Rocket in a vacuum

Problem

A rocket fires its engines in deep space. What does it “push against”, given that there is no air? Explain the physical principle in five lines.

Solution

The rocket doesn’t need to “push” against anything external: it pushes against the gas it expels itself. Consider the isolated system rocket + gas: in deep space there are no external forces, so total momentum is conserved. It starts from rest, $\vv{p}_\text{tot}=0$. The engine expels a mass of gas $m_g$ backwards with velocity $-v_g$. To conserve total momentum, the rocket (mass $m_r$) must gain forward velocity: $m_g\,(-v_g) + m_r\,v_r = 0 \;\Rightarrow\; v_r = \frac{m_g\,v_g}{m_r} > 0$ The mechanism is Newton’s third law: the rocket pushes the gas backwards, the gas pushes the rocket forwards with equal and opposite force. Neither force needs air. The vacuum is not an obstacle: in fact it removes aerodynamic drag, so a rocket works even better in space than in the atmosphere. $\ev{\text{Reaction of the expelled gas: } \vv{p}_\text{rocket}+\vv{p}_\text{gas}=0 \text{ conserved; the vacuum removes drag}}$

Links

Topics: Momentum and collisions Concepts: Conservation of momentum · Newton’s third law · Momentum Objects: Rocket