On a winter morning in 2013, a meteor the size of a four-story building screamed across the country, exploding near the city of Chelyabinsk and injuring more than 1,600 people amid widespread property damage. The chunk of rock and iron, which was 60 feet across, served as a violent reminder that Earth, bombarded daily with tons of space-going debris, periodically intersects with large planet killers—and a significant portion of those remain undocumented. After years of study and discussion, NASA is ready to launch its first effort to spare Earth the kind of calamity that extinguished the dinosaurs, crashing a space...