As demonstrated in my monograph The Sun's Path At Night, the unanimous view of the Rishonim was that the Sages of Israel believed that there is a firmament, a solid dome over the earth, upon which the sun and stars move. And I see no reason to think that the Rishonim were mistaken.
Incidentally, this sheds light on the word olam. When studying or translating rabbinic texts, people often wonder whether to translate olam as "world" or "universe," and are puzzled as to why the same world is used for both. The answer is that, in the view of Chazal, they were one and the same. Only with modern conceptions, when the Earth is a small planet floating in the vastness of space along with countless other planets and stars, is the "world" significantly different from the "universe." But in the ancient Babylonian cosmology, where the entire universe is a dome over the earth, they are one and the same structure.
This leads to the final part of Mishpachah magazine's Kolmus supplement that I had not yet discussed. The lead article on geocentrism vs. heliocentrism features a sidebar entitled "The Position of Chazal Regarding the Nature of the World." It lists four purported examples of Chazal disagreeing with the "science" of their era and eventually being proven correct. Let us examine each in turn:
1. It contrasts the non-Jewish beliefs in the world resting on pillars, water, elephants or turtles with the verse in Iyov 26:7 stating that the Earth is suspended in an empty void, citing Rashi that "the Earth is suspended in the air, held by Hashem's power." (Although note that this is not what Rashi actually says, ayin sham, v'ain kan makom leha'arich.)
Yet there are numerous other pesukim which do describe the world as resting on something - "He set the earth on its foundations; it can never be moved" (Tehillim 104), "For the pillars of the earth are God's, and he set the world upon them" (1 Samuel 2:8), "He shakes the earth from its place and makes it pillars tremble" (Job 9:6), "He spreads the earth out over the waters" (Berachos). Thus, there are a range of descriptions in Tenach, just as there are a range of descriptions in other cultures, some of which fit with modern science, many of which do not. So what system is being used here to determine when something is meant literally, and when it is meant allegorically?
2. It claims that, in contrast to other ancient scientists who thought the world to be flat or shaped like a drum or arch, the Yerushalmi and Midrash note that the earth is in the shape of a sphere.
In fact, the ancient Greeks knew full well that the earth is a sphere. Certainly most of Chazal believed the earth to be flat, as documented in my monograph and many other sources. The Yerushalmi and Midrash, at best, represent a minority of Chazal who shared the same view as the Greeks. In fact, even those sources speak about the earth being "like a ball in a dish of water," which hardly fits with the earth as we know it. Furthermore, as R. Josh Waxman notes, these sources seem to say more about Greek beliefs (perhaps subsequently adopted by Jews) than they say about Chazal's beliefs.
3. It says that while the ancient Greeks believed the celestial bodies to be made out of an unearthly quintessence, Chazal knew them to be composed of the same material substances that we have on earth.
I haven't looked into this thoroughly yet, but I'm not at all sure that the citation from Chazal (unfortunately no source is given) means what it is claimed to mean. And certainly most of the Rishonim agreed with the Greek view.
4. It cites a Midrash and Zohar which attest to people living on the other side of the world.
Yet in fact, the Midrash is referring not to Australians, but to the two-headed denizens of the subterranean netherworld (see Sacred Monsters pp. 210-212). And as for the Zohar... well, as Chasam Sofer would have said, that's not exactly evidence of what Chazal held!
In summary, since we have clearly seen that Chazal subscribed to the ancient Babylonian cosmology of the earth as a flat or near-flat disc with the rest of the universe as a dome above it, it is ludicrous to talk about Chazal being ahead of their time with regard to understanding the nature of the world and the universe.
Now, I happen to have inside info that this sidebar in Kolmus was not part of the original article, but was later added following instructions from the editor, who was concerned that the article was too maskilic and that they needed to show their True Charedi credentials. Since that is the case, and since Mishpachah is doing a very valuable job, I can't criticize them for doing their job.
But I have to do my job, too. And claiming that Chazal were ahead of their time with regard to understanding the nature of the world and the universe is not only false, but also dangerous. Creating such a false image can lead to severe disillusionment and bitterness when people discover the truth. We should be respecting Chazal as great Torah scholars who produced an astounding compendium of debate, laws and ethics - not as modern scientists.