We all have seen in school days how essential is the air (more particularly Oxygen) to keep for the process of combustion. Even human body itself breaths air to accomplish combustion(respiration) of nutrients to generate energy supporting life.
Unlike airplanes, missiles (and rockets) do not depend on atmospheric air, thats why they can be propelled into air free domains at high altitudes or more particularly in space application. air which acts as oxidizer to burn fuel in airplanes is not present at high altitudes or in space beyond Earth's atmosphere, so an oxidizer itself is mixed and stored with fuel in fuel chamber, so as long as there is fuel, its oxidizer is also present inside a missile.
It can be understood like, A bike lover wants to experience riding on moon, But his astronauts friend points him the fact there is no air in moon so his engine can not be ignited on at moon's driving circuit. The biker was desperate to ride n lunar surface so he applied the same principle working with the rocket used to carry his motorcycle to moon.
He approached his astronaut friend again with few improvements over his old made for earth bike which has a separate chamber to store air(taken from earth) along the ordinary fuel tank consisting gasoline, in this case bike need not to take air from atmosphere to burn the fuel inside engine, and accordingly it has not have an open carburetor either, which serves as air intake unit for an ordinary motorcycle.The only function now the carburetor has to provide is to mix air and fuel from two different chambers.
Rockets use the same methodology to carry the oxidizer which is not essentially air since higher rate of combustion can be obtained by more reactive agents other than air or oxygen to obtain grater acceleration.
Ballistic missiles targeting long distance object also requires to travel to outer part of atmosphere which is less air dense, hence they are also equipped with idea of storing oxidizer agent along with fuel.
We can conclude as airplanes can not travel to the air-free space, so scientist and engineers further modified the design and named it 'Rocket'.
Quick Fact : To launch something from Earth surface orbit velocity of 7.9 Kilometers per second (4.9 miles per second) is required. With this speed it takes 15 seconds to cross ozone, 150 Seconds to enter to the space (100Km orbit) , 8 hours 35 for moon, and approximately 260 days for Mars. For later 2 cases it depends upon relative position of Earth and the destination(Moon or Mars) and how much fuel you are willing to burn.
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