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Assuming vacuum exit conditions are matched by means of a suitable ejector mechanism, is the exhaust velocity of combustion products relative to static engine the same as that of a flying rocket engine?

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    $\begingroup$ Rocket engines are not velocity-dependent, they are only dependent on atmospheric pressure. Meanwhile jet engines rely on both. $\endgroup$
    – WarpPrime
    Apr 30, 2022 at 13:41

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In a technical sense, yes, the specific impulse will be the same, whether the engine is in flight or on the test stand.

In a purely physical sense, there will be differences in the internal dynamics of the rocket, because during flight, the rocket is under acceleration. This will cause a slightly higher pump outlet pressure, because of the increased gravity acting on the liquid propellants. Now, assuming that the rocket doesn't compensate for this by adjusting the main valves, the ISP may be slightly increased, because higher pressures generally slightly improve the chemistry in the combustion chamber.

But since pressure is not a driver of ISP and the pressure will only be changed slightly, the better answer is to say that the specific impulse will not be meaningfully changed.

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