For questions about rockets as they pertain to aviation. Questions about rockets in the context of space are off topic here.
A rocket engine is a reaction engine that carries both its fuel and its oxidiser with it. Monopropellant rockets use an unstable fuel which decomposes into hot gasses when brought into contact with a catalyst.
The chemical energy in the propellants is converted into heat and pressure while in a pressure chamber open on one side. The stream of gas exiting through the opening pushes the rocket in the opposite direction. Rockets need no external components to run, can operate at arbitrarily-high speeds (whereas even a scramjet, the highest-speed type of airbreathing jet-engine, tops out around mach 17), and can be made with extremely high thrust-to-weight ratios (allowing a rocket engine to impart a fairly high acceleration to even a heavy vehicle); these factors result in them being widely used for space propulsion.
However, at the relatively high air densities, low speeds, and placid flight profiles flown by most aircraft, a rocket's advantages over an airbreathing engine disappear, and, all else being equal, a rocket has a vastly-lower efficiency than an airbreathing engine (it burns far more fuel to produce the same amount of thrust), especially in dense, low-altitude air. As a result, only a few aircraft have been built to use rocket engines, mainly for experimental purposes or for very-high-performance fighters, with almost none entering mass production.
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