Rome's cultural survival

I suppose one reason Rome resonated for long after its fall was the survival of various of its cultural products.  Latin is pretty obvious.  Until the Renaissance, Western medicine was Galenic medicine (though it vanished and got reintroduced from Byzantium and the Arabs).  And astronomy was Ptolemaic astronomy.  Both were products of the late Principate.  It's a bit as if, having lost the political unity, Europeans held on to the intellectual unity, far beyond where it made sense.  Would these ideas have had the same staying power if they had not emerged in association with that dream of unity?  Ptolemaic astronomy itself seems almost like a crude metaphor for political rule from the center, having nothing to do with physical reality at all.