Rocket Thrust from Mass Flow

Thrust is momentum bookkeeping. The engine throws mass backwards at high speed; by Newton's third law the mass throws the rocket forwards with an equal and opposite force. Rate of momentum out equals force in, so $F = \dot m \, v_e$, and that is the entire derivation. A rocket needs nothing outside itself for this to work, which is why it is the only propulsion system that functions in vacuum — and why it works BETTER there, not worse. The persistent public belief that a rocket pushes against the air is exactly backwards; the air is in the way.

Two quantities in this equation are routinely misread. $\dot m$ is the TOTAL propellant flow, fuel plus oxidiser together, because both leave through the nozzle and both carry momentum. A kerolox engine running an oxidiser-to-fuel ratio of 2.5 takes 2.5 kg of liquid oxygen for every kilogram of kerosene, so the oxidiser is over 70% of that flow — and a mass flow computed from the fuel alone is wrong by a factor of three and a half. The other is $v_e$, which in this form is the EFFECTIVE exhaust velocity: it already contains whatever credit or penalty the pressure term contributes, so it is not quite the physical speed of the gas at the exit plane.

The trade this equation exposes is the central one in engine design. A given thrust can be made from a large flow at modest velocity or a small flow at high velocity, and those two engines behave completely differently. High flow, low velocity gives a chemical booster: enormous thrust, poor specific impulse, tanks emptied in minutes. Low flow, high velocity gives an ion thruster: specific impulse ten times better, thrust measured in millinewtons, burns that run for months. The rocket equation prefers the second; the launch pad demands the first; that is why every mission that leaves Earth uses chemical rockets to get off the ground and may use something else once it is up.

Because thrust and propellant consumption are locked together this way, an engine cannot be given more thrust for free. Throttling up means burning faster, which shortens the burn at a fixed propellant load. Thrust and burn time are two ends of the same rope, and which end you pull depends entirely on whether you are fighting gravity near a surface or coasting between planets.