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That turns out to be a very general principle: in any object or collection of objects, forces that only involve those objects and nothing else (\"internal forces\") cannot shift the centre of gravity. An astronaut floating in a space suit cannot shift his position without involving something else, e.g. pushing against his spacecraft. The centre of gravity--or \"centre of mass\"--is a fixed point, which cannot be moved without outside help (turning around it, however, is possible). By throwing a heavy tool in one direction, the astronaut could get moving in the opposite direction, though the common centre of gravity of the two would always stay the same.
Given a bottle of compressed oxygen, the same result follows from squirting out a blast of gas (a scene that appeared in an early science fiction film). A rocket does much the same, except that the cold gas is replaced by the much faster jet of glowing gas produced by the burning of suitable fuel The powerful rockets which lift hundreds or even thousands of tons off the launching pad depend on the same principle. If you ever watched a rocket lift off at Cape Canaveral, it is worth remembering that if you could somehow remove from the scene the launching pad, the atmosphere and the Earth, then the combined centre of gravity of the rocket and its exhaust gases would always remain where it started, at the launching point. It may seem like a roundabout way for producing motion. And yet, rockets are (at least for now) the only practical means of leaving Earth and flying into space.
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