# Internal forces and rocket thrusts

So I just started reading Goldstein's classical dynamics and I'm having a brain fart trying to understand something. I found a slide that paraphrases a part of the section, which is about systems of particles and center of mass. It is attached to this post. Particularly, Goldstein says: "In order that the motion of the center of mass be unaffected, the ejection of the exhaust gases at high velocity must be counterbalanced by the forward motion of the vehicle." So how is the motion of the center of mass unaffected by internal forces? It seems to me that motion of the center of mass is directly affected by these internal forces. Specifically, the center of mass moves or undergoes motion because of the force of thrust that emerges from the rocket, which by Newton's third law, there is an equal and opposite force that causes the rocket (and the center of mass) to move forward. Goldstein appears to consider the center of mass as a system of the exhaust and the rocket itself. Could someone clarify this?