On a number of occasions, particularly in my monograph "The Sun's Path at Night," I referred to Rabbeinu Tam's endorsement of the view of the Chachmei Yisrael that the sun, upon setting, changes direction to travel horizontally through the firmament, whereupon it changes direction again, traveling up and behind the sky. Since this is clearly incorrect, some people wanted to know if this means that following Rabbeinu Tam's view - with its ramifications regarding the time of the departure of Shabbos - has no basis.
There are some authorities who make this argument, such as Maharam Alashkar. And Prof. Shlomo Sternberg argues that Rabbeinu Tam was only offering a hypothetical explanation and that his view was never followed lehalachah until a few centuries ago (see his fascinating article here - 33 meg PDF).
On the other hand, a number of Rishonim and Acharonim adopted Rabbeinu Tam’s view regarding two stages of sunset, and many of them explicitly noted that this did not mean that they believed the Sages of Israel to have been correct regarding the sun’s path at night. See, for example, R. David ben Shlomo ibn Zimra, She’eilos U’Teshuvos Radbaz, Part IV, #282; R. Hezekiah da Silva, Kuntrus Binah Ve’Da’as (also known as Kuntrus D’vei Shamsha), pp. 5b-6a; and R. Avraham Cohen Pimentel, Minchas Kohen, Sefer Mevo HaShemesh 1:10.
But if they disagree with Rabbeinu Tam's cosmological model, why are they following his view? Some, such as R. Pimentel, give no explanation. Others say that the observations of stars behind Rabbeinu Tam's view are still valid, even if the conceptual astronomical framework was incorrect, and therefore his view is still correct. (See R. Gil Student's useful summary here.)
One may therefore wonder why I said recently that Ramban adopts Rabbeinu Tam's mistaken cosmology. A few people argued that he was just adopting Rabbeinu Tam's halachah, based on his observations, not the astronomical model. But a careful reading of Ramban shows that he actually speaks about the sun traveling through and behind the firmament -
Nevertheless, I still have two remaining questions. First is that R. Nissim of Gerona also follows Rabbeinu Tam and likewise refers to the sun passing behind the firmament:
My second question is with regard to R. Eliezer of Metz (who, incidentally, was a disciple of Rabbeinu Tam). His ruling regarding mayim shelanu is explicitly based on the premise that the Chachmei Yisrael were mistaken about the sun passing through and behind the firmament at night. But in his ruling regarding the time of bein hashmashos, he explicitly bases it upon that very mistaken cosmological worldview! What accounts for this seeming contradiction?
If anyone can suggest answers to either of these questions, I'd be indebted.