This is the solid fuel rocket motor for the Sparrow II air-to-air missile. Produced by the Aerojet-General Corporation, the motor generated 7,800 pounds of thrust for 1.8 seconds, hence its designation 1.8KS7800. The same motor was also used in the Sparrow I and other members of the Sparrow missile family.
The U.S. Navy transferred the Sparrow II to the Smithsonian in 1958.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.