On March 16, 1966, Neil Armstrong and David Scott became the first astronauts ever to dock with another spacecraft when they linked their Gemini 8 capsule to the uncrewed Agena target ship. However, the cheers had barely died down at Mission Control Houston when Scott realized they had a problem. The conjoined spacecraft had begun a gentle leftward pitch.

Armstrong and Scott watched in horror as the capsule’s gentle pitch became a tumbling motion that increased, turning the craft into a centrifuge. In desperation, Scott undocked the two ships before gravity ripped them apart. But Gemini 8 continued to spin faster. At 60 revolutions per minute, the astronauts began to slip into unconsciousness. Fighting the rising G-forces, Armstrong shut down the faulty maneuvering thrusters and fired the reentry thrusters. Slowly, the rotation eased. With the craft now very low on fuel, the two men just had to achieve one more first: the first emergency reentry in history.

The Space Race started with the Soviet Union’s launch of Sputnik 1 on October 4, 1957, the Earth’s first artificial satellite. Thereafter, the two superpowers competed with their rival Vostok and Mercury space programs for headline-grabbing “firsts,” and initially it seemed Moscow was winning. In an........

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