Common Misconceptions
Because this is a variable-mass system, Newton's second law of motion cannot directly be applied because it is valid for constant mass systems only. It can cause confusion that the Tsiolkovsky rocket equation is similar to the relativistic force equation . Using this formula with as the varying mass of the rocket is mathematically equivalent to the derived Tsiolkovsky rocket equation, but this derivation is not correct.
A simple counter example is to consider a rocket travelling with a constant velocity with two maneuvering thrusters pointing out on either side, with both firing such that their forces cancel each other out. In such a case the rocket would be losing mass and an incorrect application of would result in a non-zero but non-accelerating force, leading to nonsensical answers.
Any system with a non-constant mass must be treated as a variable-mass system.
Read more about this topic: Tsiolkovsky Rocket Equation
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