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So, it could be difficult to match the event in the NASA's database but, since we have very detailed information about this Homeric event, there is a good chance to find it. First, we know the date: December 20th. Second, we know the location: Vasiliki Lefkada Greece. Thirdly, we can estimate the time of the event: around noon. Scholars agree about the era of the Odyssey, that is around 1250BCE. So I searched between 1300 and 1200 BCE for a match and there is only one! This partial solar eclipse appeared on december 20th from 7:25 till 10:35 UTC (Universal time) that is from 10:25 till 13:35 Greek time. In the year -1246 that is 1246BCE. The maximum was at 8:55 UTC that is 11:55 hours Greek time. Just around noon. Perfect!


December 20th, 1246 BCE!
It is the special effect an solar eclipse causes! Homer described this theatrical effect pretty well. The effect takes place when the sun is partially covered by the moon. Solar eclipses appear twice to five times a year somewhere on the globe.

Ladies and Gentlemen, we have a date!