How does the thrust magnitude relate mathematically to specific impulse ($I_{sp}$)?

Answer

Thrust is proportional to Power divided by Specific Impulse

The physics governing ion propulsion dictates an inherent trade-off between how efficiently propellant is used (Specific Impulse, $I_{sp}$) and how hard the engine pushes (Thrust). The relationship is explicitly defined by the proportionality: Thrust is proportional to the input Power divided by the Specific Impulse. Therefore, maximizing $I_{sp}$—which means accelerating ions to extremely high exhaust velocities for maximum fuel economy—necessarily results in a lower thrust magnitude for any fixed power input. Conversely, increasing thrust requires either dramatically increasing input power or accepting a lower $I_{sp}$ by accelerating ions to a slower speed.

How does the thrust magnitude relate mathematically to specific impulse ($I_{sp}$)?

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