These are the fins-forward (smaller fins) and aft-of the Douglas Aircraft-built Sparrow II missile, a follow on to the Sparrow I. Dating from the mid-1950s and designed for use on Navy aircraft, the Sparrow II was a highly maneuverable air-to-air missile equipped with a more advanced guidance system than its predecessor. The Sparrow family of missiles originated in 1946 and became one of the largest and most important missile programs for the United States, the North Atlantic Treaty Organization (NATO), and other U.S. allies. A branch of the Sparrow family exists today as the AIM series of missiles.
The U.S. Navy transferred the Sparrow II to the Smithsonian in 1958.