The Odyssey is one of the great works of ancient Western literature, written eight centuries before the birth of Christ and four centuries after the fall of Troy. Generations of classicists have pored over the many lines of Homer's epic description of the long journey taken by the hero Odysseus to his home island of Ithaca. Now two scholars have found evidence to support the idea that one line, in the poem's 20th book, refers to a total solar eclipse that occurred on 16 April 1178 BC – the day when Odysseus returned home to kill his wife's suitors. If true, this would date the fall of Troy itself to precisely 1188 BC.

It takes Odysseus 10 years to reach Ithaca after the 10-year Trojan war. During his time away, his young son, Telemachus, has grown into a man and his faithful wife, Penelope, is besieged by unruly suitors desperate to gain her hand in marriage.

The Odyssey is the story of a long and great journey involving the beautiful nymph Calypso – who enslaves Odysseus for seven years as her lover – helpful divinities such as Athena and vengeful gods such as Poseidon.

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Odysseus eventually escapes from Calypso, survives a shipwreck where all his compatriots are drowned and is befriended by the Phaeacians, a race of skilled mariners who finally deliver the hero safely to Ithaca, where he takes on the guise of a beggar to learn how things stand at home.

It is during this later phase of The Odyssey that Homer is said to make reference to a total solar eclipse. The key phrase comes in a speech by the seer Theoclymenus, who foresees the deaths of the unruly young men who sought the hand of Penelope while Odysseus was away. It ends with the words: "The Sun has been obliterated from the sky, and an unlucky darkness invades the world."

The idea that The Odyssey refers to a total solar eclipse, when the Moon blocks out the Sun completely, is not new. It was first suggested by ancient scholars, but it was only in the 1920s that astronomers were able to calculate that such an eclipse over Greece around that time could only have taken place on 16 April 1178 BC.

However, few people were convinced that the passage in The Odyssey was actually a reference to a mythical total solar eclipse, never mind a real one. It might just have been poetic licence, for instance, especially as Homer is said to have written it several centuries after the events that were said to have unfolded. But two modern astronomers believe they have convincing evidence to support the 16 April eclipse by analysing other passages in the poem that refer to four other astronomical events that are known to occur quite independently of one another.

Instead of looking at when a solar eclipse occurred in history, as other astronomers had done, they investigated the timing of a new moon, the simultaneous appearance of two stellar constellations in the evening sky, and appearances of the planets Mercury and Venus. All four phenomena are mentioned in The Odyssey which gave Constantino Baikouzis of the Observatorio Astronomico de La Plata in Argentina, and Professor Marcelo Magnasco, of the Rockefeller University in New York, another way of checking the date when Odysseus is supposed to have returned to his home on Ithaca to kill his wife's suitors.

For example, six days before the slaughter of the suitors, Homer writes that Odysseus returns with the Star of Dawn, a reference to the planet Venus, which is visible at sunrise. Odysseus also sets sail to Ithaca 29-and-a-half days earlier, when the constellations Bootes and Pleiades can both be seen in the twilight sky – stars which were used for navigation by the ancient Greeks.

Magnasco and Baikouzis also point out that the day before the slaughter of the suitors, there is a new moon – a prerequisite for a total eclipse – and 33 days prior to this day Homer may be suggesting that Mercury, described as the god Hermes, is high at dawn and near the western end of its trajectory.

They calculated the pattern in which these four events occurred, from the references mentioned in The Odyssey, and compared them against patterns gleaned from 135 years of astronomical data – nearly 5,000 days. The result was they found just one date that could have been the fateful day. It was the same 16 April 1178BC that was known to have been a total solar eclipse. "What are the chances of having two different ways of dating the text and both agreeing on the same date? We calculated the chances of these two dates agreeing by chance alone is something like one in 50,000," Professor Magnasco said.

"Not only is this corroborative evidence that this date might be something important but, if we take it as a given that the death of the suitors happened on this particular eclipse date, then everything else in The Odyssey happens exactly as is described."

In the time of the ancient scholars, notably Plutarch and Heraclitus, there were suggestions that The Odyssey did refer to a total solar eclipse, a rare and dramatic event that was often taken as an omen. "Temperatures drop suddenly a few degrees, winds change, animals become restless and human faces may have a striking, exsanguinated appearance in the bluish light," the two academics write in the US journal Proceedings of the National Academy of Sciences.

"We cannot say for sure that the events described in The Odyssey really happened, of course, because some of the events are really quite fanciful. But what we want to do is to get people to go back to the text and have another look," Professor Magnasco said.

"Under the very large assumption that there was an Odysseus, there were suitors that got massacred, that it indeed took 10 years for Odysseus to get back ... yes, in that case the fall of Troy would have happened 10 years before the death of the suitors, thus in 1188BC. The current dating of the destruction layer of Troy VIIa is around 1190 plus/minus a few years."

One weak spot in the analysis, Professor Magnasco admits, is the idea of linking the appearance of planets with gods, which was a Babylonian invention that dates back to about 1000BC. There is no evidence those ideas had reached Greece by the time of Homer, hundreds of years later.

"This is a risky step in our analysis. One may say that our interpretation of the phenomena is stretching it but, when you go back to the text, you have to wonder," he said. "Even though there are historical arguments that say this is a ridiculous thing to think about, if we can get a few people to read The Odyssey differently, to look at it and ponder whether there was an actual date in it, we will be happy."