The first spectacles, designed to correct farsightedness ... "objective" lens—the convex lens at the far end of the telescope—Galileo ground a lens larger than he needed, for example.

Second, you soon want a bigger telescope. Galileo, who first trained a telescope on the night sky 400 years ago this fall, pioneered this two-step program. First, he marveled at what he could see.

Still, even Galileo recognized the ground-based uses of telescopes. After building his first telescopes, Galileo demonstrated the new instrument to the Venetian Senate, including military leaders.