If only the play were simply these two men of Florence. Their argument - over whether, as Copernicus posited, Galileo argued, and Urban disputed, the earth revolves around the sun, in apparent contradiction of the Bible and church doctrine - is a turning point in the road to modernity, and the details of their battle are more complicated than we remember from grade school.
Galileo did, after all, recant (though it's unclear whether he actually went on to whisper, "e pur si muove" - "nevertheless, it moves" - and he doesn't do so here). Moreover, Goodwin reveals both men as fascinating and complicated human beings, full of intellectual curiosity and spiritual passion.
But he has also surrounded them with a small army of secondary characters - priests, Cardinal Richelieu, Galileo's daughter the nun, hooded monks, Johannes Kepler - and then loaded them down with more argument, exposition, and flowery description than any characters on earth could carry.
What's frustrating is that, buried under the barrage of words, there are some wonderful lines. Even Kepler gets one: Describing Galileo's unprecedented use of experiment and observation, rather than unaided reason, to study the universe, he says: "Now God has found himself a philosopher with hands, and we begin to understand the wonders of Creation."
"A philosopher with hands" - such a neat distillation of Galileo's gifts. But the phrase is hidden in a full paragraph of speech, which itself is stuck in the middle of a whirl of vignettes that take us from Tuscany to France to who knows where for a glimpse of reactions to Galileo's work in each spot.