Mass driver constrained by a limited amount of onboard spacecraft power. Thrust and momentum from exhaust, per unit mass expelled, scales up linearly with its velocity (momentum = mv), yet kinetic energy and energy input requirements scale up faster with velocity squared (kinetic energy = mv). Too low exhaust velocity would excessively increase propellant mass needed under the rocket equation, with too high a fraction of energy going into accelerating propellant not used yet. Higher exhaust velocity has both benefit and tradeoff, increasing propellant usage efficiency (more momentum per unit mass of propellant expelled) but decreasing thrust and the current rate of
Thermal velocity Boltzmann constant, formula_2 is the temperature, and formula_3 is the mass of a particle, then we can write the different thermal velocities: If formula_4 is defined as the root mean square of the velocity in any one dimension (i.e. any single direction), then If formula_4 is defined as the mean of the magnitude of the velocity in any one dimension (i.e. any single direction), then If formula_4 is defined as the most probable speed, then If formula_4 is defined as the root mean square of the total velocity (in three dimensions), then If formula_4 is defined as the mean of