Rocket in deep space

Problem

A rocket is at rest in deep space. It fires its engines and accelerates. Does its centre of mass also move? And if instead we consider “rocket + expelled gases” as the system, does the centre of mass of that system accelerate?

Solution

Rocket alone. Yes, the centre of mass of the rocket alone accelerates. Relative to this system, the expelled gases have “left” and exert an external force on it (thrust): $\sum F_\text{ext} \neq 0$, so $\vec{a}_\text{CM} \neq 0$.

Rocket + gases. No, the centre of mass of the complete system rocket + expelled gases stays fixed. No external force acts on this system (we are in deep space): the forces between rocket and gases are internal and cancel. The total momentum stays zero: the rocket goes forward exactly as the gases go backward, and their common CM does not move.

This is the same principle as the explosion: internal forces redistribute momentum but do not move the centre of gravity of the whole.

Links

Topics: Centre of mass Concepts: Centre of mass · Conservation of momentum · Explosion