PHILADELPHIA  It looked like the kind of toy telescope a child might have made with scissors and tape  a lumpy, mottled tube about as long as a golf club and barely wider in girth, the color of 400-year-old cardboard, burning with age.

But near one knobby end was a bit of writing that sent Derrick Pitts, chief astronomer of the Franklin Institute here, into rapture. The tube’s focal length is “piedi 3,” the inscription said, three feet. It was in the hand of Galileo Galilei. “Absolutely amazing,” Dr. Pitts said.

Thus did Galileo, one of history’s great troublemakers, come to America.

By turning spyglasses like this to the sky 400 years ago and seeing mountains on the Moon and satellites whirling around Jupiter in contravention of the Earth-centered cosmology of Aristotle, Ptolemy and the Bible that had reigned for a thousand years, Galileo changed the world.

His discoveries propelled astronomers on a course toward discovering signs of the Big Bang and a shadowy modern cosmos suffused with dark energy and dark matter. And his tangle with the church became the template for the war between science and religion that persists to this day.