To bring down high costs, the Pentagon’s main space-launch provider is proposing a technique that sounds like a mixture of science fiction and circus act: catching rockets as they fall back to earth with an airborne hook so they can be reused.

United Launch Alliance LLC surprised many in the rocket industry this week with its plan, which would involve large helicopters with extendible booms to snare spent engines as they parachute down from the edge of space after delivering their payload.

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