This rather bedraggled looking item is the shell of a Polaris A-3 FBM, at the National Museum of Nuclear Science and History in Albuquerque, New Mexico.
Polaris was a series of two-stage solid fueled submarine-launched ballistic missiles — in fact, they were the U.S.’ first such missiles after plans for submarine use of the large early cruise missiles was abandoned in the 1950s. The Polaris program began in 1956, with the first Polaris being launched from a submerged submarine on 20 July, 1960 (this variant was later renamed the A-1). The A-2 version of the Polaris, essentially an improved A-1, went into service late in 1961.
The Polaris A-3 was a largely redesigned missile (85% new when compared with the A-2), and entered service in 1964. With a range of 2500 nautical miles (2880 statute miles / 4635 km), it could hit targets anywhere on land without needing to launch from too near a coastline. Originally equipped with a single 500-kiloton warhead, the A-3s were later refitted to carry three separate 200-kiloton warheads (although they weren’t separately targetable, they could impact up to 800 meters away from each other).
Beginning in 1963, the United Kingdom also purchased Polaris missiles and submarines and support systems. But in order to make best use of their smaller Polaris submarine force (just 4 submarines), the British Polaris missiles were outfitted via a program called Chevaline that equipped them with smaller warheads coupled with decoys and other defensive countermeasures.
The U.S. Navy retired its last Polaris missile in 1981, replacing the series first with Poseidon and later with Trident missiles. British Chevaline variants of the Polaris were in the field until 1996.