the matter of Maaser, and Shmitah, and Shmitat Kesafim, for the tradition and the deed are great pillars for instruction, and upon them it is proper to depend.