Definition of the Invariant Jet Engine Power and Resolution of the "Thrust Paradox" within Classical Mechanics

Abstract: This paper presents a critical analysis of the classical definition of jet engine useful power universally accepted in modern astronautics and theoretical physics. It is demonstrated that the traditional coupling of mechanical power to the vehicle's velocity (P = F * v) contains a fundamental methodological error. This approach makes a key internal engine parameter dependent on the observer's choice of the reference frame and results in an apparent violation of the law of conservation of energy at high velocities (broadly known as the Oberth effect or the "thrust power paradox"). The author proposes a mathematically rigorous derivation of the jet engine power equation based on the comprehensive change in the total kinetic energy of the closed system "vehicle - working fluid". It is proven that the true mechanical power of a jet engine is an invariant quantity equal to W = (Q * u^2) / 2 and is completely independent of the vehicle's speed. Based on the derived equation, an objective thermodynamic efficiency coefficient for a jet engine is formulated for the first time, taking into account the heating value and the total initial temperature of the propellant. The proposed framework completely eliminates speculative paradoxes and restores energy efficiency calculations to strict scientific logic. jet engine, engine power, Oberth effect, law of conservation of energy, Meshchersky equation, invariance, jet engine efficiency, theoretical mechanics, propulsion energy balance.