What the text says. Acts marks the turn of the voyage with a calendar note: "And when much time was spent, and the voyage was now dangerous, because the Fast was now already gone by, Paul admonished them" (Acts 27:9, ASV). "The Fast" with no further explanation is the Day of Atonement, the one commanded fast of the year, "the tenth day of this seventh month" (Leviticus 23:27; compare Leviticus 16:29 and Numbers 29:7), which in the Jewish lunar calendar falls in late September or early October.
Why that date is a warning. The ancient Mediterranean had a sailing season, and it was closing. The 1915 ISBE, summarising ancient practice, states it plainly: "The season for navigation in those seas in ancient times was from April to October. During the winter the vessels were laid up, or remained in the shelter of some suitable haven." And it gives the reason, which is not only the weather: "The reason for this was not simply the tempestuous character of the weather, but the obscuration of the heavens which prevented observations being taken for the steering of the ship", a ship navigating by sun and stars is blind under continuous overcast. Luke's clause is therefore doing real work: by saying the Fast had passed he has told a first-century reader that the ship was sailing into the closing window, which is exactly what the following narrative describes. ⚠️ The dating is Luke's own and is not disputed; what an individual master counted as too late varied, and ancient writers give somewhat different limits for when the sea was reckoned shut.
What the day itself was. It was the one day of national fasting and the only day the high priest entered the innermost room of the sanctuary. The Mishnah devotes the tractate Yoma to it. Its ritual meaning is treated fully elsewhere; what matters for the calendar is its position, ten days into the seventh month, five days before Tabernacles, which makes it the fixed autumn marker by which other things, including a voyage, could be dated.
Sources: Acts 27:9; Leviticus 16:29; Leviticus 23:27; Numbers 29:7; ISBE 1915, "Ships and Boats" and "Atonement, Day of"; Mishnah Yoma.
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