The scientists first created a rough chronology of events depicted in the "Odyssey." First, 29 days before the supposed eclipse and the massacre of the suitors, three constellations are mentioned as Odysseus sets out from the island of Ogygia, where he has spent seven years as a captive of the beautiful nymph Calypso. Odysseus is told to watch the Pleiades and late-setting Boötes and keep the Great Bear to his left. Next, five days before the supposed eclipse, Odysseus arrives in Ithaca as the Star of Dawn — that is, Venus — rises ahead of the sun.
Finally, the night before the eclipse, there is a new moon.
Also, the messenger of the gods, Hermes, is sent west to Ogygia by the king of the gods Zeus to release Odysseus and then immediately returns back east roughly 34 days before the eclipse. The researchers conjecture this trip refers to an apparent turning point of the motion of the planet Mercury. (Mercury was the Roman name for Hermes.)
Mercury completes its orbit around the sun in just roughly 88 days, compared with the year it takes Earth to do so. This means that Mercury and Earth are somewhat like two cars moving along separate lanes of a racetrack at different speeds. The effect of these motions is that Mercury occasionally appears to go backward or retrograde in the sky from our point of view, Magnasco explained. This happens for roughly three weeks at a time, about three times a year.
The scientists then searched for potential dates that satisfied all these astronomical references close to the fall of Troy, which has over the centuries been estimated to have occurred between roughly 1250 to 1115 B.C. From these 135 years, they found just one date satisfied all the references — April 16, 1178 B.C., the same date as the proposed eclipse.