Arocket moves in space because the gases are given momentum as they are expelled by the rocket engine. Consider the rocket resting in space. There is no momentum in the system. Next, the engine ignites. As the exhaust gases go in one direction, the rocket goes in the other to keep the total momentum of the system constant. This momentum change of the gases gives the rocket the "push" to go forward. We call this push, the thrust of the rocket, i.e. the force exerted on the rocket.
This thrust depends upon the speed of the exhaust gases and the mass of gas being expelled each second, sometimes called the burn rate in pounds of fuel per second. On Earth, air tends to inhibit the exhaust gases getting out of the engine. This reduces the thrust. However, in space since there is no atmosphere, the exhaust gases can exit much easier and faster, thus increasing the thrust. Therefore, the rocket engine actually works better in space than here on Earth.
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