1. Descriptions in historical records that can be used to estimate the date of Troy's fall
(1) During the reign of Menestheus, the son of Peteus, Troy was captured. [Euseb.Chron.185]
(2) During the reign of Demophon, son of Theseus, an expedition led by Diomedes, son of Tydeus, returned from Troy after the fall. [Paus.1.28.9]
(3) Troy was taken, in the first year of the reign of Demophon the son of Theseus at Athens, on the twelfth day of the month Thargelion. [Cleme.Str.1.21]
(4) Troy was taken, in the 24th of the month Thargelion. [FGrH.5.7, Plut.Camill.19]
From the above descriptions, it is inferred that the fall of Troy was the last year of the reign of Menestheus, son of Peteus, and the year Demophon, son of Theseus, ascended to the throne as King of Athens.
2. The year of enthronement of Demophon
The chronicler of the first century BC, Castor of Rhodes, tells of the reigns of successive Athenian kings and notes that in the 12th year reign of the 29th Athenian king Aeschylus, the first Olympiad was held in which Coroebus won the footrace. [Euseb.Chron.187]
The first Olympiad in which Coroebus of Eris won the footrace is known to have been in 776 BC, and the year of Aeschylus's ascension is 787 BC. [Paus.5.8.6]
Counting backward from Aeschylus according to the reigns of successive Athenians kings, Demophon, the 12th king of Athens, ascended to the throne in 1186 BC.
3. The day of Troy's fall
As for the "month" in which Troy fell, it is the month of Thargelion, which is consistent with each historical sources, but not the "day."
The writers of the Attica region notes that the day Troy fell "was a full moon," and the author of the Little Iliad reports that "the moon shone clearly." [Cleme.Str.1.21]
It is known that there was an eclipse on April 16, 1178 BC, indicating that the day was a new moon, according to the list of historical eclipses on NASA and other websites.
[Odyssey Eclipse - https://eclipse.gsfc.nasa.gov/SEhistory/SEhistory.html]
If, retroactively from this date, the full moon of the Thargelion month, which is May to June according to the current calendar, is calculated as the moon phase cycle of 29.53 days, it is as follows.
The 15th day from BC1178.4.16(new moon) is BC1178.5.1(full moon).
Intercalary year (BC1180, 1184) BC1178.5.1 - BC1186.6.1(8 * 365 + 2 - 31 = 2,891 days)
2,891 / 29.53 = 97.90044 ----- 29.53 * 98 = 2893.94 = 2894 = BC1186.5.29
Based on the above, it is estimated that the fall of Troy occurred on May 29, 1186 BC.
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