The story of America's space race with the Soviet Union and the scramble to put a man on the moon, by two who were there. Shepard and Slayton, both Mercury Seven astronauts, begin with a long, panting account of the Eagle's landing on the moon's surface, then backtrack to the beginning of the superpower missile competition in the late 1940s. They point out that the US at that time had no missile expertise whatsoever; the program was set up in Huntsville, Ala., by Wernher von Braun, the German missile genius captured from the defeated Third Reich. A German team constructed the Redstone and Jupiter rockets, but Eisenhower, who distrusted ex-Nazi scientists, eventually grounded von Braun and his German team -- until the Soviets launched a basketball-sized satellite called Sputnik. The American public was traumatized by a 1,000-pound satellite zooming across its airspace, and von Braun got the green light to launch a smaller American satellite at once. After summarizing this early history, the authors turn to the later Apollo missions, which they cover in detail (Slayton was one of the program's masterminds), as well as the eventual Soyuz-Apollo mission, a Soviet-US cooperative effort. Interesting historical material is related in a hard-boiled style, complete with dramatic re-enactments, as if the writing committee -- counting the folks who worked on the companion Turner Broadcasting documentary scheduled for fall, there are at least four authors -- had decided they needed swashbuckling prose to enliven the material. Do we really need to be told that the countdown seconds to a missile launch ""fell like withered leaves""? Still, when its corny style doesn't get the better of it, Moon Shot has its moments, and it's quite readable and detailed.