A car accelerates by pushing its tyres against the road; a swimmer accelerates by pushing water backward. Both rely on something external to push against. A rocket in the vacuum of space has no road, no water, no air — nothing external at all to push against — and yet it still accelerates, purely by expelling part of its own mass, its propellant, at high speed out the back. The reason this works at all, with total reliability, is one of physics' most fundamental conservation laws.
Momentum has to balance, with nothing left over
Conservation of momentum states that in a system with no external forces acting on it, total momentum — mass multiplied by velocity — stays constant. A rocket and its unburned fuel, sitting motionless in space, start with zero total momentum. When the engine fires, it expels burned propellant backward at high speed, giving that expelled mass a momentum in the backward direction. Because total momentum has to stay at zero (nothing external has acted on the system), the rest of the rocket must gain exactly the opposite momentum — forward — to keep the books balanced. The rocket doesn't need anything to push against externally, because it's pushing against its own expelled propellant instead, and momentum conservation guarantees that internal push produces a real, measurable acceleration on the remaining rocket.
Why the effect is proportional to how fast you throw, and how much
The Tsiolkovsky rocket equation, derived directly from momentum conservation, formalises exactly how a rocket's velocity change depends on two factors: the exhaust velocity of the expelled propellant, and the ratio of the rocket's initial mass (including fuel) to its final mass (after the fuel is burned and expelled). Higher exhaust velocity means each unit of propellant carries away more momentum, giving the rocket more "push" per unit of fuel mass expended. This is why rocket engine design invests so heavily in maximising exhaust velocity specifically — it's not simply about burning fuel faster, but about ejecting the combustion products as fast as physically achievable, since that exhaust speed directly determines how efficiently a given amount of fuel converts into the rocket's own change in velocity.
What we're still unsure about
Conservation of momentum and the Tsiolkovsky rocket equation are both rigorously derived and precisely confirmed by every spaceflight ever conducted — none of this is in dispute. The genuinely open engineering challenges lie elsewhere: achieving higher exhaust velocities more efficiently, safely, and cheaply than current chemical rocket engines allow is an active area of propulsion research, and alternative approaches — ion propulsion, nuclear thermal propulsion, and others — trade off exhaust velocity against thrust and practicality in ways engineers are still actively working through, aiming to push real spacecraft performance closer to what the underlying physics allows in principle, without yet being limited by anything the physics itself forbids.
This sits inside Conservation of Momentum, one of eight topics in Mechanics, one of five domains in Physics, one of seventeen subjects the app can quiz you on.