This is an AIM-9 "Sidewinder" missile currently on display in the museum's Cold War gallery. The Sidewinder is an air-to-air, heat-seeking weapon used by all branches of the United States Armed Forces and over two dozen allied air forces. Many other countries have copied its design for use in their own arsenals.
First developed in the 1950s, it only has a few moving parts and is easy to upgrade. Variant "X" was rolled out in 1999. Since its first deployment, the system is responsible for at least 250 air-to-air kills worldwide. It is one of the most successful weapon systems ever produced.
Read more about the system at http://www.navy.mil/navydata/fact_display.asp?cid=2200&tid=1000&ct=2.