Like Caf, I think you are missing the point here. The 'fact' that the sun revolved, or orbited, around the 'flat' earth was common belief at the time.

Around 1530 Nicolas Copernicus wrote about the idea of the earth being round, rotating around its axis each day, and traveling around the sun once a year. Of course people had believed the earth round quite a while before that, but didn't talk about it much for fear of the Catholic Church.

In the second century AD Ptolemy envisioned a geocentric universe with celestial bodies rotating around the earth. However since Ptolemy attempted to measure the circumference of the earth he obviously didn't think it was flat.

In the second century BC Posidonius attempted to measure the earth's circumference, and of course Eratosthenes attempted the measurement in the third century BC. Aristarchus of Samos, a contemporary of Eratosthenes, proposed the idea of a sun-centered universe, but Greeks in general seemed to strongly believe in an earth-centered universe because they thought earth to be the house of the gods, and therefore it would have to be the center of the universe.

All the above is fairly well known history. I suppose the Romans picked up the Greek idea of the earth being the center of the universe, they adopted most other Greek ideas. The Catholic Church tended to graft on pagan Roman/Greek ideas, they probably adopted it from them, although I've never really heard how this idea made its way into Catholic theology. If not this, then by whatever means, the Catholic Church became the defender of the idea of the earth being the center of the universe, and one risked his life to question the idea. Galileo is the most well known example of that peril.

But I don't know what the belief was among Jews in Israel around Solomon's time, the ninth century BC, as to the nature of the universe and the shape of the earth. I don't have any idea if they spent even ten minutes pondering it. Do you have any references about celestial bodies revolving around a flat earth was the prevailing idea in ninth century BC Israel? I'm not sure what to make of this assertion. OTOH, in Joshua chapter ten, a bit prior to Solomon's time, people referred to, and possibly thought of, the sun as moving (Joshua 10:12-13). But then reading "sunrise" and "sunset" in current English might lead someone hundreds of years from now to conclude we believed the sun circles the earth.

If God had wished to 'inspire' the author that the opposite was true, a fact beyond the limits of scientific investigatiob of the time, He certainly could have done so. There is no such evidence here. ... The main theme of the discussion is whether the Bible is accurate as science and as history, and this is clearly not the case.

As to what Solomon was inspired to teach, it wasn't physics. His message is that everything man does is useless except the purpose for which man was created: "Fear God and keep his commandments, for this is the whole duty of man." That message is true whether daytime is expressed as the sun rising and setting, the sun going up and going down, that the sun goes up and goes under, or that the earth rotates such that for a period of time each day the land which we inhabit is illuminated by the sun.

I don't know that God has ever taught people science, or inspired people to teach science. Again, look at Joshua chapter ten. Joshua wants God to lengthen the day so Israel can finish a battle they are winning. When Joshua asks for the sun and moon to stand still in the heavens God doesn't give Joshua a science lesson in orbital mechanics, he just grants the request.

Sometimes God or an inspired writer uses something we might call science to make a point. When Paul says that God "hath made of one blood all nations of men for to dwell on all the face of the earth" (Acts 17:26) it fits this category. We could say it is all a big lie because we know there are various types of human blood: A, B, AB, and O plus the positive and negative attributes, while Paul claims only one. But trying to shoehorn what Paul said into current blood typing would be the error, not Paul's message. This would cause us to miss his point that God made us all humans, no matter what nation we live in, and as such we are to "seek the Lord, in the hope that they might grope for Him and find Him, though He is not far from each one of us".

Likewise concentrating on the language Solomon used to describe daytime causes us to miss his important point: "of making many books there is no end; and much study is a weariness of the flesh. Let us hear the conclusion of the whole matter: Fear God, and keep his commandments: for this is the whole duty of man." (Ecclesiastes 12:13)