This is a large (6" x 12") section of parachute from the second satellite ever to be retrieved from orbit, and the first ever aerial satellite recovery.
      Project Corona was its real name, but it was codenamed "Discoverer" during the time. They were the first spy satellites.
       This satellite, Discoverer 14, was launched on August 18, 1960 and carried an advanced camera (for its day) to photograph sites of choice (namely of the Soviet Union) for the United States Central Intelligence Agency. It was the second functioning Corona satellite and the world's first successful photo reconnaissance satellite. The images it took from space were the first in history and first to be brought back to Earth (though a few prior Corona satellites tried to snap photographs, their missions failed before they were ever seen or managed to return to Earth).
       The capsule returned the exposed film back to Earth the next day in a capsule designed to survive reentry into Earth's atmosphere. It was just the second spacecraft ever retrieved from space, the first coming just a week before with Discoverer 13. It was also the first time in history that an aerial recovery was performed, in which an airplane (a C-119) snagged the capsule and its parachute from the air using a hook before it could hit the ocean.

MORE INFORMATION CAN BE FOUND HERE

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HERE

Discoverer 14 marked the:

       -Second satellite ever recovered from space
       -First photos brought back to Earth from space
       -First ever photo reconnaissance satellite
              -First real spy satellite, in other words
       -First aerial satellite recovery

       The Discoverer 14 capsule and its parachute are on display today at the US Air Force Museum in Dayton, Ohio. Discoverer 13 is on display at the Smithsonian's National Air & Space Museum (NASM) in Washington D.C.

       BELOW are two images of the front page of the New York Times from August 20 1960 that are displayed next to Discoverer 13 (though they are referring to 14) at the NASM in Washington.