Via John Scalzi's del.icio.us feed, I see that scientists claim to have pinned down exactly when Odysseus got home — roughly noon on April 16, 1178 B.C.:
Now scientists have pinned down his return to April 16, 1178 B.C., close to noon local time, according to astronomical references in the epic poem that seem to pinpoint the total eclipse of the sun on the day that Odysseus supposedly returned on.
. . . .
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.
Penelope's suitors were all dead by 12:01.
Read the whole thing, as they say.