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
Propellant mass fraction important role in the rocket equation: Where formula_10 is the ratio of final mass to initial mass (i.e., one minus the mass fraction), formula_11 is the change in the vehicle's velocity as a result of the fuel burn and formula_12 is the effective exhaust velocity (see below). The term effective exhaust velocity is defined as: where "I" is the fuel's specific impulse in seconds and "g" is the "standard acceleration of gravity" (note that this is not the local acceleration of gravity). To make a powered landing from orbit on a celestial body without an atmosphere requires the same mass