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While I was watching some videos about rocket and its engines, I saw that the principle behind it is Newton's Third Law, because while the gas is exhausted from the rocket it has a reaction force putting the rocket up.

So the reaction force produced by the gas exhaust could be written as this:

$$ F_{rocket} = F_{gas} $$

So if $F$ is constant, that would mean the acceleration of the rocket goes up as the mass goes down.

Is this correct or did I miss something?

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    $\begingroup$ That's correct. It's true for airplanes and cars you know...they get more efficient and nimble as the fuel tank empties. $\endgroup$
    – DKNguyen
    Commented Apr 15, 2023 at 16:02

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This is correct, the force increases as the propellant is consumed, and modern rocket systems will typically reduce fuel consumption rate over time to keep the acceleration in an optimal range. To calculate total impulse, you take the area under the curve for this acceleration post fuel flow rate adjustments.

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