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A rocket follows the principle of Thrust. Inside the engine, an oxidizer will combine with the fuel, causing combustion. This exerts pressure that pushes on every side of the engine, but not on the back, because there is a hole there through which the exhaust can escape. Since there is more push on the top of the rocket than on the bottom due to the hole, the rocket is pushed up into the sky.

To get to space, the rocket has to go faster than the escape velocity of earth, or it will be pulled back to earth.