It was September 12, 1962, when Pres. John F. Kennedy delivered a speech at Rice University before nearly 50,000 people. By that time, America had launched but four men into space--the suborbital flights of Alan Shepard and Gus Grissom and the nearly identical three-orbit journeys of John Glenn and Scott Carpenter. Buoyed by the success of those missions and cognizant of the danger that lay ahead, the president rearticulated his vision and reissued...