It was an epic space rescue that, in audacity and risk, echoed NASA’s campaign to save the astronauts aboard the doomed Apollo 13 moon mission. The biggest difference between the 1970 Apollo operation and the 14-month recovery of AEHF-1, an Air Force communications satellite, is that money was the only thing immediately at stake in the latter.

Granted, it was quite a lot of money: around $2 billion. And the satellite’s loss would also set back the Pentagon’s efforts to revamp its communications infrastructure as battle becomes more bandwidth-intensive.

The details of AEHF-1?s rescue, completed i...