The Rema in Toras HaOlah (1:2) states clearly that we assume rabbinic science to be infallible, and ancient rabbinic knowledge of astronomy complete.
Medrash Tehillim (19) quotes Shmuel as saying he is an expert in the streets of Nehardea as much as he is an expert in the ‘streets’ of the heavens. The Medrash asks how Shmuel knew all of that, and it answers he knew it all through the Torah.
Rabbeinu Bachyai writes in the Introduction to Chumash that all wisdom and science in existence is contained in Torah.
The Chosid Yaavatz (Ohr Hachaim) says that Chazal knew science form a Mesroah that goes back all the way to the Neviim, who knew it from Hashem, without any effort at all.
Chasam Sofer (Beshalach) writes that this is the meaning of the posuk “Ki hi chachmascha ubinascha l’einei ha’amim” – Chazal were great experts in the secular sciences and disciplines. In fact, you need to know much secular knowledge in many areas in order to properly understand the Torah – and he gives several simple examples. However, since we are supposed to be busy learning Torah – not secular science – all day and night, and Hashem has no “nachas ruach” from us learning secular studies at all, how would Chazal have known all the secular wisdom that they clearly knew, as we see they did from all of Shas?
Answer: They know it from the Torah, since the entire body of secular wisdom is included in the Torah, for the Torah is the blueprint of the world. And so, when the Goyim see that we do not study the secular science books at all – and we even disagree with them! – yet we derive all the secular knowledge, in the most precisely accurate form – from only the Sefer Torah, they will exclaim, “Am chacham v’navon hagoy hagadol hazeh!” (A similar explanation is given by the Raavad-ibn Daud. He says that the posuk refers to the philosophical truths that it took the nations centuries to develop, we knew all the time via tradition from Har Sinai.)
Once we establish that the scientific knowledge that is incorporated into Torah Shebal Peh is derived form the Torah, it has the same status as all of Chazal’s interpretaitons of the Torah — they are binding.
The Radvaz (4:232) writes that “Aggadah is part of the Torah shebal peh and is rooted in what Moshe received on Har Sinai directly from Hashem, just like the rest of Torah shebal peh”.
Chasam Sofer — Please see the Chasam Sofer in Beshalach I quoted above. He says the same thing in Drashos Chasam Sofer Vol. 1 p.100b. Our prophets and sages know all the sciences much better than the scientists even though all they learn is Torah. This is because the One Who created nature informs our sages of the correct facts. This is what amazes the Nations, as it says, Am navon v’chacham hagoy hagodol hazeh!