On display at the National Museum of Nuclear Science and History (in Albuquerque, New Mexico), it’s a Jupiter IRBM:
The Jupiter has to have one of the oddest and most confusing histories of any missile ever fielded. And this, for a weapon that was strategically useless, nearly started World War III, and which was retired within a few years of its introduction to service.
But I’m getting ahead of myself.
The development of the Jupiter IRBM was begun in 1954 by the U. S. Army’s Redstone Arsenal — intended as a longer range (1000 miles / 1600 km) derivative of the Redstone missile. Within a year, the U. S. Air Force began its own parallel development of an IRBM with similar performance (the Thor), and the Jupiter was retasked with supporting launch from submarines. In the process, it took on its trademark stocky finless shape.
But the Navy soon decided that a liquid-fueled missile would not be a safe resident on any of its ships, and so the Jupiter would be fielded as a U. S. Air Force project. But the Army continued its development, and proved out various Jupiter components on modified Redstone missiles somewhat confusingly dubbed the Jupiter A, B, and C. Note that a further-modified Jupiter C (re-renamed the Juno 1) would later launch the U.S.’ first successful satellite, Explorer 1.
Meanwhile, a few dozen Jupiter missiles were stationed in Italy and Turkey in 1961 — the locations being chosen as a result of the missiles’ relatively short range. Multiple U.S. presidents felt the Jupiters were militarily useless due to their limited mobility, short range, and slow response time. Yet they stayed in place — until their very presence provoked the Soviet Union into responding with a tit-for-tat deployment of nuclear missiles in Cuba in 1962. A subsequent secret agreement sent both the soviet missiles and the Jupiters back to their respective home nations in 1963, in the process ending the Jupiters’ service lives only 2 years after they started.