How did the Medieval church react to scientific advances?

The Church exercised only a limited direct influence on science during the middle ages. The Church did one thing that some people might consider a negative action, but it nevertheless had a positive effect. In the Condemnations of 1210 to 1277, the Church declared the physical treatises of Aristotle heretical. This had the very positive effect of freeing the scientists from an incorrect scientific model and allowing them to pursue science empirically. The empirical approach was largely a matter of acquiring data and reporting it, which was hard to proscribe. It was considered legal to continue teaching what the heretical teachings were, by the way (except in Paris); it was just not allowed to say they were true.

During the middle ages, science tended to be very practical. Theoretical astronomy was not of nearly so much interest as Metallurgy, for example. Without investigations into cosmology, science was not something that was likely to lead to questioning theology.

Also books on science might be written, but they needed to be copied by hand, so the influence of new books was not nearly as interesting to the Church as the influence of radical preachers.

Indirectly, the Church had a greater influence by sending men off on the crusades. Crusaders were exposed to new lands and new ideas. When they came home, they had different views about things than they did when they left. This promoted science a good deal.