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The Collaborative International Dictionary
air-to-air missile

Missile \Mis"sile\, n. [L. missile.]

  1. A weapon thrown or projected or intended to be projected, as a lance, an arrow, or a bullet.

  2. A rocket-propelled device designed to fly through the air and deliver a warhead of explosive materials to a target.

    Note: Numerous types of rocket-propelled missile[2] are now used in modern warfare. Some types with names indicating their range or function are: antiaircraft missile; ballistic missile; cruise missile; antiballistic missile missile; air-to-air missile; air-to-ground missile; guided missile; intercontinental ballistic missile (IBM); intermediate range ballistic missile (IRBM); surface-to-air missile.

Wiktionary
air-to-air missile

n. (context military English) A missile that is fired from an aircraft to typically attack another aircraft.

WordNet
air-to-air missile

n. a missile designed to be launched from one airplane at another

Wikipedia
Air-to-air missile

An air-to-air missile (AAM) is a missile fired from an aircraft for the purpose of destroying another aircraft. AAMs are typically powered by one or more rocket motors, usually solid fueled but sometimes liquid fueled. Ramjet engines, as used on the Meteor (missile) are emerging as propulsion that will enable future medium-range missiles to maintain higher average speed across their engagement envelope.

Air-to-air missiles are broadly put in two groups. Those designed to engage opposing aircraft at ranges of less than 30 km are known as short-range or "within visual range" missiles (SRAAMs or WVRAAMs) and are sometimes called " dogfight" missiles because they are designed to optimize their agility rather than range. Most use infrared guidance and are called heat-seeking missiles. In contrast, medium- or long-range missiles (MRAAMs or LRAAMs), which both fall under the category of beyond visual range missiles (BVRAAMs), tend to rely upon radar guidance, of which there are many forms. Some modern ones use inertial guidance and/or "mid-course updates" to get the missile close enough to use an active homing sensor.