This would prove very tricky and dangerous as religion and science don't get along pretty well.
Look at what happened to Galileo Galilei.
Actually, the way Daniel did it was when shown their first idol that was in a chamber which was tightly locked at night, he sprinkled the floor with fine powder, because the tale was that the offerings left at night disappeared in the morning. The next morning after the powder was sprinkled? It showed a hidden passage and footprints.
Then, there was a second one which was a dragon (and it was a live animal) that was rumored to be immortal and could eat anything. He figured out how to poison it.
That's the kind of science I'd use. And yeah.........you're right........sometimes it can be dangerous to do, but if you can actually show all the people where they're wrong all at once, you can come through okay, they might even think you're magic.
Copernicus and Galileo didn't have a telescope that could be used for everyone to look through, and I don't think the Church had the patience to sit through night after night of observation.
Remember.........that which you know the least about, you fear the most.