How can a rocket engine push in empty space?

A rocket engine produces thrust by sending its own exhaust away at high speed. In a chemical rocket, stored fuel reacts with a stored oxidizer inside the chamber. The reaction releases energy and produces hot gas under high pressure. A shaped nozzle allows that gas to expand and accelerates it outward.

The engine pushes gas in one direction, and the gas exerts an opposite force on the engine. The drawing sends exhaust downward, so its thrust arrow points upward. The engine does not have to push against the ground or surrounding air. Carrying an oxidizer also means the reaction need not collect oxygen from the atmosphere, unlike an air-breathing jet engine.

A simple steady example follows the exhaust’s momentum. If two kilograms leave each second at 2000 meters per second relative to the rocket, their momentum flow corresponds to 4000 newtons of thrust. That calculation assumes the nozzle’s exit pressure matches the surrounding pressure. A pressure difference adds another contribution in a more complete account.

The flow rate and exhaust speed here are supplied quantities, not predictions from the drawn chamber. Actual nozzle design links speed, pressure and flow. The diagram explains where thrust comes from; it does not determine how quickly a changing-mass rocket accelerates or which path it follows.