First, they tried an F-104. “Not enough wing or thrust,” recalls Jack Petry, a retired U.S. Air Force colonel. When NASA engineers were launching rockets at Florida’s Cape Canaveral in the 1960s, they needed pilots to fly close enough to film the missiles as they accelerated through Mach 1 at 35,000 feet. Petry was one of the chosen. And the preferred chase airplane was the McDonnell F-4 Phantom. “Those two J79 engines made all the difference,” says Petry. After a Mach 1.2 dive synched to the launch countdown, he “walked the [rocket’s] contrail” up to the intercept, tweaking closing speed...