Quick disclaimer; I'm not that well informed on many of the mechanics on space in general so sorry if this question is rather easy/basic.
Is the center of mass in a object a factor in space when there is no gravity? By gravity I mean planets or any other large body of mass that could interfere. For example if I had a rocket in space where the bottom was significantly heavier than the top and exerted force at the top would it rotate around the center of mass or the center of the object shape/volume wise?
This is all assuming its an enclosed system and the rocket had no velocity prior to the addition of the force exerted.